PRODUCTIVITY DECODING OF FINANCIAL SIGNALS

PRODUCTIVITY DECODING OFFINANCIAL SIGNALS:

A PRIMER FOR MANAGERS ONDETERMINISTIC PRODUCTIVITY ACCOUNfiNG

V

The Library BAZILJ. VAN

of tlic Witwaterstand

Johannesburg

by

WtTMEA

PUBLISHERProductivity Measurement AssociatesUnited Kingdom

This book is copyright under the Berne Convention. In termsof the Copyright Act, No 98 of 1978, no part of this book maybe reproduced or transmitted in any form or by any means,electronic or mechanical, including photocopying, recording orby information storage and retrieval system, without permissionin writing from the Publisher.

Key words:- ProductivityDecodeFinancialSignalsManagerDeterministicAccounting

Prior to publication of this book, I communicated the ofdeterministic productivity accounting to university students and tothrough lectures, articles and books which assume the reader hat anappreciation of advanced mathematics.

This book attempts to introduce another dimension to the literature thesubject. It aims at providing the non—mathematical reader an overview q theproductivity notion and relates.the "hard" (i.e., mathematicallynotion of productivity measurement to the "soft" objective of

in a manner conducive to raising productivity.

My principal business activity is training and providing consulting sqtjportto management of corporations who have decided to adoptproductivity accounting as part of the productivity management jqtjrneydescribed jn this book. In addition, I enjoy lecturing part—time inuniversities on the subject covered by this book to both andpostgraduate students in engineering and commerce faculties. Such teictingactivities revealed a need for an introductory text book which providflt anoverview of the productivity concept and the role of productivityin improving productivity.

The demand for such a book extends beyond universities into the pqlicyformation arena as governments increasingly acknowledge the need for contreteprograms to foster productivity growth. Government agencies theriforeacknowledge that they are also targets for the ideas expressed in this

To simplify the measurement component of the ideas set forth in this asimple notation is employed. A more quantitative audience is referred myother works for a rigurous algebraic specification of the axioms on thework rests.

Growing awareness of this work in academic circles is evident from theincreasing number of candidates for higher degrees who aspire to use this &jorkfor their research. It is interesting that some candidates intendthe mathematical structure while others intend taking it as given to moflitorprogress in the soft i:omponents of the productivity improvement process.

Growing awareness of this work in business circles flows from two roots, Itis stimulated in part by a management recognition thatimprovement is a good idea whose time has come. It is also stimulated injartby the activities of postgraduate university students who perceive the peedfor sound productivity measurement to underpin systematic efforts tooperations and raise productivity.

I hope that this bcok will therefore serve the needs of productivityconstituents in universities, business and government. Toupfront intellectual investment which users of the concept need to make, barehas been taken to include an expert system in the latest softwareknown as Financial Productivity Management (FPM). Hence the principal Ueascontained in this book can readily be accessed from the software inform to reinforce in the mind of the user what is stated more fullybook.

Bazil J. van.

To the Players, onsite and offsite

COPYRIGHT 1988 Basil James van Loggerenberg

PREFACE

"In their deep concerns men clever enough to dissimulate". C.P. Snow

Published by

Productivity Measurement AssociatesP.O. Box 201WITS 2050

301014429

ISBN 0 620 10540 2BDOZZO61

CONTENTS

PART A — BACKGROUND

Chapter Al TIlE PRODUCTIVITY CONCEPT

Chapter AZ PRODUCTIVITY MEASUREMENT AND PRODUCTIVITY IMPROVEMENT

Chapter A3 PRODUCTIVITY MANAGEMENT JOURNEY

Chapter A4 HOW MEASUREMENT ASSISTS PRODUCTIVITY MANAGEMENT

PART B — INPUT FUNCTIONS

Chapter Bl DATA REQUIREMENTS AND DEFAULT VALUES

PART C — AXIOMS FOR ALL REPORTS

Chapter Cl OVERVIEW OF ALL AXIOMS

Chapter C2 AXIOMS FOR FUNCTIONS IN INPUT REPORTS

Chapter C3 AXIOMS TO GENERALIZE FUNCTIONS FORNEW RESOURCE QUANTITY AND NEW RESOURCE PRICE

Chapter C4 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN PRODUCTIVITY,4CAPACITY UTILIZATION AND EFFICIENCY

Chapter C5 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN LONG TERM SHORT

TERM PRODUCT PROFIT

Chapter C6 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN LONG TERM ANQ SHORTTERM PRODUCT COST

Chapter C7 AXIOMS FOR FUNCTIONS IN PROFIT AND COST RECONCILIATIONRE PORTS

PART 0 — GRIDS FOR PERFORMANCE REPORTS AND RECONCILIATION

Chapter Dl QUANTITY GRID (LONG TERM)

Chapter D2 QUANTITY GRID (SHORT TERM)

Chapter D3 PRODUCTIVITY GRID

Chapter D4 PRODUCT COST GRID (LONG TERM)

Chapter D5 PRODUCT COST GRID (SHORT TERM)

Chapter D6 PRiCE GRID

Chapter 07 PRODUCT PROFIT GRID (LONG TERM)

CONTENTS — I

Chapter

Chapter

Chapter

Chapter

Chapter

Chapter

Chapter

D8

09

D10

011

012

D13

Dl 4

CONTENTS — 2

Chapter 12 DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSIONTO BENEFIT TO COST RATIOS

APPENDIX B - BIBLIOGRAPHY

CONTENTS — 3

PRODUCT PROFIT GRID (SHORT TERM)

PRODUCT MIX COST GRID

PRODUCT VOLUME COST GRID

INVESTMENT VARIANCE PROFIT GRID

RETURN ON REVENUE VARIANCE PROFIT GRID

TARGET ROI PROFIT GRID

GRIDS RECOMMENDED FOR PRODUCTIVITY DISCLOSURE

PART F — RESOURCE VARIABILITY (REVA

Chapter Fl 'VARIOUS CASES OF REVA

PART G — PROXY DATA

Chapter Gl PROXY PRICES AND PROXY QUANTITIES WHEN NONE ARE AVAILAWI

Chapter G2 SCORING MATRICES FOR PROXY PRODUCT QUANTITY

PART H — TRADEOFF ANALYSIS

Chapter Hl TRADITIONAL PRODUCTIVITY INDEX NUMBERS AND WORK STUDYAPPROACHES

Chapter HZ TRADITIONAL INFLATION ACCOUNTING APPROACH

Chapter H3 1RADITIONAL STANDARD COST ACCOUNTING APPROACH ANDEXPENSE TO REVENUE RATIO APPROACH

Chapter H4 DETERMINISTIC PRODUCTIVITY ACCOUNTING APPROACH

Chapter H5 COMPARISON OF TRADITIONAL STANDARD COSTING ANDPRODUCTIVITY ACCOUNTING APPROACHES

PART I — NET PRESENT VALUE

Chapter Ii DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSIONTC NET PRESENT VALUE ANALYSIS

PART E — EXAMPLE

Chapter El EXAMPLE OF INPUT VALIDATION "A" REPORT

Chapter E2 EXAMPLE OF INPUT VALIDATION "B" REPORT

Chapter E3 EXAMPLE OF INPUT VARIANCE REPORT

Chapter E4 EXAMPLE OF INPUT RELATIVE REPORT

Chapter ES EXAMPLE OF INPUT COMPACT REPORT

Chapter E6 EXAMPLE OF INPUT NORMALIZED QUANTITY AND PRICE REPORT

Chapter E7 EXAMPLE OF PROFIT BACKGROUND REPORT

Chapter E8 EXAMPLE OF PROFIT RECONCILIATION REPORT

Chapter E9 EXAMPLE OF PROFIT OVERVIEW REPORT

Chapter E1O EXAMPLE OF LONG TERM PRODUCT PROFIT REPORT

Chapter Eli EXAMPLE OF SHORT TERM PROOUCT PROFIT REPORT

Chapter E12 EXAMPLE OF COST RECONCILIATION REPORT

Chapter E13 EXAMPLE OF COST OVERVIEW REPORT

Chapter

Chapter

EI4

ElS

EXAMPLE OF LONG TERM PRODUCT COST REPORT

EXAMPLE OF SHORT TERM PRODUCT COST REPORT

Chapter E16 EXAMPLE OF PRODUCTIVITY OLD AND NEW VARIANCE REPORT

Chapter E17 EXAMPLE OF PRODUCTIVITY COMPONENT VARIANCE REPORT

Chapter E18 EXAMPLE OF PRODUCTIVITY COMPONENT OLD & NEW REPORT

PART ,J — UNIT LIFE CYCLE COST

Chapter JI DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSIONTO UNIT LIFE CYCLE COST ANALYSIS

PART K — PRODUCT NORMALIZATIONS

Chapter KI AXIOMS TO NORMALIZE NEW LEVELS OF PRODUCT QUANTITY AND PftICE

APPENDIX A - SPECIMEN EXPERT SYSTEM REPORTS

I

PART A — BACKGROUND

This part of the book presents the following 4 chapters.

Chapter Al THE PRODUCTIVITY CONCEPT

Chapter A2 PRODUCTIVITY NEASUREMENT AND PRODUCTIVITY IMPROVEMENT

Chapter A3 PRODUCTIVITY MANAGEMENT JOURNEY

Chapter A4 HOW MEASUREMENT ASSISTS PRODUCTIVITY MANAGEMENT

Chapter Al — THE PRODUCTIVITY CONCEPT

The purpose of this book is to bring to the attention of managers the notionof productivity and to expose them to a simplified form of a comprehensivemathematical structure (see Appendix B item A15 for the companionbook) which underpins proper productivity measurement. Simplyproductivity is the following quotient.

PRODUCT (i.e. OUTPUT) QUANTITYPRODUCTIVITY m (Al

RESOURCE (i.e. INPUT) QUANTITY

Whereas production refers to the conversion of resources comprising labor,material and capital (i.e. input) into goods and services of

a quotient which relates toa subset of resources used in the production process. Since usedin the production process extend beyond labor, the definition ofalso deals with resources other than labor. Yet labor plays a centrar rpl e,since capital and materials cannot produce anything unless labor theprocess. Although it is common to talk of productivity as output per oflabor input, it must be borne in mind that an increase in this canalso be driven by utilization of materials and capital

The author believes that managers should familiarise withproductivity and its proper measurement in view of the growing need fur thebenefits to be derived from productivity improvement. The relaflonshipbetween productivity measurement and productivity improvement is dftcussedin the ensuing chapter.

This chapter discusses the importance of promoting productivity growth,corrects common fallacies about the productivity concept, presents an q,jerviewof productivity measurement, identifies defects in conventionalmeasures and specifies characteristics for sound productivitywhich are satisfied by the approach defined in the companion techni4i bookcited above.

The Importance of Promoting Productivity Growth

Productivity is becoming a hot issue in the unpredictable,economic environment in which we live. It is increasingly recognized the

Al — 1

I11 productivity performance of private and public sector undertakings is theprincipal determinant of cost—effectiveness and hence viability. Leadingundertakings and government policy—makers in First, Second and Third Worldsare to varying degrees articulating a commitment to productivity improvementbecause of the rewards it brings.

C]\ The purpose of raising productivity is to increase the profitability of theJ private sector, the cost—effectiveness of thepublic sector and the realliving standard of consumers. A commitment to improve productivity createsaudiences interested in monitoring productivity trends (i.e. trackingproductivity). They range from the microcosm up to the macrocosm andinclude:

• the industrial engineer defining engineered standards (i.e productivitynorms) for labor and/or plant

• the accountant controlling a cost center within a profit center

i the product or group controller monitoring different profit centers withina business and/or different businesses

• the business economist and the financial/investment analyst monitoringlarge corporations or industries

• the rate—making officer adjudicating on a rate increase application

• the economist scrutinizing the performance of the national economy and itsunderlying sectors such as manufacturing, construction and services etc.

Productivity tracking is facilitated when measures of productivity changeare directly related to an operationally familiar measure, For example, afinancial officer would value a measure of the contribution of productivitychange to budgets for production, costs, net income or investment. Similarly,a rate—making (i.e., tariff—setting) tribunal would value a measure of the

• contribution of productivity change to the requested rate increase.

The improvement of productivity is of paramount importance where themajority of the population expects to achieve a higher standard of living thanit presently enjoys. Standard of living is measured as the consumption (ofgoods and services in the national economy) per person in the totalA\ population, and the standard of living cannot for long increase without

• increase in the production (of goods and services in the national economy) perperson employed in the total population.

The requirement that there should be increase in production per employeeshould not be construed to mean that productivity deals only with labor.

It is clear that a stable socio—political future of any country requires asound economy which will be sufficiently vigorous to provide job opportunityfor hundreds of thousands of people trying to enter the labor market. Thissituation signifies a growing economy. Economic growth will be largelydependent upon our competitiveness which, in turn, is a function ofproductivity.

The interesting aspect of productivity improvement is that it is not simplysomething for "the other party" to do, since everyone must contribute to it.The managerial cadre can play a key role in productivity improvement, sinceone of the prime reasons for a country's inadequate productivity performancemust be sought in the lack of highly skilled people together with an inability

Al — 2

to use technology to its fullest extent.

It is therefore to he expected that increasing pressure will be placed uponmanagers to focus their efforts more on the contributions they can make toincreasing productivity. The managerial cadre should be cognisant ofpressure and equip itself with knowledge related to productivity issues inorder to meet the challenge of the new situation.

Correcting Common Fallacies About Productivity

There is no commonly accepted intuitive definition of "productivity"there is, albeit imprecise, intuitive understanding of notions such as "bjm","unemployment", "inflation" and "profitability". It is thereforeto give cursory attention to the following examples of misleading rhetori&andhow they should be qualified:

• economic growth flows from a boom and not from productivity• productivity growth promotes unemployment• productivity change is irrelevant to inflation• profitability is niore important than productivity.

Informed opinion would typically correct the above ambiguities withpositions such as the following: -

• economic growth is derived from two potential sources, viz.,more resources into the production process and using such resources joreproductively. Both factors can give rise to an economic boom.

• productivity growth may cause short term retrenchments but will tocause long term increase in employment as a result of acompetitive position. The notion that productivity growth leads tounemployment flows from an incorrect perception that productivitydisplaces labor aione, specifically when capital is substituted forOn the contrary, it is clear that productivity growth can be derivedhigher materials and/or capital productivity. In this situation inthe materials and/or capital content per unit of output takes place.

• productivity growth tends to reduce inflation (defined here asprice increase) while productivity loss tends to increase inflation.

• productivity is the key, but not the sole, determinant of how sustainable agiven level of profitability (defined here as the ratio of tocapital assets) might be. High productivity tends to sustain sighprofitability while low productivity tends to erode high

To create perspective for a definition of productivity, one must ask whodetermines the level of productivity in the country. In a strict sense it istrue that anyone who works contributes to the productivity level thecountry as a whole. A comprehensive classification of the economy wguldreflect the following breakdown:

• formal sector, comprising all production of goods and services whichin the Sytem of National Accounts which is specified by internatiäpalconvention and which is subdivided into a private sector and asector.

• informal sector, comprising all production of goods and services notincluded in the System of National Accounts and which includes, inter alia,

Al — 3

the following:

• production of households

• production of small producers who evade detection by not reportingactivity to government's statistics gathering or tax collectingagencies. In the United States some estimate that exclusion of theinformal sector leads to an undercounting of up to 15% of thevalue of output in the national economy. This sector is alwaysimportant in a developing economy.

For reasons of' brevity the remainder of this book limits the followingdiscussion of productivity measurement to the formal sector.

Productivity Measurement Overview

This overview is intended to provide readers with an understanding of thepractical benefits which flow from productivity measurement. Peter Drucker,an American authority on management, makes the case for productivity'measurement as follows:—

"Without productivity objectives a business does not have direction.Without productivity measurement, it does not have control".

It is easy to appreciate why Drucker makes the above statement if one

considers the definition of productivity given above in statement (Al Al) tounderstand why leading businesses are generally preocuppied with "controlsystems" to ensure their solvency and viability.

The above definition of productivity is related first to a private sectorbusiness and then to the public sector teaching and research environments inthe ensuing discussion of productivity measurement.

Private Sector MeasuresIn the business environment final "product" refers to the goods and/or

services created for sale, while "resource" refers to the materials, labor andcapital inputs which are needed to make product. Examples of differentproductivity measures are given below for a hypothetical shirt manufacturer:—

Number of shirts producedCloth productivity = (Al Bl)

Labor productivity =

Capital productivity =

Number of shirts produced

Number of man—hours used

Number of shirts produced

Each of the above measures represents a "partial" productivity measurebecause it relates product quantity to less than all the resources needed tomake product. A "total resource" productivity measure would relate productquantity to a Rand measure which combines all the resource quantities needed

to make product. Both partial and total resource productivity measures beexpressed as an index number which would simply express in percetitage form theratio of a new (Le. current period) productivity measure to an old (j;e. baseperiod) productivity measure.

If one ignores the effect of changes in the selling price of product and inthe purchase price of resources used, the link between andsolvency becomes clear when one bears in mind that productgenerate revenue (i.e. cash inflow) for the business, whilequantities used generate expenses (i.e. cash outflow).

If, in the example of the shirt manufacturer cited above,productivity (also known as materials yield) declines from, say, 4 shk9s per10 square metres of textile used to 3 shirts per 10 square metres of7textileused because of either inferior material quality or shoddy workmanship whichdoes not withstand the scrutiny of final product quality control, willbe a decline in revenue with respect to expenses which will diluteIn this example of higher wastage rate at final product quality stage,the decline in materials productivity will be accompanied by inenergy productivity, labor productivity and capital productivitysignificantly dilute profits and perhaps jeopardise solvency.

Awareness of the connection between productivity loss and threats tq profitsis the prime driver which motivates management to institute "control"which cover both the production and financial areas. Examples of cqs',trolsin each area are discussed below.

materials yield (which is a materials productivity norm)energylaborplant

contentcontentthroughput

(which is anenergy(which is a labor(which is a capital

productivityproductivityproductivity

norm)norm)norm)

• Inventory control to ensure, consistent with the facts of lead time neededfor suppliers to supply raw material and the need for proper prcgJuctionscheduling, that quantities of raw material inventory do not morequickly than output. An acceptable deviation from this rule could ifmanagement builds raw material inventory through "hedge—buying" to floid anexpected increase in the purchase price of raw material. S4ilarly,management may decide to build finished product inventory in dSer tooptimize on production scheduling.

• Standard costing to ensure that the actual cost per unit of oqtput iscompared with he standard cost per unit of output which can be Uaed oneither a "hard' (i.e. engineered) standard or a "soft" (i.e. year)standard.

• Inflation accounting to ensure that profit is adjusted by theeffect of prce change on both revenue and expense parts of incomestatement.

• Linear programming which purports to achieve a least cost combinaL)on ofresources to product where more than one combination of tomake product is known.

Examples of control system in the production area include:

• Engineered star4ards for

(Al B2)

(Al B3)

Number of Metres of textile used

Al — 4Al — 5

Examples of control system in the financial area include:

i Credit control to ensure that goods are not supplied to prospective, new

customers whose inability, or unwillingness, to pay could lead to a baddebt which would constitute a capital productivity loss

_________________________________

• Debtors control to ensure that capital tied up in these short—term assetsdoes not, without express management intention, increase more rapidly thanoutput. Conclusion

On the positive side, management also recognizes that a well controlledbusiness achieves higher productivity and a resulting lower cost per unit of Given the case for productivity measurement, it does not follow th4t alloutput which confers a cost advantage over competitors. If the market is productivity measurement is sound or that measurement 'per willprice—sensitive, the well controlled business may use its cost advantage for automatically imprcve productivity. Productivity measurement is necessagy, butaggressive pricing which could generate more demand and thereby lead to even not sufficient, to improve productivity. Different types of measuremeht and

higher productivity, their relationship with productivity improvement are discussed next. --

Public Sector MeasuresIn the teaching and research environment final "product" refers to the

services produced, while "resource" refers to the materials, labor and capitalinputs which are needed to make product. The absence of readily identifiablespecifications of product in this environment constitutes such a datadeficiency that it is often argued that it is impossible to measureproductivity in such environment and that productivity measurement istherefore irrelevant. This "irrelevance" argument becomes an excuse for notmeasuring, and hence not managing, productivity performance.

Notwithstanding such "irrelevance" argument, it is possible to quantifyoutput measures for most areas in the teaching/research environment using a

scoring matrix based on objectives. This tool is versatile and has been usedsuccessfully for measuring output in service activities such as information,teaching, social planning and underground surveying. -

Use of the scoring matrix tool boils down to individuals involved inactivity identifying the outputs and objectives which they deem to be ofcritical importance to their activity. They then decide on the minimumachievable level of output, the current level of output and the objective(i.e. desired) level of output which they should strive to attain. Theselevels and linear (or other) interpolations are then assigned score valueswhich are combined, using a set of subjectively determined weights, into an

overall proxy measure of output. Any person interested in a more detailedexposition of the methodology can obtain additional information from theauthor.

Assuming that an acceptable definition of proxy final product could be

specified in the teaching and research environment, the following productivity.measures could be defined.

Number of proxy units producedEnergy productivity = (Al Cl)

Number of Kilowatts used

Al—6 Al—7

-t

Number of proxy units producedLabor productivity = C2)

Number of man—hours used

Number of proxy units producedCapital productivity = (A! C3)

Number of sq. metres space used

Chapter A2 - PRODUCTIVITY IMPROVEMENT AND PRODUCTIVITY MEASUREMENT

The superordinate goal of all productivity analysis is the improvement ofproductivity. To improve productivity, one must first understand thecomponents of productivity improvement. The following figure outlinesprincipal components of productivity improvement. With respect to the internalcomponents of productivity improvement, it is noted that both 'soft" (i.e.subjective, elusive) components and "hard" (i.e. objective, tangible, robust)components must display suitable characteristics before sustainableproductivity improvement can take place.

External components of productivity Improvement

The physical component is given by the natural endowment and is subject tolittle intervention by man. Climatic change can favorably affectproductivity in agriculture as, for example, the climatic regime changes fromdrought to more precipitation. Similarly, the discovery of expolitable oresat shallower depths raises productivity in mining.

The national culture of a society can change and thereby raise productivity.The acceptance of a work ethic and a profit motive by a society whose valuesystem previously devalued such notions will improve motivation, productionand productivity.

Legislation is a human invention and is subject to short—term variation.Lowering of taxes, privatisation, deregulation and change in the ofland tenure are examples of legislative intervention which raiseproductivity.

Market considerations may be conducive to raising productivity jn thefollowing respects. At minimum, increasing one's market share in a marketwhose industry potential is not declining creates an opportunity to Ipcreaseproduction and productivity provided resources used increase to lowerextent than the increase in production. Growth in market potential asimilar opportunity even under conditions of either constant market shire ordeclining market share where a corporation's production is increasing.

The forces of expansion in market potential derive from factors ;och asincrease in domestic real purchasing power, reduction of imports, inexports, and growth in vertical integration which may or may not fromtechnological change. An example of technological change

Fconvergence of markets which may inspire vertical integration is inthe computer and telecommunications industries in the United Thecomputer industry's devices today offer electronic mail transmission way ofcomputer—to—computer file transfers through telephone and packet—switching

• networks, and telecommunication equipment suppliers are entering the• industry as shown by the American Telegraph and Telephone part acquisitfon ofOlivetti.

Internal soft components of productivity Improvement

The organizational structure of a corporation is conducive to raisingproductivity when it links management accountability to prodqotivityperformance and displays organizational flexibility for timeous adaptat(pn tochanging conditions. Such an organizational structure will iiefineproductivity measures for every control point in the operation, andalso include marketing, purchasing, administration, etc., in additipn tocustomary production—related control points.

An earlier viewpoint of the importance of organizational structure is givenbelow.

The corporate culture of a corporation is conducive to raising productivitywhen it is a questioning culture which tolerates no sacred cows,proper communication and accepts that managed change in the quéi.j forimprovement is often uncomfortable but worthwhile. Such a culture {bmmitsmanagement to respond to the signals from sound productivitywhich is defined below.

The training program of a corporation is conducive to raisingwhen it is relevant to corporate needs and the skills transmitted are uud. Ahighly trained, motivated labor force is a prime ingredient forproductivity improvement.

Human resources policy of a corporation is conducive to raisingwhen it reflects an enlightened approach towards the use of humansince human acts of omission and commission underlie change i11 theproductivity of labor resources as well as the productivity of allresources such as materials, energy and capital in all its forms.

k

Figure A2.F1

A2—1 A2—2

Internal hard components of productivity improvement

The equipment (and supporting technology) used by a corporation are

conducive to raising productivity when they are the best available which can

be economically justified.

The work methods used by a corporation are conducive to raising productivitywhen they are the best available which can be economically justified. Work

methods include the following engineering ("hard system") approaches towards

improving operations: Value engineering, just—in—time, group technology, total

quality control, multiple resource planning, computer aided design, computer

aided manufacture, and so forth.

The productivity measurement system used by a corporation is conducive to

raising productivity when it is the best available which can be economically

justified. Deterministic and stochastic approaches to productivity

measurement are defined below as a prelude to a discussion of the strengths

and weaknesses of different types of productivity measurement.

Deterministic and stochastic approaches to measurement

Deterministic approaches to measurement start by defining certain equations

as axioms or identities (i.e. relationships which are always valid) and then

proceed to derive other relationships from transformations of the initialaxioms. A deterministic model permits total accuracy provided initial axioms

can be specified and the model can be populated with credible data.

Stochastic approaches to measurement start with the assumption that axioms

are not known to define the relationship in question. Stochastic approaches

therefore resort to probablistic equations which employ regressions (i.e.statistical inferences) to estimate a relationship which is not known with

certainty. A stochastic methodology is justified and plays an indispensable

role only when a deterministic one cannot be identified.

The approach presented in this volume is deterministic. The preference of

the engineering and accounting communities for rigor, precision and freedom

from ambiguity indicated at an early stage a need to develop, as far as

possible, a deterministic methodology in lieu of a stochastic one. Business

economists, industrial engineers and accountants have long used deterministic

models to appraise the performance of the individual producer establishment.

Yet the reader with econometrics training may be surprised to encounter in

this book some novel deterministic specifications in areas where stochasticspecifications are customarily found in econometric literature.

The author offers no apology for this fact, and points out that the adoption

of a stochastic methodology implies that a deterministic one cannot be

identified. On the contrary, the practitioners of stochastic methodology, for

those types of analysis for which a deterministic methodology has now been

identified, will be obliged to justify their stochastic practice.

General weakness and strength of all productivity measurement

A general weakness of all productivity measurement arises from the fact thatthe productivity quotient has no necessary causal significance. Changes in

productivity express effect and not cause. Causal insight can only be provided

by those familiar with a given operation. Ongoing productivity measurement,

known as productivity tracking, therefore poses rather than answers questions.

A2 — 3

A general strength of all productivity measurement with toproductivity improvement. efforts arises from its overall monitor as

attempts are made to change soft and hard components cited above. Ato improve productivity creates a need for productivity measurement.

productivity measurement there would be no score—card to ascertainsystematic efforts to raise productivity are bearing any fruit.

Productivity measurement is a hard component of productivity irlipregement

which can quantify the effect of productivity change on financialThe soft components must be activated to enable management to proceedeffect and thereby uncover cause so that remedial action to improvecan be formulated and implemented.

Specific weakness and strength of individual productivity measurement

To introduce this topic, the following figure presents a simplified tgAonomyof productivity measurement systems.

I

PRODUCTIVITY. MEASUREMENT TAXONOMY

MEASURES EXPRESSED INNON—FINANCIAL UNITS

•1

- MEASURES EXPRESSED INFINANCIAL UNITS

NON—NORMATIVE

MEASURES

Activity SamplingProductivity Index

NumbersEconometPi c

ModelsDeterministic

ProductivityAccounting

Inflation Accounting

DeterministicProductivityAccounting

NORMATIVEMEASURES

Engineered Standards for— Labor minutes— Materials yield— Plant production rate

DeterministicProductivityAccounting

Standard Costing

Linear ProgrammingDeterministic

ProductivityAccounting

Each of theSome of thestochastic and

Figure A2.F2

above types of productivity measure is reviewed briefly below.above measures are purely deterministic, others are purelyyet others blend deterministic and stochastic characterbtics.

AZ — 4

Non-norñiatiVe, non-financial measures

These measures are termed non—normative and non—financial because they

typically compare actual productivity levels in two accounting periods and

express the result in percentage form rather than in a currency unit.

Activity Sampling is the most elementary form of productivity measurement.

It is expressed as a percentage which is constructed from division of the

number of observations in which work takes place by the total number of

observations. It can be done through human observation or mechanical

observation by way of a camera periodically photographing an operation.

Although the activity sampling quotient for a given accounting period isdeterministic, trend values can be derived using either a deterministic or a

stochastic approach.

Change in productivity index numbers indicate the percentage change in a

given productivity quotient between two accounting periods. Although the basic

quotient for a given accounting period is deterministic, trend values can be

derived using either a determinsitic or a stochastic approach.

Econometric models are used to estimate percentage change in productivity.

They are constrained by some deterministic axioms but make extensive use of

regression analysis (i.e. a stochastic approach).

Deterministic productivity accounting contains measures which belong to this

group. All measures in this approach are purely deterministic, as indicated

by the first word in the title of the approach. Within the group of non—

normative, non—financial measures, deterministic productivity accounting

measures comprise change in index numbers which refer to value, quantity,price, productivity and price recovery. The latter indicate percentage change

in a given price recovery quotient between two accounting periods. Price

recovery is defined below. It complements the notion of productivity and canalso be defined for a single resource or an aggregation of resources.

PRDDUCT (i.e. DUTPUT) PRICEPRICE RECDVERY a

(A2 Al)RESDURCE (i.e. INPUT) PRICE

Non-normative, financial measures

These measures are termed non—normative and financial because they typicallycompare actual productivity levels in two accounting periods and express the

result on profit or on cost in a currency unit.

A primary feature of these approaches is the specification of productivitymeasures which offer a "bottom line" linkage, i.e. linkage to the financial

accounting system of the producer. Experience shows that any measure of

productivity which exists as a discrete measure unconnected to the financial

system commands limited credibility since it sooner or later sends signals

which conflict with signals from the financial accounting system. A classical

example of sqch a conflict arises when the productivity measure signalsimprovement while the financial accounting system signals deterioration.

Inflation accounting is presented by way of a numerical example in a laterchapter. All measures in this approach are normally deterministic. Itinvolves the deflation of new period revenues and costs (expressing new

quantities in new prices) to adjusted values which purport to represent new

quantities in old prices. The resulting adjusted profit pqrports toeliminate price change and to represent the effect of productivity ihange on

profits. Questions of accuracy arise from the use of deflators (Uè. .priceindex numbers which express the ratio of a new price to an old pricej.

Deterministic productivity accounting contains measures which to thisgroup. They comprise accounting variances (which will be specifj4d later)for change in different variables expressed in a currency unit.which appear in this group would compare actual performance leveh in twoaccounting periods rather than a contrast in which one of the accountingperiods contains performance targets or performance norms.

Normative, non-financial measures

These measures are termed normative and non—financial because they typicallycompare normative (i.e. standard or target) productivity in oneaccounting period with actual productivity levels in another accoun%(ng periodand express the result not in a currency unit but as a percentage oWin unitsof resource. Hence the deviation of, say, actual minutes frop4 standardminutes can be expressed either in minutes or as a percentage.

Engineered standards for 7abor minutes prescribe the number minutesspecified tasks should take. Computation. of the time sta&ard was

historically drterministic but has in recent years become more

since use of regression analysis accelerates (and hence reduces of)quantifying the time standard. Deviation of actual from standard is expressedas a percentage or in labor minutes, i.e., labor resource units. I

Engineered standards for materials yield prescribe the resourcecontent per unit of product. Computation of the standard yield fiows fromspecified assumptions on product quality and materials It istypically deterministic but would be stochastic in the event of hiatisticalinference being used to quantify the relationship. Deviation of acçual fromstandard is uxpressed as a percentage or as a materials quantityj:i.e., inmaterials resource units.

Engineered standards for plant production rate prescribe a plant productionrate with respect to specified operating conditions. of theproduction rate standard is typically deterministic but would be inthe event of 5tatistical inference being used to quantify the re44ionship.Deviation of actual from standard is expressed as a percentage, machine—

hours, i.e., in capital resource units, or in units of production orlost.

Deterministic productivity accounting contains measures which to thisgroup. Although input data into this approach can be either determjoistic orstochastic in origin, deterministic productivity accounting datain a purely deterministic manner. Within the group of normative, non-financial measures, deterministic productivity accounting measuret comprisechange in index numbers which refer to value, quantity, price,and price recovery as defined above.

A2—6A2-5

I

Normative, financial measures

These measures are termed normative and financial because they typicallycompare normative (i.e. standard or target) productivity levels in oneaccounting period with actual productivity levels in another accounting periodand express the effect on cost or on profit in a currency unit.

Standard costing typically compares cost or profit based on standardproductivity levels and standard prices with cost or prodit based on actualproductivity levels and prices. The standards are defined using either a

deterministic approach or a stochastic approach, but the data are subsequentlymanipulated in a purely deterministic manner as explained by way of a

numerical example in a later chapter. -

Linear Programming is applied to situations where more than one combinationof resources to make product is known. This purely deterministic techniquewould compute total cost of production associated with each "recipe" toascertain which method of making product minimizes cost and hence maximizesprofit. It does not show a contribution per resource to explain changes inthe variables with which it deals.

Deterministic productivity accounting contains measures which belong to thisgroup. It typically compares cost or profit based on standard productivitylevels and standard prices with cost or prodit based on actual productivitylevels and prices. The standards are defined using either a deterministicapproach or a stochastic approach, but the data are subsequently manipulatedin a purely deterministic manner as explained by way of a numerical example ina later chapter. Although the deterministic productivity accounting approachapparently coincides with that of standard costing, it will later be shownthat its measures are significantly different and can contradict, withjustification, signals from standard costing.

Defects in conventional productivity measurement

Figure A2,F2 lists different approaches towards productivity measurement.They can be classified into conventional approaches (all of which are in someway flawed) and a new approach known as deterministic productivity accounting.The latter approach has been developed by the author to eliminate the flawscontained by conventional approaches which comprize all other approacheslisted in figure A2.F2 above.

This book does not provide a detailed demonstration of the defects inherentin the various conventional approaches to productivity measurement employed byeconomists, accountants and engineers. However, later chapters will providefor the non—mathematical reader numerical examples to expose the weaknesses ofproductivity index numbers, standard costing and inflation accounting. Forthe mathematical reader a list of defects in conventional productivitymeasurement would cite:

• unjustified use of a differential operator when a difference operator isrequi red

• failure to rationalize the attribution of higher ordered interactions whena difference operator is employed

• dimensionally improper arithmetic operations

• use of ordinary differences when partial differences are required

• use of a stochastic methodology when a deterministic one can be

The above list of defects signifies that none of themeasurement approaches provides systematic insight into productivityand itsassociated financial impacts. This limitation arises because ofthe conventional measurement approaches possesses thecan be prescribed for sound productivity measurement.

Characteristics of sound productivity measurement

Although the purpose of all productivity measurement is control, soundproductivity measurement has more demanding characteristics. It withrespect to a private sector business, employ full accounting rigor to:

• provide simple and unambiguous signals to improve profits;

• break down change in profit into the underlying contributions froip eachresource in production (i.e. materials, energy, labor, and

i break down the contributions to profit change from each resource iHto a

productivity term and a price recovery term to isolate the ofdisparate change in product price vis—a—vis resource price

• break down the productivity- term into a capacity utilization term qud anefficiency term (i.e. differentiate short—range fromshort—range potentially controll able factors);

• use the price recovery term to evaluate whether productivity lqs orproductivity gain for a given resource is appropriate;

• transform the above measures of change in profit intomeasures for cnange in profitability, change in cost per unit ofand change in performance index numbers (e.g. productivity indexand

• provide consistent signals for profit improvement regardless of the- unitsin which the measure is expressed.

Translation of the above features from a private sector businessto the the public sector environment entails substituting the notion costfor the notion of profit and the notion of resource price for the notldn ofprice recovery. -

Deterministic productivity accounting is a new approach towards productivitymeasurement which does possess the characteristics prescribed soundproductivity measurement and which is free of the defects cited above.

When is productivity measurement unnecessary ?

There is one situation in which productivity measurement is notfor proper control. It is the case of the small business in whichis responsible for the 5 business phases represented by

• production, marketing, credit control and planning. In such a situatthji, thefive human senses could be sufficient to gather the information forproper control and productivity measurement would therefore be

A2 — 8A2 — 7

•

•1.

Productivity measurement is merely a component of the productivityimprovement process which is holistic by nature. If isolated from other softcomponents discussed above, productivity measurement will fail to thrive and

in consequence not contribute to productivity improvement. The processwhereby managers could strive to pilot the migration of an organisation fromproductivity measurement to productivity improvement is described by theproductivity management journey in the next chapter.

The productivity management journey is defined as a path whichcould take to proceed from productivity measurement to a sustainedto productivity improvement. The process of productivity managementcan be reduced to the 5 stages shown in the following diagram.

The above productivity management journey path is not the sole path whichmanagement could take, yet it does offer a logical sequence for startingactivities which lead to sustained productivity improvement. Although 5

stages would be activated in the above sequence, each stage needs toactive as management attention passes to the next stage. A

commitment to productivity improvement needs the concurrent operation allstages shown above. Each is discussed in more detail below.

Stage 1 - Productivity Measurement

This stage is the starting point of the productivity management journey. Itrepresents a hard component (i.e., a component which is andmathematically definable). The method of productivity measurement asDeterministic Productivity Accounting recognizes that the followingidentity applies to revenue, cost and capital.

VALUE = QUANTITY x PRICE(in 5) (in units) (in s/unit) (A3 fl)

Revenue refers to product (i.e., goods and/or services produced). Costresources refer to leased capital equipment, labor and materialscosts with respect to profit defined as operating income beforeThe definition of cost resources could be extended to include deprec4flion,

Chapter A3 - PRODUCTIVITY MANAGEMENT JOURNEYConclusion

PRODUCTIVITY MANAGEMENT

Figure A3.F1

A2—9A3—l

interest paid and other finance—related charges with respect to profit defined

as taxable income. Capital resources refer to fixed capital assets and to

working capital assets.

Deterministic Productivity Accounting employs the above value axiom to

derive various other axioms which include the following:

PRODUCT QUANTITY

PRODUCTIVITY a(A3 Bi)

RESOURCE QUANTITY

PRODUCT PRICE

PRICE RECOVERY a(A3 Cl)

RESOURCE PRICE

The above measures are then applied to uncover the financial effect of,

inter alia, productivity change and price recovery change of each cost

resource and capital resource used in a given operation.

The limitation of all productivity measurement is that it focusses on effect

rather than cause and is therefore a mechanism for posing rather than

answering questions. The strength of Deterministic Productivity Accounting is

that it provides an overall financial monitor of all systematic effort to

raise productivity.

Stage 2 - Productivity Diagnosis

This stage represents a soft component (i.e., a component which is

intangible and cannot be mathematically defined). It strives to proceed

beyond effect to uncover cause and hence to explain the reasons for

productivity change. Its strength is that it attempts to answer questions

posed by measurement, Yet it will fail whenever the corporate cultureresists ascertainment of cause.

Success in the productivity diagnosis stage depends upon management's

ability to create and nurture an open, questioning culture in which there are

no sacred cows to which the cause of productivity improvement can be held

hostage. Quality circles which are effective can be an example of such

desirable attributes in the corporate culture of an organization.

Stage 3 - Productivity Plan

This stage represents hard and soft components. Using the insights gained

by productivity diagnosis, this stage strives to formulate a productivity plan

which identifies what changes are needed to move the organization from itscurrent productivity levels to target productivity levels which are specified

in this stage and which are included in budgets.

A productivity plan typically contains hard components which includes

equipment, measures such as key performance ratios, productivity and price

recovery targets, as well as other engineering—based hard systems such as

value engineering, multiple resource planning and just—in—time control

systems. A productivity plan also contains soft components (i.e., changes in

organization, training and culture). This stage requires a clear specificationof objectives, strategy and tactics needed in the soft components to ensure

that the hard components of the plan will be achieved. It would also

A3 - 2

introduce productivity measurement as an overall financial monitor of effortto raise productivity.

Stage 4 Productivity Disclosure

This stage represents a hard component. It involves disclosing tg internaland external audiences the family of grids defined byProductivity Accounting as the profit grid, productivity grid, grid,price grid and cost grid. The grids preserve confidentiality of nuSric dataand simply show position with respect to defined segments in jach grid.Disclosure of the grids could start with internal audiences and ththteafter beextended to include external audiences.

Disclosure to internal audiences within the organization creates •awarenessof the productivity concept, assists its assimilation within the corporateculture and prepares the organization for the major step ofdisclosure to external audiences. External audiences are intended functionas a proxy for competition in markets where there are few In thecase of a private sector undertaking the external audience investorsand consumers, whereas in the case of a public sector a

central or local government body, the external audience comprizes :taxpayersand consumers.

Productivity disclosure to external audiences represents the acid test ofmanagement commitment to the notion of productivity Onceinitiated, this stage cannot easily be revoked and will inevitably to thefollowing stage.

Stage 5 - Productivity Accountability

This stage represents a soft component. It involvesaccountability for productivity performance disclosed by the grids specifiedabove.

Specifically, it relates to actual productivity performance well as

planned productivity performance. Actual productivity wouldrelate! actual productivity in a given accounting period to that indicated by

either a prior actual accounting period or a budget for theperiod. Planned productivity performance would relate planned ina given budget to that indicated by either a prior actual

a prior accounting period.

Irrespective of the signal from the grids at the time of initial disclosureto an external audience, management stands to gain credit from the action ofexternal disclosure. If the initial grids signal inproductivity, management is praised for candor in disclosing dfleriorationand, by inference, for committing itself to reverse the direction f$om one ofdeterioration to one of improvement in productivity. On the hand, ifthe initial gvids signal improvement in productivity, management :4p praisedfor good performance and, by inference, for committing itself sustainimprovement in productivity.

Management accountability for disclosed productivity willmotivate management to respond to signals from ongoing fl4ductivitymeasurement, productivity diagnosis and productivity planning. - In otherwords, productivity accountability will induce management to walkdown the path of productivity improvement. -

A3 — 3

C

The Outcome - Productivity Improvement

This stage represents hard and soft components. It will not be possible toattain and maintain productivity improvement unless hard and soft componentscited above are continually melded together. Productivity improvement wouldbe detected through productivity measurement and communicated to stakeholdersthrough productivity disclosure. Stakeholders are defined as suppliers,producers and consumers. Suppliers include the suppliers of labor, materialsand capital resources. In the case of the private sector investors supplyinvestment capital and are included in the definition of suppliers. In thecase of the public sector taxpayers supply investment capital and are includedin the definition of suppliers.

A disclosed, healthy productivity and price recovery track record would tendto reduce uninformed consumer resistance to increase in product price from a

private business, increase in utility rate from a rate—regulated utility orincrease in tax rate from central or local government. Instead it offersobjective facts which indicate the extent to which the producer achievesproductivity growth to finance the absorption of resource price increase whichhe does not recover from consumers by way of an increase in the product price,utility rate or tax rate. Hence the difference between the resource priceincrease and that which is recovered from the consumer would constitute priceunder—recovery and the transfer of a subsidy from the producer to theconsumer.

Conclusion

The productivity management journey contains hard and soft components. Itcan determine the extent of sustainable productivity improvement and hencecompetitive strength, the safety of the investment and the extent to which theproducer can afford to subsidise the consumer.

The productivity management journey can be usefully compared with themanagement of the flight path of an aircraft in the following manner. The

flight of an aircraft is managed by the pilot who is dependent upon bothdirect sensing devices, which provide data on fuel supply, speed etc., andremote sensing devices such as a radar altimeter which provides data on heightabove the earth, Throughout the flight altimetry provides ongoinginformation on the changing topographical features of the earth surface belowthe aircraft. The pilot can elect to disregard remotely sensed altimetricdata and thereby imperil the aircraft.

p

Similarly, the role of productivity measurement is to provide remote sensingof the financial consequences of the changing productivity terrain whicharises from movement of the organization through time and space. The managercan elect to disregard remotely sensed productivity data and thereby imperilthe organization.

Both altimetry and productivity measurement represent hard components withsoft objectives. They seek, respectively, to influence the decision behaviourpattern of the pilot managing the flight path of the aircraft and the managercharged with managing the productivity journey of the organization.

Success in the soft and hard components described in chapter A2 will impactupon productivity and hence financial performance as monitored bydeterministic productivity accounting. In the productivity management journeyproductivity measurement should therefore be seen as a background activity todetect productivity change and calibrate efforts to improve productivity.

A3—4

Chapter A4 - HOW MEASUREMENT ASSISTS PRODUCTIVITY MANAGEMENT

The purpose of this chapter is to define in practise how measurementprovides information to enable management to make better decisions,operations and progress along the productivity management journey.

Productivity Diagnosis for Management

The total resource productivity measurement approach described in this bookmeasures the profit contribution of each resource in terms of capacityutilization, efficiency, and price recovery. Using this information candiagnose which resources contribute significantly to higher profit potágtialwhich can be attained by better allocation of resources. k-

The price recovery term for each resource is used to determineproductivity gain or loss is appropriate for that resource. Subject t( anyappropriate constraints, resources making the less favorable toprice recovery should be targeted for productivity growth (i.e., reduced usageper unit of output) which must more than offset any trade—off productIvityloss (i.e., increased usage per unit of output) from resources making tha'morefavorable contributions to price recovery.

It is appropriate to contrast short term price recovery with efficiency (forshort—term control cycles). It is also appropriate to contrast long, termprice recovery with productivity (for long—term control cycles) since ip thelong term, all resources are variable and, hence, controllable. - Thiscomparison permits the systematic substitution of cheap resources forexpensive resources to optimize profit consistent with the length of thecontrol cycle. Since this approach provides bottom—line measures of chanfl incapacity utilization, efficiency, and price recovery for eachmanagement can pinpoint where productivity improvement efforts will thegreatest beneficial impact on the business.

Some corporations have attempted to analyze their productivity usingconventional approaches such as partial production measures, totalproductivity index numbers, inflation accounting, and/or standard Tcostaccounting. None of these conventional measurement approaches, howk.ver,provides systematic insight into productivity change and itsfinancial impacts. This limitation arises because none of the conventionalmeasurement approaches possesses the characteristics that can befor sound productivity measurement as specified in chapter A2 thediscussion of Characteristics of sound productvity measurement.

Management Control

The approach presented in this book shows that it is possible to thebottom—line impact of change in productivity and change in price recovery foreach resource used in the operation of a business. This fact hassignificance because it permits management to gauge the bottom—line dellareffect of change in the allocation of individual resources withincontrol points. This argument is explained below with respect to bgth alow level control print and a higher level control point.

Even if it is unable to influence price recovery because of itsto control product and resource prices, management at a low level cöwtrolpoint such as a production control point has some prospect of

A4 — 1

the efficiency term in the productivity change. Management at a low levelcontrol point which offers no control of price recovery can still use the

price recovery measure to validate its targets for productivity change.

Sound productivity targeting requires a net positive tradeoff from

changes in resource allocation which give rise to productivity gain

on resources which are used less intensively and to productivity loss on

resources which are used more intensively as a result of planned

substitutions. Business profit improves when relatively cheaper resources

are substituted for relatively dearer resources.

The price recovery variance per resource enables management to determine

whether resources making the least favorable contribution to price recoveryare targeted for productivity growth.- Productivity growth is achieved by

tolerating less than offsetting productivity loss in resources making a more

favorable contribution to price recovery. In this manner the price recovery

variance is used to validatE the direction of productivity change for each

resource.

The sign and magnitude of the bottom—line impact of the price recovery

variance for each resource can send different types of signals to various

levels of control points in a business. For example, negative pricerecovery for a given resource signifies that product price increase does notrecover the extent of price increase for that resource. From this signaldifferent control points may draw the following types of inference.

• A production control point may infer that it should strive throughresource reallocation to target that resource for productivitygrowth (i.e., reduced usage per unit of production).

• A purchasing control point may infer that it should strive, ifpossible, to lower the specification for that resource to achieve a

favorable purchasing variance.

• A production planning control point may infer that it should explore

a make—versus—buy option for that resource, and this analysis may

identify technological gaps that the research and development functioncould explore.

Existing control systems explore the above questions by way of discreteinitiatives which drive specific studies of these questions. The

proposed control system would expliciXly integrate the price recovery

signal, with its decomposition by resource, into the basic profit variance

analysis which is seen by management. This would help management focus

on what questions it should be asking on the setting of productivitytargets for selected individual resources or sets of resources.

At a higher level control point which makes decisions on both production

and product pricing, management may trade price recovery variance offagainst productivity variance in the following manner. If a product

experiences a price elasticity of demand greater than positive unity,management may decide to reduce product price (and hence opt for less

A4 — 2

favorable price recovery variance) to generate more—than—offsettjpg profitfrom production volume (and hence opt for more favorableproductivity variance which flows principally from improvqG capacityutilization).

This possibility of measuring for each resource the ofproductivity change and price recovery change to change in profit, suggeststhat their agjregation permits explaining the origin of in theincome statement as portrayed in the 9—box diagram on the cover book,

Summary

Profitability can be described as the result of the contribution of pricerecovery and productivity. Although management cannot always pricerecovery, it can always influence productivity. The first step influenceproductivity contributions of all resources used is to adopt a soun4 method bywhich they can be measured.

Sound productivity measurement possesses characteristics (a,j specifiedearlier) which should underpin all systematic efforts to raiseregardless of whether those efforts originate from high—level contSl pointssuch as the management committee or low—level control points such as costcenter expense budgets in a plant.

The model discussed above and the PM software implementation of the model

used in this book provide an analytical tool that can be used validateother studies focusing on improving productivity through such as

vertical integration, investment, technological change,incentive schemes, and training.

• A financialintegrationunattractiveprofitabilityquestion.

planningshould be

on costin the

control point may inferinvestigated if the make

grounds and there existsbusiness sector supplying the

that reverseoption is

acceptableresource in

L

A4 — 3

PART B — INPUT FUNCTIONS

part of the book presents the following chapter.

Chapter 81 DATA REQUIREMENTS AND DEFAULT VALUES

Chapter Bi DATA REQUIREMENTS AND DEFAULT VALUES

The 10 input functions (i.e. user specified functions) required by the modelare defined in this chapter. If the user fails to provide informationby the model, use is made of either default values (which are definedchapter) or proxy values (which are defined in Part G of the book).

The distinction between default values and proxy values is soajçwhatarbitrary, but is nonetheless clearly defined. With the exception of thefunction TARGET RETURN ON IN VESTMENT, whose default value is set at oldintrinsic return on investment, all default values of input functions setat 0 or at 1. In contrast, proxy values assume a wider range ofvalues as shown in Part 0.

The 10 input functions required from the user are specified in stateRents(81 Al) through (81 32).

Q (QUANTITY FUNCTION) is a user specified functibn.(81 Al)

dimension is typically given in physical units.(81

The above suite of statements refers to the level of a function. It dbtinesthe Quantity function which is specifed by the user on the basic partitthr ofaccounting data. This function is dimensioned and is typically expressed insome physical unit such as tons, work—hours etc. It is defined forand resource.

There is no default value for the quantity function, and its proxy valutc isdefined in Part.G of the book. 2

P (PRICE FUNCTION) is a user specified function.(81 hI)

P dimension is given in currency unit / physical units.(81

The above suite of statements refers to the level of a function. It detjnesthe Price function which is specifed by the user on the basic partitin ofaccounting data. This function is dimensioned and is typically insome currency unit divided by physical units. It is defined for product andresource.

There is no default value for the price function, and its proxy isdefined in Part 0 of the book.

81—1

W (INTERVAL WIDTH FUNCTION) is a user specified function.

W dimension is given in days or other unit of time.

(81 Cl)

(81 C2)

The above suite of statements refers to the level of a function. It definesthe user specified interval Width. This function is dimensioned and istypically expressed in some unit of time such as hours, shifts or days of a

given intensity. This feature of the model would, for example, allow a chainstore user to weight, say, a Saturday with a greater intensity than a Monday.This function is defined for product and resource.

Function W is important in the following two cases:

— high frequency control cycles (i.e., a month and shorter periods), sinceit is misleading to compare, say, an 18 workday month such as Februarywith a 22 workday month such as March.

— a change in th.e closing month for an accounting year could give rise todiffering numbers of months per year when the last of the old years andthe first of the new years are compared.

The following entity rule of function W is implemented in the axioms and isspecified below:

Function W is applied to function Q(U), i.e., product Quantity

Function W is applied to function Q(N), i.e., cost resource Quantity

Function W is applied to function T(K,), i.e., target rate of returnin turn applied toP(K) representingresource asset Price.

The value functions for revenue (i.e., product value), operating expense(i.e., cost resource value) and target profit (i.e., cost of capital) allcontain a time component in contrast with the value function for capitalassets (i.e., capital asset value) which is time free. In other wordsreve4lile, cost and target profit values are time bound since they refer to a

flow concept with respect to a time interval such as a month, quarter or yearwhereas asset value is time free since it refers to a point concept such as

the value at close of business on the last business day within such timeinterval

Given the axiom Value = Quantity * Price, a value function which has a timecomponent in the left hand expression creates a need to distribute the timecomponent to either the quantity function or the price function in the righthand expression. The above entity rule of function W signifies that the timecomponent in the value function is distributed to the quantity function forproduct and cost resources, and to the price function for capital resourcesvia function T (for Target return on investment) in a manner which is shown inthe following figure.

In the following figure, RAW DATA refers to the form of data at source,while DATA ENTRY refers to how data must be transformed before entry todistribute the time component from the value function to the quantity functionor the price function according to the entity rule of W specified above.

FIGURE B1.F1 DISTRIBUTING THE TIME COMPONENTFROM VALUE TO QUANTITY OR PRICE

ENTITY CAIEIONYDINENSION OF

QUANTITY FUNCTIONDESCRIPTIV4

OF DATA

FUNCTIONS APPEARING IN INPUT

OLD INTERAAL

VALIDATION NtAC41T

NEN

ENTITY 0 (product U or cost roosore, N) deys worked VAN DATA

Roe Qo Ps No To

A DC DC1000 DO 1D ID

Von Re Po

F OR1440 60 DO

days worked DOTA ENTVV DODD 10 DD ID 1440 NO D4

ENTDTT D (product U or coot rooource N) ml leased RAN DATA 1000 00 20 Il 1440 60 24 5

ml o doyo Teased DATA ENTRY 1000 ADO 16 Il[10 a Il]

1440 040 0,0

[60 0 4]

ENTITY C (capital reooorce wooeD 'jaDe, K)

(capital reoeerce taroet profit T)

ml leased

ml leased

ml loosed

RAN DATA

DATA ENTRY

DATA CREATED

1000 50 DO ID 20%

1000 10 20 Il 200

200 50 4 Il[20 o 00%)

[lOO0ll/lD)_J

1440 60 04 !INRO 00 24 ISO

216 00 3,0

[00 a

)lOTeD/l&I.

Poe = OLD VALUE One NEA VALUE

Re = OLD QUANTITY Qe = NEW QUANTITY

Po OLD PRICE Pn = NCA P01CC

Ne = OLD INTERVAL 01010

To = OLD TVROET VETOONON INVESTMENT

An NEW INTERVAL

Tn NEW TAOOET RAVURNON

The above figure shows that the old interval refers to 12 days while thg pewinterval refers to g days. It shows how the changing time component isapplied to productn cost resource and capital data to distribute the ttimecomponent from value into quantity or price.

Entity A in the above figure refers to a product and a cost resource. Itrequires no adjustment before data entry since the dimension of the quantityfunction, given as hours worked, already contains a time component.product or cost resource quantity function which already contains a fleeComponent needs no adjustment before data entry.

Entity B in the above figure refers to a product and a cost resource. Itrequires adjustment to its quantity function before data entry because thedimension of its quantity function, given as square meters leased, containt notime component. The quantity function is adjusted to introduce a timecomponent through multiplying the raw quantity function, given in sqparemeters leased, by the interval width function, given in days, to create. anadjusted quantity function, given in square meters leased * days. fryproduct or cost resource quantity function which contains no time compqt5entneeds the above adjustment before data entry.

Entity C in the above figure refers to a capital resource. It requiresadjustment to its function T (for Target return on investment) to ensure thatit applies the time component to the price function and not to thefunction. The capital resource quantity should always be loaded with no timecomponent since the time component is contained in the compensation rate givenby function T.

81—2 81—3

which iSfunctioncapital

The default value for the width function W is I unit of time. The modeluses the quotient of new interval width and old interval width and therebycreates a quotient of dimensionless unity when I unit of time is entered for,say, each of two years containing 365 days. A default value would bewhen the user specifies a quantity function but omits to specify a widthfunction. Proxy values for the width function arise when a proxy product or a

proxy cost resource is required, as specified in Part G of the book.

T is a dimensionless function.

(Cl DI)

(Cl D2)

The above suite of statements refers to the level of a function. It definesthe user specified Target return on investment which is used to define thetarget profit level by individual element of capital investment. It is definedonly for capital resources.

The default value for both old target return on investment and new targetreturn on investment is the function for old intrinsic return on investmentwith respect to a specified contrast. It is used when the user specifiescapital asset value but omits to specify a target return on investment. A

proxy value for target return on investment arises when proxy capital isrequired, as specified in Part G of the book.

S (RISK WEIGHT FOR INVESTMENT) is a user specified function.

S is a dimensionless function.

(Cl El)

(Cl E2)

The above suite of statements refers to the level of a function. It definesthe user specified risk weight on investment which is one of the functionsused to distribute the intrinsic profit level to the individual elements ofcapital investment.

The default value for risk weight for investment is dimensionless unity. Itis used when the user specifies capital quantity and price but omits tospecify a risk weight for investment. A proxy value for the risk weight forinvestment arises when proxy capital is required, as specified in Part G ofthe book.

REM (RESOURCE VARIABILITY RATIO) is a user specified function.

REV/i is a dimensionless function.(Cl F2)

The above suite of statements refers to change in the level of a function.It defines thenormalization function which is the REsource VAriability ratio.This variable is defined on a contrast. Its function is to separate long termcontrol from short term control measures as shown

Part F of the book is devoted to a more detailed discussion of REVA. Atthis stage it is sufficient to say that this function constitutes a

variability coefficient which is applied to the ratio of product quafltitychange to prescribe the ratio by which resource quantity should change forconstant efficiency. Hence, for example, a REVA value of positive unitywould be prescribed for a resource which is deemed by the cost tobe purely variable with respect to a given change in the level ofquantity (i.e. deemed by the economist to be subject to constant returii toscale). Similary, a REVA value of zero would be prescribed for a resiurcewhich is deemed by the cost accountant to be purely fixed with respect a

given change in product quantity (i.e. deemed by the economist to be subjectto variable returns to scale).

The default value for REVA, for both cost resources and capitalis dimensionless unity. It is used when the user specifies a resourcefunction but omits to specify REVA. A proxy value for REVA for a caAitalresource arises when proxy capital is required, as specified in Part Gbook. Since there is never need for a proxy cost resource, there isheed for a proxy value for REVA for a cost resource.

B1—4 Bl—5

U

T (TARGET RETURN ON INVESTMENT) is a user specified function.

Figure B1.F2 -. BREAKDOWN CREATED BY REVA (RESOURCE VARIABILITY RATIQI

LONG TERM CONTROL SHORT TERM CONTROL CAPACITY UTILIZATIONVARIANCE VARIANCE VARIANCE

Efficiency variance Capacity utilization= in new prices + variance in new

Productivity variancein new prices

Long termprice recoveryvan ance

Long termproduct profitvan ance

Long termresource pricevariance

Long termproduct costvariance

Short term= price recovery

variance

Short term= product profit

variance

Short term= resource price

variance

Short term= product cost

variance

Capacity utilization+ term in price recovery

variance -

Capacity utilization+ term in product

profit variance

Capacity utilization+ term in resource

variance

Capacity utilization+ term in product cost

variance

(Cl Fl)

RATIO OF TARGET ClAP/GE IN EFFICIENCY is a user specified function.(BI Gi)

RATIO OF TARGET C/lANGE IN EFFICIENCY is a dimensionless function.(Bl Ga)

The above suite of statements refers to change in the level of a function.

It defines the function for ratio of target change in efficiency. Thisvariable is defined on a contrast. Its function is to contribute to thespecification of the new resource quantity required for efficiency variance toachieve targeted change in efficiency, as will be shown in statement (C3 Al).

The default value is zero, and there is no proxy value for this function.

RATIO OF TARGET CHANGE IN PRODUCTIVITY is a user specified function.(Bl Hl)

RATIO OF TARGET CHANGE IN PROOUCTIVITY is a dimensionless function.(Bl H2)

The above suite of statements refers to change in the level of a function.It defines the function for ratio of target change in productivity. Thisvariable is defined on a contrast. Its function is to contribute to thespecification of the new resource quantity required for productivity varianceto achieve targeted change in productivity, as will be shown in statement(C3 A4).


RATIO OF TARGET CHANGE IN RESOURCE PRICE is a user specified function.(Bl Ii)

RATIO OF TARGET CHANGE IN RESOURCE PRICE is a dimensionless function.(Bl 12)

The above suite of statements refers to change in the level of a function.It defines the function for ratio of target change in resource price. Thisvariable is defined on a contrast. Its function is to contribute to thespecification of the new resource price required for (short or long term)resource price variance to achieve targeted (short or long term) resourceprice variance, as will be shown in statement (C3 Dl).


RATIO OF TARGET CHANGE IN PRICE RECOVERY is a user specified function.(B1 J1)

RATIO OF TARGET CHANGE IN PRICE RECOVERY is a dimensionless function.(BI J2)

The above suite of statements refers to change in the level of a function.It defines the function for ratio of target change in price recovery. Thisvariable is defined on a contrast. Its function is to contribute to thespecification of the new resource price required for (short or long term)price recovery variance to achieve targeted (short or long term) pricerecovery variance, as will be shown in statement (C3 02).


The discussion of the 10 user specified input functions is concluded.

Bl—6

PART C — AXIOMS FOR ALL REPORTS



Chapter C2 AXIOMS FOR FUNCTIONS IN INPUT REPORTS

Chapter C3 AXIOMS TO GENERALIZE FUNCTIONS FORNEW RESOURCE QUANTITY AND NEW RESOURCE PRICE

Chapter C4 AXTONS FOR FUNCTIONS TO MEASURE CHANGE IN PRODUCTIVITY,CAPACITY UTILIZATION AND EFFICIENCY

Chapter C5 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN LONG TERM ANQ SHORTTERM PRODUCT PROFIT

Chapter C6 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN LONG TERM ANQ SHORTTERM PRODUCT COST

Chapter C7 AXIOMS FOR FUNCTIONS IN PROFIT AND COST RECONCILIATIONREPORTS


There are three published notations which express the axioms and rglatedmathematical concepts specified by deterministic productivity Theyhave been developed to reach audiences with differing levels ofappreciation. Notation I is presented in this book and is aimed themanager whose formal mathematical experience is limited to highalgebra. Notations 2 and 3 assume a more advanced level of matheniflicalappreciation in the reader and are described in the Appendix B bibliography.

The reader who has mathematical training at the tertiary level should notethat notation I axioms do not pretend to be definitive and general. Theymerely present a special case which is sufficient to illustrate the basiv ideaunderpinning the v?rious measures. Whenever there is need in this book fur a

more complex algebraic expression than can be accommodated by the limitAtionsimposed by notation 1, a verbal explanation of the concept is provided.

Notation 3, which is definitive and general, employs differenceranging from ordinary differences of degree one and order one to pfltialdifferences of higher degree and higher order. By contrast, Iexcludes the higher degree property and employs difference equationsfrom ordinary differences of degree one and order one to partialof degree one and higher order. Such restriction to degree onesuppressing reference to the interval width function W in the ensuingalthough its effect has been illustrated in chapter BI.

Although notation I is intended to serve the needs of users of the softwareimplementations of this work which have been approved by the author, isinadequate for those who wish to write a comprehensiveimplementation. Such need can only be served by the notation 3

k

Cl — 1

Cell

(5) , (6)

Report

Input Validation "A" Report

Input Compact Report

C2—2

I Chapter C2 AXIOMS FOR FUNCTIONS IN INPUT REPORTS

This chapter presents axioms for the 6 Input Reports implemented in the 1988software release of determinstic productivity accounting. Examples of theaxioms and their reports appear in chapters [1 through E6.

INTRINSIC PROFIT

This measure refers to the level of a function, and its dimensionalcoefficient is a currency unit. Numerical examples for old and new intervalsappear in the following references.

Chapter Cell Report

El (1) , (2) Input Validation "A" Report

E5 Input Compact Report

The following two axioms are self—explanatory. The second expressions ineach axiom provide the mneumonic for the functions which appear in the firstexpression.

OLD INTRINSIC PROFIT a OLD TOTAL REVENUE - OLD TOTAL COST RESOURCES

PRDFITo7d a REVENUEoId — COSTo7o'(C2 El (1))

NEW INTRINSIC PROFIT a NEW TOTAL REVENUE — NEW TOTAL COST RESOURCES

PRDFITneW a REVENUEnew — CDSTnew(C2 El (2))

The words OLD and NEW refer to different accounting periods employed for a

contrast. They could be two historical periods, two forecast (i.e., budget)periods, any permutation of historical and forecast data for a givenoperation, or two different operations making similar product with respect toany permutation of historical and forecast data.

The following axioms define the average intrinsic return on investment fortotal capital resources valued at asset valuation as distinct from targetprofit valuation.

INTRINSIC RETURN ON INVESTMENT

This measure refers to the level of a function, and its dimensionalcoefficient is dimensionless. Numerical examples for old and new intervalsappear in the following references which explain the significance of the timecomponent introduced by the intrinsic profit dividend (i.e., numerator).

Chapter Cell Report


ES Input Compact Report

OLD INTRINSIC PROFITCo a

OLD TOTAL ASSET VALUE OF CAPITAL RESOURCES (K ROWS)

(C2 ci (3))WHERE Co = OLD INTRINSIC (ACTUAL) RETURN ON INVESTNENT

NEW INTRINSIC PROFITCn a

NEW TOTAL ASSET VALUE OF CAPITAL RESOURCES (K ROWS)

(C2 Rj (4))WHERE Co = NEW INTRINSIC (ACTUAL) RETURN ON INVESTMENT

TARGET PROFIT VALUE

This measure refers to the level of a function, and itscoefficient is a currency unit. Numerical examples for old and new irflervalsappear in the following references.

Chapter

El

ES

The following axioms define the target profit for each capital asset. Thismeasure defines a dollar cost value of capital assets per unit of time whichplaces capital and cost resources on to the same footing. Henceforth it willbe possible to treat capital and cost resources in exactly the same forpurposes of productivity measurement and analysis.

OLD TARGET PROFIT VALUE (Ti)

a OLD CAPITAL ASSET VALUE (Xi) * OLD TARGET RETURN ON CAPITAL

= Vo(Ki) *To(C2 El (5))

NEW TARGET PROFIT VALUE (Ti)

a NEW CAPITAL ASSET VALUE (Ki) * OLD RETURN ON CAPITAL

= Via (Xi) *. To

(C2 (6))

TARGET PROFIT PRICE

This measure refers to the level of a function, and itscoefficient is a currency unit divided by the dimension to which thequantity refers. Numerical examples for old and new intervals thefollowing references.

Chapter Cell Report


ES Input Compact Report

This measure refers to the level of a function, and its dimensionalcoefficient is a currency unit. Numerical, examples for old and new intervalsappear in the following references.

Chapter Cell Report

El (9) , (10) Input Validation 'A' Report


The following axioms define the total target profit for all capital assets.

OLD TOTAL CAPITAL RESOURCES VALUE (T ROWS)

a SUM OF OLD CAPITAL VALUES (T ROWS)(C2 El (9))

MEW TOTAL CAPITAL RESOURCES VALUE (T ROWS)

a SUM OF NEW CAPITAL VALUES (T ROWS)

TOTAL RESOURCES VALUE

This measure refers to the level of a function, and its dimensionalcoefficient is a currency unit. Numerical examples for old and new intervalsappear in the following references.

Chapter Cell Report


E5 Input Report

The following axioms define the total resource value as the sum of totalcost resource value and total target profit for all capital assets.

This measure refers to the level of a function,coefficient is a currency unit. Numerical examples forappear in the following references.

Chapter Cell Report



The following axioms define offtarget profit as the difference betweenintrinsic profit and target profit. It represents the deviation of 'targetprofit (i.e., dollar cost of capital) from available profit.

OLD OFFTARGET PROFIT m OLD INTRINSIC PROFIT — OLD TARGET PROFIT(C2 Ei (13))

C2—3 C2—4

The following axioms define the target profit price for each capital asset.This measure contains the time component referred to in the previous measure.

OLD TARGET PROFIT PRICE (Ti)

m OLDCAPITAL ASSET PRICE (Ki) * OLD RETURN ON CAPITAL

= Po (Ki) * To(C2 El (7))

NEW TARGET PROFIT PRICE (Ti)

m NEW CAPITAL ASSET PRICE (Ki) * OLD RETURN ON CAPITAL

= Pn(Ki) *Tn(C2 El (8))

TOTAL CAPITAL RESOURCES TARGET PROFIT VALUE

OLD TOTAL RESOURCES VALUE

m OLD TOTAL COST RESOURCES VALUE

+ OLD TOTAL CAPITAL RESOURCES VALUE (T ROWS)

NEW TOTAL RESOURCES VALUE

m NEW TOTAL COST RESOURCES VALUE

+ NEW TOTAL CAPITAL RESOURCES VALUE (T ROWS)

OFFTARGET PROFIT VALUE

(C2 EJ (11))

(C2 (12))

and itsold and new

(C2 El (10))

NEW OFFTARGET PROFIT a NEW INTRINSIC PROFIT — NEW TARGET PROFIT(C2 (14))

RESOURCE VARIABILITY RATIO (REVA)

This measure refers to change in the level of a function, aod itsdimensional coefficient is dimensionless. Numerical examples for a(defined as an old interval vs. new interval pair) appear in the foTTowingreferences.

Chapter Column Report

E2 A Input Validation "B' Report

E5 A Input Compact Report

REVA represents REsource VAriability. It is discussed in statements Fl)and (Bl F2), as well as in chapter Fl.

INTRINSIC RETURN ON INVESTMENT

This measure refers to the level of a function, and its dimensionalcoefficient is dimensionless. Numerical examples for Co and Cn, for old andnew intervals respectively, appear in the following references.


E2 D , H Input Validation "B" Report

RISK WEIGHT

This measure refers to the level of a function, and itscoefficient is dimensionless. Numerical examples for old and new

in the following references.


E2 E , I Input Validation "B" Report

So represents old interval risk weight for a capital resource.

Sn represents new interval risk weight for a capital resource.

Function S is discussed in statements (Bi El) and (Bi E2).

INTRINSIC VALUE VARIANCE

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples formeasure for each product and resource appear in the following references.


E3 A Input Variance Report

The mneumonic for this function is VALUEintrinsic. It measures the intribsic• change between two intervals before any adjustment is made for the effectjf a

- gap between the two periods and differing interval widths. This functiow isdefined for.each product and each resource. V/lLUEintrinsfc is used to specify

C2—5 C2—6

Co represents old interval intrinsic return on investment for aresource.

• (C2

Function Co for total capital resources is discussed insupporting chapter El cell (3). Function Co for an individual cqitalresource employs the old risk weight So and is derived from an axiomappears in the book on difference calculus cited as bibliography item inAppendix B of this book.

Co represents new interval intrinsic return on investment for a ca&talresource.

(C2 E2 LiE)

Function Cn for total capital resources is discussed in statqthentssupporting chapter El cell (4). Function Cn for an individualresource employs the new risk weight Sn and is derived from an axiom jjhichappears in the book on difference calculus cited as bibliography item inAppendix B of this book,

INTERVAL WIOTH

This measure refers to the level of a function, and its dimensionalcoefficient is a unit of time such as months or days. Numerical examples forold and new intervals appear in the following references.


E2 B , F Input Validation "B" Report

Wuo represents old interval width for a product, andWo represents old interval width for a resource.

(C2 E2 Bl)

Wun represents new interval width for a product, andWn represents new interval width for a resource.

(C2 E2 B2)

Function W is discussed in statements (Bl Cl) and (Bl C2).

TARGET RETURN ON INVESTMENT

This measure refers to the level of a function, and its dimensionalcoefficient is dimensionless. Numerical examples for old and new intervalsappear in the following references.


E2 C , C Input Validation "B" Report

To represents old interval target return on investment for a capitalresource.

(C2 E2 Cl)

Tn represents new interval target return on investment for a capitalresource.

(C? E2 C2)Function T is discussed in statements (Bl Dl) and (Bl D2).

(C2 E2

(C2 E2

the function I$7intrinsic later in this chapter. VALUE VARIANCE

VALUEintrinsic a VALUErieW — VALUEo1d(C2 E3 A)

INTERVAL GAP VARIANCE

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples for thismeasure appear in the following references.


E3 B Input Variance Report

The mneumonic for this function is VALUEgap. It adjusts for a gap betweenold and new intervals. It assumes a zero value when the intervals arecontiguous and are therefore separated by zero gap. VALUEgap is used tospecify the function Ajigap later in this chapter.

The function VALUEgap represents interval gap variance for each.product andeach resource.

(C2 E3 B)

The axiom for this function involves a AX divisor and appears in the book ondifference calculus which appears as bibliography item A15 in Appendix B ofthis book.

INTERVAL WIDTH VARIANCE

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples for thismeasure appear in the following references.


E3 C Input Variance Report

The mneumonic for this function is VALUEwIdth. It adjusts for differentinterval widths in old and new intervals. It assumes a zero value when theinterval widths are equal. VALUEwidth is used to specify the function lit/widthlater in this chapter.

The function VALUEwidth represents interval gap variance for each productand each resource.

(C2 E3 C)

The axiom for this function appears in the book on difference calculus whichappears as bibliography item A15 in Appendix B of this book.

C2—7

This measure refers to change in the level of a function, aQj itsdimensional coefficient is a currency unit. Numerical examples and a çjlagramfor this measure appear in the following references.


E3 D Input Variance Report. See also Figure E3.F1

The mneumonic for this function is VALUEchange. It reflects change in valueafter adjustments have been made for interval gap and interval width. Thisfunction is defined for each product and each resource. VALUEchaoge usedto specify the function AV later in this chapter.

VALUEchange a VALUEnew — VALUEo1d (in our simplified example)

= VALUEintrinsic (Column A in our simplified example)(C2 P1)

Since our example assumes no interval gap and equal interval width jn oldand new intervals, the above specification suppresses reference to andwidth although the; appear in the axiom for this column given in the bcjblc ondifference calculus which appears as bibliography item A15 in Appendix/B ofthis book.

PURE VDLUNE VARIANCE

This measure refers to change in the level of a function, arni itsdimensional coefficient is a currency unit. Numerical examples and a diagramfor this measure appear in the following references.


E3 E Input Variance Report. See also Figure E3.F2

The mneumonic for this function is VOLUMEoJd. It reflects the purevariance contribution to change in value after adjustments have been forinterval gap and interval width. VOLUMEoJd is used to specify the functions

and later in this chapter.

VOLUME01d(u) ( Qun — Quo J * Puo(C2 E3 £1)

VOLUMEoJd(U) a SUM ALL VOLUMEoJd(u)(C2 E3 f2)

VOLUMEo1d a [ Qo — QoJ * PoE3

VOLUMEo1d(T) a SUM ALL VOLUMEoJd(C2 ES E4)

Since our example assumes no interval gap and equal interval width in oldand new intervals, the above specification suppresses reference to and

C2 — 8

width although they appear in the axiom for this column given in the book on - PRICErep(u) m (Qun — Quo) * (Pun — Puo]difference which appears as bibliography item A15 in Appendix B of (C2 E3this book. . PRICErep(U) SUM ALL PRIrep(u)

(C2 E3PRICErep m (Qn — Qo] * (Pn — Po]

(C2 E3PURE PRICE VARIANCE PRICErep(I) SUN ALL PRIrep

(C2 E3 44)

This measure refers to change in the level of a function, and its Since our example assumes no interval gap and equal interval width in olddimensional coefficient is a currency unit. Numerical examples and a diagram and new intervals, the above specification suppresses reference to gap and

for this measure appear in the following references. width although they appear in the axiom for this column given in the book ondifference calculus which appears as bibliography item A15 in Appendix 4 of

Chapter Column Report this book.

E3 F Input Variance Report. See also Figure E3.F3ADJUSTED PRICE VARIANCE

The mneumonic for this function is PRICEo7d. It reflects the pure pricevariance contribution to change in value after adjustments have been made for This measure to change in the level of a function, and itsinterval gap and interval width. PRICEo1d is used to specify the function dimensional coefficient is a currency unit. Numerical examples and aAVoid later in this chapter. for this measure appear in the following references.

Chapter Column 'ReportPRICEo1d(u) a Quo * (Pun — Puo]

(C2 E3 Fl) E3 F + C Input Variance Report. See also Figure E3.F5PRICEo1d(U) a SUM ALL PRICEoJd(u)

(C2 E3 F2)PRICEo7d a Qo * (Pn — Po] The mneumonic for this function is PRICEneW. It reflects the sum of uure

(C2 E3 F3) price and repricing variance contributions to change in valuePRICEoJd(I) a SUM ALL PRICEo1d adjustments have beet made for interval gap and interval width. PRICEnety" is

(C2 E3 F4) used to specify the function IsPnew later in this chapter.

Since our example assumes no interval gap and equal interval width in old -

and new intervals, the above specification suppresses reference to gap and PRICEneW(u) m Qun * (Pun — Puo]

width although they appear in the axiom for this column given in the book on (C? E3 Ii)difference calculus which appears as bibliography item A15 jn Appendix B of PRICEnew(U) a SUM ALL PRICEnew(u) -

this book. (C? E3 Hg)PRICEnew a Qn * (Pn — Po]

(C? E3

REPRICING VARIANCE PRICEnew(I) a SUM ALL PRICEnew(C? £3 U4)

This measure refers to change in the level of a function, and its Below each of the above axioms, statement references cite Hi to H4dimensional coefficient is a currency unit. Numerical examples and a diagram these functions do not appear in any report but are the sum of two existingfor this measure appear in the following references. columns as cited below in the numerical examples for this measure.

Chapter Column Report Since our example assumes no interval gap and equal interval width in' oldand new intervals, the above specification suppresses reference to gap and

£3 C Input Variance Report. See also Figure E3.F4 width although they appear in the axiom for this column given in the book ondifference calculus which appears as bibliography item A15 in Appendix U ofthis book.

The mneumonic for this function is PRICErep. It reflects the repricing(i.e., interactive or joint volume and price) variance contribution to changein value after adjustments have been made for interval gap and interval width. CHANGE IN RELATIVES

The function PRICErep is used to specify the function APnew in a laterchapter.

The next six functions provide data on percentage changes in relatives forvalue, quantity and price with respect to all product made and resources

C2—g C2—1O

A relative is a dimensionless which is the quotient of two measureswhich refer to the same function at two different points in time and/or space.Axioms in subsequent chapters make extensive use of change in relatives whichappear in this chapter. A relative is also known as an index number.

Since this book is used as a help—file for computer implementations of themodel and computer monitors are not yet geared to handle the A and A symbols,a modification of such notation appears on a computer screen as shown inchapter E4.

CHANGE In INTRINSIC VALUE RELATIVE

This measure refers to change in the level of a function, and itsdimensional coefficient is dimensionless. Numerical examples for this measureappear in the following references.


E4 A Input Relative Report

The mneumonic for this function is Afiintrinsic. It is read as delta V hatintrinsic. The A signifies "change in". Symbol V refers to a valuefunction. Presence of a hat A signifies that the measure is dimensionless.After the j7intrinsic the symbol (u) signifies an individual product, thesymbol (U) signifies total products in the case of multiple products, theabsence of a symbol signifies an individual resource and the symbol (I)signifies total resources.

Atjintrinsic is used to specify the function PROFlTintrinsic in chapter C7

and the function COSTintrinsic in chapter C8.



E4 B Input Relative Report

The mneumonic for this function is Aj7width. It represents the INTERVALWIDTH EFFECT contribution to CHANGE in INTRINSIC VALUE RELATIVE Ai7intrinsic.At/width is read as delta V hat width. The A signifies "change in". Symbol V

refers to a value function. Presence of a hat A signifies that the measure isdimensionless. After the Vwidth the symbol (u) signifies an individualproduct, the symbol (U) signifies total products in the case of multipleproducts, the absence of a symbol signifies an individual resource and the

CHANGE In VALUE RELATIVE

This measure refers to change in the level of a function, itsdimensional coefficient is dimensionless. Numerical examples and a :diagramfor this measure appear in the following references.


E4 C Input Relative Report. See also Figure E4.F1

ES H Input Compact Report

The mneumonic for this function is Ajl. It represents the CHANGE IN THEVALUE RELATIVE contribution to CHANGE in INTRINSIC VALUE RELATIVE Aiule,trinsiconce the interval width effect has been factored out. Aji is read as V

hat. The A signifies "change in". Symbol V refers to a value tunction.Presence of a hat A signifies that the measure is dimensionless. Afteb the Vthe symbol (u) signifies an individual product, the symbol (U) signiftps totalproducts in the case of multiple products, the absence of a symbol iigniflesan individual resource and the symbol (I) signifies total resources. 1'

AV is used to the function PROFlTrevenue in chapter C7 and can beused to specify alternative axioms for the function PROFIT1ong in ch4pter C5

and the function COSTlong in chapter C6.

At/ m

VALUEo ld(C2 Cl)

CHANGE Ii (OLD-PRICE-WEIGHTED) LASPEYRES QUANTITY RELATIVE

This measure refers to change in the level of a function, itsdimensional coefficient is dimensionless. Numerical examples and a

for this measure appear in the following references.


E4 D Input Rdlative Report. See also Figure E4.F2

I Input Compact Report

The mneumonic for this function is 14o7d. It represents the

C2 — 11. C2 — 12

symbol (I) signifies total resources.

At/width is used to specify the function PROFITwidth in chapter C7 pnd thefunction COSTwidth in chapter CS.

At/width a VALUEwidth / VALUEoJd(C2 51)

I

At/intrinsic a VALUEintrinsic / VALUEoJd

INTERVAL WIDTH EFFECT In the value relative

(C2 E4 Al)

VALUEchange

E5

WEIGHTED CHANGE in QUANTITY RELATIVE i4old which is read as delta Q hat oldand known as change in the Laspeyres quantity relative. The A signifies"change in". Symbol Q refers to a quantity function. Presence of a hatsignifies that the measure is dimensionless. The word old signifies that oldprices are used to weight (i.e., aggregate) quantity changes. After thethe symbol (u) signifies an individual product, the symbol (U) signifies totalproducts in the case of multiple products, the absence of a symbol signifiesan individual resource and the symbol (I) signifies total resources.

is used later in this chapter to specify the function Qne,representing new resource quantity normalized for constant efficiency, aedQnp, representing new resource quantity normalized for constant productivity.It can also be used to specify alternative axioms for functions Y and E inchapter C4 and function COSTlong in chapter C6.

VOLUMEo lda

VALUEo Id(C2 E4 Dl)

CHANGE IN THE UNWEIGHTED CHANGE IN TOTAL PRODUCT QUANTITY RELATIVE


Chapter

E4 page 5

The mneumonic for this function is It represents the UNWEIGHTED

CHANGE in TDTAL PRDDUCT QUANTITY which is read as delta Q hat(dimensionally improper) of U. The A signifies "change in". Symbol Q refersto a quantity function. Presence of a hat A signifies that the measure isdimensionless. The word dim signifies a dimensionally improper addition (as

distinct from a dimensionally proper addition which flows from the use ofprice weights) to aggregate quantity changes. After the the symbol (U)signifies total products in a multiple product situation.

Although is never shown in any report, it is used to specify thefunctions COSTvolume and COSTmix in chapter C8.

CHANGE IN THE (NEW-QUANTITY-WEIGHTED) PAASCHE PRICE RELATIVE




E4 E Input Relative Report. See also Figure E4.F3

The mneumonic for this function is It represents the NEW—QUANTITY—WEIGHTED CHANGE in PRICE RELATIVE which is read as delta P hat diw andkeown as change in the Paasche price relative. The A signifies in".Symbol P refersto a price function. Presence of a hat A signifies themeasure is dimensionless. The word new signifies that new quantities usedto weight (i.e., aggregate) price changes. After the Pnew the (u)signifies an individual product, the symbol (U) signifies total prodwts inthe case of multiple products, the absence of a symbol signifies an individualresource and the symbol (I) signifies total resources.

Function LtPnew(U) is used later in this chapter to specify the Pnrrepresenting new resource price normalized for constant price

APnew a

(C2 f4 El)

CHANGE IN THE (OLD-QUANTITY-WEIGHTED) LASPEVRES PRICE RELATIVE

This measure refers to change in the level of a function, abd itsdimensional coefficient is dimensionless. Numerical examples and a

for this measure appear in the following references. -


F Input Relative Report. See also Figure E4.F4

The mneumonic for this function is Sold. It represents the OLD—QUANTITY—WEIGHTED CHANGE in PRICE RELATIVE /sPold which is read as delta P hat ai4 andknown as change in the Laspeyres price relative. The A signifies "changp in".Symbol P refers to a price function. Presence of a hat A signifies tim themeasure is dimensionless. The word old signifies that old quantities er-a- usedte weight (i.e., price changes. After the Pold the (u)signifies an individual product, the symbol (U) signifies total inthe case of multiple products, the absence of a symbol signifies an indfjtidualPesource, and the symbol (I) signifies total resources. -

APold(I) can be used in chapter C6 to specify an alternative forfunction Z which represents resource price variance. -

PRICEo ld(U)A?old(U) a

___________

VALUE0Id(U)

A-.

PRICEnew

VALUEo1d ÷ VOLUMEo1d

a

E4

[SUM Qun — SUM Quo] for total products

(C2 E4 D2)SUM Quo for total products

C? — 14

(C2 E4 El)

J

&i__

CHANGE IN THE GENERAL PRICE RELATIVE The mneumonic for this function is Qne. It represents new resource quantitynormalized for constant (i.e., old) efficiency with respect to new production.It prescribes a new level of resource quantity, given a new level of pfdduct

This measure refers to change in the level of a function, and its - quantity, assuming that old efficiency level is maintained in newdimensional coefficient is dimensionless. Numerical examples for this measure interval. This function recognizes the existence of a step functionappear in the following references. indicates that a portion of resource quantity can be subject to

capacity utilization and should therefore remain fixed while productChapter Column Report changes. Qne prescribes a level of resource usage in the new interval Ipsed

upon movement along the step function which recognizes that in the shortE4 G Input Relative Report. resource usage is nut necessarily variable with respect to product

This function is therefore used for short term control analysis to£5 J Input Compact Report. step function refers.

In the following axiom interval width is built into the function as

The mneumonic for this function is It represents change in the cited in the discussion in this chapter of statement (C2 E4 Dl).Paasche price relative with a default value of change in the Laspeyres pricerelative when the Paasche price relative is not defined. The lattersituation occurs with respect to an entity deletion (i.e., an entity for which Qne a Qo * [1 + REVA * AQold(1J)]no quantity is defined in the new interval although a quantity was defined in (C2 F))the old interval).

£Pgen is used in the Input Compact Report to illustrate Qne = Qo where REVA = 0 when the resource quantity is prescribes tostay fixed despite product

for relatives the axiom (1 + IsV.) m (1 ÷ * [1 + APnewJ change.- (C2 II)

which derives from VALUE a QUANTITY * PRICE.Qne = Qnp where REVA = 1 when the resource quantity is prescribed to

i— where IsPnew exists vary in direct proportion toAPgen a quantity change.

L__. LPo7d where NPnew does not exist (C2 fl)(C2 £4 Cl) -

The above condition appears to single and multiple products as well as to NEW RESOURCr QUANTITY NORMALIZED FOR CONSTANT PRODUCTIVITY

single and multiple resources.

This measure refers to the level of a function, and itsNORMALIZED NEW QUANTITY AND NEW PRICE coefficient is the dimension to which the quantity function refers.

examples and a diagram for this measure appear in the following referencea,

The next three functions provide data on normalized new quantity and new Chapter Column Reportprice. The two possibilities for normalization are designated productnormalizations and resource normalizations. They are mutually exclusive and - E6 Qnp Input Normalized quantity and Price Reportare set out in Figure E6.Fl in chapter £6. This chapter specifies axioms forresource normalization. Product normalizations are provided for the advanced Ki See figure K1.Flreader in chapter KI.

The mneumonic for this function is Qnp. It represents new resourceNEW RESOURCE QUANTITY NORMALIZED FOR CONSTANT EFFICIENCY normalized for constant (i.e., old) productivity with respect to new prutjuct

quantity. It prescribes a new level of resource quantity, given a new leve' ofproduct quantity, assuming that old productivity level is maintained in

the level of a function, and its dimensional new interval. This function ignores the existence of the step func$Joncoefficient is the dimension to which the quantity function refers. Numerical described above and assumes resource usage is fully variable with respecU toexamples and a diagram for this measure appear in the following references, change in product quantity. It is therefore relevant to long -term

analysis since it deals with both the fixed and variable ofChapter Column Report resource usage, because in the long term all resources are variable with

respect to change in product quantity.E6 Qne Input Normalized Quantity and Price Report

In the following axiom interval width is built into the function tsQold(Vj asFl See figure Fl.F1 through F5 cited in the discussion in this chapter of statement (C2 E4 Dl).

C2-15 C2-16

j

This measure refers to the level of a function, and its dimensionalcoefficient is a currency unit divided by the dimension to which the resourcequantity function refers. Numerical examples and a diagram for this measureappear in the following references.


E6 Par Input Normalized Quantity and Price Report

KI See figure Ki.F2

The mneumonic for this function is Par. It represents new resource pricenormalized for constant (i.e., old) price recovery with respect to new productprice. It prescribes a new level of resource price given a new level ofproduct price assuming that the old price recovery level is maintained in thenew interval. Par is used for long term and short term control analysis.

In the following axiom interval width is built into the function Li2new(U) ascited in the discussion in this chapter of statement (C2 E4 El).

Par m Po * [1 + APaew(U)J(C2 Hi)

Chapter C3 - AXIOMS TO GENERALIZE FUNCTIONS FORNEW RESOURCE QUANTITY ANO NEW RESOURCE PiHCE

The purpose of this chapter is to generalize the functions for new resourcequantity and new resource price given in the Chapter C2. Axioms areto generalize the functions by adding the letter "g" to the function shown

below as well in Figure C3.Fi which appears thereafter.

qa, representing new resource quantity, becomes a special case of the more

general function Qag

Qne, representing new resource quantity adjusted for old efficiency, becomesa special case of the more general function Qaeg

Qap, representing new resource quantity adjusted for old produc4ivity,becomes a special case of the more general function Qapg

Pa, representing new resource price, becomes a special case of tk moregeneral function Png

Par, representing new resource price adjusted for old pricebecomes a special case of the more general function Parg.

Di 02

-

03

Cl

Bl

C2

B2

C3

B3

Al A2 A3

flnnrr

Dl D2

—.—--------—

RI B2

Al A2 A3

Po Pnrg

The above generalizations are used to introduce targeted inproductivity, price recovery and resource price. They are also toascertain, for example, what efficiency change is needed to offset ?esourceprice change for budgeting purposes.

Axioms for each of the above functions are specified below, and thereafter aappendix to this chapter provides the algebraic derivation of the

relevant axioms.

C3 — 1

Qap e Qo * (I + I4old(U)J

NEW RESOURCE PRICE NORMALIZED FOR CONSTANT PRODUCTIVITY

(C2 Gl)4..

C2—17

Figure C3.F1 GENERALIZING NEW RESOURCE QUANTITY AND PRICE

BEFORE GENERALIZINGNEW RESOURCE QUANTITIESAND NEW RESOURCE PRICES

AFTER GENERALIZINGNEW RESOURCE QUANTITIESAND NEW RESOURCE PRICES

Qnp

Qne

Qn

Qo

Cl C2 C3

Qng

Qo

Po Pn Pnr

Generalizing the function Qn into Qng

The function Qng generalizes the 7 functions shown in statement (C3 A7).The functions which appear in the right hand expression are specified below asa prelude to the specification of statement (0 A7).

Qnet a Qne / (1 + TARGET CHANGE IN EFFICIENCY](C3 Al)

= new resource quantity required for efficiency variance to achievetargeted change in efficiency.

The RATIO OF TARGET CHANGE IN EFFICIENCY is specified by the user, and itsdefault value is zero such that the default Qnet = Qne.

Qnez a Qne*Po/Pn(C3 A2)

= new resource quantity required for efficiency variance to offsetshort term resource price variance.

It is noted that Qnez = Qne when Pn = Po, i.e., zero efficiency variance andzero resource price variance.

Qner a Qne * Pnr / Pp(C3 A3)

= new resource quantity required for efficiency variance to offsetshort term price recovery variance.

It is noted that Qner = Qne when Pnr = Pn, i.e., zero efficiency varianceand zero price recovery variance.

Qnpt a Qnp / (1 + RATIO OF TARGET CHANGE IN PRODUCTIVITY](C3 A4)

= new resource quantity required for productivity variance toachieve targeted change in productivity

The RATIO OF TARGET CHANGE IN PRODUCTIVITY is specified by the user, and itsdefault value is zero such that the default Qnpt = Qnp.

Qnpz a Qnp*Po/Pn(C3 A5)

= new resource quantity required for prQductivity variance to Offsetlong term resource price variance

It is noted that Qnpz = Qnp when Pn = Po, i.e., zero productivity varianceand zero resource price variance.

Generalizing the function Qne Into Qneg

The function Qneg generalizes the 3 functions shown in statement (C3 B4}.The functions which appear in the right hand expression are specified belowa prelude to the specification of statement (C3 B4).

Qned e Qo * [1 + REVA *(C3 Dl)

= new resource quantity required for old efficiency usingtotal product

It is noted that Qned = Qne when = /4old(U), i.e., whentotal product quantity change and weighted total product quantity change

a function which is not used in the 19DBrelease of deterministic productivity accounting, but which wiU be used in:afuture release.

Sum of boxes Dl for all products in all operations

Sum of boxes Al for all products in all operations(0 B2)

= ratio for change in total product quantities with respect tocollapse cf all operations into a single operation.

The above function is used in the specification of functions Qnec and Qnpc

which are specified in this chapter.

C3—2 C3—3

Qnpr a Qnp * Pnr / Pn(C3 A6)

= new resource quantity required for productivity variance to offsetlong term price recovery variance

It is noted that Qnpr = Qnp when Pnr = Pn, i.e., zero productivityand zero price recovery variance.

Qng e Qn , Qnet , Qnez , Qner , Qnpt , Qnpz , Qnpr(C3 A7)

= new resource quantity in its most general form.

The above statement zignifies that Qng can •be represented by any of thefunctions specified in the right hand expression. Hence it generalizpsfunction Qn as well as functions specified in statements (C3 Al)(C3 A6).

______________________________________- .-

Qnec m Oa * (1 + REVA * liQo7dcalap(U)](C3 83)

= new resource quantity adjusted for old efficiency with respect tethe collapse of all operations into a single operation.

It is noted that Qnec = One when I4aldcalap(U) = i.e., when thereis no change in the mix of product quantities across all operations.

Oneg = Qne , Qned , Qnec(C3 84)

= new resource quantity adjusted for old efficiency in •its mostgeneral form.

The above statement signifies that Qneg can be represented by any of thefunctions specified in the right hand expression. Hence it generalizesfunction One as well as all functions specified in statements (C3 81) through(C3 B3).

Generalizing the function Qnp into Qnpg

The function Qnpg generalizes the 3 functions shown in statement (C3 C3).The functions which appear in the right hand expression are specified below asa prelude to the specification of statement (C3 C3).

Qnpd a 00 * [1 +(C3 Cl)

= new resource quantity required for old productivity usingunweighted total product quantities.

It is noted that Qnpd = Qnp when = i.e., when unweightedtotal product quantity change and weighted total product quantity change areequal

Qnpc m Qo * [1 +(C3 C2)

= new resource quantity adjusted for old productivity with respect tethe collapse of all operations into a single operation.

It is noted that Qnpc = Qnp when t4oldco!ap(U) = i.e., when thereis no change in the mix of product quantities across all operations.

Qnpg a Qnp , Qnpd , Qnpc(C3 C3)

= new resource quantity adjusted for old productivity in its mostgeneral form.

The above statement signifies that Qnpg can be represented by any of thefunctions specified in the right hand expression. Hence it generalizesfunction Qnp as well as all functions specified in statements (C3 Cl) through(C3 C2).

Generalizing the function Pn into Png

The function Png generalizes the 6 functions shown in statement D7). Thefunctions which appear in the right hand expression are specified b*low as aprelude to the specification of statement (C3 D7).

Pnt a Pa * (1 + RATIO OF TARGET CHANGE IN RESOURCE PRICE](C3 01)

= new resource price required for(short or long term) resource price variance to achieve targeted(short or long term) resource price variance.

The RATIO OF TARGET CHANGE IN RESOURCE PRICE is specified by the &4er, andits default vaNe is zero such that the default Pnt = Pa.

Pnrt m Pnr / [1 + RATIO OF TARGET CHANGE IN PRICE RECOVERY](C3 D2)

= new resource price required for(short or long term) price recovery variance to achieve targeted(short or long term) price recovery variance.

The RATIO OF TARGET CHANGE IN PRICE RECOVERY is specified by the andits default value is zero such that the default Pnrt = Pnr.

Pnez One*Po/On03)

= new resource price required for efficiency variance to oftsetshort term resource price variance

It is noted that Pnez = Pa when One = On, i.e., zero efficiency variance andzero resource price variance.

Pner a One * Pnr / On04)

= new resource price required for efficiency variance to offsetshort term price recovery variance

It is noted that Pner = Pnr when One = On, i.e., zero efficiency varianceand zero price recovery variance.

Pnpz a Onp * Pa / OnD5)

= new resource price required for productivity variancelong term resource price variance

It is noted that Pnpz = Pa when Qnp = Qn, i.e., zero productivity varianceand zer? resource price variance.

C3—4 C3—5

H

Pnpr a Qnp * Pnr / Qn(C3 06)

= new resource price required for productivity variance to offsetlong term price recovery variance

It is noted that Pnpr = Pnr when Qnp = Qn, i.e., zero productivity varianceand zero price recovery variance.

Png m Pn , Pnt , Pnrt , Pnez , Pner , Pnpz , Pnpr(C3 07)

= new resource price in its most general form.

The above statement signifies that Png can be represented by any of the

functions specified in the right hand expression. Hence it generalizesfunction Pn as well as all functions specified in statements (C3 Dl) through

(C3 06).

Generalizing the function Pnr Into Pnrg

The function Pnrg generalizes the 3 functions shown in statement (C3 ES).The functions which appear in the right hand expression are specified below asa prelude to the specification of statement (C3 ES).

Sum (Qun * Pun] / Sum Qun — Sum (Quo * Puo] / Sum Quoe

Sum (Quo * PuoJ / Sum Quo(C3 El)

= ratio of unweighted (dimensionally improper) change in totalproduct prices.

This statement specifies a function which is not used in the 1988 release efdeterministic productivity accounting, but which will be used in a future

release.

Pnrd a Pa * (1 + tsfidim(U)](C3 E2)

= new resource price required for old price recovery using

unweighted total product prices.

It is noted that Pnrd = Pnr when Ispdim(U) = i.e., when unweightedtotal product price change and weighted total product price change are equal

This statement specifies a function which is not used in the 1988 release at

deterministic productivity accounting, but which will be used in a future

release.

C3—-6

Sum of boxes A2 + 82 for all products in a77 operAtionsIsPnewcolap(U) a

Sum of boxes Al + Bl for all products in all operationsE3)

= ratio for change in total product prices with respect to thecollapse of all operations into a single operation.

The above function is used in the specification of function Pnrc which isspecified in this chapter. if

Pnrc a Po * (1 + bPnewcolap(U)]E4)

= new resource price adjusted for old price recovery with tothe collapse of all operations into a single operation. '

It is noted that Pnrc = Pnr when /sPnewcolap(U) = i.e., when tine rateof product price change for all operations is equal to that for 4' givenoperation.

Pnrg a Pnr , Pnrd , Pnrc(Q,i E5)

= new resource quantity adjusted for old productivity in Rn most• general form.

The above statement signifies that Pnrg can be represented by any pf thefunctions specified in the right hand expression. Hence itfunction Pnr as well as all functions specified in statements (C3 fl) and(13 E4). if

-i

13 — 7

Qaez (new resource quantity required forefficiency variance to offsetshort term resource price variance)

e r e EFFICIENCY VARIANCE SHORT TERM

IN NEW PRICES + RESOURCE PRICE VARIANCE

[Qne—Qa]*Pa +Qae*(Po—Pa](C3

_Qn*Pa+Qae*[Po—Pa] = 0(C3

= — Qae * [Pa + Po — Pa](C3

= Qae * Po(C3

= Qae*Po/Pa

= Qaez

Qaer (new resource quantity required forefficiency variance to offsetshort term price recovery variance)

e r e EFFICIENCY VARIANCE SHORT TERM

IN NEW PRICES + PRICE RECOVERY VARIANCE = 0

[Qae—Qa] *Pa +Qae* [Par—Pa] = 0

(C3 Gl)

*Pa+Qae* [Par—Pa] = 0(C3 G2)

— Qae * [Pa + Par — Pa](C3 G3)

= Qae * Par(C3 G4)

= Qae*Par/Pa = Qaer(C3 G5.l)

= Qaer(C3 G5.2)

w h e r e PROOUCTIVITY VARIANCE LONG TERMIN NEW PRICES + RESOURCE PRICE = 0

[Qap—Qa]*Pa +Qap*(Po—Pa] =0(C3 111)

Qa*Pn+Qap*[Po—Pa] = 0(C3

= —Qap*[Pa+Po—Pa](C3

= Qnp*Po(C3 U4)

= Qap*Po/Pa(C3

= Qapz(C3

Qapr (new resource quantity required forproductivity variance to offsetlong term price recovery variance)

w ii e e PROOUCTIVITY VARIANCE LONG TERMIN NEW PRICES + PRICE RECOVERY VARIANC[ = 0

(Qap—Qa]*Pa +Qap*(Par—Pa] =0(C3 fl)

* Pa + Qap * [Par — Pa] = 0

(C3 12)

— Qap * [Pa + Par — Pa](C3 )3)

= Qap * Par(C3 14)

= Qap*Par/Pa(C3

= Qapr(C3

C3—8 C3—9

TECHNICAL APPENDIX TO CHAPTER C3 DERIVATION OF Qapz (new resource quantity required forproductivity variance to offsetlong term resource price variance)

DERIVATION OF

Qaez = Qa wh

=> Qae * Pa

— Qa * Pa

=> Qa*Pa

=> Qa

DERIVATION OF

=0=0

Fl)

F2)

F3)

F4)

(C3 F5.1)

(C3 F5.2)

Qapz = Qa

=> Qap * Pa —

a — Qa * Pa

=> Qa*Pa

=> Qa

DERIVATION OF

Qapr = Qa

Qaer = Qa wh

=> Qae * Pa — Qa

— Qa * Pa =

=> Qa*Pa

a Qa

H

a

Qap * Pa — Qa

—Qa*Pa =

Qa * Pa

Qa

DERIVATION OF Pnez (new resource price required forefficiency variance to offsetshort term resource price variance)

Pnez = Pn w h e r e EFFICIENCY VARIANCE SHORT TERNIN NEW PRICES + RESOURCE PRICE VARIANCE =

[Qne—QnJ*Pn +Qne*(Po.-PnJ = 0

(C3 JI)

=> Qne*Pn—Qn*Pn+Qne*(Po_pn] = 0(C3 J2)

=> —Qn*Pn = —Qne*[Pn+Po—PnJ(C3 J3)

=> Qn*Pn = Qne*Po(C3 J4)

=> - Pn = Qne*Po/Qn(C3 J5.1)

= Pnez(C3 J5.2)

DERIVATION OF Pner (new resource price required forefficiency variance to offsetshort term price recovery variance)

Pner = Pn w h e r e EFFICIENCY VARIANCE SHORT TERMIN NEW PRICES + PRICE RECOVERY VARIANCE = 0

(Qne—QnJ*Pn +Qne*(Pnr—PnJ = 0

(C3 KI)

Qn*Pn+Qne*[Pnr—PnJ = 0

(C3 K2)

= —Qne* (Pn+Pnr—PnJ(C3 K3)

= Qne * Pnr(C3 K4)

= Qne*Pnr/Qn(C3 K5.l)

= Pner(C3 K5.2)

Pnpz (new resource price required forproductivity variance to offsetlong term resource price variance)

w h e r e PROOUCTIVITY VARIANCE LONG TERMIN NEW PRICES + RESOURCE PRICE VARIANCE 0

[Qnp—QnJ*Pn +Qnp*(Po—PnJ(C3

-Qn*Pn+Qnp*(Po—PnJ = 0

(C3 L?1

= —Qnp*[Pn+Po—PnJ(C3-

= Qnp*Po(C3

= Qnp * Po / Qn(C3

= Pnpz(C3

DERIVATION OF Pnpr (new resource price required forproductivity variance to offsetlong term price recovery variance)

a Qnp * Pn —

— Qn * Pp

'=> Qn *Pp

a Pn

w h e r e PROOUCTIVITY VARIANCE LONG TERMIN NEW PRICES + PRICE RECOVERY VARIANCE 0

(Qnp-QnJ*Pn +Qnp*(Pnr-PnJ(C3 Nfl

Qn*Pi-i-Qnp*(Pnr—PnJ = 0(C3 Mfl

= —Qnp*(Pn-i-Pnr—Pnj(C3

= Qnp-kPnr(C3 M4;

= Qnp*Pnr/Qn(C3

= Pnpr(C3

C3—l0 C3—1l

• DERIVATION OF

Pnpz = Pp

r> Qnp * Pp

a - Qn * pp

=> Qp*Pp

a Pp

It

Qne *

— Qn * pp

=>

=>

=>

=>

Pnpr = Pp

Qp * pp

pp

Chapter C4 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN PRODUCTIVITY,CAPACITY UTILIZATION AND EFFICIENCY

This chapter presents axioms for various performance reports implemented in

the 1988 software release of determinstic productivity accounting. The

concept of a "performance" measure relates product to resource. For example,intrinsic profit is a performance measure because it relates revenue (i.e.,product value) to expense (i.e., cost resource value). Similarly, measures ofchange in productivity, capacity utilization and efficiency reviewed in thischapter are performance measures because they are generated from informationon product quantity, resource quantity and resource price.

PRODUCTIVITY CHANGE

Change in productivity arises from change in the (fixed and variablecomponents) of resource content per unit of product quantity. The change inproductivity of an individual resource can be measured in the following 5 waysgiven by statements (C4 Al) through (C4 AS).

CHANGE IN RESOURCE QUANTITY OUE TO PRODUCTIVITY CHANGE

= Qnp — Qn(C4 Al)

This measure refers to change in the level of a function, and itsdimensional coefficient is the physical unit to which the resource quantityrefers. A numerical example for this measure appears in the followingreferences.


E6 Qn , Qnp Input Normalized Quantity and Price report

PRODUCTIVITY VARIANCE IN OLD PRICES

Yold = (Qnp — QnJ * Po(C4 A2)

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples and a diagranfor this measure appear in the following references.


£16 B Productivity Old & New Variance Report. See figure E16.F1

PRODUCTIVITY VARIANCE IN NEW PRICES

Ynew = (Qnp — Qn] *(C4 A3)

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples and a diagran

C4 —

1



£9 0 Profit Overview Report. See figure E9.Fl

Productivity variance in new prices is decomposed into contributiqns fromcapacity utilization variance in new prices and efficiency variance in newprices. There are 13 segments for this breakdown in the chapter D3presentation of the Productivity Grid.

PERCENTAGE CHANGE IN PRODUCTIVITY IN OLD PRICES

= Yold / [VALUEo7d + VOLUNE07d](q A4)




£16 £ Productivity Old & New Variance Report. See figuru El6.F2

PERCENTAGE CRINGE IN PRODUCTIVITY IN NEW PRICES

A7new = Ynew / V'lLUEnew(Cf A5)

This measure refers to change in the level of a function, &nd itsdimensional coefficient is dimensionless. Numerical examples and a diagramfor this measure appear in the following references.


£10 0 Long Term Product Profit Report. See figure

CAPACITY UTILIZATION CHANGE

Change in capacity utilization arises from change in the fixed ofresource content per unit of product quantity. The change inutilization of an individual resource can be measured in the waysgiven by statements (C4 81) through (C4 85).

CHANGE IN RESOURCE QUANTITY USED DUE TO CAPACITY UTILIZATION CHANGE

= Qnp — Qne

(Cf 81)

This measure refers to change in the level of a function, itsdimensional coefficient is the physical unit to which the resourcerefers. A numerical example for this measure appears in the fjllowingreferences. - -'

C4-2

1

Chapter Column Report EFFICIENCY CHANGE

E6 Qne , Qnp Input Normalized Quantity and Price report Change in efficiency arises from change in the variable component resourcecontent per unit product quantity and/or change in the underutilized fixedcomponent of resource quantity. The change in efficiency of an

CAPACITY UTILIZATION VARIANCE IN OLD PRICES resource can be measured in the following 5 ways given by statements Cl)through (C4 C5).

Lold = [Qnp — QneJ*Po(C4 B2)

CHANGE IN RESOURCE QUANTITY USED DUE TO EFFICIENCY CHANGE

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples and a diagram = Qnd — Qn

for this measure appear in the following references. Cl)

Chapter Column Report This measure refers to change in the level of a function, itsdimensional coefficient is the physical unit to which the resource

E18 B Productivity Component Old & New Report. See figure E18.F1 refers. A numerical example for this measure appears in thereferences.

CAPACITY UTILIZATION VARIANCE IN NEW PRICES Chapter Column Report

Lnew = (Qnp — QneJ * E6 Qn , Qne Input Normalized Quantity and Price report(C4 B3)

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. Numerical examples and a diagram EFFICIENCY VARIANCE IN OLD PRICES

for this measure appear in the following references.Eold = [Qne — QnJ*Po

Chapter Column Report (C$ C2)

E9 I Profit Overview Report. See figure E9.F3 . This measure refers to change in the level of a function, itsH . dimensional coefficient is a currency unit. Numerical examples and a

for this measure appear in the following references. -.

PERCENTAGE CHANGE IN CAPACITY UTILIZATION IN OLD PRICES Chapter Column Report

pAtold = Lold / (VALUE0Jd + VOLUMEo7d + EoJdJ E18 E Productivity Component Old & New Report. See E18.F2

(C48fl

This measure refers to change in the. level of a function, and its EFFICIENCY VARIANCE IN NEW PRICES

dimensional coefficient is dimensionless. Numerical examples and a diagramfor this measure are not provided. Enew = (Qne — QnJ * Pn

C3)

PERCENTAGE CHANGE IN CAPACITY UTILIZATION IN NEW PRICES This measure refers to change in the level of a function, itsdimensional coefficient is a currency unit. Numerical examples and a

Atnew = Lnew / rVALUEOOW + EnewJ for this measure appear in the following references.(C4 B5)


This measure refers to change in the level of a function, and its4 1

dimensional coefficient is dimeAsionless. Numerical examples and a diagram ES 0 Profit Overview Report. See figure E9.F2

Hfor this measure appear in the following references.

Chapter Column ReportPERCENTAGE CHANGE IN EFFICIENCY IN OLD PRICES

U E17 0 Productivity Component Variance Report. See figure E17.F2= Eold / (VALUE0Jd + VOLUMEoIdJ

(Q4 C4)

C4 -3 C4 -4

This measure refers to change in the level of a function, and its Chapter CS AXIOMS FOR FUNCTIONS TO NEASURE CHANGE IN LONGdimensional coefficient is dimensionless. Numerical examples and a diagram AND SHORT TERM PRODUCT PROFITfor this measure are not provided.

This chapter presents axioms for product profit performance reportsPERCENTAGE CHANGE IN EFFICIENCY IN NEW PRICES implemented in the 1988 software release of determinstic pro4uctivity

accounting. Measures of change in price recovery and product profitlsrnew = Enew / VALUEnew in this chapter are performance measures because they are from

(C4 CS) information on product quantity, resource quantity and product pj4ce andresource price.

This measure refers to change in the level of a function, and itsdimensional coefficient is dimensionless. Numerical examples and a diagramfor this measure appear in the following references. PRICE RECOVERY CHANGE

Chapter Column Report .

Change in price recovery arises from change in the relation of prodit$ priceE17 E Productivity Component Variance Report. See figure E17.F2 to resource price. The change in price recovery of an individual resdiirce can

be measured in the following 9 ways given by statements (C5 Al)• (C5 AS).

CHANGE IN RESOURCE PRICE ASSOCIATED WITH PRICE RECOVERY CHANGE

= Pnr — Pn

• (Ce: Al)

This measure refers to change in the level of a function, itsdimensional coefficient is a currency unit divided by the physical unit towhich the resource quantity refers. A numerical example for this

in the following references.


E6 Pn , Pnr Input Normalized Quantity and Price report

PRICE RECOVERY VARIANCE (FOR OLD PRODUCTION)

Rold = Qa * [Per —

(c A2)This measure refers to change in the level of a function, its

- dimensional coefficient is a currency unit. This measure is clean itnses Qo which is free of any productivity change component sinceconstant productivity at the old production level. Numerical examples iwe notprovided.

PRICE RECOVERY VARIANCE (FOR NEW PRODUCTION)

Rnew = Qn*[Pnr — Pc]

This measure refers to change in the level of a function, end itsdimensional coefficient is a currency unit. This measure isbecause it uses Qn which contains a productivity change component. Nijjericalexamples are not provided.

C4-5 CS-i

4—

Rshort = Qne * (P1w — PnJ

This measure refers to change •in the level of a function, and itdimensional coefficient is a currency unit. This measure is clean because L

uses Qne which is free of any efficiency change component since it assumes

constant efficiency at the new production level. Numerical examples and a

diagram for this measure appear in the following references.


£9 H Profit Overview Report. See figure E9.F2

LONG TERM PRICE RECOVERYVARIANCE (FOR NEW PRODUCTION)

Riong = Qnp * fPnr — PnJ

This measure refers to change in the level of a function, and I.

dimensional coefficient is a currency unit. This measure is clean because L

uses Qnp which is free of any productivity change component since it assumes

constant productivity at the new production level. Numerical examples and a

diagram for this measure appear in the following references.


E9 EProfit Overview Report. See figure E9.F1

PERCENTAGE CHANGE IN PRICE RECOVERY FOR OLD PRODUCTION

= Rold / [VALUE07d + PRICE0JdI

This measure refers to change in the level of a function, and i

dimensional coefficient is dimensionless. Numerical examples are not provides

PERCENTAGE CHANGE IN PRICE RECOVERY FOR NEW PRODUCTION

= Rnew / VALUEneW

This measure refers to change in the level of a function, and ii,

dimensional coefficient is dimensionless. Numerical examples are not

PERCENTAGE CHANGE IN SHORT TERN PRICE RECOVERY (FOR NEW PRODUCTION) H

CRshort = Rshort / (VALUEneW + Enew]

This measure refers to change in the level of a function, and i

dimensional coefficient is dimensionless. Numerical examples and a dirfor this measure appear in the following references.

C5 — 2


?9)

E1O E Long Term Product Profit Report. See figure E1O.F1

PRODUCT PROFIT CHANGE

Change in product profit arises from change in the relation of product priceto product cost which includes a target profit for cost of capital. •roductprofit change is therefore the complement of product cost change.they account for product price change.

The •change in product profit of an individual resource can be inthe following 2 ways given by statements (CS 81) through (C5 82).

SHORT TERM PRODUCT PROFIT VARIANCE (FOR NEW PRODUCTION)

= Qne * Pnr — Qn *(CS

This measure refers to change in the level of a function,a currency unit. Numerical examples and a diagram

this measure appear in the following references.

sapter Column Report

F Profit Overview Report. See figure E9.F2

iort term product profit variance is decomposed into fromficiency variance in new prices and short term price recoveryere are 13 segmerics for this breakdown in the chapter 08 presentation pf the

Term Product Profit Grid.

CS — 3

SHORT TERN PRICE RECOVERY VARIANCE (FOR NEW PRODUCTION)

(CS A4)Eli E Short Term Product Profit Report. See figure

PERCENTAGE CHANGE IN LONG TERN PRICE RECOVERY (FOR NEW PRODUCTION)

= R7ong / (VALUEnew + Ynew)

This measure refers to change in the level of a function, itsdimensional coefficient is dimensionless. Numerical examples and a jjiagramfor this measure appear in the following references.


(C5 All

(CS A8)

LONG TERM PRODUCT PROFIT VARIANCE (FOR NEW PRODUCTION) Chapter C6 AXIOMS FOR FUNCTIONS TO MEASURE CHANGE IN LONG TERNAND SHORT TERM PRODUCT COST

PROFITPong = Qnp * Pnr — Qn * Pn(CS 82)

This chapter presents axioms for product cost performance reportsThis measure refers to change in the level of a function, and its implemented in the 1988 software release of determinstic

dimensional coefficient is a currency unit. Numerical examples and a diagram -. accounting. Measures 'if change in resource price and product cost infor this measure appear in the following references. this chapter are performance measures because they are generated

information on product quantity, •resource quantity and resource price.Chapter Column Report

E9 C Profit Overview Report. See figure E9.F1 RESOURCE PRICE CHANGE

Long term product profit variance is decomposed into contributions from

productivity variance in new prices and long term price recovery variance. Change in resource price of an individual resource can be measured in theThere are 13 segments for this breakdown in the chapter D7 presentation of the following 9 ways given by statements (C6 Al) through (C6 A9).Long Term Product Profit Grid.

CHANGE IN RESOURCE PRICE

= Po — Pn

(C6 A!)

This measure refers to change in the level of a function and itsdimensional coefficient is a currency un.it divided by the physical unit towhich the resource quantity refers. A numerical example for this meOureappears in the following references.


E6 Pn , Po Input Normalized quantity and Price report

RESOURCE PRICE VARIANCE (FOR OLD PRODUCTION)

laid = Qo * (P0 — Pn](C6

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. This measure is clean ituses Qo which is fre! of any productivity change component since it

productivity at the old production level. Numerical examplesprovided.

RESOURCE PRICE VARIANCE (FOR NEW PRODUCTION)

mew = Qn * (Po — PnJ

(C6A3i

This measure refers to change in the level of a function, and itsdimensional coefficient is a currency unit. This measure is contamits4tedbecause it uses Qn which contains a productivity change component. Numericalexamples are not provided.

C5—4 C6—1

SHORT TERM RESOURCE PRICE VARIANCE (FOR NEW PRODUCTION)

Zshort = Qne * (P0 — Pnj(C6 A4)

This measure refers to change in the level of a function, anddimensional coefficient is a currency unit. This measure is clean because I

uses Qne which is free of any efficiency change component since it assunsconstant efficiency at the new production level. Numerical examples anddiagram for this measure appear in the following references.


E13 H Cost Overview Report. See figure E13.F2

LONG TERM RESOURCE PRICE VARIANCE (FOR NEW PROOUCTION)

Ziong = Qnp * (Po — Pn]

This measure refers to change in the level of a function, and Pdimensional coefficient is a currency unit. This measure is clean becauseuses Qnp which is free of any productivity change component since itconstant productivity at the new production level. Numerical examples anddiagram for this measure appear in the following references.


E13 E Cost Overview Report. See figure E13.F1

PRODUCT COST CHANGE

Change in product cost (which includes a target profit for cost of capitsl)f an individual resource can be measured in the following 2 ways giventatements (C6 Ri) through (C6 B2).

SHORT TERM PRODUCT COST VARIANCE (FOR NEW PRODUCTION)

COSTshort = Qne * Pa — Qn * Pn(C6 Ri)

us measure refers to change in the level of a function, and itsnensional coefficient is a currency unit. Numerical examples and a diagram

this measure appear in the following references.

bct Column Report

E13 F Cost Overview Report. See figure E13.F2

term product cost variance is decomposed into contributions fromiciency variance in new prices and short term resource price

nre are 13 segments for this breakdown in the chapter D5 presentation of (lienrt Term Product Cost Grid.

LONG TERM PROOUCT COST VARIANCE (FOR NEW PRODUCTION)

COSTlong = Qnp * Pa — * Pn(C6 B2)

This measure refers to change in the level of a function, and itswnsional coefficient is a currency unit. Numerical examples and a diagfim

this measure appear in the following references. -:

Column Report

C Cost Overview Report. See figure E13.F1

term product cost variance is decomposed into contributions frqmctivity variance in new prices and long term resource price varianàj.e are 13 segments for this breakdown in the chapter 04 presentation of itue'Term Product Cost Grid.

PERCENTAGE CHANGE IN LONG TERM RESOURCE PRICE (FOR NEW PRODUCTION)

7/ong = — Ziong / (VALUE01d + VOLUMEoJd + Yold](C6

5 measure refers to change in the level of a function, andmensional coefficient is dimensionless. Numerical examples and a diaØamr this measure appear in the following references.


i4 E Long Term Product Cost Report. See figure E14.F1

Attention is drawn to the footnote on the final page of chapter E15.

ii

4

it11

ft

PERCENTAGE CHANGE IN RESOURCE PRICE FOR OLD PRODUCTION

lxYold = — Zo7d / VALUEo7d

This measure refers to change in the level of a function, •anddimensional coefficient is dimensionless. Numerical examples are not provide

PERCENTAGE CHANGE IN RESOURCE PRICE FOR NEW PRODUCTION

A7new = — Znew / (VALUEoJd + VOLUMEoJd]

This measure refers to change in the level of a function, and I'dimensional coefficient is dimensionless. Numerical examples are not

PERCENTAGE CHANGE IN SHORT TERN RESOURCE PRICE (FOR NEW PRODUCTION)

ts7short = — Zshort / (VALUE0Jd + VOLUNEod + Eold](C6 AR)

This measure refers to change in the level of a function, anddimensional coefficient is dimensionless. Numerical examples and a d€for this measure appear in the following references.

Chapter Column ReportE15 E Short Term Product Cost Report. See figure E15.F1

C6 — 2 C6 — 3

— — — — — — — — — — — — a a' U • ——

AXIOMS FOR FUNCTIONS IN PROFIT AND COST RECONCILIATION PART D — GRIDS FOR PERFORMANCE REPORTS AND RECONCILIATION RERQRTS


Chapter D2 QUANTITY GRID

Chapter D3

(SHORT TERM)

PRODUCTIVITY GRID

Chapter D4 PRODUCT COST GRID

Chapter D5

TERM)

PRODUCT COST GRID

Chapter D6

(SHORT TERM)

PRICE GRID

Chapter

Chapter

D7

D8

PRODUCT PROFIT GRID (LONG TERM)

PRODUCT PROFIT GRID

Chapter D9

(SHORT TERM)

PRODUCT MIX COST GRID

Chapter 010 PRODUCT VOLUME COST GRID

Chapter

Chapter

D1I

D12

INVESTMENT VARIANCE PROFIT GRID

RETURN ON REVENUE VARIANCE

D13

PROFIT

TARGET ROl

GRID

GRID

Chapter C7

The axioms for functions in the Profit Reconciliation Report are simplerequire no special comment. They are specified in chapter E8 and a

supported by the explanantions in the profit reconciliation grids definedchapters Dli, 012 and 013.

Similarly, the axioms for functions in the Cost Reconciliation Report a

simple and require no special comment. They are specified in chapter E12 aare supported by the explanantions in the cost reconciliation grids definedchapters D9 and 010.

C7 — 1

Chapter

The following grids appear in this book and are classified as shown.

DIFFERENCE GRIDS [Y —

PERFORMANCE GRIDS

ProductivityL T Product CostS T Product CostL T Product ProfitS T Product Profit

L T QuantityS T QuantityPrice

PRODUCT GRIDS V kX

RECONCILIATION GRIOS

Product Mix Product VolumeInvestmentReturn on Revenue

I

Target Profit

he author has specified other grids which are omitted from this book sincey are not yet incorporated in any software implementation ofaccounting. They can be made available upon request.

01 — I

I

POTENTIALGAIN TOCONSUMER

% CHANGE IN RESOURCE QUANTITYFOR CONSTANT PRODUCTIVITY

DISCHARGE

OVERREACT 0'0 -

0

CONSTANTPRODUCTIVITY

4-

ii

ORBIT 0

FAVORS

PRODUCER

HARMS

PRODUCER

+

these two changes we plotted on the above grid, it is possible to howChapter 01 QUANTITY GRIO (LONG TERN)change in production and/or in usage determine productivity change.

This chapter presents the axioms underpinning the 13 segments which make This grid enables one to categorize productivity into the variousthe long term quantity grid. These measures refer to change in the level of as shown. The horizontal axis scales the change in resource quantity:t'index

number and the vertical axis scales the change in product quantitya function, and their dimensional coefficient is dimensionless.index number The diagonal line connects all points where inproduct quantity equals change in resource quantity. Along this lThe noproductivity change takes place.Figure D1.F1 - LONG TERN QUANTITY GRID

The 5 areas above the diagonal signify productivity growth aS arefinancially favorable, the 3 areas along the diagonal signify coPjstantproductivity and are financially neutral, while the 5 areas below thesignify productivity decline and are financially unfavorable to the

LIFTOFF strategic segment (financially unfavorable)

(Y axis — A' axis) < 0

0 C Y axis < x axis

_________________ __________________

The LIFTOFF segment represents increasing production accompanied bydeclining productivity because growth in resource usage exceeds inproduction > This situation favors the suppliers ofresources because of the increasing demand for resources. It can arise irp theearly (i.e. weak) phase of increasing demand for product, and is typfcally

'Censtrued by management as a transient stage which precedes migration tcu theORBIT segment. Productivity decline increases long term product cost thatin the long term this situation will undermine competitiveness and theviability of the producer. Productivity decline in the producerharms the supplier because it reduces the security of outlet.

FIRST QUADRANT dlagoial (financially neutral)

00

LI FTOFF

0 - % CHANGE INRESOURCEQUANTITY

POTENTIALLOSS TOCONSUMER

0

0

HOARD

HA RN S

SUPPLIER

SELFDESTRLICT

FAVORS

SUPPLIER

Y = PERCENTAGE CHANGE IN RESOURCE QUANTITY NEEDED FORCONSTANT (i.e., OLD) PRODUCTIVITY

=

= [Yold(I) + VOLold(I)) / V/ILUEoId(I)

X = PERCENTAGE CHANGE IN RESOURCE QUANTITY

[Yaxis — Xaxisj = 0

=

0 < Yaxis = Xaxis

= V0Lold(I) / VALUE0Id(I)

DIAGONAL = CONSTANT (i.e., OLD) PRODUCTIVITY

- A' = 0

Productivity change is driven by change in the product quantity index numberand/or change in the resource Quantity index number If,

The FIRST QUADRANT diagonal segment represents increasing prodqctionaccompanied by constant productivity because growth in resource usage ehualsgrowth in production (I4old(I) = This situation favora" thesuppliers of resources because of the increasing demand for resourcesconditions of constant resource quantity content per unit of product.roductivity has zero effect on long term product cost which in the long"term

Will hence be influenced solely by resource price change.

ORBIT strategic segment (financially favorable)

0 < [Y axis — A' axis)

0 < Xaxis C Yaxis

01—2 ' 01—3

irhe ORBIT segment is the ideal segment. It represents increasing produLtionccempanied by increasing productivity because growth in production

UPPER VERTICAL AXIS segment (financially favorable)

o c (V axis — X axis]

o = Xaxis < Yaxis

The above segment represents increasing production accompanied by increasingproductivity because growth in production occurs while resource usage staysconstant. This situation has a neutral direct effect on the suppliers ofresources because of the constant demand for resources despite decliningresource content per unit of product. Productivity growth reduces long termproduct cost, so that in the long term this situation will enhancecompetitiveness and the viability of the •producer. Productivity growth in theproducer indirectly favors the supplier because it increases the security ofoutlet.

DISCHARGE strategic segment (financially favorable)

o < (Y axis — X axis]

Xaxis < 0 < Yaxis

The DISCHARGE segment represents increasing production accompanied by

increasing productivity because growth in production occurs despite decline irresource usage. This situation directly harms the suppliers of given r::TTTbecause of the decreasing demand for such given resources. It can arise underconditions of increasing production and resource substitution where, say,labor is discharged and replaced by capital and the weighted average resourcequantity change reflects decline in resource usage. Productivityreduces long term product cost so that in the long term this situation willenhance competitiveness and the viability of the producer. Productivity growtFin the producer indirectly favors the supplier because it increases I.security of outlet. Yet it must be borne in mind that ifquantities of resources are discharged, the resulting contraction of inccreceived by the suppliers of such resources could reduce overall demandproduct.

HORIZONTAL AXIS' segment (financially favorable)

0 < (Y axis — X axis]

X axis < 0 = V axis

The above segment represents unchanged production accompanied by increasirproductivity because production stays constant while resource usage declines.This situation has a directly unfavorable effect on the suppliers ofbecause of the declining demand for resources and resulting declining resourcer,

The OVERREACT segment represents decreasing production accompanied byincreasing productivity because decline in resource usage exceeds inproduction. This situation directly harms the suppliers of resourcesef the decreasing for resources. Productivity growth in the prothicerindirectly favors the supplier because it increases the security of Itcan arise in the later (i.e. strong) phase of decreasing demand for product,and is typically construed by management as an essential step to reduce longterm product cost and enhance competitiveness in order to protect theviability of the producer.

THIRD QUADRANT diagonal (financially neutral)

[V axis — Xaxis] = 0

V axis = X axis < o

The THIRD QUADRANT diagonal segment represents decliningmn.nied by constant productivity because decline in resource usage equalsin production = I4old(U)). This situationsuppliers of resources because of the declining demand for resources uqderconditions of constant resource quantity content per unit of product.

r has zero effect on long term product cost which in the longwill hence be influenced solely by resource price change

HOARD strategic segmeit (financially unfavorable)

(V axis — X axis] < 0

V axis < x axis < o

The HOARD segment represents decreasing production accompanied by decreasjngproductivity because decline in production exceeds decline in resourceThis situation directly harms the suppliers of resources because ofecreasing demand for resources. It can arise in the early (i.e. weak) ph4se

F decreasing demand for product. Productivity decline increases longproduct cost so that in the long term this situation willcompetitiveness and the viability of the producer. Productivity decline-inthe producer indirectly harms the supplier because it reduces the security- ofoutlet.

growth in resource usage > This situation favorssuppliers of resources because of the increasing demand for resources despitedeclining resource content per unit of product. It can arise in the later(i.e. strong) phase of increasing demand for product. Productivity growthreduces long term product cost, so that in the long term this situation willenhance competitiveness and the viability of the producer. Productivitygrowth in the producer indirectly favors the supplier because it increases thesecurity of outlet.

content per unit of product. Productivity growth reduces long term productcost, so that in the 1ong term this situation will enhance andthe viability of the producer. Productivity growth in the producerfavors the supplier because it increases the security of outlet. -

OVERREACT 'strategis scgment (financially favorable)

o < (V axis — X axis]

Xaxis < Vaxis < 0

1-

ii.9

Dl—4 DI — 5

LOWER VERTICAL AXIS segment (financially unfavorable)

(Y axis — X axis] < 0

Y axis C 0 = X axis

The above segment represents declining production accompanied by decliningproductivity because production declines occurs while resource usage stays

constant. This situation has a neutral direct effect on the suppliers of

resources because of the constant demand for resources despite increasingresource content per unit of product. Productivity decline increases long termproduct cost, so that in the long term this situation will erode

competitiveness and the viability of the producer. Productivity decline in

the producer indirectly harms the supplier because it reduces the security of

outlet.

SELFDESTRIJCT strategic segment (financially unfavorable)

(Yaxis — Xaxis] < 0

Yaxis < 0 C laxis

The SELFDESTRLJCT segment represents decreasing production accompanied by

decreasing productivity because resource usage is increasing despite the

decline in production. This situation is in the short term favorable to the

suppliers of resources because of the increasing demand for resources. This

situation in the long term harms the suppliers of resources becauseproductivity decline raises long term product cost, undermines competitivenand hence the viability of the producer. It can arise in the early (i.e. w...,.,phase of decreasing demand for product when management views the decline in

demand as a short term phenomenon and proceeds to introduce more resources to

gear the production system for a long term increase in demand.

RIGHT HORIZONTAL AXIS segment (financially unfavorable)


V axis = 0 < X axis

The above segment represents unchanged production accompanied by declininfproductivity because production stays constant while resource usage increases.This situation has a directly favorable effect on the suppliers of resources

because of the increasing demand for resources and resulting increase IT,

resource content per unit of product. Productivity decline increases long ternproduct cost, so that in the long term this situation will erode

competitiveness and the viability of the producer. Productivity decline in

the producer indirectly harms the supplier because it reduces the security or

outlet.

AXIS ORIGIN segment (financially neutral)

[V axis — X axis] = 0

V axis = = X axis

The above segment (i.e. that which appears between all segments definedabove) represents constant production accompanied by constantbecause constant production and constant resource usage are maintained. Inthe long term this situation neither favors nor harms the of

..es because of the constant demand for resources. Constantproduct cost so that long term residence in the AXIS

N segment will signify that product cost change will be drivefl byresource price change alone. I-

— I I

ILLDl — 6

Dl — 7

This chapter presents the axioms underpinning the 13 segments which makethe short term quantity grid. These measures refer to change in the levela function, and their dimensional coefficient is dimensionless.

Figure O2.Fl - SHORT TERM QUANTITY GRID

Efficiency change is driven by change in the resource quantity index nun

needed for constant efficiency LØeff(I) and/or change in the resource quantiindex number If these two changes are plotted on the above grid,

I

This grid enables one to categorize efficiency into the various segments asThe horizontal axis scales the change in resource quantity index

(/4old(I)) and the vertical axis scales the change in resource quantityneeded for constant efficiency The diagonal line connects 'Callpeints where change in product quantity equals change in resource quantity.Ashort this line no efficiency change takes place.

The 5 areas above the diagonal signify efficiency growth and arefavorable, the 3 areas ashort the diagonal signify constant efficiencyfinancially neutral, while the 5 areas below the diagonal signify efficlqncydecline and are financially unfavorable to the producer.

The LIFTOFF segment represents increasing target usage needed for constantefficiency accompanied by declining efficiency because growth in resource

exceeds growth in target usage needed for constant((I) > This situation favors the suppliers of

because of the increasing demand for resources. It can arise in the eflly(i.e., weak) phase of increasing demand for product, and is

by management as a transient stage which precedes migration toIT segment. Efficiency decline increases short term product cost and dan

'mine competitivaness and the viability of the producer..d in the producer indirectly harms the supplier because it reduces :the

(rity of outlet.

:::T QUADRANT diagonal (financially neutral)

(V axis — X axis] = 0

0 < V axis = axis

The FIRST QUADRANT diagonal segment represents increasing target usAgeeded for constant efficiency accompanied by constant efficiency becAuse

h in resource usage equals growth in target usage needed foriciency = This situation favors the

sources because of the increasing demand for resources under conditions ofvariable component of resource quantity content per unit of

,ftonstant efficiency has zero effect on short term product cost which in jheiert term will hence be influenced solely by resource price change.

T strategic segment (financially favorable)

0 < [V axis — K axis]

0 < Xaxis < Vaxis

he ORBIT segment is the ideal segment. It represents increasing targetneeded for constant efficiency accompanied by increasing

D2 — 2

Chapter 02 QUANTITY GRID (SHORT TERN)possible to see how change in target usage needed for constant effickpcy

and/or in usage determine efficiency change.

CONSTANTEFFICIENCY

% CHANGE IN+ RESOURCE

QUANTITY

LIFTOFF strategic segment (financially unfavorable)

1.

if

t

(V axis — K axis] < 0

0 < Yaxis < Xaxis

% CHANGE IN RESOURCE QUANTITYPOTENTIAL FOR CONSTANT EFFICIENCYGAIN TOCONSUMER % I

ORBIT #

DISCHARGE IFAVORS + p4 LIFTOFF

PRODUCER I+ 0-•

+1HARMS OVERREACT #PRODUCER p4 -

SELFOESTRUCT

HOARDPOTENTIALLOSS TOCONSUMER

HARMS FAVORS

SUPPLIER SUPPLIER

Y = PERCENTAGE CHANGE IN RESOURCE QUANTITY NEEDED FOR

CONSTANT (i.e., OLD) EFFICIENCY

=

= (Eold(I) + VOLold(I)] / VALUE01d(I)

X = PERCENTAGE CHANGE IN RESOURCE QUANTITY

=

= VOLo1d(I) / VALUEoIO(I)

DIAGONAL = CONSTANT (i.e., OLO) EFFICIENCY

=y—x=0

D2 — 1

because growth in target usage needed for constant efficiency exceeds gro"in resource usage > This situation favors the suppliof resources because of the increasing demand for resources despite declini.variable component of resource content per unit of product. It can arisethe later (i.e. strong) phase of increasing demand for product.growth reduces short term product cost, so that in the short term this -

situation will enhance competitiveness and the viability of the producer.

Efficiency growth in the producer indirectly favors the supplier because itincreases the security of outlet.


o < fY axis — K axis]

0 = K axis C Y axis

The above segment represents increasing target usage needed for constant

efficiency accompanied by increasing efficiency because growth in target usageneeded for constant efficiency occurs while resource usage stays constant.

This situation has a neutral direct effect on the suppliers of resources

because of the constant demand for resources despite declining resource

content per unit of product. Efficiency growth reduces short term product

cost, so that in the short term this situation will enhance competitiveness

and the viability of the producer. Efficiency growth in theindirectly favors the supplier because it increases the security of outlet.

DISCHARGE strategic segment (financially favorable)

o c fYaxis — Xaxis]

K axis c 0 < Y axis

The DISCHARGE segment represents increasing target usage needed for constaiefficiency accompanied by increasing efficiency because growth in targetneeded for constant efficiency occurs despite decline in resource usage.situation directly harms the suppliers of given resources because of Udecreasing demand for such given resources. It can arise under conditions' ci

increasing target usage needed for constant efficiency and resourci

substitution where, say, labor is discharged and replaced by capital and thi

weighted average resource quantity change reflects decline in resourceEfficiency increase reduces short term product cost so that in the short tthis situation will enhance competitiveness and the viability of the producerEfficiency growth in the producer indirectly favors the supplier because I,

increases the security of outlet. Yet it must be borne in mind that i

significant quantities of resources are discharged, the resulting contractiof income received by the suppliers of such resources could reduce overeli.

demand for product.

LEFT HORIZONTAL AXIS segment (financially favorable)

o < fY axis — K axis]

K axis < 0 = Y axis

The above segment represents unchanged target usage needed forefficiency accompanied by increasing efficiency because target usage neec

02 — 3

for constant efficiency stays constant while resource usage declines. Thissituation has a directly unfavorable effect on the suppliers ofbecause of the decUning demand for resources and resulting declining ra4ourcecontent per unit of product. Efficiency growth reduces short termcost, so that in the short term this situation will enhanceend the viability of the producer. Efficiency growth in the prAducerindirectly favors the supplier because it increases the security of outflt.

OVERREACT strategis segment (financially favorable)

0 c (V axis — K axis]

Kaxis C Yaxis < 0

The OVERREACT segment represents decreasing target usage needed forefficiency accompanied by increasing efficiency because decline in rOourceusage exceeds decline in target usage needed for constant efficiency,? Thissituation directly harms the suppliers of resources because of the decreasingdemand for resources. Efficiency growth in the producer indirectly favori thesupplier because it increases the security of outlet. It can arise thelater (i.e. strong) phase of decreasing demand for product, and is typicallyconstrued by management as an essential step to reduce short term costand enhance competitiveness in order to protect the viability of the prQAucer.

THIRD QUADRANT diagunal (financially neutral)

[Y axis — K axis] = 0

The THIRD QUADRANT diagonal segment represents declining target usage k5peded'ir constant efficiency accompanied by constant efficiency because decljeje inresource equals decline in target usage needed for constant

= LtQeff(J)). This situation harms the suppliers of resourcesthe declining demand for resources under conditions of constant variable...,..,it of resource quantity content per unit of product. Cogstantciency has zero effect on short term product cost which in the short? term

11 hence be influenced solely by resource price change.

WARD strategic segment (financially unfavorable)

(Y axis — K axis] < 0

HOARD segment represents decreasing target usage needed foraccompanied by decreasing efficiency because decline in target

e needed for constant efficiency exceeds decline in resource usage.[This,uation directly harms the suppliers of resources because of the

lenand for resources. It can arise in the early (i.e. weak) pha,4 ofJecreasing demand for product. Efficiency decline increases short term pSduct

so that in the short term this situation will undermineI the viability of the producer. Efficiency decline in therectly harms the supplier because it reduces the security of outlet.;

V axis < K axis < 0

V axis = K axis C 0

D2 — 4

The above segment represents declining target usage needed for constao.efficiency accompanied by declining efficiency because target usage needed forconstant efficiency declines occurs while resource usage stays constant. Thisituation has a neutral direct effect on the suppliers of resources becausethe constant demand for resources despite increasing resource content per oniof product. Efficiency decline increases short term product cost, so that i

the short term this situation will erode competitiveness and the viabilitythe producer. Efficiency decline in the producer indirectly harms thosupplier because it reduces the security of outlet.

SELFOESTRUCT strategic segment (financially unfavorable)


Y axis < 0 c X axis

The SELFDESTRUCT segment represents decreasing target usage needed forconstant efficiency accompanied by decreasing efficiency because resource.usage is increasing despite the decline in target usage needed forefficiency. This situation is in the short term favorable to the suppliers

of the increasing demand for resources. This situation in?

the short term harms the suppliers of resources because sustained efficiencydecline raises short term product cost, undermines competitiveness and hencrthe viability of the producer. It can arise in the early (i.e. weak) phase of

decreasing demand for product when management views the decline in demand asshort term phenomenon and proceeds to introduce more resources to gear thetarget usage needed for constant efficiency system for a short term increasein demand.

RIGHT HORIZONTAL AXIS segment (financially unfavorable)

[V axis — X axis] C 0

The above segment represents unchanged target usage needed forefficiency accompanied by declining efficiency because target usage needed farconstant efficiency stays constant while resource usage increases. Thin;situation has a directly favorable effect on the suppliers of resourceo,because of the increasing demand for resources and resulting increase io,resource content per unit of product. Efficiency decline increases shortproduct cost, so that in the short term this situation will erodecompetitiveness and the viability of the producer. Efficiency decline in theproducer indirectly harms the supplier because it reduces the security ofoutlet.

Y axis = 0 c X axis


[V axis — XaxisJ = 0

Yaxis = 0 = Xaxis

The above segment (i.e. that which appears between all segments deflnedabove) represents constant production accompanied by constantbecause constant production and constant target resource usage neededconstant efficiency are maintained. In the short term this situation nelkher.favors nor harms the soppl i ers of resources because of the constantresources. Constant productivity has a neutral effect on product cost soshort term residence in the AXIS ORIGIN segment will signify that productchange will be driven by resource price change alone.


[V axis — X axis] < 0

V axis c 0 = X axis

ftii

ft

D2—5 D2 — 6

a

Chapter D3 PRODUCTIVITY GRID

This chapter presents the axioms underpinning the 13 segments which make up

the productivity grid. These measures refer to change in the level offunction, and their dimensional coefficient is a currency unit.

Figure D3.Fl - PRODUCTIVITY GRID

= Enew(I)

DIAGONAL = CONSTANT PRODUCTIVITY VARIANCE IN NEW PRICES

= Y + X = 0 = Ynew(I)

The PRODUCTIVITY GRID presents an analysis of change in productivity. I

graphs the PRODUCTIVITY VARIANCE, the CAPACITY UTILIZATION VARIANCE and th

EFFICIENCY VARIANCE which appear in the PROFIT OVERVIEW and COST OVERVIE

reports. The horizontal axis of the PRODUCTIVITY grid scales the change i

efficiency, and the vertical axis scales the change in capacity utilizationBoth axes employ the same numerical scale. The diagonal line representconstant productivity because it connects all points where the change i

efficiency is exactly offset by an opposite change in capacity utilization.

D3 — 1.

Starting with the WIN segment, and proceeding in anti—clockwise order, themeaning of each of the above 13 case segments is defined below. The ofsix case segments which do not occur along axes or the diagonal are intendedte characterize descriptions rather than prescriptions ofperformance. They do not relate to the short term and must be quaiifiedshould any compelling contrary considerations be relevant.

WIN strategic segment (financially favorable)

0 c [V axis + Xaxis]

0 c Vaxis , Xaxis

In the WIN strategic segment the producer gains cost advantage through gainin capacity utilization and gain in efficiency. Such improvements prisebecause increased capacity utilization signifies the allocation of the fixedcomponent of cost across a higher production volume, while the incr4asedefficiency flows from reduction in the level of the fixed component of

cost and hence signifiesImprovement which attends movement down the learning curve. -

This strategic segment represents increasing capacityaccompanied by increasing productivity because efficiency gain also fakesplace. This situation harms the suppliers of resources because of' thedecreasing resource content per unit of product. The LONG TERM QUANTITY GRIDshows which of the 5 possible cases of productivity growth pertains to' thissituation, and the SHORT TERN QUANTITY GRID shows which of the 5

eases of efficiency grOwth pertains to this situation.

Both effects tend to deter competitors, particularly if thecapacity utilization arises from increased market share. Improved productivity

Thenefits the producer because he saves resources by holding some re$urcefixed while increasing production (i.e. increasing caflcity

utilization) or by reducing the variable resource content per unit of-production (i.e. increasing efficiency). Increase in capacity utili2ftion-'favors the supplier because it brings nearer the point at which full —

would create an opportunity for the supplier toIncrease in efficiency harms the supplier because it the

'resource content per unit of product.

UPPER VERTICAL AXIS Ltrategic segment (financially favorable)

0 < [V axis + X axis]

0 = X axis c V axis

This strategic segment represents increasing capacityaccompanied by increasing productivity because of constant efficj4pcy.Improved productivity favors the producer because it reduces productIncrease in capacity utilization favors the supplier because it bringsthe point at which full capacity utilization would create an opportunity' forthe supplier to more resource.

CAPACITY UTILIZATIONVARIANCE

WIN

POTENTIALGAIN TOCONSUMER

+ EFFICIENCYVARIANCE

CONSTANTPRODUCTIVITY

b4 GANBLE

tFAVORSPRODUCER SQUANDER

I,

HA RN S

PRODUCER

POTENTIALLOSS TOCONSUMER

I''I EXCEL

LOSE

FAVORS

SUPPLIER

RECOUP

HA RN S

SUPPLIER

Y = CAPACITY UTILIZATION VARIANCE IN NEW PRICES

= Lnew(I)

X = EFFICIENCY VARIANCE IN NEW PRICES

03 — 2

S

GAMBLE strategic segment (financially favorable)

o < (Y axis + X axis]

X axis < 0 < Y axis

In the GAMBLE strategic segment the producer gambles through reducirefficiency and eroding his cost advantage which flows from increased capacilutilization.

This strategic segment represents increasing capacity utilizaticaccompanied by increasing productivity because capacity utilization gaff

impovement exceeds efficiency loss. This situation favors the supplier ci

resources because he benefits from increased capacity utilization and tffincreasing resource content per unit of product which arises from reduced.

efficiency.

SECOND QUADRANT diagonal (financially neutral)

(V axis + X axis] = 0

X axis < 0 C Y axis

This strategic segment represents increasing capacity utilizataccompanied by constant productivity because capacity utilization impovemen

is exactly offset by efficiency loss.

This situation has a neutral effect on the short term cost position of t,

producer because the damage created by reduced efficiency is temporai'i.

masked by higher capacity utilization but will become apparent once there i

decline in capacity utilization. This situation favors the supplierresources because he benefits from increased capacity utilization and tL

increasing resource content per unit of product which arises froni reduce

efficiency.

SQUANDER strategic segment (financially unfavorable)

(Y axis + K axis] C 0

Kaxis C 0 < Y axis

In the SQUANDER strategic segment the producer squanders the cost advantag

conferred by capacity utilization gain through more than offsetting reductirin efficiency.

This strategic segment represents increasing capacity utilizattcaccompanied by decreasing productivity because capacity utilization impovemer

is exceeded by efficiency loss. This situation favors the supplier c

resources because he benefits from increased capacity utilization and rincreasing resource content per unit of product which arises from reduu

efficiency.

This strategic segment represents constant capacity utilizationdecreasing productivity because decline in efficiency takes place. This

tuation harms the producer because of unfavorable impact of productjvityis on product cost, but favors the supplier of resources because he

the increasing resource content per unit of product which arises ,cfromefficiency.

In the LOSE strategic segment the producer incurs cost disadvantage'dine in capacity utilization and decline in efficiency. •Suchises because decreased capacity utilization signifies the allocation of the

rnmnnn 'cnt of cost across a lower production volume, while the decflpingncy i from increase in the level of the fixed component of: cost

id/or the variable component of cost per unit of product. Suchsignifies movement back up the learning curve.

This strategic segment represents declining capacity utilizationry declining productivity because efficiency loss also takes place.

uation favors the suppliers of resources because of the increasing resQurceintent per unit of product. The LONG TERM QUANTITY GRID shows which thepossible cases of productivity loss pertains to this situation, and the

ORT TERM QUANTITY GRID shows which of the 5 possible cases of efficilcncypertains to this situation.

Both effects tend to encourage competitors, particularly if theapacity utilization arises from declining market share. Reduced productivity

...s the producer because it increases product cost. Decline inlization harms the supplier because it defers the point at which ]'ullacity utilization would create an opportunity for the supplier to prawidee resource. Decline in efficiency favors the supplier it

the resource content per unit of product.

VERTICAL AXIS segment (financially unfavorable)

Vaxis C 0 = Kaxis

This strategic segment represents declining capacity utilization accomp4flieddeclining productivity because of constant efficiency. Decltgiing

:cductivity harms the producer because it increases product cost andcompetition. Decline in capacity utilization harms the supplier

ause it defers the point at which full capacity utilization would anportunity for the supplier to provide more resource.

LEFT HORIZONTAL AXIS strategic segment (financially unfavorable)

(V axis + K axis] < 0

K axis < 0 = V axis

LOSE strategic segmeut (financially unfavorable)

(V axis + K axis] C 0

V axis , K acis C 0

:1

.4

I.

(V axis + Kaxis] C 0

I

03 — 3 03 — 4

RECOUP strategic segment (financially unfavorable)

(Y axis + X axis] < 0

Y axis ( 0 < X axis

In the RECOUP strategic segment the producer reduces the cost disadvantageinflicted by capacity utilization decline through less than offsettingimprovement In efficiency.

This strategic segment represents declining capacity utilization accompaniedby decreasing productivity because capacity utilization decline exceedsefficiency gain. Declining productivity harms the producer because itincreases product cost and can encourage competition. This situation harms

the supplier of resources because he is disadvantaged by decline in capacityutilization and the declining resource content per unit of product whicharises from reduced efficiency.

FOURTH QUADRANT diagonal (financially neutral)

EY axis + X axis] = 0

Y axis < 0 < X axis

This strategic segment represents declining capacity utilization accompaniedby constant productivity because capacity utilization decline is exactlyoffset by efficiency gain.

This situation has a neutral effect on the short term cost position of theproducer because the benefit afforded by higher efficiency is temporarilymasked by lower capacity utilization but will become apparent once there isincrease in capacity utilization. This situation harms the supplier ofresources because he is disadvantaged by declining capacity utilization and

the declining resource content per unit of product which arises from higherefficiency.

EXCEL strategic segment (financially favorable)

0 < [Y axis + X axis]

Y axis < 0 < X axis

In the EXCEL strategic segment the producer excels through increasingefficiency to more than offset his cost disadvantage which flows fromdeclining capacity utilization. On balance he therefore reduces his productcost despite the lower capacity utilization.

This strategic segment represents declining capacity utilization accompaniedby increasing productivity because capacity utilization decline is exceeded byefficiency gain. This situation harms the supplier of resources because he isdisadvantaged by declining capacity utilization and the decliningcontent per unit of product which arises from higher efficiency.

This strategic segment represents constant capacity utilizationincreasing productivity because gain in efficiency takes place. This

::tion favors the producer because of the favorable impact of.n on product cost, but has an unfavorable impact on the suppler ofsources because of the decreased resource content per unit ofcompanies efficiency improvement.

This strategic segment represents constant capacity utilizationby constant productivity because efficiency remains constant. Thishas a neutral impact on the producer because of zero productivity onproduct cost, and it has a neutral effect on the supplier of resourcesof the constant resource content per unit of product whose level notchanged.

RIGHT HORIZONTAL AXIS segment (financially favorable)

o < (V axis + X axis]

V axis 0 < X axis

S ORIGIN segment (financially neutral)

(Y axis + K axis] = 0

Y axis = 0 = K axis

D3 — 5D3 — 6

Chapter 04 PRODUCT COST (LONG TERM)

This chapter presents the axioms underpinning the 13 segments which makethe long term product cost grid. These measures refer to change in the levelof a function, and their dimensional coefficient is a currency unit.

V = PRODUCTIVITV VARIANCE IN NEW PRICES

= Ynew(I)

X = LONG TERM RESOURCE PRICE VARIANCE

= Zlong(I)

DIAGONAL = CONSTANT LONG TERM PRODUCT COST VARIANCE

= Y + X = 0 = COSTlong(I)

The LONG TERM COST GRIO presents an analysis of change in long term prodaj

cost. It graphs the LONG TERM PROOUCT COST VARIANCE, the PRODUCTIVI1

VARIANCE and the LONG TERM RESOURCE PRICE VARIANCE which appear in the 0

OVERVIEW reports. The horizontal axis of this grid scales the change

resource price normalized for constant productivity, and the vertical a:

scales the change in productivity. Both axes employ the same numerici

scale. The diagonal line represents constant long term product cost

04—1

It connects all points where the change in productivity is exactly offset byan opposite change in resource price normalized for constant productivity.

The sign convention on this grid should be borne in mind. The positivesign signifies favorable to the bottom line and the negative sign signiFIesanfavorable to the bottom line. Productivity increase favors the bottom flneand attracts a positive sign, while productivity decrease harms theline and attracts a negative sign. In contrast, resource price increjseharms the bottom line and commands a negative sign, while resourcedecrease favors the bottom line and commands a positive sign.

Starting with the COAST segment, and proceeding in anti—clockwise order, themeaning of each of the above 13 case segments is defined below. The nameçofSix case segments which do not occur along axes or the diagonal are inteuded4a characterize typical descriptions rather than rigid definitions. They

relate to the short term and must be qualified should any compellingcontrary considerations be relevant.

strategic segment (financially favorable)

o < [V axis + X axis]

o < Yaxis , Xaxis

This strategic segment represents increasing productivity accompanied byproduct cost because the favorable effect ol productivity incre3se

magnified by the favorable effect of resource price decrease. Thisharms the suppliers of resources because of both the

source content per unit of product and the decrease in resource price. - theIDUCTIVITY and QUANTITY GRIDS show which of the 5 possible cases of

growth pertains to this situation.

The threat of new competitors is less serious than in the RALLY or DELUDEsegments (which are described below) because improved productivity makes

structure more competitive in addition to the favorable effect of:-resource price decline.

VERTICAL AXIS strategic segment (financially favorable)

o < [V axis 4 X axis]

0 = Xaxis < Yaxis

is strategic segment represents increasing productivity accompanied bycreasing product cost because the favorable effect of productivity

accompanied by the neutral effect of constant resource price, istuation harms the suppliers of resources because of the decreasing resoàtcefltent per unit of prriduct. The PRODUCTIVITY and QUANTITY GRIDS showthe S possible cases of productivity growth pertains to this situation.

he threat of new competitors hinges upon their ability to beor to buy rosources cheaper.

Figure D4.F1 - LONG TERM COST GRID

PRODUCTIVITYVARIAMCE

ERSE

+RETARD

+

COAST

REDUCES

LONG TERMPRODUCT

$ COST

LOMG TERMRESOURCE

—0 PRICEVARIANCE

CONSTANTLONG TERMPRODUCT

COST

HARMS

SUPPLIER

FAVORS

SUPPLIER

INCREASESLONG TERM

PRODUCTCOST

+DELUDE

SUCCUMB

RALLY

4 p

FAVORS HARMS

SUPPLIER SUPPLIER

I04 — 2

This strategic segment represents increasing productivity accompanied by.declining product cost because the favorable effect of productivity impovementexceeds the unfavorable effect of resource price increase.productivity increase more than absorbs resource price increase and reversesgrowth in (i.e. reduces) the level of product cost. This situation harms thesuppliers of resources because of the decreasing resource content per unit ofproduct, bu.t also favors the suppliers of resources because of the increase inresource price. The PRODUCTIVITY and QUANTITY GRIDS show which of the 5

possible cases of productivity growth pertains to this situation.

New competitors are unlikely to attempt entry in such circumstances.


(Yaxis + Kaxis] = 0

Xaxis < 0 < Yaxis

This strategic segment represents increasing productivity accompanied by

constant product cost because the favorable effect of productivity impovementis exactly offset by the unfavorable effect of resource price increase. Thissituation harms the suppliers of resources because of the decreasing resourcecontent per unit of product, but also favors the suppliers of resourcesbecause of the increase in resource price. The PRODUCTIVITY and QUANTITY

GRIDS show which of the 5 possible cases of productivity growth pertains tothis situation.


RETARD strategic segment (financially unfavorable)

(Yaxis + Xaxis] c 0

X axis < 0 < Y axis


increasing product cost because the favorable effect of productivityimpovement is more than offset by the unfavorable effect of resource priceincrease. Hence productivity increase less than absorbs resource priceincrease and retards growth in the level of product cost. This situation,harms the suppliers of resources because of the decreasing resource contenUper unit of product, but also favors the suppliers of resources because of theresource price increase. The PRODUCTIVITY and QUANTITY GRIDS show which of thel5 possible cases of productivity growth pertains to this situation.


HORIZONTAL AXiS strategic segment (financially unfavorable)


Xaxis < o = Yaxis

This strategic segment represents constant productivity accompanied byproduct cost because the neutral effect of constant productivity is

accompanied by the unfavorable effect of resource price increase. Thishas a neutral effect on the suppliers of resources because of the

constant resource content per unit of product, and favors the ofPesources because of the resource price increase. The PRODUCTIVITY and'. LONG

:TERM QUANTITY GRIDS show which of the 3 possible cases ofvproductivity pertains to this situation.

Competitors will pose a threat if they can match the productivity levei and-buy resources cheaper.

strategic segment (financially unfavorable)

(Y axis + X axis] c 0

V axis , X axis < 0

• This strategic segment represents decreasing productivity byproduct cost because the unfavorable effect of

productivity is accompanied by the unfavorable effect of resourceIncrease This situation favors the suppliers of resources because of

increasing resource content per unit of product and the resource ericeThe PRODUCTIVITY and QUANTITY GRIDS show which of the 5

cases of productivity decline pertains to this situation.

Competitors would pose a threat once they perceive the productivity dç;linerepresent movement back up the learning curve which narrows the

cost gap. Productivity improvement is therefore required to widen the•gap and deter competitive entry.

VERTICAL AXIS segment (financially unfavorable)

(Y axis + X axis] c 0

Yaxis c 0 = Xaxis

This strategic segment represents decreasing productivity accompanied byIncreasing product cost because the unfavorable effect of productivity dflline

:is accompanied by the neutral effect of constant resource price. TThisfavors the suppliers of resources because of the increasing

per unit of product, and has a neutral effect on the ofresources with respect to the constant resource price. The PRODUCTIVITy- andQUANTITY GRIDS show which of the 5 possible cases of productivitypertains to this situation.

Competitors would pose a threat once they perceive the productivity declineto represent movement back up the learning curve which narrows the competitivetest gap. Productivity improvement is therefore required to widengop and deter competitive entry.

REVERSE strategic segment (financially favorable)

o < (V axis + X axis]

X axis c 0 < Y axis

D4 — 3 D4—4

11

RALLY strategic segment (financially unfavorable)

(Y axis + X axis] c U

Yaxis < 0 C Xaxis

This strategic segment represents decreasing productivity accompaniedincreasing product cost because the unfavorable effect of productivity declineexceeds the favorable effect of resource price decrease. This situationfavors the suppliers of resources because of the increasing resource contentper unit of product, and harms the suppliers of resources because of the

resource price decrease. The PRODUCTIVITY and QUANTITY GRIDS show which of

the 5 possible cases of productivity decline pertains to this situation.

Competitors would pose a threat once they perceive the productivity declirto represent movement back up the learning curve which narrows the -

cost gap. Productivity improvement is therefore required to widen the cost

gap and deter competitive entry.

FOURTH QUADRANT diagonal (financially neutral)

(V axis + XaxisJ = 0

Y axis < 0 < X axis

This strategic segment represents decreasing productivity accompanied bj

constant product cost because the unfavorable effect of productivity declinis exactly offset be the favorable effect of resource price decrease. TT

situation favors the suppliers of resources because of the increasingcontent per unit of product, and harms the suppliers of resources because i

the resource price decrease. The PRODUCTIVITY and QUANTITY GRIDS show whiiof the 5 possible cases of productivity decline pertains to this situation.

Competitors would pose a threat once they perceive the productivity declineto represent movement back up the learning curve which narrows the competitivecost gap. Productivity improvement is therefore required to widen thegap and deter competitive entry.

DELUDE strategic segment (financially favorable)

0 < (V axis + X axis]

V axis < 0 < X axis

This strategic segment represents decreasing productivity accompanied frdecreasing product cost because the unfavorable effect of productivity decliois more than offset by the favorable effect of resource price decrease. T:.

situation favors the suppliers of resources because of the increasing resourcontent per unit of product, and harms the suppliers of resources becausethe resource price decrease. The PRODUCTIVITY and QUANTITY GRIDS show wh

of the 5 possible cases of productivity decline pertains to this situation.

Competitors would pose a threat once they perceive the productivity dec11

to represent movement back up the learning curve which narrows the competiticost gap. Productivity improvement is therefore required to widen the cgap and deter competitive entry.

IT HORIZONTAL AXIS segment (financially favorable)

0 < (V axis + X axis]

Y axis = 0 < X axis

This strategic segment represents constant productivity accompanicif byiecreasing product cost because the neutral effect of constant isaccompanied by the favorable effect of resource price decrease.;ituation has a neutral impact on the suppi iers of resources because of the:onstant resource content per unit of product, and harms the ofresources because of the resource price decrease. The PRODUCTIVITY and -IONG

QUANTITY GRIDS show which of the 3 possible cases ofroductivity pertains to this situation.

Competitors will pose a threat if they can match the productivity level andy resources even cheaper.

ORIGIN segment (financially neutral)

(V axis + Xaxis] = 0

V axis = U = X axis

This strategic segment represents constant productivity accompanieq bytonstant product cost because the neutral effett of constant productivity isaccompanied by the neutral effect of constant resource price. This

a neutral impact on the suppliers of resources because of the conttanturce content per unit of product and the constant resource price.7 The

.,.JUCTIVITY mnd QUANTITY GRIDS show which of the 3 possible cases of conflant'oductivity pertains to this situation.

will pose a threat if they can outperform the productivityend buy resources even cheaper.

U

04 — 5 04 — 6

L

Chapter D5 PRODUCT COST (SHORT TERM)

This chapter presents the axioms underpinning the 13 segments which makethe short term product cost grid. These measures refer to change inlevel of a function, and their dimensional coefficient is a currency unit.

Figure D5.F1 - SHORT TERM COST GRID

all points where the change in efficiency is exactly offset anepposite change in resource price normalized for constant efficiency.

The sign conventipn on this grid should be borne in mind. The positivesign signifies favorable to the bottom line and the negative sign signjties

to the bottom line. Efficiency increase favors the bottom;ts a positive sign, while efficiency decrease harms the bottom line and'i a negative sign. In contrast, resource price increase harms the

tom line and commands a negative sign, while resource price decreasebottom line and commands a positive sign.

Starting with the COAST segment, and proceeding in anti—clockwise theof each of thti above 13 case segments is defined below. The namea of

a case segments which do not occur along axes or the diagonal arecharacterize typical descriptions rather than rigid definitions. do

it relate to the short term and must be qualified should anycontrary considerations be relevant. -

I strategic segment (financially favorable)

0 c [Y axis X axis]

CONSTANT EFFICIENCY REDUCES

SHORT TERM VARIANCE SHORT TERM

PRODUCT PRODUCT

COST COST

REVERSE

Ii

ICOAST

HARMS RETARD

SUPPLIER - + SHORT TERMRESOURCE

•j PRICE

VARIANCE

FAVORS +SUPPLIER b4 DELUDE

-SUCCUMB

RALLY

INCREASESSHORT TERN

PRODUCT FAVORS HARMS

COST SUPPLIER SUPPLIER

V = EFFICIENCY VARIANCE IN NEW PRICES

= Enew(I)

x = SHORT TERM RESOURCE PRICE VARIANCE

= Zshort(I)

DIAGONAL = CONSTANT SHORT TERM PRODUCT COST VARIANCE

= Y + X = 0 = CoSTshort(I)

The SHORT TERM COST GRID presents an analysis of change in short tproduct cost. It graphs the SHORT TERM PRODUCT COST VARIANCE, theVARIANCE and the SHORT TERM RESOURCE PRICE VARIANCE which appear in the COS

OVERVIEW reports. The horizontal axis of this grid scales the changeresource price normalized for constant efficiency, and the vertical a'"scales the change in efficiency. Both axes employ the same numerical scale.The diagonal line represents constant short term product cost because

05 — 1

o < Y axis , X axis

nis strategic segnent represents increasing efficiency accompanied bylining product cost because the favorable effect of efficiency increase isnified by the favorable effect of resource price decrease. This situationins the suppliers of resources because of both the decreasing resdurce

t per unit of product and the decrease in resource price. The SHORTV GRID shows which of the 5 possible cases of efficiency

ains to this situation.

The threat of new competitors is less serious than in the RALLY or OEIVOEegments (which are described below) because improved efficiency makes 4he

structure more competitive in addition to the favorable effect ofresource price decline, -

ER VERTICAL AXIS strategic segment (financially favorable)

0 < (Y axis + X axis]

0 = Kaxis < Yaxis

"s strategic segment represents increasing efficiency accompanied bylecreasing product cost because the favorable effect of efficiency increasv isccompanied by the neutral effect of constant resource price. This situatfonarms the suppliers of resources because of the decreasing resourcer unit of product. The SHORT TERM QUANTITY GRID shows which of thp 5

ssible cases of efflciency growth pertains to this situation. •

¶ke threat of new competitors hinges upon their ability to bemductive or to buy resources cheaper.

05 — 2

REVERSE strategic segment (financially favorable)

o < [V axis + X axis]

X axis < 0 < V axis

This strategic segment represents increasing efficiency accompanieddeclining product cost because the favorable effect of efficiency impovemelexceeds the unfavorable effect of resource price Increase. Hence efficieru

Increase more than absorbs resource price increase and reverses growth(i.e. reduces) the level of product cost. This situation harms the supplirof resources because of the decreasing resource content per unit of producibut also favors the suppliers of resources because of the increase in resounprice. The SHORT TERM QUANTITY GRID shows which of the 5 possible casesefficiency growth pertains to this situation.



(Y axis + X axis] = 0

X axis C 0 < Y axis

This strategic segment represents increasing efficiency accompanied L,

constant product cost because the favorable effect of efficiency impoverneni

is exactly offset by the unfavorable effect of resource price increase. ThU

situation harms the suppliers of resources because of the decreasingcontent per unit of product, but also favors the suppliers of resobecause of the increase in resource price. The SHORT TERM QUANTITY G

shows which of the 5 possible cases of efficiency growth pertains tosituation.


RETARD strategic segment (financially unfavorable)

(V axis + X axis] C 0

Kaxis < 0 < Vaxis

This strategic segment represents increasing efficiency accompanied b,

increasing product cost because the favorable effect of efficiency impoveeenis more than offset by the unfavorable effect of resource price increaseHence efficiency increase less than absorbs resource price increase a

retards growth in the level of product cost. This situation harmssuppliers of resources because of the decreasing resource content per unitproduct, but also favors the suppliers of resources because of the resourc

price increase. The SHORT TERM QUANTITY GRID shows which of the S possibl.cases of efficiency growth pertains to this situation.


05 — 3

I:1

I

lEFT HORIZONTAL AXIS strategic segment (financially unfavorable)

This strategic egment represents constant efficiency accompaniqq byincreasing product cost because the neutral effect of constant efficierity is

companied by the unfavorable effect of resource price increase. Thistion has a neutral effect on the suppliers of resources because of thetnt resource content per unit of product, and favors the of

because of the resource price increase. The SHORT TERM

shows which of the 3 possible cases of constant efficiency pertaIns tothis situation.

Competitors will pose a threat if they can match the efficiency level andbuy resources cheaper.



Y axis , X axis < 0

strategic segment represents decreasing efficiency accompanied byicreasing product cost because the unfavorable effect of declining

accompanied by the unfavorable effect of resource price increase. Thisituation favors the suppliers of resources because of both the

'eseurce content per unit of product and the resource price The)RT TERM QUANTITY GRID shows which of the 5 possible cases of effidency

!cline pertains to this situation.

Competitors would pose a threat once they perceive the efficiency declfne tomovement back up the learning curve which narrows the

cest gap. Efficiency improvement is therefore required to widen the gapdeter competitive entry.


(V axis + X axis] < 0

strategic segment represents decreasing efficiency accompanied byincreasing product cost because the unfavorable effect of efficiency declineis accompanied by the neutral effect of constant resource price. Thissituation favors the suppliers of resources because of the increasing respurce

per unit of product, and has a neutral effect on the ofesources with respect to the constant resource price. The SHORF TERMJANTITY GRID shows which of the 5 possible cases of efficiency

r.'taths to this situation.

* Competitors would pose a threat once they perceive the efficiency decliiie towesent movement back up the learning curve which narrows the compe,Utive

)st gap. Efficiency improvement is therefore required to widen the cqfl gapdeter competitive entry.

D5 — 4


Xaxis < 0 = Vaxis

V axis < 0 = X axis

I

RALLY strategic segment (financially unfavorable)

axis + X axis] < 0

Yaxis < 0 < Xaxis

This strategic segment represents decreasing efficiency accompaniedincreasing product cost because the unfavorable effect of efficiencyexceeds the favorable effect of resource price decrease. This situatifavors the suppliers of resources because of the increasing resource contenper unit of product, and harms the suppliers of resources because of thresource price decrease. The SHORT TERM QUANTITY GRID shows which of thepossible cases of efficiency decline pertains to this situation.

Competitors Mould pose a threat once they perceive the efficiency decl.ine torepresent movement back up the learning curve which narrows the competiticost gap. Efficiency improvement is therefore required to widen the cost gapand deter competitive entry.

FOURTH QUADRANT diagonal (financlilly neutral)

(Yaxis + Xaxis'] = 0

Y axis c 0 < X axis

This strategic segment represents decreasing efficiency accompanied by

constant product cost because the unfavorable effect of efficiency declineis exactly offset be the favprable effect of resource price decrease, Thissituation favors the suppliers of resources because of the increasing resourcecontent per unit of product, and harms the suppliers of resources because of

the resource price decrease. The SHORT TERM QUANTITY GRID shows which of th5 possible cases of efficiency decline pertains to this situation.

Competitors would pose a threat once they perceive the efficiency declinerepresent movement back up the learning curve which narrows the competitivecost gap. Efficiency improvement is therefore required to widen the cost gapand deter competitive entry.

DELUDE strategic segment (financially favorable)

0 c (Yaxis + Xaxis]

Y axis < 0 c X axis

This strategic segment represents decreasing efficiency accompanieddecreasing product cost because the unfavorable effect of efficiency decliris more than offset by the favorable effect of resource price decrease. TLsituation favors the suppliers of resources because of the increasing resouncontent per unit of product, and harms the suppliers of resources becausethe resource price decrease. The SHORT TERM QUANTITY GRID shows which of5 possible cases of efficiency decline pertains to this situation.

Competitors would pose a threat once they perceive the efficiency declinerepresent movement back up the learning curve which narrows the competitircost gap. Efficiency improvement is therefore required to widen the costand deter competitive entry.

D5 — 5

IGHT HORIZONTAL AXIS segment (financially favorable)

V axis = 0 < X axis.

This strategic segment represents constant efficiency accompanied bydecreasing product cost because the neutral effect of constant isaccompanied by the favorable effect of resource price decrease.situation has a neutral impact on the suppliers of resources because of the-enstant resource content per unit of product, and harms the supplieiss ofesources because r.f the resource price decrease. The SHORT TERM QUAHTITYRID shows which of the 3 possible cases of constant efficiency to

situation.

uuv#ctitors will pose a threat if they can match the efficiency level andnay resources even

V axis = 0 A' axis

This strategic segment represents constant efficiency accompanied byConstant product cost because the neutral effect of constant isaccompanied by the neutral effect of constant resource price. This siti4tion

a neutral impact on the suppliers of resources because of the coriflantnurce content per unit of product and the constant resource price. TheiT TERM QUANTITY GRID shows which of the 3 possible cases of

pertains to this situation.

Competitors will pose a threat if they can outperform the efficiency ievel.1 buy resources cheaper.

D5 — 6

.4

0 c (V axis + A' axis]


(V axis + A' axis] = 0

Chapter D6 PRICE GRID

This chapter presents the axioms uiiderpinning the 13 segments which make

the price grid. These measures refer to change in the level of, aand their dimensional coefficient is dimensionless.

Figure D6.Fl - PRICE GRID

Pricerecovery change is driven by change in the product price index nuni..

tsPnew(U) and/or change in the resource price index number APoJd(I). If

D6 - 1

s grid enables one to categorize price recovery into the various'n. The horizontal axis scales the change in resource price index

old(I)) and the vertical axis scales the change in product priceber (APnew(U)). The diagonal line connects all points where changQ induct price equals change in resource price. Along this line no Qriceavery change takes place. -

'e 5 areas above the diagonal signify price over—recovery and arencially favorable, the 3 areas along the diagonal signify constantvery and are financially neutral, while the 5 areas below the

price under—recovery decline and are financially unfavorable tw theoducer.

e TRAIL segment represents increasing product price accompanie4 bylining price recovery because growth in resource price exceeds induct price (lsPolci(T) > APnew(U)). In this situation the suppliero a higher price which the producer less than fully recovers from2 thesumer. The produ:er therefore subsidizes the consumer to the extent the

under—recovery. Price under—recovery represents an inverted priceolla which deters new competitors. This deterrent makes the ofproducer more safe provided he finances price under—recovery::from

creased productivity.

QUADRANT diagonal (financially neutral)

(Y axis — X axis) = 0

o < Yaxis = Xaxis

ie FIRST QUADRANT diagonal segment represents increasing product price)mpanied by constant price recovery because growth in resource price eqpals

Dwth in product price = In this situation thenefits from a higher price which the producer fully recovers from: the

sumer. The producer therefore transfers no subsidy to the cons)aoer.itant price recovery has a neutral effect on profits and on the ofcompetitors.

I strategic segment (financially favorable but unsafe)

0 < [V axis —. X axis]

o < Xaxis < Vaxis

SPURT segment represents increasing product price byprice recovery because growth in product price exceeds growth in

price > In this situation the supplier benpfits

D6 — 2

changes are plotted on the above grid, it is possible to see how chatwe tnduct price and/or in resource price determine price recovery change.

strategic segmnnt (financially unfavorable but safe)

[V axis — X axis] < 0

0 < Vaxis < Xaxis

% CHANGE INCONSUMER PAYS PRODUCT PRICE CONSTANT

SUBSIDY TO PRICE

PRODUCER p4 RECOVERY

(UNSAFE) SPURT p4

GOUGE

p4 TRAIL

PRODUCER p4

% CHANGE INRESOURCE

PRICE

HARMS p4

PRODUCER SHAVE

p4

0SLASH

PARE

0PRODUCER PAYSSUBSIDY TO

4CONSUMER

HARMS FAVORS (SAFE)SUPPLIER SUPPLIER

Y = PERCENTAGE CHANGE IN RESOURCE PRICE NEEDED FORCONSTANT (i.e., OLD) PRICE RECOVERY

= AThsew(U)

= Rlong(I) / [VALUEPeW(I) + Ynew(I)]

X = PERCENTAGE CHANGE IN RESOURCE PRICE

=

= PRIold(I) / VALUEoJd(I)

DIAGONAL = CONSTANT (i.e., OLD) PRICE RECOVERY

=y—x=o

from a higher price which the producer more than recovers from theThe producer therefore extracts a subsidy from the consumer to the extentthe price over—recovery. Price over—recovery represents a price umbrell

which attracts new competitors. This incentive for new competitors makes t,position of the producer less safe regardless of whether or not he increase.

productivity.

UPPER VERTICAL AXIS segment (financially favorable but unsafe)


o = Kaxis < Yaxis

The above segment represents increasing product price accompanied

increasing price recovery because growth in product price occurs while

resource price stays constant. In this situation the supplier derives neutralbenefit from zero change in resource price despite which the producer

increases product price. The producer therefore extracts a subsidy from the

consumer to the extent of the price over—recovery. Price over—recovery

represents a price umbrella which attracts new competitors. This incentivefor new competitors makes the position of the producer less safe regardless ef-iwhether or not he increases productivity.

GOUGE strategic segment (financially favorable but unsafe)


X axis < 0 < Y axis

The GOUGE segment represents increasing product price accompanied by

increasing price recovery because growth in product price occurs despite

decline in resource price. In this situation the supplier is harmed by

decline in resource price despite which the producer increases product price.:The producer therefore extracts a subsidy from the consumer to the extent oh

the price over—recovery. Price over—recovery represents a price umbrell.

which attracts new competitors. This incentive for new competitors makes the

position of the producer less safe regardless of whether or not he increases

productivity.

LEFT HORIZONTAL AXIS segment (financially favorable but unsafe)

o < [Y axis — X axis]

X axis < 0 = Y axis

The above segment represents unchanged product price accompaniedincreasing price recovery because product price stays constant while resouri

price declines. In this situation the supplier is harmed by the declineresource price despite which the producer maintains a constant product prY

The producer therefore extracts a subsidy from the consumer to the extentthe price over—recovery. Price over—recovery represents a price umbrel

which attracts new competitors. This incentive for new competitors makes ti

position of the producer less safe regardless of whether or not he increas'

productivity.

DO — 3

The SHAVE segment represents decreasing product price accompanieØ byincreasing price recovery because decline in resource price exceeds inproduct price. In this situation the supplier is harmed by a lowerprice which the producer less than concedes to the consumer. The proelqcer

extracts a subsidy from the consumer to the extent of the TWice-——recovery. Price over—recovery represents a price umbrella which attr*cts

competitors. This incentive for new competitors makes the positionof whether or not he increases productivity.

The THIRD QUADRANT diagonal segment represents declining productaccompanied by constant price recovery because decline in resource pHceequals decline in product price (APold(I) = LtPnew(U)). In this situation -tesupplier is harmed by -e lower resource price which the producer fully concrijieso the consumer. The producer therefore transfers no subsidy to the consqür.onstant price recovery has a neutral effect on profits and on the

competitors.

PARE strategic segment (financially unfavorable but safe)


Y axis C X axis < 0

The PARE segment represents decreasing product price accompanied bycreasing price recovery because decline in product price exceeds decline in

esource price. In this situation the supplier is harmed by a lower resdurcerice which the producer less than transfers to the consumer. Theerefore subsidizes the consumer to the extent of the priceice under—recovery represents an inverted price umbrella which deterswtitors. This deterrent makes the position of the producer more

he finances price under—recovery from increased productivity.

_..!R VERTICAL AXIS segment (financially unfavorable but safe)

(Yaxis — Xaxis] C 0

Y axis < 0 = X axis

lie above segment represents declining product price accompanied by declininga recovery because product price declines occurs while resource price stays

estant. In this situation the supplier derives neutral benefit from flroange in resource price despite which the producer reduces product price:lhe

DO — 4

strategis segment (financially favorable but unsafe)

0 < (V axis — X axis]

X axis < V axis < 0

QUADRANT diagonal (financially neutral)

(V axis — X axis] = 0

Y axis = X aris C 0

producer therefore transfers a subsidy to the consumer to the extent ofprice under—recovery. Price under—recovery represents an inverted priumbrella which deters new competitors. This deterrent makes the positionthe producer more safe provided he increases productivity.

SLASH strategic segment (financially unfavorable but safe)


Yaxis < 0 < Xaxis -

The SLASH segment represents decreasing product price accompanied

decreasing price recovery because resource price is increasing despitedecline in product price. In this situation the supplier benefitshigher price which the producer does not recovers from the consumer

producer therefore subsidizes the consumer to the extent of the price L.

recovery. Price under—recovery represents an inverted price umbrelladeters new competitors. This deterrent makes the position of the produce

more safe provided he finances price under—recovery from Increase

productivity.

RIGHT HORIZONTAL AXIS segment (financially unfavorable but safe)

[Y axis — X axis] < 0

Y axis = 0 < X axis

The above segment represents unchanged product price accompanied

declining price recovery because product price stays constant while reseurt

price increases. In this situation the supplier benefits from a higher pr4

which the producer does not recovers from the consumer. The producer theresubsidizes the consumer to the extent of the price under—recovery.under—recovery represents an inverted price umbrella which deterscompetitors. This deterrent makes the position of the producer more

provided he finances price under—recovery from increased productivity.

AXIS ORIGIN strategic segment (financially neutral)

jY axis — K axis] = 0

V axis = 0 = K axis

The AXIS ORIGIN segment (i.e. that which appears between all segme

defined above) represents constant product price accompanied by constantrecovery because both product price and resource price are maintaiconstant. This situation has a neutral effect on the consumer and produc'

because neither receives a subsidy from the other, Constant price recove

has a neutral effect on profitability so that residence in the AXIS ORI

segment will signify that profitability change will be driven by productichange alone.

Chapter D7 PROFIT GRID (LONG TERM)

This chapter presents the axioms underpinning the 13 segments which mak. uplong term quantity grid. These measures refer to change in the leve of

a function, and their dimensional coefficient is a currency unit.

The LONG TERM PROFIT GRID presents an analysis of change in long term"ict profit. It graphs the LONG TERM PRODUCT PROFIT VARIANCE,

CTIVITY VARIANCE and the LONG TERM PRICE RECOVERY VARIANCE whichthe PROFIT OVERVIEW report. The horizontal axis of this grid

iange in long term price recovery (i.e., normalized for

D7 — 1

Figure D7.F1 - LONG TERM PROFIT GRID

PRODUCTIVITYVARIANCE

PURSUE

AWAKEN

+FINETUNE

CONSTANTLONG TERMPRODUCT

PROFIT

HARMS

SUPPLIER

FAVORS

SUPPLIER

DECREASEDLONG TERMPRODUCT

PROFIT

INCREASEDLONG TERMPRODUCT

$ PROFIT

LONG TERMPRICERECOVERYVARIANCE

SCUTTLE

PROOUCER PAYSSUBSIDY TO

CONSUMER (SAFE)

sq

- SCRAMBLE

SALVAGE

CONSUMER PAYSSUBSIDY TOPRODUCER (UNSAFE)

F

k

L

Y = PROOUCTIVITY VARIANCE IN NEW PRICES

= yn&w(r)

X = LONG TERM PRICE RECOVERY

= Rlong(I)

DIAGONAL = LONG TERM PRODUCT PROFIT VARIANCE

= PROFIT7ong(I)

=Y+X=O

06 —

productivity), and the vertical axis scales the change in productivity. Bothaxes employ the same numerical scale. The diagonal line represents constantlong term product profit because it connects all points where the change inproductivity is exactly offset by an opposite change in long term pricerecovery normalized for constant productivity.

Starting with the AWAKEN segment, and proceeding in anti—clockwise order,the meaning of each of the above 13 case segments is defined below. Thenames of six case segments which do not occur along axes or the diagonal areintended to characterize typical •strategic reponses rather than rigidprescriptions. They do not relate to the short term and must be qualifiedshould any compelling contrary considerations be relevant.

AWAKEN strategic segment (financially favorable and partly unsafe)

0 < [Yaxis + Xaxis]

- 0 < Y axis , X axis


increasing long term product profit because price over—recovery also takesplace. This situation harms the suppliers of resources because of thedecreasing resource content per unit of product. It also harms the consumerbecause he pays to the producer a subsidy equivalent to the price over—recovery. The QUANTITY and PRODUCTIVITY GRIDS show which of the 5 possiblecases of productivity growth pertains to this situation, and the PRICE GRID

shows which of the 5 possible cases of price over—recovery pertains to thissituation.

Awaken a business in this strategic segment. The combination of increasinglong term product profit and umbrella pricing could trigger the entry ofcompetitors. However, even if competitive entry completely eliminates theprice umbrella, this business would reflect lower, but still positive,in long term product profit on account of productivity gain. The danger isnot as severe here as it is in the Scramble strategic segment.

UPPER VERTICAL AXIS strategic segment (financially favorable and safe)

o < [V axis + XaxisJ

o = Xaxis < Yaxis

This strategic segment represents increasing productivity accompanied byincreasing long term product profit because constant long term price recoverytakes place. This situation harms the suppliers of resources because ofdecreasing resource content per unit of product. It is also neutral toconsumer and producer because neither pays a subsidy to the other. The-QUANTITY and PRODUCTIVITY GRIDS show which of the S possible cases efproductivity growth pertains to this situation, and the PRICE GRID shows whichof the 3 possible cases of constant price recovery pertains to this situation,

In the UPPER VERTICAL AXIS strategic segment the entire productivity pie is -

retained by the producer to improve profitability.

D7 — 2

PURSUE strategic Legment (financially favorable and safe)

0 < [V axis + Xaxis]

Xaxis < 0 < Vaxis

This strategic segment represents increasing productivity accompapied byIncreasing long term product profit because productivity impovement' exceedsprice under—recovery.. This situation harms the suppliers of Vesourcesbecause of the decreasing resource content per unit of product. 'It alsofavors the consumer because he receives from the producer a subsidy qqpivalentto the price under—recovery. The QUANTITY and PRODUCTIVITY GRIDS whichof the S possible cases of productivity growth pertains to this situation, andthe PRICE GRID shows which of the S possible cases of price underrecovery

¾ perthins to this situation.

In the PURSUE strategic segment the productivity pie is shared befween theproducer and the consumer. -

Pursue the same path in a business in this strategic segment. This is themost favored of segments because productivity gain is being used td financethe creation of an inverted price umbrella consistent with longterm product profit. Despite improving long term product profit, newcompetitors are unlikely to attempt entry in the face of an invertüd priceumbrella and the productivity growth registered by the business.

SECOND QUADRANT diagonal (financially neutral and safe)

[V axis + Xaxis] = 0

Xaxis < 0 < Vaxis

This strategic segment represents increasing productivity byconstant long term product profit because productivity impovement is:: exactlyoffset by price under—recovery. This situation harms the suppljers ofresources because of the decreasing resource content per unit of product. It

- also favors the consumer because he receives from the producerequivalent to price under—recovery. The QUANTITY and PRODUCTIVITY GRIDSshow which of the 5 possible cases of productivity growth pertains -to thissituation, and the PRICE GRID shows which of the 5 possible cases ef priceunder—recovery pertains to this situation.

In the SECOND QUADRANT diagonal strategic segment the entire productivitypie is transferred by the producer to the consumer by way of pricj' under—

j.recovery.

FINETUNE strategic segment (financially unfavorable and safe)

[V axis + X axis] < 0

Xaxis < 0 .c Yaxis

This strategic segment represents increasing productivity bydecreasing long term product profit because productivity isexceeded by price under—recovery. This situation harms the supp[fers of

because of the decreasing resource content per unit of Italso favors the consumer because he receives from the producer

It

07 — 3

In the FINETUNE strategic segment a benefit which is more than the entireproductivity pie is transferred from the producer to the consumer. Thproducer dilutes profitability to the extent of the decline in long tL.product profit to finance the excess of the benefit over the productivity ph

Fine—Tune a business in this strategic segment. It has the samegrowth and inverted price umbrella characteristics as the Pursue stratisegment, but the balance between them requires fine—tuning. This can beeither by reducing the extent of the negative long term price recovery orfurther inversion of the price umbrella, provided it is more then offsetfurther increases in productivity growth.

LEFT HORIZONTAL AXIS strategic segment (financially unfavorable and safe)

(V axis + X axis) < 0

X axis < 0 = Y axis

This strategic segment represents constant productivity accompanieddecreasing long term product profit because price under—recovery takes plaiThis situation has a neutral impact on the suppliers of resources becausethe constant resource content per unit of product. It is also favorsconsumer because he receives from the producer a subsidy equal to the prunder—recovery. The QUANTITY and PRODUCTIVITY GRIDS show which of thepossible cases of constant productivity pertains to this situation, and U

PRICE GRID shows which of the 5 possible cases of price under—recoveipertains to this situation.

In the LEFT HORIZONTAL AXIS strategic segment there is no productivityto share between producer and consumer.

SCUTTLE strategic segment (financially unfavorable and partly unsafe)

(V axis + X axis) < 0

V axis , X axis < 0

This strategic segment represents decreasing productivity accompanieddecreasing long term product profit because price under—recovery also tplace. This situation favors the suppliers of resources because of tincreasing resource content per unit of product. It also favors the consun'because he receives from the producer a subsidy equivalent to the price underecovery. The QUANTITY and PRODUCTIVITY GRIDS show which of the 5 possibcases of productivity decline pertains to this situation, and the PRICE Ishows which of the 5 possible cases of price under—recovery pertains to tsituation.

In the SCUTTLE strategic segment there is no productivity pie to s:..between producer and consumer. Instead there is a productivity deficit.

Scuttle (i.e., abandon) a business in this strategic segment. Thistypically a dying business with high fixed cost which is unable to recover

D7 — 4 -

This strategic segment represents decreasing productivity accompaniej$ byecreasing long term product profit because constant long term priceekes place. This situation favors the suppliers of resources because oftheecreasing resource content per unit of product. It is also neutra toonsumer and producer because neither pays a subsidy to the other. The

and PRODUCTIVITY GRIDS show which of the S possible cases ofpreductivity decline pertains to this situation, and the PRICE GRIDwhich of the 3 possible cases of constant price recovery pertains to-4his

ion.

In the LOWER VERTICAL AXIS strategic segment there is no productivity piç toshare between producer and consumer. Instead there is a productivity

LVAGE strategic segment (financially unfavorable and unsafe)

(Y axis + X axis) < 0

Yaxis c 0 < Xaxis

This strategic segment represents decreasing productivity accompanigØ bydecreasing long term product profit because productivity decline exceeds pricever—recovery. This situation favors the suppliers of resources of:.a increasing resource content per unit of product. It also harms theDnsumer because he pays to the producer a subsidy equivalent to the pricever—recovery. The QUANTITY and PRODUCTIVITY GRIDS show which of 5

cases of productivity decline pertains to this situation,GRID shows which of the 5 possible cases of price over—recovery perUins

this situation.

the SALVAGE strategic segment there is no productivity pie to oAarebetween producer and consumer. Instead there is a productivity deficit. -

calvage a business in this strategic segment. Performance profit is:lining because productivity loss exceeds the price recovery gain creat.d by

umbrella pricing situation. Relief from dependence on umbrella isincentive to try to restore productivity levels and reversn the long eterm

roduct profit decline. The threat of newcomers entering under the pjiceis lower than in the next strategic segment.

DURTH QUADRANT diagonal (financially neutral and unsafe)

V axis C 0 < X axis

This strategic segment represents decreasing productivity byonstant long term product profit because productivity decline is

D7 — 5

a

equivalent to the price under—recovery. The QUANTITY and PRODUCTIVITY GRT'

show which of the 5 possible cases of productivity growth pertains to U

situation, and the PRICE GRID shows which of the 5 possible cases of p.

under—recovery pertains to this situation.

reduct price increase the full extent of the resource price increase to ghicht is exposed.

VERTICAL AXIS segment (financially unfavorable and partly unsafe)

(Y axis + X axis) < 0

V axis c 0 = X axis

(V axis + X dxis) = 0

offset by price over—recovery. This situation favors the suppliersresources because of the increasing resource content per unit of product.also harms the consumer because he pays to the producer a subsidy equivalrto the price over—recovery. The QUANTITY and PRODUCTIVITY GRIDS show whiof the 5 possible cases of productivity decline pertains to this situaticand the PRICE GRID shows which of the 5 possible cases of price over—recoverpertains to this situation.

In the FQURTH QUADRANT diagonal strategic segment there is no productivitpie to share between producer and consumer. Instead there is a producti.;deficit.

SCRAMBLE strategic segment (financially favorable and unsafe)


V axis < 0 < X axis

This strategic segment represents decreasing productivity accompaniedincreasing long term product profit because productivity decline is more t..offset by price over—recovery. This situation favors the suppliers o

resources because of the increasing resource content per unit of product. I

also harms the consumer because he pays to the producer a subsidy equivale-to the price over—recovery. The QUANTITY and PRODUCTIVITY GRIDS showof the 5 possible cases of productivity decline pertains to this situationand the PRICE GRID shows which of the 5 possible cases of price over—recoverpertains to this situation.

In the SCRAMBLE strategic segment there is no productivity pie tobetween producer and consumer. Instead there is a productivity deficit.

Scramble to protect a business in this strategic segment. Performance pis increasing because the umbrella pricing gain exceeds (and Ii

camouflages) productivity loss. The threat of new competitors is real becausof both umbrella pricing and increasing long term product profit. Furthermoreproductivity loss narrows the productivity gap between this business and tlow productivity levels of newcomers to the market. A quick turnaroundproductivity loss to gain is needed, since competitive erosion of theumbrella could transform this business from increasing to decreperformance profit.

RIGHT HORIZONTAL AXIS segment (financially favorable and unsafe)


Y axis = 0 C X axis

to share between producer and consumer.

5 ORIGIN segment (financially neutral)

(V axis + X axis] = 0

V axis = 0 = A' axis

This strategic soqment represents constant productivity accompanied byconstant long term product profit because constant price recovery takesThis situation has a neutral impact on the suppliers of resources becausi' of'ie constant, resource content per unit of product. It also has a

t on consumer and producer since neither pays a subsidy to the other,[Theand PRODUCTIVITY GRIDS show which of the 3 possible cases of

productivity pertains to this situation, and the PRICE GRID shows which otthe3 possible cases of constant long term price recovery pertains tosituation.

In the AXIS ORIGIN strategic segment there is no productivity pie to 4!arebetween producer and consumer.

The advanced reader will appreciate the grid rule on the following page,

D7 — 7

This strategic segment represents constant productivity accompanied b,

increasing long term product profit because price over—recovery takes placeThis situation has a neutral impact on the suppliers of resources because o

the constant resource content per unit of product. It is also harms tkconsumer because he pays to the producer a subsidy equal to the price overecovery. The QUANTITY and PRODUCTIVITY GRIDS show which of the 3 possi'cases of constant productivity pertains to thi situation, and the PRICE G

shows which of the 5 possible cases of price over—recovery pertains to +

situation.• In the RIGHT HORIZONTAL AXIS strategic segment there is no productivity p1

D7 — 6

Figure D7.F2 - GRID RULE

LINK BETWEEN LONG TERM PROFIT GRID AND 48 BOX DIAGRAM

SEGMENT LONG TERM PROFITPERFORMANCE

CONSEQUENCE

PRODUCTIVITYCONDITION

PRICERECOVERYCONDITION

SCRAMBLE

RIGHT HORIZONTAL

AWAKEN

UPPER VERTICAL

PURSUE

FINANCIALLY FAVORABLE

Qn * Pn Qnp * Pnr

Qn * Pn < Qnp * Pnr

Qn * Pn < Qnp * Pnr

Qn * Pn < Qnp * Pnr

Qn * Pn < Qnp * Pnr

Qn > Qnp

Qn = Qnp

Qn < Qnp

Qn < Qnp

Qn < Qnp

Pn < Pnr

Pn < Pnr

Pn < Pnr

Pn = Pnr

Pn > Pnr

2ND QUADRNT DIAGNL

where

or

AXIS ORIGIN

4TH QUADRNT DIAGNL

where

or

FINANCIALLY NEUTRAL

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn * Pn = Qnp * Pnr

Qn < Qnp

Qn = Qnpr

Qn < Qnp

Qn = Qnp

Qn > Qnp

Qn = Qnpr

Qn > qnp

Pn > Pnr

Pn > Pnr

Pn = Pnrp

Pn = Pnr

Pn < Pnr

Pn < Pnr

Pn = Pnrp

FINETUNE

LEFT HORIZONTAL

SCUTTLE

LOWER VERTICAL

SALVAGE

FINANCIALLY UNFAVORABLE

Qn * Pn > Qnp * Pnr

Qn * Pn > Qnp * Pnr

Qn *Pn > Qnp * Pnr

Qn * Pn > Qnp * Pnr

Qn * Pn > Qnp * Pnr

Qn < Qnp

Qn = Qnp

Qn > Qnp

Qn > Qnp

Qn > Qnp

Pn > Pnr

Pn > Pnr

Pn > Pnr

Pn = Pnr

Pn < Pnr

07 — 8

Chapter 08 PROFIT GRID (SHORT TERM)

This chapter presents the axioms underpinning the 13 segments which make upshort term quantity grid. These measures refer to change in the of

a function, and their dimensional coefficient is a currency unit.

Figure D8.F1 - SHORT TERM PROFIT GRID

The SHORT TERM PROFIT GRID presents an analysis of change in short)roduct profit. It graphs the SHORT TERM PRODUCT PROFIT VARIANCE, the

FICIENCY VARIANCE and the SHORT TERM PRICE RECOVERY VARIANCE whiche PROFIT OVERVIEW report. The horizontal axis of this grid scales (heange in short term price recovery (i.e., normalized for constant

and the vertical axis scales the change in efficiency.

08 — 1

CONSTANTSHORT TERMPRODUCT

PROF IT

EFFICIENCYVARIANCE

PURSUE

INCREASEDSHORT TERMPRODUCT

$ PROFIT

b1 +

FINE b1

TUNE -

AWAKEN

HARMS

SUPPLIER

FAVORS

SUPPLIER

+ SHORT TERMPRICE

+ RECOVERYVARIANCE

SCUTTLE

SCRAMBLE

'I,'

SALVAGEDECREASEDSHORT TERMPRODUCT

PROFIT PRODUCER PAYSSUBSIDY TO

CONSUMER (SAFE)

CONSUMER PAYSSUBSIDY TOPRODUCER (UNSAFE)

Y = EFFICIENCY VARIANCE IN NEW PRICES

= Enew(I)

X = SHORT TERM PRICE RECOVERY VARIANCE

= Rshort(I)

DIAGONAL SHORT TERM PRODUCT PROFIT VARIANCE

= PROFITshort(I)

= 'I + X = 0

axes employ the same numerical scale. The diagonal line represents constantshort term product profit because It connects all points where the change inefficiency Is exactly offset by an opposite change in short term price,recovery normalized for constant efficiency.

Starting with the AWAKEN segment, and proceeding in anti—clockwise order,the meaning of each of the above 13 case segments is defined below. Thenames of six case segments which do not occur along axes or the diagonal areintended to characterize typical strategic reponses rather than rigidprescriptions. They do not relate to the short term and must be qualifiedshould any compelling contrary considerations be relevant.

AWAKEN strategic segment (financially favorable and partly unsafe)

o < (Vax/s + lax/sfo < Vax/s , lax/s

This strategic segment represents increasing efficiency accompanied by

increasing short term product profit because price over—recovery also takesplace. This situation harms the suppliers of resources because of thedecreasing resource content per unit of product. It also harms the consumerbecause he pays to the producer a subsidy equivalent to the price oversrecovery. The SHORT TERM QUANTITY GRID shows which of the 5 possible casesof efficiency growth pertains to this situation, and the PRICE GRID shows'which of the 5 possible cases of price over—recovery pertains to thissituation.

Awaken a business in this strategic segment. The combination of increasingshort term product profit and umbrella pricing could trigger the entry of new

competitors. However, even if competitive entry completely eliminates theprice umbrella, this business would reflect lower, but still positive, changein short term product profit on account of efficiency gain. The danger isnot as severe here as it is in the Scramble strategic segment.

UPPER VERTICAL AXIS strategic segment (financially favorable and safe)

o < (V ax/s + I ax/sf

o = I ax/s c V ax/s

This strategic segment represents increasing efficiency accompanied by'increasing short term product profit because constant short term price-recovery takes place. This situation harms the suppliers of resourcesbecause of the decreasing resource content per unit of product. It is alsoneutral to consumer and producer because neither pays a subsidy to the other.The SHORT TERM QUANTITY GRID shows which of the 5 possible cases of efficiencrgrowth pertains to this situation, and the PRICE GRID shows which of the 3

possible cases of constant price recovery pertains to this situation.

In the UPPER VERTICAL AXIS strategic segment the entire efficiency pie isretained by the producer to improve profitability.

DR — 2

PURSUE strategic segment (financially favorable and safe)

0 < (Vax/s + lax/sflax/s < o < Yax/s -

This strategic segment represents increasing efficiency accompaniect by'increasing short term product profit because efficiency impovement exnedsprice under—recovery. This situation harms the suppliers of resoqgcesof the decreasing resource content per unit of product. It £lsofavors the consumer because he receives from the producer a subsidyto the price under—recovery. The SHORT TERM QUANTITY GRID shows which

of efficiency growth pertains to this situation, and thePRICE GRID shows which of the 5 possible cases of pricepartains to this situation.

In the PURSUE strategic segment the efficiency pie is shared between - kheproducer and the consumer.

Pursue the same path in a business in this strategic segment. This is ' themost favored of segments because efficiency gain is being used to finance thecreation of an inverted price umbrella consistent with increasing short Lrmproduct profit. Despite improving short term product profit, new'are unlikely to attempt entry in the face of an inverted price umbrellathe efficiency growth registered by the business.

SECOND QUADRANT diagonal (financially neutral and safe)

(Vax/s + lax/sf = 0

- lax/s < a < Vax/s

This strategic segment represents increasing efficiency accompanied by'constant short term product profit because efficiency impovement is exactly'offset by price under—recovery. This situation harms the suppliersresources because of the decreasing resource content per unit of product. Italso favors the consumer because he receives from the producer aeqoivalent to the price under—recovery. The SHORT TERM QUANTITY GRID shbwswhich of the 5 possible cases of efficiency growth pertains to this situatfçjai,'eod the PRICE GRID shows which of the S possible cases of price under—recoyfrypertains to this situation.

In the SECOND QUADRANT diagonal strategic segment the entire efficiency &etransferred by the producer to the consumer by way of price

FINETUNE strategic segment (financially unfavorable and safe)

(Vax/s + lax/sf C 0

I ax/s c 0 c V ax/s

This strategic segiaent represents increasing efficiency accompanied bydecreasing short term product profit because efficiency impovement isby price under—recovery. This situation harms the suppliers ofbecause of the decreasing resource content per unit of product. It aHofavors the consumer because he receives from the producer a subsidy equival'4jitto the price under—recovery. The SHORT TERM QUANTITY GRID shows which of

D8—3

5 possible cases of efficiency growth pertains to this situation, and the

PRICE GRID shows which of the S possible cases of price under—recoveypertains to this situation.

In the FINETUNE strategic segment a benefit which is more than the entirefficiency pie is transferred from the producer to the consumer. Th

producer dilutes profitability to the extent of the decline in short telproduct profit to finance the excess of the benefit over the efficiency pie.

Fine—Tune a business in this strategic segment. It has the same efficientgrowth and inverted price umbrella characteristics as the Pursue strategisegment, but the balance between them requires fine—tuning. This can be don

either by reducing the extent of the negative short term price recovery orfurther inversion of the price umbrella, provided it is more then offsetfurther increases in efficiency growth.

LEFT HORIZONTAL AXIS strategic segment (financially unfavorable and safe)

(V axis + Xaxisj < 0

X axis < 0 = V axis

This strategic segment represents constant efficiency accompanied hidecreasing short term product profit because price under—recovery takes place.This situation has a neutral impact on the suppliers of resources because of

the constant resource content per unit of product. It is also favors the

consumer because he receives from the producer a subsidy equal to theunder—recovery. The SHORT TERM QUANTITY GRID shows which of the 3 possiblecases of constant efficiency pertains to this situation, and the PRICE GRI

shows which of the 5 possible cases of price under—recovery pertains to thissituation.

In the LEFT HORIZONTAL AXIS strategic segment there is no efficiency pie to

share between producer and consumer.

SCUTTLE strategic segment (financially unfavorable and partly unsafe)


V axis , X axis < 0

This strategic segment represents decreasing efficiency accompanied by

decreasing short term product profit because price under—recovery also taketplace. This situation favors the suppliers of resources because ofincreasing resource content per unit of product. It also favors the consumtbecause he receives from the producer a subsidy equivalent to the pricerecovery. The SHORT TERM QUANTITY GRID shows which of the 5 possible cases

of efficiency decline pertains to this situation, and the PRICE GRID shewr

which of the 5 possible cases of price under—recovery pertains to thlcsituation.

In the SCUTTLE strategic segment there i.s no efficiency pie to share betweenproducer and consumer. Instead there is a efficiency deficit.

Scuttle (i.e., abandon) a business in this strategic segment. Thistypically a dying business with high fixed cost which is unable to recover hiproduct price increase the full extent of the resource price increase to which

DR — 4

dt is exposed.

LOWER VERTICAL AXIS segment (financially unfavorable and partly unsafe)


V axis < C = X axis

This strategic segment represents decreasing efficiency accompaniq4 bydecreasing short term product profit because constant short term twicerecovery takes pluce. This situation favors the suppliers ofbecause of the increasing resource content per unit of product. It is 'alsoneutral to consumer and producer because neither pays a subsidy to the ojher.The SHORT TERM QUANTITY GRID shows which of the 5 possible cases ofdecline pertains to this situation, and the PRICE GRID shows which of 3possible cases of constant price recovery pertains to this situation.

In the LOWER VERTICAL AXIS strategic segment there is no efficiency toshare between producer and consumer. Instead there is a efficiency deficIt.

SALVAGE strategic segment (financially unfavorable and unsafe)

(V axis + X axis] c 0

Yaxis < 0 < Xaxis

This strategic segment represents decreasing efficiency accompanied bydecreasing short term product profit because efficiency decline exceedsrover_recovery. This situation favors the suppliers of resources ofthe increasing resource content per unit of product. It also harms theconsumer because he pays to the producer a subsidy equivalent to the pciceover—recovery. The SHORT TERM QUANTITY GRID shows which of the 5

cases of efficiency decline pertains to this situation, and the PRICEshows which of the 5 possible cases of price over—recovery pertains to thissituation.

In the SALVAGE strategic segment there is no efficiency pie to share betweenproducer and consumer. Instead there is an efficiency deficit.

Salvage a business in this strategic segment. Performance profit isdeclining because efficiency loss exceeds the price recovery gain by

'an umbrella pricing situation. Relief from dependence on umbrella prici4 isan incentive to try to restore efficiency levels and reverse the short termproduct profit decline. The threat of newcomers entering under theumbrella is lower than in the next strategic segment.

!OURTH QUADRANT diagonal (financially neutral and unsafe)

(Vaxis + = 0

V axis < 0 c A' axis

This strategic segment represents decreasing efficiency accompanied byconstant short term product profit because efficiency decline isoffset by price over—recovery. This situation favors the ofresources because of the increasing resource content per unit of It

F;!

08 — 5

S

also harms the consumer because he pays to the producer a subsidy equivato the price over—recovery. The SHORT TERM QUANTITY GRIO shows which of5 possible cases of efficiency decline pertains to this situation, andPRICE GRIO shows which of the 5 possible cases of price over—recovery pertato this situation.

In the FOURTH QUAORANT diagonal strategic segment there is no efficienc'to share between producer and consumer.. Instead there is a efficideficit.

SCRAMBLE strategic segment (financially favorable and unsafe)


Yaxis < 0 < Xaxis

This strategic segment represents decreasing efficiency accompaniedincreasing short term product profit because efficiency decline is more U.

offset by price over—recovery. This situation favors the suppliersresources because of the increasing resource content per unit of product.also harms the consumer because he pays to the producer a subsidyto the price over—recovery. The SHORT. TERM QUANTITY GRIO shows which of5 possible cases of efficiency decline pertains to this situation, andPRICE GRIO shows which of the 5 possible cases of price over—recovery pertato this situation.

In the SCRAMBLE strategic segment there is no efficiency pie tobetween producer and consumer. Instead there is a efficiency deficit.

Scramble to protect a business in this strategic segment. Performance pis increasing because the umbrella pricing gain exceeds (and h_,..

camouflages) efficiency loss. The threat of new competitors is real becauseboth umbrella pricing and increasing short term product profit. FurthermorEefficiency loss narrows the efficiency gap between this business and theefficiency levels of newcomers to the market. A quick turnaround fiefficiency loss to gain is needed, since competitive erosion of the p

umbrella could transform this business from increasing toperformance profit.

RIGHT HORIZONTAL AXIS segment (financially favorable and unsafe)


Y axis = 0 c X axis

This strategic segment represents constant efficiency accompaniedincreasing short term product profit because price over—recovery takes plarThis situation has a neutral impact on the suppliers of resources becausethe constant resource content per unit of product. It is also harmsconsumer because he pays to the producer a subsidy equal to the price e

recovery. The SHORT TERM QUANTITY GRIO shows which of the 3 possible c

of constant efficiency pertains to thi situation, and the PRICE CR10 s

which of the 5 possible cases of price over—recovery pertains to tsituation.

In the RIGHT HORIZONTAL AXIS strategic segment there is no efficiency pieshare between producer and consumer.

08 — 6

i,d5 strategic segment represents constant efficiency accompanied byshort term product profit because constant price recovery takes

3ce. This situation has a neutral impact on the suppliers ofresource content per unit of product. It also has a

eutral impact on consumer and producer since neither pays a subsidy to tháther. The SHORT TERM QUANTITY CR10 shows which of the 3 possible cases of'stant efficiency pertcins to this situation, and the PRICE CR10 shows whichthe 3 possible cases of constant short term price recovery pertains toLuat ion.

In the AXIS ORIGIN strategic segment there is no efficiency pie to shareetween producer and consumer.

The advanced reader will appreciate the grid rule on the next page.

08 — 7


[Yaxis + Xaxis] = 0

Y axis = 0 = I axis

The PRODUCT MIX COST GRID presents an analysis of the product mix yariancewhich appears in the COST RECONCILIATION REPORT. It graphs changelii unweighted product quantity against percentage change inqaantity to reveal the effect on cost of change in product mix. Bpjh axesemploy the same numerical scale. The isovalue diagonal represents zerodifference betweei the two axes and signifies constant product mix beç4use itcannects all points where the percentage change in unweighted productis equal to percentage change in weighted product quantity.

LINK 8ETWEEN SHORT TERM PROFIT GRID AND 48 BOX DIAGRAM

Figure D8.F2 - GRIDE RULE Chapter D9 PRODUCT MIX COST GRID

This chapter presents the axioms underpinning the 13 segments which make upproduct mix cost grid. These measures refer to change in the of a

fanction, and their dimensional coefficient is a currency unit.

Figure D1.F1 - PRODUCT MIX COST GRID

% CHANGE IN UMWEIGHTEDPRODUCT QUANTITY

DISGUISE

DILUTE

THICKEN

SEGMENT SHORT TERM PROFITPERFORMANCE

CONSEQUENCE

EFFICIENCYCONDITION

PRICERECOVERY

CONDITION

SCRAMBLE

RIGHT HORIZONTAL

AWAKEN

UPPER VERTICAL

PURSUE

FINANCIALLY FAVORABLE

Qn * Pn < Qne * Pnr

Qn * Pn < Qne * Pnr

Qn * Pn c Qne * Pnr

Qn * Pn < Qne * Pnr

Qn * Pn < Qne * Pnr

Qn > Qne

Qn = Qne

Qn c Qne

Qn C Qne

Qn C Qne

Pn < Pnr

Pn < Pnr

Pn < Pnr

Pn = Pnr

Pn > Pnr

2ND QUADRNT DIAGNL

where

or

AXISORIGIN

4TH QUADRNT DIAGNL

where

or

FINANCIALLY NEUTRAL

qn * Pn = Qne * Pnr

Qn * Pn = Qne * Pnr

Qn*Pn = Qne*Pnr

Qn*Pn=Qne*Pnr

Qn * Pn = Qne * Pnr

Qn*Pn = Qne*Pnr

Qn*Pn = Qne*Pnr

Qn < Qne

Qn = Qner

Qn < Qne

Qn=Qne

Qn > Qne

Qn = Qner

Qn > Qne

Pn > Pnr

Pn > Pnr

Pn = Pnre

Pn=PnrPn < Pnr

Pn < Pnr

Pn = Pnre

FINETUNE

LEFT HORIZONTAL

SCUTTLE

LOWER VERTICAL

SALVAGE

FINANCIALLY UNFAVORABLE

Qn * Pn > Qne * Pnr

Qn * Pn > Qne * Pnr

Qn*Pn>Qne*Pnr

Qn * Pn > Qne * Pnr

Qn*Pn > Qne*Pnr

Qn < Qne

Qn = Qne

Qn>Qne

Qn > Qne

Qn > Qne

Pn > Pnr

Pn > Pnr

Pn>PnrPn = Per

Pn C Pnr

1-+

'4

% CHANGE IN4 WEIGHTED

PRODUCTQUANTITYSOFTEN

jJ'4

HARDEN

CONCEAL

'4

Y = PERCENTAGE CHANGE IN UNWEIGHTEDPRODUCT QUANTITY

IN WEIGHTEDPRODUCT QUANTITY

= PERCENTAGE CHANGE

=

= VOL0!d(LJ) / VALUEoJdflJ)

DIAGONAL = CONSTANT (i.e., OLD) PRODUCT MIX

= Y — X = 0

D8 — 8D9 — 1

S

The product mix variance refers to multiple products within an operation. Itassumes a zero value when there is a single product within an operation orwhen multiple products within a given operation all change to the same -

proportion between old and new intervals (i.e. remain in constant relation toone another and hence in constant mix). Change in product quantity ismeasured in the following two ways:

— percentage change in weighted product quantity (using old product prices asweights to combine unlike product quantities in old and new intervalsrespectively into dimensionally proper aggegations which are calladweighted production), and

— percentage change in unweighted product quantity (using no weights tocombine unlike product quantities in old and new intervals respectivelyinto dimensionally improper aggegations which are called unweightedproduction).

THICKEN strategic segment (financially unfavorable)

[Yaxis — Xaxis] < 0

o < Yaxis < Xaxis

The THICKEN segment represents an increase in unweighted productionaccompanied by a larger increase in weighted production. This situationgives rise to a unfavorable (i.e. negative) product mix variance and signifiesthat between the old and new intervals the product quantities which employhigh price weights increased relative to the product quantities which employlow price weights. Such change thickens the product mix.

FIRST QUADRANT diagonal (financially neutral)

[V axis — Xaxis] = 0

o < V axis = K axis

The FIRST QUADRANT diagonal segment (i.e. that which appears betweenTHICKEN and DILUTE segments) represents an increase in unweighted productionaccompanied by an identical increase in weighted production. This situationgives rise to a zero product mix variance and signifies that between the oldand new intervals the product quantities which employ high price weightsincreased by a proportion equal to that of the product quantities which employlow price weights. Such change holds the product mix constant.

DILUTE strategic segment (financially favorable)

o < [V axis — K axis]

o < Xaxis < Yaxis

The DILUTE segment represents an increase in unweighted productionaccompanied by a lesser increase in weighted production. This situation',gives rise to a positive product mix variance and signifies that between thaiold and new intervals the product quantities which employ high pricedeclined relative to the product quantities which employ low price weights.Such change dilutes the product mix.

D9 — 2

ii



a = Kaxis < Vaxis

The UPPER VERTICAL AXIS segment (i.e. that which appears between DILUTE and£DISGUISE segments) represents an increase in unweighted production accthnpanied

a zero change in weighted production. This situation gives nsa: to aproduct mix variance and signifies that between the old new

'intervals the product quantities which employ high price weights duclinedrelative to the product quantities which employ low price weights .J' Suchchange "reduces the density" of the product mix.

DISGUISE strategic segment (financially favorable)


K axis < U < V axis

The DISGUISE segment represents an increase in unweighteda decline in weighted production. This situation rise

ste a positive product mix variance and signifies that between the old newthe product quantities which employ high price weights

to the product quantities which employ low price weights. I- Suchincrease in unweighted production disguises (i.e. contradicts) moresignificant decline in weighted production.

LEFT HORIZONTAL AXIS segment (financially favorable)

0 < [V axis — K axis]

The LEFT HORIZONTAL AXIS segment (i.e. that which appears between DiSGUISEand SOFTEN segments) represents zero change in unweighted productionaccompanied by a decline in weighted production. This situation rise

a positive product mix variance and signifies that between the old newintervals the product quantities which employ high price weights

to the product quantities which employ low price weights. Suchchange "reduces the density" of the product mix. —

SOFTEN strategic segment (financially favorable)

0 < [Yaxis — Xaxis]

Kaxis < Vaxis < 0

The SOFTEN segment represents a decline in unweighted productiona greater decline in weighted production. This situation gives a

pesitive product mix variance and signifies that between the old new'intervals the product quantities which employ high price weightsYelative to the product quantities which employ low price weights. Suchchange softens the product mix.

Dg — 3

K axis < 3 = V axis

THIRD QUADRANT diagonal (financially neutral) RIGHT HORIZONTAL AXIS segment (financially unfavorable)

rv axis — X axis] = 0

V axis = X axis < 0

The THIRD QUADRANT diagonal segment (i.e. that which appears between SOFTEN

and HARDEN segments) represents a decline in unweighted production accompaniedby an identical decline in weighted production. This situation gives rise toa zero product mix variance and signifies that between the old and neW

intervals the product quantities which employ high price weights declined by aproportion equal to that of the product quantities which employ low priceweights. Such change holds the product mix constant.

HARDEN strategic segment (financially unfavorable)


V axis c X axis c 0

The HARDEN segment represents a decline in unweighted production accompanied'by a lesser decline in weighted production. This situation gives rise to a

negative product mix variance and signifies that between the old and new!

intervals the product quantities which employ high price weights increased!relative to the product quantities which employ low price weights. Such?

change hardens the product mix.


fY axis — X axis] c 0

V axis C 0 = A' axis

The LOWER VERTICAL AXIS segment (i.e. that which appears between HARDENa decline in unweighted production accompanied by

a zero change in weighted production. This situation gives rise to a

negative product mix variance and signifies that between the old and new

intervals the product quantities which employ high price weights increasedrelative to the product quantities which employ low price weights. Such

change "raises the density" of the product mix.

CONCEAL strategic segment (financially unfavorable)

(V axis — K axis] <

0 < Xaxis -

The CONCEAL segment represents a decline in unweighted productieiaccompanied by an increase in weighted This situation gives riseto a negative product mix variance and signifies that between the old and em

intervals the product quantities which employ high price weights increasedrelative to the product quantities which employ low price weights. Such

decline in unweighted production conceals (i.e. contradicts) the more

significant increase in weighted production. -

(V axis — K ax!s] < 0

V axis = 0 C K axis

T- The RIGHT HORIZONTAL AXIS segment (i.e. that which appears betweenand THICKEN segments) represents zero change in unweighted productiánaccompanied by an increase in weighted production. This situation givesto a negative product mix variance and signifies that between the old andintervals the product quantities which employ high price weights increasjdPelative to the product quantities which employ low price weights.

"raises the density" of the product mix.


[V axis — K-axis] = 0

V axis = 0 = K axis

'The AXIS ORIGIN segment (i.e. that which appears between alldefined above) represents zero change in unweighted production accompaniedtero change in weighted production. This situation gives rise to aproduct mix variance.

Log — 4 Dg — 5

a

ri:

PRODUCT VOLUME COST GRID

This chapter presents the axioms underpinning the 9 segments which make up,

the product volume cost grid. These measures refer to change in the level ofa function, and their dimensional coefficient is a currency unit.

Figure D1O.FI - PRODUCT VOLUME COST GRID

—

The PRODUCT VOLUME COST GRID presents an analysis of the product volume

variance which appears in the COST RECONCILIATION REPORT. It graphspercentage change in unweighted product quantity against the old intervallevel of cost (i.e. resource value) to prescribe what change in cost levelrequired to maintain, with respect to the new interval unweighted productquantity, the old interval relation of resource value to unweighted productquantity. The axes employ different numerical scales, and the grid'specifies no isovalue diagonal.

The product volume variance prescribes the extent to which resource valueshould change assuming:

010—1-

— constant resource price between old and new intervals, and

— constant resource quantity per unit of unweighted product quantity Ltweenold and new intervals (i.e. constant productivity using

• dimensionally improper, product quantities)

The PROOUCT VOLUME COST GRID contains 9 segments which prescribe thefollowing cost change with or without capital resources.

— cost decrease with respect to CURTAIL and RELEASE segments

zero cost change with respect to the 4 axis segments and the axis interceptsegment

- cost increase with respect to LIMIT and EXTEND segments.

Starting with the EXTEND segment, and proceeding in anti—clockwise £*Vder,the eeaning of each of the above 9 case segments is defined below. The uaeesof four case segments which do not occur along axes describe the exppctedeffect on cost of change in unweighted product volume rather than amotive for varying the level of unweighted product volume. They notrelate to the short term and must be qualified should any compelling contraryconsiderations be relevant.

EXTEMD strategic segment (financially favorable)

0 < (—Vax/s * Xaxis]

0 < Vax/s , Xaxis

The EXTEND segment refers to an old interval positive resource value a

positive percentage change in unweighted product quantity. Hencepercentage change iii inweighted product quantity, assumes a negative and

-gives rise to a negative sign for the segment. In this segment the ne9jtiveproduct volume prescribes the extent to which cost should increfle to

the old interval positive cost per unit of unweighted product oh: thehigher production base in the new interval

The UPPER VERTICAL AXIS segment refers to an old interval zerovalue and a negative percentage change in unweighted product quantity. - Hence

minus percentage change in unweighted product quantity, assugks a

'positive sign and gives rise to a zero value sign for the segment. In-tthis'segment the zero product volume variance prescribes a zero cost tomaintain the old interval zero cost per unit of unweighted product oft thelower production base in the new interval . -

Chapter DiD

% CHANGE IN UNWEIGHTEDPRODUCT QUANTITY

RELEASE EXTEND

+OLDRESOURCE

VALUE- +

LIMIT CURTAIL

V = PERCENTAGE CHANGE IN UNWEIGHTEDPRODUCT QUANTITY

=

X = OLD RESOURCE VALUE

= VALUE0Pd(I)

PRODUCT VOLUME COST VARIANCE

= — V * K = COSTvoJumeUPPER VERTICAL AXIS strategic segment (financially neutral)

- 0 = (—Vax/s * Xaxis]

K axis = 0 < V axis

010 — 2

a

(— V axis * x axis] C 0

X axis < 0 < V axis

The RELEASE segment refers to an old interval negative resource value andpositive percentage change in unweighted product quantity. Hence zero minupercentage change in unweighted product quantity, assumes a negative sign aoi

gives rise to a positive sign for the segment. In this segment the positiviproduct volume variance prescribes the extent to which cost should decrease timaintain the old interval negative cost per unit of unweighted prodyct on thi

lower production base in the new interval.

LEFT HORIZONTAL AXIS strategic segment (financially neutral)

0 = (— V axis * X axis]

X axis < 0 = Y axis

The LEFT HORIZONTAL AXIS segment refers to an old interval negative resourcevalue and zero percentage change in unweighted product quantity. Hence zero

minus percentage change in unweighted product quantity, assumes a zero valUe

and gives rise to a zero sign for the segment. In this segment the zero

product volume variance prescribes a zero cost change to maintain the oldinterval negative cost per unit of unweighted product on the same productioubase in the new interval. -

LIMIT strategic segment (financially favorable)

0 < f—Yaxis * Xaxis]

V axis , X axis C 0

The LIMIT segment refers to an old interval negative resource value and a

negative percentage change in unweighted product quantity. Hence zero min'lis-

percentage change in unweighted product quantity, assumes a positive sign and

gives rise to a negative sign for the segment. In this segment the negativeproduct volume variance prescribes the extent to which cost should increase tomaintain the old interval negative cost per unit of unweighted product on th&lower production base in the new interval.

LOWER VERTICAL AXIS segment (financially neutral)

0 = 1— Y axis * X axis]

Y axis < 0 = X axis

The LOWER VERTICAL AXIS segment refers to an old interval zero resourcevalue and a positive percentage change in unweighted product quantity. Hence

zero minus percentage change in unweighted product quantity, assumes Inegative sign and gives rise to a zero value sign for the segment. In thissegment the zero product volume variance prescribes a zero cost change to

maintain the old interval zero cost per unit of unweighted product on the

higher production base in the new interval. -

(— V axis * X axis] > 0

Vaxis < 0 < Xaxis

The CURTAIL segment refers to an old interval positive resource value and a:negative percentage change in unweighted product quantity. Hence zeS minuspercentage change in unweighted product quantity, assumes a positive fign andgives rise to a positive sign for the segment. In this segment the jpsitiveproduct volume variance prescribes the extent to which cost should tomaintain the old interval positive cost per unit of unweighted product'on the

-lower production base in the new interval.

RIGHT HORIZONTAL AXIS segment (financially neutral)

0 = (— V axis * X axis]

V axis = 0 < X axis

The RIGHT HORIZONTAL AXIS segment refers to an old interval 1:psitiveresource value and zero percentage change in unweighted product

-Hence minus percentage change in unweighted product quantity, zerovalue and gives rise to a zero sign for the segment. In this thezero product volume variance prescribes a zero cost change to oldinterval positive cost per unit of unweighted product on the same pSoluctionbase in the new iiterval


= [— V axis * X axis]

V axis = 0 = X axis

The AXIS ORIGIN segment refers to an old interval zero resource vaiue andzero percentage change in unweighted product quantity. Thevariance assumes a zero value and prescribes that zero change in iust isrequired to maintain the old interval zero cost per unit of unweighted Øroducton the same production base in the new interval.

RELEASE strategic segment (financially unfavorable)-

CURTAIL strategic segment (financially unfavorable)

I

D1O— 3 010 — 4

This chapter presents the axioms underpinning the 9 segments which ni-'-the investment variance profit grid. These measures refer to change inlevel of a function, and their dimensional coefficient is a currency

The INVESTMENT VARIANCE GRID presents an analysis of the investment variaiwhich appears in the PROFIT RECONCILIATION REPORT. It graphs change inassets against the old interval target ROI (return on investment) to prescwhat change in profit must be earned to maintain the old target ROI on theinterval level of net assets. The axes employ different numerical s

and the grid specifies no isovalue diagonal

Starting with the GROW segment, and proceeding in anti—clockwise order,meaning of each of the above 9 case segments is defined below. The namesfour case segments which do not occur along axes describe the expected e

on profit of change in assets rather than prescribe a motive for varyinglevel of assets. They do not relate to the short term and must be qualifshould any compelling contrary considerations be relevant.

Dli — 1


0 < (V axis * K axis]

0 < Yaxis , Xaxis

GROW segment assumes a positive value and prescribes how much iaorejfit is required to earn the old positive target return on investment theositive change in assets between old and new intervals.

'PER VERTICAL AXIS strategic segment (financially neutral)

0 = TV axis * K axis]

K axis = 0 < Y axis

This segment assumes a zero value and prescribes that zero change inis required to earn old zero target return on investment on the positive

in assets between old and new intervals.


(V axis * X axis] < 0

Kaxis < 0 Yaxis

The LOSE segment assumes a negative value and prescribes how much profit isby applying the old negative target return on investment to the

tive change in assets between old and new intervals.

HORIZONTAL AXIS strategic segment (financially neutral)

0 = (V axis * K axis]

K axis < 0 Y axis

This segment assumes a zero value and prescribes that zero change in profitrequired to earn the old negative target return on investment on the

ange in assets between old and new intervals.


0 < [V axis * X axis]

V axis , K axis < 0

The SAVE segment assumes a positive value and prescribes how much profit is;aved by not having to concede the old negative target return on

in assets between old and new intervals.

Chapter Dli INVESTMENT VARIANCE PROFIT GRID

Figure D1l.Fl - INVESTMENT VARIANCE GRID

CHANGE INASSET LEVEL

LOSE GROW

+

+

OLD

TARGETROI

SAVE SHRINK

Y = CHANGE IN ASSET LEVEL

VKn — VK0

x= OLD TARGET RETURN ON INVESTMENT

To

CHANGE IN INVESTMENT VARIANCE

= Y*x = PROFiTasset

Dii — 2

LOWER VERTICAL AXIS segment (financially neutral) Chapter 012 RETURN ON REVENUE VARIANCE PROFIT GRID

0 = (Y axis * X axis]This chapter presents the axioms underpinning the 9 segments which up

y axis < 0 = X axis return on revenue profit grid. These measures refer to change thelevel of a function, and their dimensional coefficient is a currency unit

This segment assumes a zero value and prescribes that zero change in profitis required to earn the old zero target return on investment on the negativechange in assets between old and new intervals. ' Figure D12.Fl - RETURN ON REVENUE GRID

SHRINK strategic segment (financially unfavorable) , % CHANGE IN '

REVENUE )-"(V axis * Xaxis] < 0 '4"

V axis c 0 c X axis

The SHRINK segment assumes a negative value and prescribes how much less SPREAD INCREASE N,

profit is required by not having to apply the old positive target return an - , ,r' '

investment on the negative change in assets between old and new intervals. +OLD OFF

RIGHT HORIZONTAL AXIS segment (financially neutral) - PROFIT-

0 = (V axis * X axis]CONTAIN REDUCE

Vaxis = 0 c Xaxis

This segment assumes a zero value and prescribes that zero change in profitis required to earn the old positive target return on investment on the zero

t change in assets between old and new intervals.V = PERCENTAGE CHANGE IN REVENUE

AXIS ORIGIN segment (financially neutral) = Loji(U)

= [V axis * X axis] ' 7 = OLD OFFTARGET PROFIT

V axis = 0 = X axis OLD INTRINSIC PROFIT

This segment assumes a zero value and prescribes that zero change in profit' — OLD TARGET PROFIT

is required to earn the old zero target return on investment on the zero

change in assets between old and new intervals. RETURN ON REVENUE VARIANCE

= V * X = PROFlTrevenue

The RETURN ON REVENUE VARIANCE GRID presents an analysis of the returg onrevenue variance which appears in the PROFIT RECONCILIATION REPORT. - It

graphs percentage change in revenue against the old interval level ofofftarget profit to prescribe what change in profit is required to mainta ii in

• the new interval the old interval ratio of offtarget profit to revenue. 'Theokes employ different numerical scales, and the grid specifies nodiagonal

Starting with the iNCREASE segment and proceeding in anti clockwisethe meaning of each of the above g case segments is defined below. The iiiomesof four case segments which do not occur along axes describe the

011 — 3 012 — 1

effect on profit of change in return on revenue rather than prescribe a

motive for varying the level of revenue. They do not relate to the short

term and must be qualified should any compelling contrary considerations be

relevant.

INCREASE strategic segment (financially favorable)

o < (V axis * X axis]

U < Y axis , X axis

The INCREASE segment refers to an old interval positive offtarget profit anda positive percentage change in revenue. The return on revenue variance

assumes a positive value and prescribes how much more profit is required to

maintain the old interval ratio of positive offtarget profit to revenue on thehigher revenue base in the new interval.

UPPER VERTICAL AXIS strategic segment (financially neutral)

o = (V axis * x axis]

X axis = U C Y axis

The UPPER VERTICAL AXIS segment refers to an old interval zero offtarget

profit and a positive percentage change in revenue. The return on revenue

variance assumes a zero value and prescribes that zero profit is required to

maintain the old interval ratio of zero offtarget profit to revenue on the

higher revenue base in the new interval

SPREAD strategic segment (financially unfavorable)

(Y axis * X axis] c U

X axis < U C V axis

The SPREAD segment refers to an old interval negative offtarget profit and apositive percentage change in revenue. The return on revenue variance

assumes a negative value and prescribes how much extra loss (i.e. negative

profit) is required to maintain the old interval ratio of negative offtargetprofit to revenue on the higher revenue base in the new interval.


U = (V axis * X axis]

X axis < U = V axis

The LEFT HORIZONTAL AXIS segment refers to an old interval negative

offtarget profit and zero percentage change in revenue. The return on

revenue variance assumes a zero value and prescribes that zero change in

profit is required to maintain the old interval ratio of negative offtargetprofit to revenue on the same revenue base in the new interval

CONTAIN strategic segment (financially favorable)

U C (V axis * X axis]

V axis , X axis c U

The CONTAIN segment refers to an old interval negative offtarget profit anda negative percentage change in revenue. The return on revenue

a positive value and prescribes how much profit should (i.eloss should be reduced) by not having to maintain the old interval rfljo ofnegative offtarget profit to revenue on the lower revenue base in the newinterval

LOWER VERTICAL AXIS segment (financially neutral) -


V axis C U = X axis

The LOWER VERTICAL AXIS segment refers to an old interval zero oftt,argetprofit and a negative percentage change in revenue. The return onvariance assumes a zero value and prescribes that zero profit is tomaintain the old interval ratio of zero offtarget profit to revenue thelower revenue base in the new interval. -

REDUCE strategic segment (financially unfavorable)

(V axis- * X axis] < U

Yaxis < U < Xaxis

The REDUCE segment refers to an old interval positive offtarget profit and anegative percentage change in revenue. The return on revenue

a negative value and prescribes how much less profit is required tomaintain the old interval ratio of positive offtarget profit to revenue thelower revenue base in the new interval.

RIGHT HORIZONTAL AXIS segment (financially neutral)


V axis = U C X axis

The RIGHT HORIZONTAL AXIS segment refers to an old interval pqpitiveofftarget profit and zero percentage change in revenue. The onrevenue variance assumes a zero value and prescribes that zero in

- profit is required to maintain the old interval ratio of positiveprofit to revenue on the same revenue base in the new

012 —

I

012 — 3

AXIS ORIGIN segment (financially neutral) Chapter D13 TARGET ROl PROFIT GRID

0 = (Y axis * K axis]This chapter presents the axioms underpinning the 9 segments which malce up

y axis = a = x axis the target profit grid. These measures refer to change in the level afunction, and their dimensional coefficient is a currency unit.

The AXIS ORIGIN segment refers to an old interval zero offtarget profit and

zero percentage change in revenue. The return on revenue variance assumeszero value and prescribes that zero change in profit is required to maintain Figure D13.FI - TARGET ROl PROFIT GRIDthe old interval ratio of zero offtarget profit to revenue on the same revenuebase in the new interval.

CHANGE INTARGET ROI

EXPOSE EXPAND

+NET ASSETSIN NEWINTERVAL

+ -

RETRIEVE CONTRACT

V = CHANGE IN LEVEL OF TARGET RETURN ONINVESTMENT

= Tn — To

X = NET ASSETS IN NEW INTERVAL

= VKn

TARGET RETURN ON INVESTMENT VARIANCE

= * K = PROFITtaroi

The TARGET ROl VARIANCE GRID presents an analysis of the target ROl variancewhich appears in the PROFIT RECONCILIATION REPORT. It graphs intarget ROI against the new interval level of net assets to prescribe whatchange in profit is required to earn the new target ROI on the newlevel of net assets. The axes employ different numerical scales, and theglid specifies no isovalue diagonal.

Starting with the EXPAND segment, and proceeding in anti—clockwise orjer,the meaning of each of the above 9 case segments is defined below. TheOf four case segments which do not occur along axes describe theeffect on profit of change in target return on investment ratherprescribe a motive for varying the level of target return on investment.

012—4 013—1

o = IY axis * X axis]

X axis = U < Y axis

This segment assumes a zero value and prescribes that zero change in profit

is required to earn the positive change in target return on the zero asset

level in the new interval.

EXPOSE strategic segment (financially unfavorable)

LY axis * X axis] < 0

X axis C 0 < Y axis

The EXPOSE segment assumes a negative value and prescribes the extent

which less profit need be earned by applying the positive change in targ

return on investment to the negative assets level in the new interval


Q = fY axis * x axis]

Xaxis C 0 = Yaxis

This segment assumes a zero value and prescribes that zero change in preft!

is required to earn the zero change in target ROI on the negative asset

in the new interval

This segment assumes a zero value and prescribes that zero change in profitis required to earn in the new interval a lower target ROl on the zero'l in the new interval.

The CONTRACT segment assumes a negative value and prescribes how much lessprofit is required to earn in the new interval a lower target ROI thepositive asset level in the new interval

HORIZONTAL AXIS segment (financially neutral)

0 = [V axis * X axis]

Yaxis = U < Xaxis

This segment assumes a zero value and prescribes that zero change in Ps'ofitrequired to earn the zero change in target ROl on the positive asset levelthe new interval.

'5 ORIGIN segment (financially neutral)

0 = [V axis * Xaxis]

V axis = 0 = X axis

This segment assumes a zero value and prescribes that zero change in profitis required to earn the zero change in ROI on the zero asset level in the newiterval

do not relate to the short term and must be qualified should any compelling

contrary considerations be relevant.

EXPAND strategic segment (financially favorable)

o C (Y axis * X axis]

o < Y axis , X axis

The EXPANO segment assumes a positive value and prescribes how much mo

profit is required to earn the positive change in target return on inves.tment

on the positive asset level in the new interval.

UPPER VERTICAL AXIS strategic segment (financially neutral)

LOWER VERTICAL AXIS segment (financiallyneutral)

0 = [V axis * X axis]

V axis < 0 = X axis

CONTRACT strategic segment (financially unfavorable)

[V axis * X axis] < a

Vaxis < 0 c Xaxis

p

I

Lt

RETRIEVE strategic segment (financially favorable)

o c [V axis * X axis]

V axis , X axis < 0

The RETRIEVE segment assumes a positive value and prescribes how much prel

is saved by having to concede in the new interval a lower target ROI on I

negative asset level in the new interval.

013 — 2 013 — 3

Chapter D14 GRIDS RECOMMENDED FOR PRODUCTIVITY DISCLOSURE

This chapter identifies the grids which are appropriate for productivitydisclosure which is defined in part A of the book.

Figure D14.Fl - PERFORMANCE GRIDS FOR PRODUCTIVITY DISCLOSURE

In the following figure grids are presented in an order which differsfrom that given in the preceding figure. This order presents the

5 sum grids (in which the zero isovalue diagonal = V axis + X axis)

whichare followed

3 difference grids

Figure D14.F2

ProductivityGrid

ShortTermQuantityGrid

LongTermQuantityGrid

ShortTermCostGrid

LongTermCostGrid

ShortTermProfitGrid

LongTermProfitGrid

.

PriceGrid

COSTCENTER

PROFITCENTER

COSTCENTER

PROFITCENTER

COST

CENTER

PROFITCENTER

COST

CENTER

COST

CENTER:

PROFITCENTER

PROFITCENTER

PROFITCENTER

by the

(in which the zero isovalue diagonal = V axis — X axis).

- DATA SOURCES FOR GRIDS FOR PRODUCTIVITY

SHtWT TERMQUARTIlEGRID

LENIG TERCI

COST GRID

0 CENTERI COAST2 RERER3E3 RETARE4 SRCCRNI

RALLY6 RELORE

SRONT TERM

PROFIT GRID

I CENTERI AWAKEN2 PARYYE3 FINETRRE4 OCOTTLES SALRACE6 SCRAWRLE

TERN

PROFIT GRID±0 CENTER1 AWAKEN2 PARYAE3 FINETYREV OCATTLES SALVAGE6 SCRAMILE

PRWACTIAITTORIR

CENTER

1 62W2 ORWRLE3 SRUANAER4 LOSE5 ARTOAN6 EACEL

IRENT TERNCOOT GRID

CENTER

I COAST2 RERERTE3 RETARD4 RACER MR

I RALLY6 DELUDE

tootReerelowReport

OFFICIENCTAMIANCEIN NEW PRICES

Column 0

Row: TotalReooorteo

LERO TERNRAW WIITT

GRID

S CENTER1 LIFIOFF2 ARRIT3 OIRCVAROE4 OVERREACT

WOARD

6 SELFSESSYACT

O CENTER2 LIFTOFFO ERIIT3 RISCRARGE4 OVERREACT5 WAAREN SELFEESIRACT

RERTICAL AS S

CootOverviewReport

PRARACTIRSTOWAR lAN C E

IN NEW PRICES

Colomv E

Row: TotalReooorceo

PRICE- GRID

CEWTER

4 TRAILo SPORT4 RUSE5 SVAAE

FARE

* SLASA

LLj'2PhSOENTAGE

IN

3

ENOvol Total

Income

ProfitOverviewReport

EFFICIENCYTARIANCEIN NEW PRICES

Column 0

Roe: TotalReooorceo


FREN2ACTIRITTRARIANCEIN NEW PRICER

Coloov 0

Roe: TotalReooorceo

The above grids are suitable for productivity disclosure with respect to

cost center and profit center control points in a business.

The following figure summarizes the sources of information for each ofabove 8 performance grids.

D14 — 1

Coot or ProFitOoero lowReport

CVPVCITYUTILIZATIONRARUANCE

IN NEW PRICER

Colomv I

Woe: TotalReooorceo

IvpotCoopoctAdjoo tedReport

FERCLNYAGE

CVAWGE INOAAWTITT

Colown I

Row: TotalIncome

(to ld( I(+YALARL01d(IlI/ WALOEo14(I)

TotalReooorcoo

RU IZRNRAL AOIR

H

tootOverviewNeport

MART TERNREIRIRCE PRICENON lANCE

Column W

CootOverviewReport

LONG TERNRESMJRCE PRICERARIARCE

Column E

ProFitOverviewReport

SWCNT TERNPRICE RECORERYRN1IAWCE

Colomv W

Row: TotalRoooorceo

Coot or ProFItOverviewReport

EFFICIENCYWAR lANCE

IN NtN PRICES

Colown 0


LONG TERNPAICE RCCSVEATVARIANCE

Colomo E

Row: TotalReoourcoo

lopotCompactAdjuotedReport

PERCENTAGE

CRANGE INOUANTITT

Coloioo I

Now: Total Row: TotalReooorcoo Roooorcno

InputCompactAdjuotedReport

PERCENTAGE

CWANGE IN

IRANYITA

Colomo I

tC4000E IN

Roe: TotalR000urceo

Row: Total Wow: Total Wow: TotalReooorceo Roooorcoo Roooorcno

k

D14 — 7

PART E - EXAMPLE OF REPORTS

This part of book presents the following 18 chapters. Although thereare more reports specified in the scientific book on difference towhich this book refers, the following 18 reports are sufficient to iltustratethe scope of the reporting mechanism.

Chapter El EXAMPLE OF INPUT VALIDATION 'A" REPORT


E3 EXAMPLE OF INPUT VARIANCE REPORT


Chapter E5 EXAMPLE OF INPUT COMPACT REPORT



Chapter EB EXAMPLE OF PROFIT RECONCILIATION REPORT


Chapter ElO EXAMPLE OF LONG TERM PRODUCT PROFIT REPORT

Chapter EI1 EXAMPLE OF SHORT TERM PRODUCT PROFIT REPORT IChapter E12 EXAMPLE OF COST RECONCILIATION REPORT

Chapter EI3 EXAMPLE OF COST OVERVIEW REPORT

Chapter E14 EXAMPLE OF LONG TERM PRODUCT COST REPORT

Chapter E15 EXAMPLE OF SHORT TERM PRODUCT COST REPORT

Chapter E16 EXAMPLE OF PRODUCTIVITY OLD AND NEW VARIANCE REPORT

Chapter E17 EXAMPLE OF PRODUCTIVITY COMPONENT VARIANCE REPORT

Chapter E1B EXAMPLE oF PRODUCTIVITY COMPONENT OLD & NEW REPORT

Chapter El EXAMPLE OF INPUT VALIDATION "A" REPORT

This chapter presents the axioms which define the Input Validatiup "A"Report and an example. Selected cells are assigned numbers ranging frpe (I)through (18) to indicate that the ensuing text in this chapter willthe derivation of their numerical values. 1

The purpose of this report is to provide data on value, quantity and priceto validate data entry. This report complements Input Validation "B" report.

El — 1

E1—2 E1—3

1989/09/Il PPM INPUT VALIDOTIFAI 0" REP80T

BUSINESS A1981 vs. 1989

Values are in DOLLARS

OLD (REFEDENCE) INTERVAL NEW (DEVIEW) INTEUVAL

INDEX ENTITY VALUE QUANTITY PRICE VALUE QUANTITY PRICI

I IU U C I E FL

INCOME:

UI Prsduct aI 6000.01 150.00 40.00000 1901.00 000.00 44.10000

02 Prsduct a2 4000.00 84.00 11.00001 9100.00 — — 140.00 60.00004

I(IXTAL INCOME 10000.00 18001.00

COST REX OIJRCES:

Ni Naterial a 8000.00 400.00 20.00000 12540.00

= 5,0%

570.00 22.00000

ITOTAL OPERATING EXPENSES 8000.00 12540.00

CAPITAL RESU1RCES:Ti Equipment a

[7) (8

1100.00 (5) 8.00 250.00100 3500.00 (6) 10.00 350.0000

TOTAL CAPITAL REOOJRCES 1000.00 (9) 3500.00 [II)

TOTAL RESO'JRCES 10000.00 (II) 16040.00 (12) I

TARSET PROFIT (13] 1960.00 (14)I

INTRINSIC PROFIT 2000.00 (1) . - 5460.00 [2) -

CAPITAL RESWRCES:KS Equipment a 40000.00 8.00 5001.00001 70000.00 10.00 7000.00014

ITOTAL CAPITAL RESWRCES 40000.00 71005.A0 I—

IRE1SRN 001 INOESTNENT (0) 5.00 [3) 7.80 (4) I

PUN CT I ON S Tstal Individual Tstal Individual

cest resnurce

prndsctcsst ressurcetarget prsfltcapital assetssr Sarget preP it

VOn

ANn

ATsADs

VusOne

Yts• VAn

Ye

RueRevQtaRAn

Ru

PusPenPEnPksPs

NonANn

ATnVOn

• NunYenVtnVAnAn

QusQnnQtnRAnRn

Pun

Pen

PinPA'Pn

,

'

Return On Onnesteent Cs

Cell (1)

Ce

CAPITAL ASSET VALUE

RETURN ON INVESTMENT

Cell (3)

OLD INTRINSIC (ACTUAL) RETURN ON INVESTNENT

OLD INTRINSIC PROFITCo

OLD TOTAL ASSET VALUE OF CAPITAL RESOURCES (K ROWS)

= $2000,O / $40000,0

Capital asset values are defined with respect to a point in time, e.g., thefinal day of a control period such as a month, quarter or year. They areiRdicated by sKe rows in the numeric computer reports and do not necessarilychange in response to change in the control period as shown below.

CONTROL PERIOO Month Quarter Year

REVEIIUE $100 $500 $1500

COST $80 $450 $1200

PROFIT $20 $50 $300

$2500 $2500 $2500

-0,8% 2,0% 12,0%

Cell (4)

,-Cn

= 7,8%

Target profit is indicated by rows in the numeric computer reportsrefers to the control period to which return on investment (ROl) relates. ThisIs determined by the control period to which revenue and cost relate, e.g.; ayear, quarter, month, etc. Target profit therefore represents a cost: ofCapital for the control period to which revenue and cost refer.

In our example, Old Target ROI (To) = Old Intrinsic ROl (Co) (5,0%) and

New Target ROl (Tn) = Old Intrinsic ROI (Ce) (5,0%)

Cell (2)

NEW INTRINSIC (ACTUAL) RETURN ON INVESTNENT

NEW INTRINSIC PROFIT

OLD INTRINSIC PROFIT e OLD TOTAL REVENUE — OLD TOTAL COST RESOURCES

PROFITo1d REVENUEo!d — COSToJd

= $I0000,O — $8000,O

$2000,0 :.

NEW INTRINSIC PROFIT NEW TOTAL REVENUE — NEW TOTAL COST RESOURCES

PROFITnoW a REVENUEnoW — COSTnew

= $18000,0 — $1254O,O

NEW TOTAL

= $546O,O /

ASSET VALUE OF CAPITAL RESOURCES (K ROWS)

$ 70000,0

$5460,0

Cell (5)

OLD TARGET PROFIT VALUE (Ti)

E OLD CAPITAL ASSET VALUE (Ki) * OLD TARGET RETURN ON CAPITAL

= Vo(Ki) *To

= $40000,0 * 5,0%

= $2000,0

Cell (6)

NEW TARGET PROFIT VALUE (Ti)

E NEW CAPITAL ASSET VALUE (Ki) * OLD RETURN ON CAPITAL

= Vn(Ki) *Tn

$70000,0 * 5,0%

$3500,0

Cell (7)

OLD TARGET PROFIT PRICE (Ti)

OLD CAPITAL ASSET PRICE (Ki) * OLD RETURN ON CAPITAL

= Po (Ki) * To

= $5000,0 * 5,0%

= $250,0

Cell (8)

NEW TARGET PROFIT PRICE (Ti)

NEW CAPITAL ASSET PRICE (Ki) * OLD RETURN ON CAPITAL

= Pn (Ki) * Tn

= $7000,0 * 5,0%

= $350,0

Cell (9)

OLD TOTAL CAPITAL RESOURCES VALUE (T ROWS)

SUM OF OLD CAPITAL VALUES (T ROWS)

= $2000,0

Cell (10)

NEW TOTAL CAPITAL RESOURCES VALUE (T ROWS)

E SUN OF NEW CA°ITAL VALUES (T ROWS)

= $3500,0

Cell (11)

OLD TOTAL RESOURCES VALUE

E OLD TOTAL COST RESOURCES VALUE

+ OLD TOTAL CAPITAL RESOURCES VALUE (T ROWS)

= $8000,0 + $2000,0

= $10000,0

:-Cell (12)

NEW TOTAL RESOURCES VALUE

E NEW TOTAL COST RESOURCES VALUE

£

÷ NEW TOTAL CAPITAL RESOURCES VALUE (T ROWS)

= $12540,0 + $3500,0

Cell (14)

NEW OFFTARGET PROFIT NEW INTRINSIC PROFIT - NEW TARGET PROFIT

= $5460,0 — $3500,0

$16040, 0

Cell (13)

OLD OFFTARGET PROFIT OLD INTRINSIC PROFIT

= $2000,0

— OLD TARGET PROFIT

— $2000,0

$0, 0

E1—4

L

$ 1960,0

El — 5

N/H NOT

INTERNAL KEN (REVIEW) INTERVAL

INDEA ENDITT

OLD (REFERENCE)INTERVAL TARGET INTRINSIC RISK INTERVAL TAROET INTRINSIC

RENA DAYS ROI)G) RRI (8) WEIGHT DAYS RGI)S) Vol )S)

F S H

I IA D C D E

INCENSE:

UI Product aI N/AI N/A N/A

N/A I N/A N/A N/A N/A N/A

1 N/AN/A

a

1 1.880 1.800

Column E2 A

REVuI represents REsource VAriabilitY and is discussed in statements (B] F

and (81 F2).

Column E2 B

Woo represents old interval width for a product and Wa represents

interval width for a resource. Function W is discussed in statements (81

and (81 C2).

Column E2 C

To represents old interval target return on investment for a cai

resource. Function T is discussed in statements (81 01) and (81 02).

Column E2 D

Co represents old interval intrinsic return on investment for a cap

resource. Function Co for total capital resources is discussed in staten!

supporting chapter El cell (3), Function Co for an individual ca'

resource employs the old risk weight So and is derived from an ark:appears in the book on difference calculus cited as bibliography itemAppendix B of this book.

Column E2 E

So represents old interval risk weight for a capital resource. Function Sdiscussed in statements (81 El) and (81 E2).

Wun represents new interval width for a product and Wn represents'erval width for a rosource. Function W is discussed in statements (81 tj)d (81 C2). -'

Tn represents new interval target return on investment for aesource. Function T is discussed in statements (81 Dl) and (81 02).

represents new interval intrinsic return on investment for a1source. Function Cn for total capital resources is discussed inipporting chapter El cell (4). Function Cn for an individual capitalDseurce employs the new risk weight Sn and is derived from an axiomopears in the book on difference calculus cited as bibliography item A15sendix B of this book.

represents new interval risk weight for a capital resource. Function £ Hdiscussed in statements (81 El) and (81 E2)

E2 I


This chapter presents the axioms which define the Input Validation

Report and an example.

The purpose of this report is to provide data on REVA, interval wT

target return on investment, intrinsic return on and risk weight

validate data entry. This report complements the Input Validation 'H

report.

IDea/ON/UIFPN INPUT RALIDNTIENS 'I' ENTITT REP88T

DUllNESS A1888 vs. 1888

nE2F

Column E2 C

FDNCTIDND Nue

REAA No To

E2 H

Ave

Cu Iv No Dv Ce

E2 — 1 - E2 — 2

Chapter E3 EXAMPLE OF INPUT VARIANCE REPORT

This chapter presents the axioms which define the Input Variance Report and

an example. The mathematically trained reader is reminded that the variancesin this book are not the square of a standard deviation. They are differenceequations expressed in a currency unit, and range from ordinary differences efdegree one and order one to partial differences of higher degree and of higherorder.

The purpose of this report is to create variances arising from change in thefunctions which appear in the Input Validation "A" and "B" reports. They -areused to construct the functions which appear in the Input Relative Report and

to construct some of the functions which appear in the Cost reports.

PPM INPUT RAeIANCE ENTITY REPAST

BOSINESS Aegeevo. IRAN

Values are In 00I.LPAS

INleiNsic IVTEVVAL INTERVAL PURE PURE

VALUE GAP ROOm VALUE RALURE PRICE

INRES ENTITY VARIANCE VARIANCE VARIANCE VARIANCE VARIANCE VARIANCE

E + P + II I j A B +' C +0

INCASE:US Product alAl Product aO

—

2100.0 2900.0 0000.0 675.0 211.0

5100.0 5100.0 3000.0 1200.0 000.0

1121.;TOTAL INCeNE ROOtS R000.0 5000.0 ieis.e

CAST RESOURCES:

NI Material a - 4540.0 - - 4540.0 — 3400:0 800.0 - 340.0

3410.0 RVV.U 340.1I

ITOTAL OPERATING EAPENSES NR4V.U 454V.R

=CAPITAL RESOURCES:

Ti EVuIPISeOL a 1505.5 1500.0 500.0 eoo.e 200.0

TOTAL CAPITAL RESOURCES 1500.0 1500.0 500.0 800.0 200.0

=ITOTAL RESOURCES 4540.5 6040.0 3900.2 1600.0 140.0

CAPITAL RESOURCES:KO Equipment a 30000.0 30000.0 10000.0 16000.0 4002.0

IITOTAL CAPITRL RESOURCES 30005.5 30000.0 IR005.V 16000.0 4000.0

=

=

$8900$9100

—

— $4000 $5100 for product U2

= $18000 — $10000 $8000 for TOTAL PROOUCTS

=

=

=

$12540$3500

$16040

—

—

—

$8000$2000

$10000

$4540 for cost resource NI$1500 for capital resource TI

$6040 for TOTAL RESOURCES

=

=

=

$1960$5460

$70000

—

—

—

0

$2000$40000

$1960 OFFTARGET PROFIT

$3460 INTRINSIC PROFIT$30000 for capital resource Ki

'

The function VALLJEintrinsic measures the intrinsic change between twointervals before any adjustment is made for the effect of a gap between thetwo periods and differing interval widths.

Column E3 B

The function V.4LUEgap adjusts for a gap between old and new intervals. Itassumes a zero value when the intervals are contiguous as shown in our examplebecause 1989 and 1988 are contiguous. The axiom for this column involvesdivisor and appears in the book on difference calculus which asbibliography' item AI5 in Appendix 8 of this book.

Column E3 C

The function VALUEWIdtA adjusts for different interval widths in old and I0ewintervals. It assumes a zero value when the interval widths are equal tasshown in our example where they are set at unity for both periods.axiom for this column appears in the book on difference calculus which appe4rsas bibliography item AlS in Appendix B of this book.

Column E3 0

The function VALUEchange reflects change in value after adjustmentsbeen made for interval gap and interval width. Since our example assumes jointerval gap and equal interval width in old and new intervals, thespecification suppresses reference to gap and width although they appear linthe axiom for this column given in the book on difference calculus whijjhappears as bibliography item A15 in Appendix B of this book.

Figure E3.Fl VALUE VARIANCES IN CHAPTER E3

Column F3 0, Column E3 0

VALUE VALUE VARIANCEFOR PRODUCT FOR RESOURCEVALUEchange(u) = A VALUEchange = B

REPRICING

VARIANCE

TARGET PROFIT

IINTVINSSC PROFIT

1960.0

3460.0

1960.0 1000.0

3460.0

275.0

1600.0

501.0

1075.0 785.0

P U N C 1 1 5 N S RALAEIntrInuic AALSEqap AALAEuIdLh RALUCchange VOLUNEo1d

Column E3 A

VALUEintrinsic VALUEnew — VALUEo7d

PRICEuId PRICErep

Puo Pun

VALUEchange (a)

a Van — Vito

= Qun*Pun — Quo*Pao

0

Po Pn

VALUEchange

a Vn — Vo

= Qn*Pn — Qo*Po

A

VALUEchange a V/1LUEITeW — VALUEo!d

= VALUEintrinsjc (Column A in our simplified example)

E3 — 2

Column E3 E

The function VOLUMEoId reflects the pure volume variance contribution to

change in value after adjustments have been made for interval gap and intervalwidth. The function VOLUMEo1d is used to specify the functions and

in a later chapter. Since our example assumes no interval gap and equal

interval width in old and new intervals, the following specification

suppresses reference to gap and width although they appear in the axiom for

this column given in the book on difference calculus which appears as

bibliography item A15 in Appendix B of this book.

Figure E3.F2 VOLUME VARIANCES IN CHAPTER E3

Column E3 F

The function PRICFo!d reflects the pure price variance tochange in value after adjustments have been made for interval and

i. The function PRICEoId is used to specify the function in a later- "r. Since our example assumes no interval gap and equal interval width inand new intervals, the following specification suppresses referencewidth although they appear in the axiom for this column given in the

on difference calculus which appears as bibliography item A15 in Appendix ofthis book.

Figure E3.F3 PRICE VARIANCES IN CHAPTER E3

PRICE VARIANCE PRICE VARIANCEFOR PRODUCT FOR RESOURCEPRICEo7d(u) = A PRICE0Id = B

Qun -

Puo Pun

PRICEo !d(u)

a * [Pun — Puo]

Qn

Qo * (Pn — P0]

$2000,O$3000,O

$5000,O

for cost resource Nifor capital resource Ti

150,0 * [ 44,5 — 40,0] =

80,0 * [ 65,0 — 50,0] =for product Uifor product U2

for TOTAL PRODUCTS

for cost resource Nifor capital resource

for TOTAL RESOURCES

VOLUMEoJd(U) a ( Qun — Quo J * Puo

[200,0 — 150,0 1 * 40,0 =

[140,0 — 80,0 ] * 50,0 =

VOLUME01d(U) a SUM ALL VOLUMEoJd(u)

VOLUMEOId a ( Qn — Qo] * P0

for product Uifor product U2

for TOTAL PRODUCTS

Eold(u) a Quo * [Pun — Puo]

[570 — 400 1* 20,0 = $3400,O

10 — 8 1* 250,0 = $ 500,0

VOLUMEo1d(I) a SUM ALL VOLUMEoId $3900,O for TOTAL RESOURCES

$ 675,0$ 1200,0

a SUM ALL PRICEo7d(u) $1875,O

a Qo * (Pn — Po]

400,0 * [ 22,0 — 20,0] = $ 800,08,0 * [350,0 — 250,0] = $ 800,0

CEo7d(I) a SUM ALL PRICEo1d $1600,0

E3 — 4E3—3 -

Column E3 C

The function PRICErep reflects the joint quantity—price variancecontribution to change in value after adjustments have been made for intervalgap and interval width. Since our example assumes no interval gap and e#:1

interval width in old and new intervals, the following specificationsuppresses reference to gap and width although they appear in the- axiom for

this column given in the book on difference calculus which appears as


Figure E3.F4 REPRICING VARIANCES IN CHAPTER E3

Column E3 G Column E3 G

REPRICING VARIANCE REPRICING VARIANCEFOR PRODUCT FOR RESOURCE

PRICErep(u) = A PRICErep = B

Puo Pun

PRICErep (u)

e fQun—QuoJ*(PUP—PLlO]

Po Pn

PRICErep

a (Qn — QoJ*[Pn — Pa]

Column E3 F + Column U C

The function PRICEncr.v reflects the sum of pure price variance andvariance contributions to change in value after adjustments have beeninterval gap and interval width. The function PRICEnew is used to specify thefunction A7new in a later chapter. Since our example assumes no interval flpand equal interval width in new and new intervals, the following specificfl'lonsuppresses reference to gap and width although they appear in the axiomthis column given in the book on difference calculus which appears -asbibliography item AIS Appendix B of this book.

Figure E3.F5 ADJUSTED PRICE VARIANCES IN CHAPTER E3

Column E3 F + [3 G Column E3 F + E3 G

ADJUSTED PRICE VARIANCE ADJUSTED PRICE VARIANCEFOR PRODUCT FOR RESOURCEPRICEnew(e,) A PRICEnew = B

•

Puo Pun

PRICEnew(u)

aQur*[Pun—Pua]

Po Pn

PRICEnew

a

PRICErep(u) a (Qun — Quo] * (Pun — PuoJ

[200,0 — 150,0] * [44,5 — 40,0] = $ 225,0 for product UI[140,0 — 80,0] * [65,0 — 50,0] = $ 900,0 for product U2

PRICErep(U) a SUM ALL PRIrep(u) $1125,D for TOTAL PRODUCTS

PRICErep a (Qn — Qo] * (Pn — Po]

[570 — 400] * [ 22

[10— 8]*[350

PRICErep(I) a SUM ALL PRirep

570,0 * [ 22,0 — 20,0] = $1140,010,0 * [350,0 — 250,0] = $I000,o

for cost resource Nifor capital resource

PRICEnew(u) a Qun * [Pun — Puo]

200,0 * [ 44,5 — 40,0] = $ 900,0140,0 * [ 65,0 — 50,0] = $2100,0

for product UIfor product U2

PRICEnew(1J) a SUM ALL PRICEnew(u) $3000,D for TOTAL PRODUCTS

PRICEnew a Qn * (Pn — Po]

— 20,0] = $340,0 for cost resource Ni— 250,0] = $200,0 for capital resource

$540,0 for TOTAL RESOURCES

E3 — 5

PRICEnew(I) a SUM ALL PRICEnew $2i40,0 for TOTAL RESOURCES

E3 — 6


This chapter presents the axioms which define the Input Relative Report and

an example.

The purpose of this report is to provide data on percentage changes in

relatives for value, quantity and price with respect to both product and

resource. A relative is a dimensionless quantity which is the quotient of twomeasures which refer to the same function at two different points in time

and/or space. Axioms in subsequent chapters make extensive use of change in

relatives which appear in this chapter.

1988/09/01 FPN INPUT RELATIVE ENTITY REPcNT


Percentage CHANGE inINTERVAL VALUE LASPEYRES

WIDTH EFFECT RELATIVE qUANTITY

IA B C 0 C F 0

INCOME:

01 Product al02 Product a2

48.3333 48.3333 33.3333 11.2500 11.1000 11.2001

127.8000 127.0002 70.0000 30.0000 30.0000 30.0022

ITOTAL INCOME 00.0000 80.0000 SO.0000 20.0000 18.7000 20.0022

COST RESOURCES:

NI Material a 50.7500 — —— 56.7000 — 42.5000 10.0000 20.0000 20.0000

IIIOTAL OPERATINI EUPERSES 50.7500 - 56.7500 02.5000 10.0000 60.0000 10.0001

CAPITAL RESOURCES:TI Equipment a 75.0000 75.0000 21.0000 40.0000 00.0000 40.0000

ITOTRI CAPITAL RESOURCEST

75.0000 75.0000 25.0000 40.0000 00.0000 40.0002

39.0000 15.3057 16.0000 15.3811ITOTAL RESOURCES 60.4000

IIRIRINSIC PROFIT I173.0000 173.0000 80.0000 51.6607 53.7500 '52.6667

CAPITAL RESOURCES:

IEI Equipment a 75.0000 75.0000 20.0000 40.0000 40.0000 40.0000

IITOTOL CAPITAL RESOURCES

I78.0000 78.0000 20.0000 40.0000 40.0000 40.0000

anintrivaic APwidth an AQold Apnee Apolddefuult

Since this book is used as a help—file for computer implementations of the

model and computer monitors are not yet geared to handle the A and A symbols,a modification of such notation appears on a computer screen as shown below.

Column E4 A The computer Screen displays Aj7intrinsic as IVintrinsic.

AVintrinsic m VALUEintrinsic / V/1LUEoId

AVintrinsic(u) = $2900 / $6000 = 48,3333% for product Ui

$5100 / $4000 = 127,5000% for product Ui

$8000 /$10000 = 80,0000% for TOTAL PROOUCTS

= $4540 / $8000 = 56,7500% for cost resource Ni

/ $2000 = 75,0000% for cap resource TI

10000 = 60,4000% for TOTAL RESOURCES

E4 — 1

Column E4 A gives the CHANGE in INTRINSIC VALUE RELATIVE AVintrinsic shichis read as delta 'V hat intrinsic. The A signifies °change in". Vrefers to a value function. Presence of a hat A signifies that the is

- dimensionless. After the jiintrinsic the symbol (u) signifies an indiv{Øualproduct, the symbol (U) signifies total products in the case of mulflpleproducts, the absence of a symbol signifies an individual resourcesymbol (I) signifies total resources.

This function is used to compute intrinsic cost variance and theprofit variance which appear later chapters.

Column E4 B The computer screen displays Ajiwidth as IVwidth.

At/width m VALUEwidth / VALUEo1d

This column gives the AVwidth INTERVAL WIOTH EFFECT contribution to CIh4NGEin INTRINSIC VALUE RELATIVE Aj7intrinsic. is read as de7ta V

width. The A signifies "change inc. Symbol V refers to a value function.Presence of a hat A signifies that the measure is dimensionless. After

the symbol (2!) signifies an individual product, the symbol (U)signifies total products in the case of multiple products, the absence jif a

-symbol signifies an individual resource and the symbol (I) signifies totalresources.

Since our example assumes equal interval widths for all entities, thisfunction assumes a zero value in Column B above. This function is usej tospecify in later chapters axioms for cost width variance and profitvariance.

IROEO - ENTITYIIRTRINSC VALUE

RELATIVE

PMICHEPRICE

LA5PE ORES 0E4OEVL -

PRICE PRICE

FUN

AVintrinsic(u) =

At/intrinsic(U) =

At/intrinsic = $1500

Atiintrinsic(I) = $6040

A

II

41

E4 — 2

Column E4 C The computer screen displays AV as IV.

This column gives the Aj7 CHANGE IN THE VALUE RELATIVE contribution to CHANGEin INTRINSIC VALUE RELATIVE Aj7intrinsic once the interval width effect has

been factored out. Aj7 is read as delta V hat. The A signifies change in.Symbol V refers to a value function. Presence of a hat signifies that themeasure is dimensionless. After the ji the symbol (u) signifies an individualproduct, the symbol (U) signifies total products in the case of multipleproducts, the absence of a symbol signifies an individual resource and thesymbol (I) signifies total resources.

Column E4 C Column E,4 C

PERCENTAGE CHANGE IN PERCENTAGE CHANGE INVALUE RELATIVE VALUE RELATIVEFOR PRODUCT FOR RESOURCE

AV(u) Al?

QunA

Quo

Puo Pun

a A/BA = VALUEchange(u)

a Qun*Pun — Quo*Puo

B = VALUEo1d(u)

a Quo*Puo

QnC

Qo

P0 Pn

a C/B

A = VALUEchange

a Qn*Pn — Qo*Po

B = VALUEo1d

a Qo*Po

The following two examples show the computation of the change in the totalproduct value relative and change in the total resource value relative.

VALUEchange(U) $ 8000AV(U) a =

______

= 0,8 = 80,0000% FOR TOTAL PRODUCTS

VALUEo1d(U) $10000

VALuEchange(I) $ 6040AV(I) a =

______

= 0,604 = 60,4000% FOR TOTAL RESOURCES

VALUE01d(I) $10000

Column C4 0 The computer screen displays as IQold.

This column defines the OLD—PRICE—WEIGHTED CHANGE in QUANTITY RELATIVE goldwhich is read as delta Q hat old and known as change in the Laspeyres::lative. The A signifies change in. Symbol Q refers to a quantityPresence of a hat A cignifies that the measure is dimensionless. The oldsignifies that old prices are used to weight (i.e., aggregate) quaqtitychanges. After the Qold the symbol (u) signifies an individual product; thesymbol (U) signifies total products in the case of multiple products; theabsence of a symbol signifies an individual resource and the symbol (I)signifies total resources.

will in a later chapter be used to specify axioms fort Qne,representing new resource quantity normalized for constant andQnp, representing new resource quantity normalized for constant productivity.

Figure CHANGE IN LASPEYRES QUANTITY INDEX NUMBERSIN CHAPTER E4

Col umii E4 0 Col umn E4 D

PERCENTAGE CHANGE IN PERCENTAGE CHANGE INOLD—PFflCE—.WEIGHTED OLD—PRICE—WEIGHTEDQUANTiTY RELATIVE QUANTITY RELATIVEFOR PEODUCT FOR RESOURCE

QunM

Quo

B

Puo Pun

A

a

B =

a Quo*Puo

Qn

C

Qo

D

Po Pn

a C / B

C = VOLUMEo1d

a (Qn — Qo] * Po

B = VALUEo1d

a Qo*Po

The following two examples showpeyres (i.e., old—price—weighted)total resources

VOLUMEo1d(U) $ 5000a

____________

=

______

= 0,5 = 50,0000% FOR TOTAL PRODUCTSVALUE01d(U) $10000

Figure E4.F1 CHANGE IN VALUE INDEX NUMBERS IN CHAPTER E4

the computation of the change in thequantity relative for total product and

E4 — 3

VOLUMEo1d(I) $ 3900a =

______

= 0,39 = 39,0000% FOR TOTALVALUEo1cJ(f) $10000

E4 — 4

Quo Quo

UI 150,0U2 80,0

SUM 230,0

340,0 — 230,0=

______________

230,0

Column E4 EFor comparison we now calculate the UNWEIGHTED CHANGE in TOTAL PRODUCT

QUANTITY which is read as delta Q hat (dimensionally improper) of U.,The A signifies "change in". Symbol Q refers to a quantity function. Presenceof a hat A signifies that the measure is dimensionless. The word dimsignifies a dimensionally improper addition (as distinct from a dimensionallyproper addition which flows from the use of price weights) toquantity changes. After the the symbol (U) signifies total products in a

multiple product situation.

(SUM Quo — SUM Quo] for total products

SUM Quo for total products

200,0140,0

340,0

The computer screen displays LCpnew as IPnew.

This column defines the NEW—QUANTITY—WEIGHTED CHANGE in PRICE APnewwhich is read as delta P hat new and known as change in the pricerelative. The A signifies "change in". Symbol P refers to a pricePresence of a hat A signifies that the measure is dimensionless. The word newsignifies that nrw quantities are used to weight (i.e., aggregate). pricechanges. After the Pnew the symbol (u) signifies an individual thesymbol (U) signifies total products in the case of multiple theabsence of a symbol signifies an individual resource and the (I)signifies total resources.

Function APnew(U) will in a later chapter be used to specify an forPnr representing new resource price normalized for constant price recovjry.

Figure V4.F3 CHANGE IN PAASCHE PRICE INDEX NUNBERSIN CHAPTER E4

= 0,4782609 = 47,82609%

Although is never shown in any report, it is used in a laterchapter to specify axioms for functions Qnpd, COSTvolume and CQSTmix.

The computer screen displays I4dim as IQdiin.

Column E4 E Column E4 E

PERCENTAGE CHANGE IN PERCENTAGE CHANGE INNEW—QUANTITY—WEIGHTED

PRICE RELATIVE PRICE RELATIVEFOR PRODUCT FOR RESOURcEAPnew(u) APnew

Quo

A

Puo Pun

APncw(u) e A/BA = PRICEnew(u)

aQun*(Pun—Puo]

B = VALUEo1d(u)i- VOLUMEo1d(u)

sQun*Puo

Qn

Qo 0 C

Po Pn

APnew a C/BC = PRICEnew(i)

eQo*(Pn—Po]

B = VALUEo1d+ VOLUMEo1d

aQn*Po

The following two examples show the computation of the change in the(i.e., new—quantity—weighted) price relative for total product andresources.

PRICEnew(U) $ 3000 FORAPnew(U) e

__________________________

=

______

= 20,0000% TOTALVALUEo1d(U) + VOLUME01d(U) $15000

PRICEnew(I) $ 2140 FORàVnew(I) e

__________________________

=

______

= 15,3957% TOTALVALUEoJd(I) + VOLUME01d(I) $13900 RESOURCES

E4—5 E4—6

Column E4 F The computer screen displays Aflold as IPold.

This column defines the OLD_QUANTITY—WEIGHTED CHANGE in PRICE RELATIVE IsPold

which is read as delta P hat old and known as change in the Laspeyres price

relative. The A signifies "change in". Symbol P refers to a price function.

Presence of a hat A signifies that the measure is dimensionless. The word ol

signifies that old quantities are used to weight (i.e., aggregate) pr

changes. After the the symbol (u) signifies an individual product,

symbol (U) signifies total products in the case of multiple products,

absence of a symbol signifies an individual resource, and the symbol

signifies total resources.

Function APold(I) will in a later chapter be used to specify axioms

function Z which represents resource price variance.

Figure E4.F4 CHANGE IN LASPEYRES PRICE INDEX NIJNBERSIN CHAPTER E4

Column E4 G

This column is defined as change in the Paasche price relative with adefault value of change in the Laspeyres price relative when the Paascherelative is not defined. The latter situation occurs with respect tq anentity deletion (i.e., an entity for which no quantity is defined in pewinterval although a quantity was defined in the old interval).

APnew where Kflnew exists

where /fPnew does not exist

The above condition appears to single and multiple products as well as tosingle and multiple resources.

Change in the genera! price relative

Column E4 F Column E4 F

PERCENTAGE CHANGE INOLD_QUANTITY—WEIGHTEDPRICE RELATIVEFOR RESOURCEAPold

PERCENTAGE CHANGE INOLD_QUANTITY—WEIGHTEDPRICE RELATIVEFOR PRODUCTAPold(u)

Qun

QuoB A

Puo Pun

APold(u) a A / B

A = PRICEoId(u)

a Quo * (Pun —

Po Pn

APold a C/DC = PRICEoJd

a Qo * (Pn — Po]

B = VALUE0Id(u) D = VALUEoId

aquo*PUo aQo*Po

The following two examples show the computation of the change in

Laspeyres (i.e., old_quantity—weighted) price relative for total product ai

for total resources.

PRICE01d(U) $ 1875APold(U) a =

______

= 18,7500% FOR TOTAL PRODUCTS

VALUE01d(U) $10000

PRICEo1d(I) $ 1600APold(I) a =

______

= 16,0000% FOR TOTAL RESOURCES

VALUE01d(I) $10000

E4—7 -E4 — B

Chapter E5 EXAMPLE OF INPUT COMPACT REPORT

This chapter presents the axioms which define the Input Compact Report and

an example.

The purpose of this report is to provide data on value, quantity and price(together with their percentage changes where relevant) to facilitate the

derivation of the Input Quantity and Price report shown in the next chapter.The Input Compact Report consolidates key information from •preceding Input

reports once possible differences in interval width between old and new

intervals have been factored out. This adjustment is indicated in the words

"ADJUSTED FOR ZERO INTERVAL WIDTH CHANGE" which appear in the report title.

1968/09/01 FPM INPAT COMPACT REPOUT ADJuSTED 1042 ZERO INTERVAL WIDTH CHANGE

90516055 A1987 as. 1988

Values are On COLLARS

c. Old (Reference) Interval —no——— New Interval adjusted ——— <———— Percent tRANCE In

INDEX ENTITY REVA VALRE QUANTITY PRICE VALUE QUANTITY PRICE VALVE QUANTITY PRICE

IN 8 C 0 0 F 6) 8 1 JI

INCORE:RI Product al 6000.9 150.9 40.000 8900.0 200.0 44.100 48.333 33.333 11.210

92 Product a2 4000.0 80.0 10.000 9100.0 140.0 61.000 127.500 75.000 30.000

TOTAL INC04IE 10000.8 10000.0 80.000 10.000 20.000

COST RESOURCES:

NI Materiel a 1.00 8000.0 400.0 20.000 12540.0 510.2 22.000I

56.750 42.500 10.000

(TRIAL OPERATING EXPENSES 8000.0 12540.0 (50.750 42.500 10.000

CA;ITAL RESOURCES: - --TI Equiposent a 2000.0 8.0 200.000 3100.0 10.0 310,000

I

75.OAO 25.000 00.000

(TOTAL CAPITAL RESOURCES 2000.9 3500.0 (75.000 25.000 40

(TOTAL RESOURCES )10000.0 16040.0 60.400 39.000 28.1

(OFF TAROET PROFIT 2960.0 )100.000 06.122 78.1

(INTRINSIC PROFIT — - 2000.0 — 5460.0 —— )173.000 80.000

CAPITAL RESOURCES:

UI Eqaipment a 4OOUO.0 8.0 5OU0.000 70000.0 20.0 7000.000(

75.OUO 25.000 40.000

(TOTAL CAPITAL RESOURCES 40000.0 70000.0 75.000 25.000 40.000

)RETOAN 044 IHAESTNENT (5) 5.0 7.8 I

PUNt 79860 Ruse Ion Poe Vunn Run Pun

ROVA You Re Pe Ann Qn Fn

Ce Cn

Column E5 A

This column reflects REV/I which appears in Input Validation 0B'shown in chapter E2 column A.

Column E5 B

This column repeats old values which appear in the Input Validation °A"

Report shown in chapter El column A. It also repeats the old intrinsic rate!

of return from the same source.

This column lists new values adjusted for any inequality in Interval widthoetween old and new intervals. Since our example assumes equal intai)ovalwidth in old and new intervals, the data in this column do not refer to widthalthough width appears in the axiom for this column given in the ondifference calculus which appears as bibliography item A15 in Appendix a ofu)s book.

Our example therefore simply repeats new values which appear in the iv-,putTlidation Report Shown in chapter El column 0. It also repeatsthe same source.

This column lists new quantities adjusted for any inequality in intervalbetween old and new intervals. Since our example assumes equalin in this column do not refer to wtdthlthough width appears in the axiom for this column given in the boot onlifference calculus which appears as bibliography item A15 in Appendix ofs book.

Our example therefore simply repeats new quantities which appear in:t Validation Report shown in chapter El column E.

E5 G

column repeats new prices which appear in the Input Validationeport shown in chapter El column F.

lumn ES H

TiS column repeats change in the value relative Aj7 which appears in theit Relative Report shown in chapter E4 column C.

imn ES I

column repeats change in the Laspeyres quantity relative whichppRars in the Input Relative Report shown in chapter E4 column 0.

iumn ES J

Otis column repeats change in the Paaschm price relative APnew whichpthe Input Relative Report shown in chapter E4 column E.

E5 — 2

This column repeats old quantities which appear in the Input Validatios4 CACshown In chapter El column B.

ES 0

This column repeats old prices which appear in the Input Validation°°"rt shown in chapter El column C

:::i E5 E

'0

'O

Column ES F1!

00(u) UQeld(o(00(0) 000ld(UIàY UQeld09(1) AQnldI2)

Report:4

E5 — 1


This chapter presents the axioms which define the Input Normalized Quantityand Price Report and an example.

First it is necessary to comment on the product and resource normalizationswhich appear In the following figure.

The left side 12—box diagram is discussed in chapter Ki. It is aimed atthe advanced reader who wishes to scrutinize axioms dealing with productnormalizations in lieu of resource normalizations. The right side 12—box

diagram is discussed in this chapter. It is aimed at all readers as they am

required to understand the functions comprizing resource normalizations, i.e.,functions which comprize normalized new resource quantity and normalized new

resource price.

PRODUCT RESOURCE

NORMALIZATIONS NORMALIZATIONS

specified in specified inChapter Ki Chapter E6

Puo Pun Punr Po Pn Pnr

The purpose of this report is to provide data on quantity and price togethwith the normalized quantities and prices which are relevant to resources. Tdata appearing in this report form the foundation of all performanvariances, and their corresponding percentage changes, which appear in c

and profit reports.

IC:

a2150.00 200.0040.00 140.00

I

40.0000 44.500050.0005 05.0000

COSIRESmIRCEST

I Rn Qn Qne Rap, Pu Pn PinI

TI

RI

Material a

CAPITALEquipment a

CAPITALEquipeia,5 a -=

400.00 570.00

4.00 10.00

8.00 10.00

600.00 600.00 20.0000 22.0050 24.0200-

6.00 12.00 250.0005 350.0000 '8.00 12.00 5000.0000 7000.0000

This column lists new quantities adjusted for any inequality in intervalwidth between old and new intervals. Since our example assumes 'equalinterval width in old and new intervals, the data in this column do notwidth although width appears in the axiom for this column given in thç -bookdifference calculus which appears as bibliography item hiS in B of'5 book.

Our example therefore simply repeats new quantities which appear iq the.t Validation cAn Report shown in chapter El column E.

This column lists new resource quantities normalized for constant (I.e.,efficiency with respect to new production. In the following1Mnterval width is buflt into the function as cited in theof chapter E4 column C.

0 Qo * (1 + REVA * I4old(U)]

40D * {l + 1,0 * O,5J = 6OD for cost resource NI8 * [1 + 0 * D,5J = 8 for capital resource Tl

= Qo where REVA = 0 when the resource quantity is presci-ibeci tostay fixed despite product quarqitychange.

= Qnp where REVA = 1 when the resource quantity is prescribed tovary in direct proportion toquantity change, as shown below.

= Qo * (1 + REI'A * IQoldflJ)] appears on the computer screen.

E6 — 2

1988/09/51FPN INPUT NC8IRRLIZEU 5208TITR AND PRICE REPORT

BUSINESS A1988 cm. 1988

Figure E6.F1 12 BOX DIAGRAMS FOR PRODUCT AND RESOURCE NORMALIZATIONS

Quo and Qo

This column repeats old quantitiesshown in chapter El column 8.

and Qn

from the Input Validation cAn

Qne

Qne

E6 — 1

Qne

5-

Qnp

This column lists new resource quantities normalized for constant (i.e.,old) productivity with respect to new product quantity. In the followingaxiom interval width is built into the function I4old(U) as cited in thediscussion of chapter E4 column 0.

Qnp a Qo * [1 +

400 * [1 + 0,5 ] = 600 for cost resource NI

8 * [1 + 0,5 1 = 12 for capital resource TI

Function Qnp assumes full variability of resource quantity with respect tochange in product quantity.

Qnp = Qo * (1 + IQold(U)J appears on the computer screen.

Pua and Pa

This column repeats old prices from the Input Validation "A" Report shown inchapter El column C.

Pun and Pn

This column lists new quantities adjusted for any inequality in intervalwidth between old and new intervals. Since our example assumes equalinterval width in old and new intervals, the data in this column do not referto width although width appears in the bookon difference calculus which appears as bibliography item A15 in Appendix B ofthis book.

Our example therefore simply repeats new prices which appear in the InputValidation "A" Report shown in chapter El column F.

Pnr

This column lists new resource prices normalized for constant (i.e.,price recovery with respect to new product price. In the followinginterval width is built into the function APnew(U) as cited in theof chapter E4 column E.

Pnr a Po * [1 + AThiew(U)J

20 * [1 + 0,2 1 = 24 for cost resource Ni

250 * [1 + 0,2 J = 300 for capital resource Tl

For = Po * [1 + IPnew(U,)J appears on the computer screen.


This chapter presents the axioms which define the Profit Background Reportand an example. The report is self—explanatory.

PPM PROFIT O4CK0000RO REPeOT

1988 VS. 1989

are OOLLARO

OPERATICMOLD

ONTEROALMEW

INTERVALOLD

INTERVAL INTERVALMEW INTRINSIC

REVENuE REOENOE

=

COST COSTINIVIN5IC

PVOFOTINTRINSIC PROFIT

morn VARIANCE

F 0 N C T 1 0 9 S REVEROES1d REVENOEVVW COST,]d COSTnew POOFIToSA

E7 A

OLD INTERVAL REVENUE

r_lumn E7 B

PROFITVVW nherent

a OLD TOTAL INCOME

= 110000,0r:.t

'4NEW INTERVAL REVENUE e NEW TOTAL INCOME

= 118000,0

Column E7 C

OLD INTERVAL COST a OLD TOTAL COST RESOURCES

= 18000,0lumn El D

NEW INTERVAL COST = NEW TOTAL COST RESOURCES

= 112540,0Iumn E7 E

OLD INTERVAL PROFIT a OLD INTRINSIC PROFIT

= 12000,0column E7 F

NEW INTERVAL PROFIT a NEW INTRINSIC PROFIT

= 15460,0:olumn El C

CHANGE IN PROFIT = NEW INTRINSIC PROFIT a OLD INTRINSIC PROFIT

$5 460,0— $2 000,0

13460,0

E7 — .1E6—3 -

FPM PROFIT RECcNICILIATIOI REPORT

80018050 A1988 vs. 1989

Values are In OOLLARS

/'.i \JA

Chapter E8 EXAMPLE OF PROFIT RECONCILIATION REPORTColumn E8 0

RETURN ON REVEIWE VARIANCE only for T rowsPROFITre venue e 01.0 OFFTARGET PROFIT

10 2 \2= Vko*(Co To]

= Vko*(Co — Co]

There arechapter 012.

Column E8 C

* CHANGE IN TOT PRODUCT VALUE RE4ATIVE

*. AV(U)] WHERE Vo refers to K row

* Aji(U) (by default To =Co)30,0 c±C)

A

9 segments defined in the Return on Revenue Variance in

This chapter presents the axioms which define the Profit ReconciliatiooReport and an example. The profit reconciliation variance is the differencebetween intrinsic profit variance, which is seen by comparing profit levels intwo income statements, and long term performance profit variance, which is thecomponent of intrinsic profit variance relevant to productivity analysis and

long term price recovery analysis.

The purpose of this report is to specify the components of the profitreconcil iation variance.

198 8/09/01

PROFIT INTERVAL INTERVAL RETURN 01 TAREET CVVNSE IN

ENTITY RECENCILIATIEN PROFIT GAP PROFIT 81010 REVENUE RSI IN505TNENI

- - VARIANCE VARIANCE VARIANCE VARIANCE VARIANCE VVRIVNCE

A = 8 + C + U + E +

COST RESOJRCEI:NaEarIal a

ITOTAL OPERATING EVPEVSE5 - —- — - -— -

-I

CAPITAL RESENRCE5:EquVpnenE a 1500.00 1500.01

ITOTAL CAPITAL RESOORCES 1500.001500.00

I

TOTAL RESENRCES 1500.00 1500.00

F 0 N C T I 0 N S PROFITOeCOS PROFITgap PROFITwIdEA

Column E8 F

CHANGE IN INVESTMENT VARIANCE only for T rows

PROFITasset m To * ( Vkn — Vko J

= Co * ( Vkn — Vko ] (by default To = Co)

= 0,05 * [70000,0 — 40000,OJ = 31500,0 for capital resource

$1500,O for Total Resources -.

There are g segments defined in the Investment Variance Grid in chapter 011..

Column EB EI

TARGET ROI VARIANCE only for T rows

PROFITtaroi e Vkn * [ Tn — To ]

PROFITrRve,un PROFITEarOI PROFITa5snI

umn E88

VARIANCE (PROFITwIdt/i)

The function PROFITwidth adjusts for different interval widths in old andnew intervals. It assumes a zero value when the interval widths are aslown in our example where they are.set at unity for both periods. Thethis column appears in the book on difference calculus which asliography item A15 in Appendix B of this book.

INTER VAL PROFIT GAP VARIANCE (PROFITgap)

The function PROFITgap adjusts for a gap between old and new intervals. itsumes a zero value when the intervals are contiguous as shown in our exaooplermIIe 1989 and 1988 are contiguous. The axiom for this columnin the book on difference calculus which as1iography item A15 in Appendix B of this book.

iron E8A

PROFIT RECONCILIATION VARIANCE

a PROFIT + PROFIT + PROFIT + PROFIT + PROFITasset taroi revenue width gap

= 0+ + 0 +

= Vkn * (Co — Co] (bydefault Tn = Co = To)

= $1500,o + 0 +

$0, 0

There are 9 segments defined in the Target Return on Investment Variano

Grid in chapter 013.

£8 — 1

0 cost0 + 0 + 0 = $1500,o capJtaj

$l500,o Tqtal

£8 — 2


This chapter presents the axioms which define the Profit Overview

Report and an example.

The purpose of this report is to provide an overview of both long term and

short term variances which make up the product profit variance. This report

is complemented by additional reports which, inter a7ia, provide percentage

changes for the variances shown in this report.

1988/09/01 PPM PROFIT OVERVIEW REPa8T

BUSINESS a1980 vs. 1989


INTRINSIC PROP REC80 TERN PRODUCT— L880 TERM SHOiT TERM SHORT TERM CAPACITY

ENTITY PRRPIT —dIlATION PRODUCT IRITT PRICE PROEUCT EFFICIENCY PRICE 0Th

VYROUNCE RARIONCE PROFIT RARIARCE RECOVERY PROFIT VARIANCE RECOVERY VARIANCE

U I + CC 0 + E F 0 + 8 Ii

COST REOER1RCES: =

Material a 18600 1860.0 660.0 1l0O.R 1860.0 660.0 1200.0

TOTAL OPERATSNS EXPENSES I1860.0 1860.0 660.0 0200.0 1860.0 660.0 1000.0

CAPITAL RESWRCES:Equipment a —

—— 1600.0 1500.0 100.0 700.0—

608.0: 1100.0— 700.0 — 485.0— 1800.0

TOTAL CAPITAL REOWRCES I1800.0 1100.0 100.0 780.8 800.0— 2180.0— 708.0— 400.0— 1400.0

I

!T0b0. RE501RCES I3000.0 1000.0 1060.8 1360.0 = 680.0 708.0 60.0- 800.0

P 8 N C T I 09 S PROPITintrinsic PROPSTrecon PROFITYOng mew Rlnng PROFIT5VOrC Enen

The following text defines long term product profit variance, short term

product profit variance, and the capacity utilization term in long term

product profit variance.

Figure E9JI - LOMO TERM PERFORMAMCE VARIAMCES IM CHAPTER

Column Eg C Column E5 0 Column E9 E

LONG TERM PR000CTIVITy LONG TERMPI<ODUCT VARIANCE PRICE RECOVERYPROFIT VARIANCE IN NEW PRICES VARIANCEPh'OFIT7ong = A Ynew = B Rlong = C

ES — 1

There are 13 segments in the long term product profit grid in chapter

ES — 2

Po Pn Pnr

A =

a Qnp * Pnr — Qn * Pn

Rshort

Po Pn Pnr

Lena

B = Ynew

[Qnp — Qn] *

C = Riong

a Qnp * (Pnr — Pn]

Column ES C

LONG TERM

rlong a

PRCDUCT PROFIT VARIANCE

Qnc' * Pnr — Qn *

600 * 24 — 570 * 22 = $1860,O for cost resource

12 * 300 — 10 * 350 = $ 100,0 for capital resource

$1960.0 for Total Resources

VARIANCE IN NEW PRICES

— Qn 7*Pn

— 570,0 * 22,0 = $ 660,0 for cost resource

— 10,0 3 * 350,0 = $ 700,0 for capital resource

$1360,0 for Total Resources

There are 13 segments in the productivity grid in chapter 03.

Column E9 E

LONG TERM PRICE RECOVERY VARIANCE

Riong a Qnp * [ Pnr — Pn J

600,0 * [ 24,0 — 22,0

12,0 * [ 300,0 — 350,0 3

There are 13 segments in the long term price recovery grid in chapter D6.

Column E9 F

SHORT TERM PRODUCT PROFIT VARIANCE

rlTshort a Qne * Pnr — Qn *

600,0 * 24,0 — 570,0 * 22,0 = $1860,0 for cost resource8,0 * 300,0 — 10,0 * 350,0 $1I00,0- for capital

$ 760,0 for Total Resource

There are 13 segments in the short term profit grid in chapter 07.

Column E9 0

PRODUCTIVITY

Ynew a f Qnp

600,0

12,0

Figure E9.F2 - SHORT TERM PERFORMANCE VARIANCES IN CHAPTER E9

$1200, 0

= $ 600,0-

$ 600,0

for cost resource

for capital resource

for Total Resources

E9 — 3 Eg—4

Enew a [ Qne — Qn ] *

600,0 — 570,0 1 * 22,0 = $660,O for cost resource

8,0 — 10,0 ] * 350,0 = $700,0- for capital resource

$ 40,0- for Total Resources

There are 13 segments in the efficiency grid in chapter D5.

Column E9 H

SHORT TERM PRICE RECOVERY VARIANCE

Rshort a Qne * ( Pnr — Pn J

600,0 * [ 24,0 — 22,0 1 =

8,0 * [ 300,0 — 350,0 ] =

There are 13 segments in the short term price recovery grid in chapter D6.

Column E9 C

CAPACITY

PROFITcut a

- Column E9 F

UTILIZATION TERM IN PRODUCT PROFIT VARIANCE

PROFIT1ong — PROFITshort

= (Qnp — Qne ]*Pnr600,0 — 600,0 1 * 24,0 = $ 0,0 for cost resource12,0 — 8,0 ] * 300,0 = $1200,0 for capital resource

$1200,O for Total Resources

This variance is in September 1988 not shown in any report of any softwareimplementation, It is shown above as the link between long termvariance and short term product profit variance.

Column E9 G

EFFICIENCY VARIANCE IN NEW PRICES

Figure E9.F3 - CAPACITY UTILIZATION TERM INPERFORMANCE VARIANCES IN CHAPTER E9

NOT REPORTED Column E9 I NOT REPORTED

CAPACITY CAPACITY CAPACITYUTILIZATION UTILIZATION UTILIZATIONTERN iN VARIANCE TERM INPRODUCT IN NEW PRICES PRICE RECOVERYPROFIT VARIANCE VARIANCEPROFITcut = A Lnew = 8 Rcut = C

$1200,O for cost resource

$ 400,0- for capital resource

$ 800,0 for Total Resources

Pn Pnr P0 Pn Pnr

A = PROFITcut

a [Qnp — Qne] * Pnr

B = Lnew

a(Qnp—Qne]*pp

C = Rcut

a[Qnp — QneJ*(Pnr — Pn]

E9 — 5 [9 — 6

Column E9 I

CAPACITY UTILIZATION VARIANCE IN NEW PRICES

Lnew [Qnp — Qne J*Pn

[600,0 — 600,0] * 22,0 = $ 0,0 for cost resource

12,0 — 8,0 ] * 350,0 = $1400,O for capital resource


There are 13 segments in the capacity utilization grid in chapter D4.

Column E9 E - Column E9 H

CAPACITY UTILIZATION TERM IN PRICE RECOVERY VARIANCE

Raft a Rlong — Rshort

= fQnp —Qne ] *[Pnr — Pn 3

[600,0 — 600,0] * [ 24,0 — 22,0] = $ 0,0

12,0 — 8,0] * [300,0 — 350,0] = $200,0—

$200,0- for Total Resources

This variance is in September 1988 not shown in any report of any software

implementation. It is shown above as the link between long term pricerecovery variance and short term price recovery variance.

Column E9 B

PROFIT RECONCILIATION VARIANCE

PROFITrecon See chapter E8 column A.

$1850,0 = $1B60,O for cost resource

$1500,0 + $ 100,0 = $1600,0 for capital resource


Column ElO A

LONG TERM PROOL'JT PROFIT VARIANCE

PROFIT1ong is presented in chapter E9 figure E9.F1 and column E9 C.

Column ElO B


Ynew is presented in chapter E9 figure E9.F1 and column E9 0.

Column E1O C

LONG TERN PRICE RECOVERY VARIANCE

is presented in chapter £9 figure E9.F1 and column [9 [.

It Chapter E1O EXAMPLE OF LONG TERN PRODUCT PROFIT REPORT

This chapter presents the axioms which define the Long Term Product PcofitReport and an example.

The purpose of the report is to show variances and percentage inlong term profit change.

988/09/01 FPM LONG TERM PROOIUCT POOFIT REPONT

DUllNESS A1988 v, 1889

Values are I' DOLLARS

for cost resource


ENTITY PRWUCTPROFIT

A

PRONUCTI RIOTVARIANEE

9

powucnvIlTpRicr!kcovEoyPRICE RECOVERY VARIANCE IARIPJXCE

VARIANCE C CVANOE CNAOOE

+ C I) E

COOT RESOUOCES:

Material a 1880.000 660.000 1200.000 9.2632

TOTAL OPERATING EXPENSES 1860.000 660.000 1200.000 9.2032

CAPITAL RESWRCES:!

Equipme'L a 100.000 700.002 600.OSO— 20.0000 14.2857—

FONCTIONS PROFITOsng Ynew bong

A

INTRINSIC PROFIT VARIANCE

PROFIT a PROFIT + PROFIT

intrinsic recon long

4

E9 — 7 £10 — 1

a

Column ElO D Column E10 E

PERCENTAGE CHANGEPRODUCTIVITYIN NEW PRICES

AVnew

IN PERCENTAGE CHANGE INLONG TERMPRICE RECOVERY

Po Pn Pnr P0 Pn Pnr

A7new a A / B a C / 0

A = Ynew C = Riong

a [Qnp — Qnj * Pn a Qnp * (Pnr — PnJ

B = VALUEnew 0 = VALUEnew + Ynew

mQn*Pn mqnp*Pn

Qnp

Qne

Qn

Qo

Column ElO D

PERCENTAGE CHANGE IN PRODUCTIVITY IN NEW PRICES

a Ynew / VALUEnew

$660 / $12540 = 5,2632% for cost resource

$700 / $3500 = 20,0000% for capital resource

$1360 / $16040 = 8,4788% for Total Resources

Column ElO E

PERCENTAGE CHANGE IN LONG TERM PRICE RECOVERY

a Riong / (VALUEnew + Ynew 3

$1200,O / [$12540,0 +

$ 600,0— / [$ 3500,0 +

$ 600,0 / [$16040,O +

Column Eli A

SHORT TERM PRODUCT PROFIT VARIANCE

PROFITshort is prese:ited in chapter E9 figure E9.F2 and column E9 F.

EFFICIENCY VARIAICE IN NEW PRICES

is presented in chapter E9 figure E9.F2 and column E9 G.

lumn Eli C

SHORT TERM PRICE RECOVERY VARIANCE

,lort is presented in chapter E9 figure E9.F2 and column E9 H.

Figure E10.Fi - CHANGE IN PERFORMANCE INDEX NUMBERSIN CHAPTER ElO

Chapter Eli EXAMPLE OF SHORT TERM PRODUCT PROFIT REPORT

This chapter presents the axioms which define the Short Term Product profitReport and an example. The purpose of the report is to show andpercentage changes in short term profit change.

rPM SHOUT TERN PROUUCI PROFIT REPOUT

NOSINESS A1988 vs. 1989

Values are In DOLLARS

ENTITYPROSUCT EFFICIENCY PRICE RECOVERY VARIANCE VARIANCEPROFIT VARIANCE VARIANCE % CWINGE CROSGE

COST RESOURCES:Material a 1800.000 660.000 1200.001 5.2632 ' 9.0909

TOTAL OPERATING EXPENSESI — — 1860.000 660.000 — 1200.000 5.2832

Equlpi,ent a 1100.000- 700.000— 400.000— 20.6000-TOTAL CAPITAL RESOURCES

I 1100.000- 700.000— 406.000—

J4.2857_

20.0000—TOTAL RESOURCES

J 760 000 48 000 900 000 2494— p5

0000I

hurt

$660,O] = 9,0909% for cost resource

$700,0] = 14,2857%- for capital resourc

$1360,O] 3,4483% for Total

ElO — 2 Eli — 1

Chapter E12 EXAMPLE OF COST RECONCILIATION REPORT

This chapter presents the axioms which define the Cost ReconciliatitrnReportand an example. There is no Cost Background Report. The Cost ReconcfliationReport serves to combine for cost analysis the functions which ProfitBackground and ProFit Reconciliation Reports perform for profitIn the following report the column E cost reconciliation variance is thedifference between the column C intrinsic cost variance, which is seen bycomparing cost levels in two income statements, and the column D termproduct cost variance, which is the component of intrinsic cost Oriancerelevant to productivity analysis and long term resource price

The purpose of this report is therefore to indicate the old and costlevels from the intrinsic cost variance is derived, and to spec{fy thecomponents of the cost reconciliation variance.

C 5 4 EE P 4 + + I,

8000.0 12510.0 4540.0— 540.0— 4000.0— 3826.1— 173.9—EXPENSES

I0000.0 12540.0 4540.0— 540.0— 4000.0— 3026.1' 173.9—p

L

2000.0 3500.0 1520.0- 500.0- 1000.0- 43.5-I 2000.0 3500.0 1500.0— 500.0— 1000.0— oso.o:I 10000.0 16040.0 6040.0— 1040.0— 5000.0—

217.4_I

Figure EI1.F1 - CHANGE IN PERFORMANCE INDEX NUMBERSIN CHAPTER Eli

Column Eli D Column Eli E

PERCENTAGE CHANGEEFFICIENCYIN NEW PRICESlsrnew

IN PERCENTAGE CHANGE INSHORT TERMPRICE RECOVERY

Po Pn Pnr Po Pn Pnr

AEnew a A/BA C = Rshort

a(Qne—QnJ*Pn aqne*[Pnr—Pn]

B = VALUEnew U = VALUEnew + Enew

aqn*pn aQne*Pn

ENTITY

PPM COST RECONCILIATION REPLO2T


Values are In DOLL000

OLD NEW INTRINSIC LONG TERN COST RECLOI INTERVAL INTERVAL P0000CTINTERVAL INTERVAL COST PROSUCT -CILIOTION COST GAP COST WIDTH 0010MW MbCOST COOT VARIANCE COST WAOIANCE VARIANCE VARIANCE ONVEIOVTEP EFrECTA — I

Column Eli 0

PERCENTAGE CHANGE IN EFFICIENCY IN NEW PRICES -

Atnew a Enew / VALUEnew

$660 / $i2540 = 5,2632% for cost resource

$700— / $3500 = 20,0000%- for capital resource

$ 40— / $16040 = 0,2494%- for Total Resources

Column Eli E

PERCENTAGE CHANGE IN SHORT TERN PRICE RECOVERY

a Rshort / (VALUEnew + Enew

$1200,0 / [$12540,O + $66O,0 ] = 9,0909% for cost resource! I

$ 400,0— / [$ 3500,0 ÷ $700,O—] = 14,2857%— for capital resoUA

$ 800,0 / [$16040,0 + $ 40,0—] = 5,0000% for Total Resoun

ElI — 2

1';P U N C T I 0 N S CGSTo1d COOTnee COSTintrinsIc COST9ong COSTrecon COSTgap COSTWIdEN COSTyolume

:olumn E12 A

OLD INTERVAL COST

'OSTo7d a VALUEO !L1

$ 8000,0 for cost resource

$ 2000,0 for capital resource

$l0000,0 for Total Resources

E12 8

NEW INTERVAL COST

OSTnew a VALUEnew

$12540,O for cost resource

$ 3500,0 for capital resource

$16040,O for Total Resources

E12 — I

Column E12 C

INTRINSIC COST VARIANCE

COSTintrinsic a COSTa1d

$8000

$2000

Column E12 D

LONG TERM

COST1ong a

= 5540,0- for cost resource

= $500,0- for capital resource


VARIANCE

COSTwidth + COSTv0 lame + COSTmIx

= 0,0 + 0,0 + 53826,1— + 5173,9— = 54000,0- for cost

= 0,0 + 0,0 + $ 956,5— + $ 43,5— = 51000,0- for capi

$5000.0- for Total

(see chapter E4 page 5)

= 53826,1- for cost resource= $ 956,5- for cost resource


appears on the computer screen.

the Product Volume Grid in chapter 011.

COSTmIx a (Qnpd — QnpJ * Pa WHERE Qnpd = Qa * (1 + Mdim(U)J

= Va * — (see chapter £4 page 5)

$8000 * [0,4782609 — 0,5 ] = $173.9- for cost resource

$2000 * [0,4782609 — 0,5 = $ 43,5- for capital resource

5217,4- for Total

= Va * (IQdim(U) — IQold(U)J appears on the computer screen.

There are 9 segments defined in the Product Mix Grid in chapter Dli.

Column E12 F

INTERVAL COST GAP VARIANCE (COSTgap)

The function COSTgap adjusts for a gap between old and new intervals.assumes a zero value when the intervals are contiguous as shown in our examibecause 1989 and 1988 are contiguous. The axiom for this column involves adivisor and appears in the book on difference calculus which appears

bibliography item AlS in Appendix B of this book.

Column E12 8

INTERVAL COST WIDTH VARIANCE (COSTwidth)

The function COSTwidth adjusts for different interval widths in old andintervals. It assumes a zero value when the interval widths are equal

shown in our example where they are set at unity for both periods. The axi,

for this column appears in the book on difference calculus which appears


E12 — 2

In columns £12 H and E12 I shown above, the first right hand expresstonsy Qnpd which represents new resource quantity normalized for

ductivity using unweighted (dimensionally improper) product quantities..s composition is indicated by the constraint shown alongside the fft-st

.'ight hand expression of the axiom covered by column £12 H above.

El? — 3

— COSTnew

— $12540 =

— $ 3500 =

$4540- for cost resource

$1500- for capital resource

$6040- for Total Resources

= — Vo * I4dim(U)

— $8000 * 0,4782609— $2000 * 0,4782609

PRODUCT COST VARIANCE

Qnp*Po — Qn*Pn

600 * 20 — 570 * 22

12*250 — 10*350

Column E12 H

PRODUCT VOLUME UNWEIGHTED VARIANCE

COSTvolame m [Qo — Qnpd] * Pa where Qnpd = Qo * (1 +

COSTvo lame = — Va * IQdim(U)

There are 9 segments defined in

E12 I

PRODUCT MIX EFFECT

Column El? E

COST RECONCILIATION

COSTrecon a COSTgap +

I

Chapter E13 EXAMPLE OF COST OVERVIEW REPORT

This chapter presents the axioms which define the Cost Overview Report and

an example.

The purpose of this report is to provide an overview of both long term and

short term variances which make up the product cost variance. This report iscomplemented by additional reports which, inter al/a, provide percentagechanges for the variances shown in this report.

1988/AM/Al PPM COST OREORSEA AEPCIOT


— -—— Aalues are In DOLLARS

IN001MSIC COST 8ECOS LOSS TERN PROSUCT— 1880 TEAM SMOST TERM SAOTT TEAM CI

ENTITY COST -CILIATImI PRCOOCT TASTY AESmIACE P0000CT EFFICIENCY AESC4JACE

AURSYACE AmBIANCE COST AmBIANCE PRICE COST AAAIUNCE PAICE RI

A • B 4 CC D + E F 0 + A

COST RE5000CES:Material a 0540.0— AOOS.O— SASS— 080.0 1200.0— 540.0— 080.0 1200.0—

TOTAL OPERATING EUPEASES 454A.O- 4000.0- 540.0- 1000.0- 540.0- 080.0 1000.0-

CAPITAL RE5008CES:Equipiavnt a ISSO.0— 1000.0— 500.0— 700.0 1200.0— 1500.0— 700.0— 800.0— 1400.0

ITOTAL CAPITAL RE500RCES I1500.0— 1000.0— 500.0— 700.0 0200.0- 1500.0- 700.0— 800.0- 140011

ITOTAL RE5008CES = 8040.0— 5000.0— ;OAO.T 1380.0 2400.0— SOAO.O— AO.O— 2000.0— lASSOI

F 0 8 C T I 0 N S COSTT,trI,slc COSTrecon COSTlong Once Zlong COSTohorL

The following text defines long term product cost variance, short termproduct cost variance, and the capacity utilization term in long term productcost variance.

Cumn E13

LONG TERM PRODUCT COST VARIANCE

Qnp * Po — Qn * Pn

600 * 20 — 570 * 22 = $54O,O- for cost resource

12 * 250 — 10 * 350 = $500,O- for capital resource

$IO4O,O- for Total Resources

There are 13 segments defined in the long term cost grid in chapter DY.

Figure E13.F1 - LONG TERM PERFORMANCE VARIANCES IN CHAPTER E13

A

Column E13 C Column E13 D Column E13 E

LONG TERM PRODUCTIVITY LONG TERMPRODUCT COST VARIANCE RESOURCE PRICEVARIANCE IN NEW PRICES VARIANCECOSTlong = A Ynew = B Zlong = C

Po Pn Prir

= COSTlong

e Qnp * Po — Qn * Pn

=B÷C

Po Pn Pnr Po Pn Pnr

B = Ynew C = Zlong

(Qnp — QnJ * Pn m Qnp * [Po — PnJ

Enow 0 short Lnoo

m

E13 — I

PRODUCTIVITY VARIAMCE IN NEW PRICES

is presented in chapter E9 figure E9.F1 and column E9 0.

E13 — 2

TERM RESOURCE PRICE VARIANCE

Qnp *[Po — Pn ]600,0 * [ 20,0

12,0 * [ 250,0

Column E13 F Column E13 G Column E13 H

SHORT TERM EFFICIENCY SHORT TERM

PRODUCT COST VARIANCE RESOURCE PRICE

VARIANCE IN NEW PRICES VARIANCE

COSTshort = A Enew = B Zshort = C

Qnp1

QneA over

P0 Pn Pnr

A = COsTshort

Qne * Pa — Qn * Pn

=B+C

Qnp Qnp

Qne Qne

B

C

Pa Pn Pnr P0 Pn Pnr

B = C = Zshort

(Qne — Qnj * Qne LP0 — PnJ

Column E13 F

SHORT TERM PRODUCT COST VARIANCE

COSTshort Qne * Pa — Qn *

600,0 * 20,0 — 570,0 * 22,0 = $ 540,0- for cost resource I8,0 * 250,0 — 10,0 * 350,0 = $1500,0- for capital


There are 13 segments defined in the short term cost grid in chapter 09.

E13—3

E13 G

EFFICIENCY VARIAPCE IN NEW PRICES

is presented in chapter E9 figure E9.F2 and column E9 G.

SHORT TERM RESOURCE PRICE VARIANCE

Qne * [ Pa — Pn .1

600,0 * [ 20,0 — 22,0 1

8,0 * [ 250,0 — 350,0 1

Iumn E13 C - Columi, E13 F

CAPACITY UTILIZATION TERM IN PRODUCT COST VARIANCE

COSTiang — CO5Tshort

Column E13 E

LONG

Ziong

There are 13 segmentschapter 08.

— 22,0 ] = $1200,O- for cost resource

— 350,0 ] = $1200,0- for capital resource


defined in the long term resource price grid in

Figure E13.F2 - SHORT TERM PERFORMANCE VARIANCES IN CHAPTER E13

= $1200,0- for cost resource

= $ 800,0- for capital resource


Figure E13.F3 - CAPACITY UTILIZATION TERM INPERFORMANCE VARIANCES IN CHAPTER E13

NOT REPORTED Column E13 I NOT REPORTED

CAPACITY CAPACITY CAPACITYUTILIZATION UTILIZATION UTILIZATIONTERM IN VARIANCE TERM INPRODUCT COST IN NEW PRICES RESOURCE PRICEVARIANCE VARIANCECOSTcut = A Lnew = B Zcut = C

Po Pn Pnr

A = COSTcut = Loid

a [Qnp — Qne] * Pa

=B+C

Pa Pn Pnr Po Pn Pnr

B = Lnew C = Zcut = — Lrep

(Qnp — Qne] * Pn a (Qnp—Qne]*(Po—PnJ

Laid

E13 — 4

Cha!ter E14 EXAMPLE OF LONG TERN PRODUCT COST REPORT

This chapter presents the axioms which define the Long Term Prqjuct CostReport and an example.

The purpose of the report is to show variances and percentage inlong term cost change.

PROSOCTI VIII RE50JRCE PRICE RARIANCt VARIANCERARIARCE VARIANCE V V CHANGE

COST RESOVRCES:Naterlal a 540.000— 660.000 1100.000— 10.0000

TOTAl OPERA1560 EXPENSES 540.000- 660.000 1200.005— 5.2632:. 50.0050

CAPEIALRES mmcEquipment a soo.ooo— 700.000 1200.000— 20.0000 - 40.0000

Column E14 C

LONG TERM RESOURCE PRICE VARIANCE

?long is presentcd in chapter £13 figure E13.F1 and column £13 E. -

r

1006/09/01 PPN LONG TERN PRCCUCI COST AEPHAT

NOSINESS A1900 vs. 1909

- Values are I, 20L1065

ENTITI1010 TERN

PROS XC I

COST

Lold is presented in chapter £18 figure E18.F1 and column £18 B.

Although Lo7d appears as CAPACITY UTILIZATION OLO PRICE VARIANCE in the

Productivity Component Old and Mew Report presented in chapter E18, COSTcut is

in September 1988 not reported as CAPACITY UTILIZATION TERM IN PRODUCT COST

VARIANCE in any report of any software implementation. It is shown above as

the link between long term product cost variance and short term term product

cost variance.

Column E13 I


Lnew is presented in chapter £9 figure E9.F3 and column

E Column E13 H -

CAPACITY UTILIZATION TERM IN RESOURCE PRICE VARIANCE

Zcut m Ziong — Zshort

= —Lrep

= (Qnp —Qne j*( Po — Rn]

600,0 — 600,0 3 * [ 20,0 — 22,0] $ 0,0 for cost resource

12,0 — 8,0] * [ 250,0 — 350,0] = $400,O- for capital resource

$400,O- for Total Resources

This variance is in September 1988 not shown in any report of any software

implementation. It is shown above as the link between long term resource

price variance and short term resource price variance.

£13 — 5 -

FANC 11090

Column E14 A

COOTiveg I've flung 07lsng

LONG TERN PRODUCT COST VARIANCE

COST/ong is presented in chapter £13 figure E13.F1 and column £13 C.

Column E14 B


Ynew is presented in chapter £9 figure E9.F1 and column £9 D.

£14 — I

Column EM D Column E14 E

PERCENTAGE CHANGEPRODUCTIVITYIN NEW PRICESA7new

IN PERCENTAGE CHANGE INLONG TERNRESOURCE PRICEA7long

Po Pn Pnr Po Pn Pnr

A?new a A/B a -C /0A = Ynew C = Ziong

mTQnp_QnJ* Pn aqnp*[Po —PnJ

B = VALUEnew

mqn*Pn

0 = VALUEo7d

eQnp*Po

+ VOLold+ Yold

Column E14 D

PERCENTAGE CHANGE IN PRODUCTIVITY IN NEW PRICES

AVnew is presented in chapter E1O figure E1O.Fl and column ElO 0.

Column E14 E

PERCENTAGE CHANGE IN LONG TERM RESOURCE PRICE

Lt7long a — Ziong / [VALUEoId + VOLold + Yold ]

— 51200,0— / [58000,0 + 53400,0 + $ 600,0] = 10,0000% for cost

— $1200,0— / [5 2000,0 + $ 500,0 + $ 500,0] = 40,0000% for capital

— $2400,0— / [510000,0 + 53900,0 + 51100,0] = 16,0000% for Total

Attention is drawn to the footnote at the bottom of the final page

chapter E15. It/relates to IQiong.

umn E15 A

SHORT TERM PRODUCT COST VARIANCE

Tshort is presented in chapter E13 figure E13.F2 and column E13 F.

olumn ElS B


is presented in chapter E9 figure E9.F2 and column E9 0.

olumn E15 C

SHORT TERN RESOURCE PRICE VARIANCE

'short is presented in chapter E13 figure E13.F2 and column E13 H.

Figure E14.F1 - CHANGE IN PERFORMANCE INDEX NUMBERSIN CHAPTER E14

E1S EXAMPLE OF SHORT TERN PRODUCT COST REPORT

This chapter presents the axioms which define the Short Term Product CostReport and an example.

The purpose of the report is to show variances and percentage inshort term cost change.

PPM sHmT TERN CasT PERFOSVGAAICE REP%T

NOsINEss A5968 vs.

are lv ScuMs

ENTITYsVmT TERM

PR HAG C T

COST

58681 TERMEFFICIENCY REIeIRCE PRICE

VARIANCE VARIANCE

EFFICIENCY PRICEVARIANCE 44ARIANCE% CHANGE CHANGE

I 549.000— 660.000 1100.001— 5.2630

62 SHOES 540.000— 660.000 1200.OOO— .2631

1500.000— 700.000— 800.000— 10.0000— - 4P.OOOO

1500.000 10.0000 fl??.

FUNCTIONS COSTslisrE E,ew Eshurt Atvew

E14 — 2 ElS — 1

Column E15 D Column E15 E

PERCENTAGE CHANGE

EFFICIENCYIN NEW PRICES

IN PERCENTAGE CHANGE INSHORT TERMRESOURCE PRICEts2short

Po Pn Pnr Po Pn Pnr

a!new a A/B A7short a — C/U

A = Enew C = Zshort

a/Qne_Qnj* Pn aqne*(Po —Pn]

B = VALUEnew 0 = VALUEo!d + VOLold

eQn*Pn aqne*Po+ Eold

Column E15 0

PERCENTAGE CHANGE IN EFFICIENCY IN NEW PRICES

Isrnew is presented in chapter Eli figure Eil.Fl and column Eli D.

Column E15 E

PERCENTAGE CHANGE IN SHORT TERN RESOURCE PRICE

â7short a — Zshort / (VALUE07d + VOLold + Eold .1

— $1200,O— / [$ 8000,0 + $3400,O + $ 600,0] = 10,0000% for cost

{$ 2000,0 + $ 500,O + $ 500,0—] = 40,0000% for capit..

{$i0000,0 + $3900,0 + $ 100,0 ] = 14,2857% for Total

— $ 800,0— /

— $2000,0— /


Chapter E16 EXAMPLE OF PRODuCTIVITY OLD AND NEW VARIANCE

This chapter presents the axioms which define the Productivity Old qggl NewVariance Report and an example. The purpose of this report is to diEomposeproductivity variances in new prices into an old price component- arepricing component, and to provide corresponding percentage changes.

PPM PROUUCII VIII OLD & REV VARIANCE IEPCRT

905INESD A1908 us. 1989

Values are I, DOLLARS

ENTITY REV PRICEVARIANCE

::::::: ::__:OLD PRICE REPRICING REV PRICE

- PRICEVARIANCE VARIANCE 0 CHARGE - S CHANCE

I

- I

N60.101 601.011 60.008 5.1631 9.2632660.008

700.800

600.008

500.000

60.000

200.000

5.2632

20.0000

--: 0.2632I

20.0000NL CAPITAL RESOURCES

I 700.080 500.000 200.000 20.0000 '20.0000

FORE 2 IONS AsiA Vrep AVuew . A7s1d

Ftgure E16.F1 - PRODUCTIVITY VARIANCES IN CHAPTER E16

Column Ei6 A Column E16 B Column E16 C

PRD0UCTIVITY PRODUCTIVITY PRODUCTIVITYVARIANCE VARIANCE VARIANCEIN NEW PRICES IN OLD PRICES REPRICING TERM

FOOTNOTE Column E4 F

[For each resource

For Total Resources isPold(I)

E15 — 2

Column E14 E Column E15 E

a bjlong a b2short -:

a L2long(I) > = c ts7short(I)

Po Pn Pnr Po Pn Pnr

A=Ynew B=Yold

a[Qnp—Qn]*pn a[Qnp—Qn]*po

C = Yrep

a (Qnp — QnJ*(Pn — PoJ

E16 — 1

Column E16 A


Ynew is presented in chapter E9 figure E9.F1 and column E9 D.

Column E16 B

PRODUCTIVITY VARIANCE IN OLD PRICES

Yold a (Qnp — QnJ * P0

[600,0 — 570] * 20,0

12,0 — 10] * 250,0

Column E16 C

PRODUCTIVITY VARIANCE REPRICING TERM

Yrep a [Qnp — QnJ * I Pn — Po J

[600,0—570] * [ 22,0 — 20,0] = $60,000 for cost resource

12,0 — 101 * [300,0 — 250,0] = $200,000 for capital resource


E16 U

PERCENTAGE CHiINGE IN PRODUCTIVITY

AYnew is presented in chapter ElO in

umn E16

PERCENTAGE CHANGE

old a Yold

$ 600

$ 500

$1100

/ [V/1LUEo1d + VOLUMEoJd]

/ [$ 8000 + $3400

/ [$2000 +$500

/ [$10000 + $3900

Column E14 D Column E14 El

a

> = < AYold(I)

E16 — 3


= $ 600,000 for cost resource

= $ 500,000 for capital resource


Column E16 D

PERCENTAGE CHANGEPRODUCTIVITYIn NEW PRICES

IN

Column E16 E

PERCENTAGE CHANGE INPRODUCTIVITYIN OLD PRICES

Qnp

Qne A

Qnp

Qn

Qne C

Qo B

Qn

Qo D

Po Pn

AVnew a A / B

Po Pn Pnr

A=)'new

. AVoid a C / D

a [Qnp — QnJ * Pn

C=Yold

B VALUEnew

a (Qnp — QnJ * Po

aQn*PnD = VALUEo/d + VOLoJd

E

IN NEW PRICES

figure E10.F1 and column ElO 0.

IN PRODUCTIVITY IN OLD PRICES

= 5,2632% for cost

= 20,0000% for capitai

= 7,9137% for Total

E16 — 2

For each resource

For Total Resources

Chapter E17

This chapter presents the axioms which define the Productivity Component

Variance Report and an example. The purpose of this report is to decompose

productivity variances in new prices into contributions from capacityutilization variance in new prices and efficiency variance in new prices, and

to provide corresponding percentage changes.

ENTITY

PPCGOUCTIVIU CAPACITY OTILIZAOION EYIICIENCY CAPACITY

NEW NEW PRICE NEW PRICO UTILIZATION

VARIANCE YAeIANCE VAVIANCE S CHANGE

I

A I + C 0 1

CosT eEsoJeCEs:MateriAl a - 650.000 660.000 5.2632

TeTA. APEP.AIING EXPENSEs o&o.onn 600.003

CAPITAL REsOURCES:Equipment a 100.000 1400.000 100.000— 00.0000 20.0000-

110161 CAPiTAL eEsIoIecEs lnn.eno 1400.000 100.000- 50.0000

ITOIAL stoweCEs 1360.000 1400.000 40.000— 6.7500

Figure E17.FI - PRODUCTIVITY VARIANCES IN CHAPTER E17

Eli — 1E17 — 2

EXAMPLE OF PRODUCTIVITY COMPONENT VARIANCE REPORT

1980/09101 PPM PRONOCTI VITO VARIANCE REPONT

ROSINESS A1906 vs. 1909

Values are in 0011805

Column E17 A


Ynew is presented in chapter E9 figure E9.F1 and column E9 D.

Column E17 B


Lnew is presented in chapter E9 figure E9.F3 and column E9 I.

Column E17 C


Enew is presented in chapter E9 figure E9.F2 column E9 C.

Column Eli A Column Eli B Column Eli C

PRODUCTIVITY CAP UTILIZTN EFFICIENCY

VARIANCE VARIANCE VARIANCE

IN NEW PRICES IN NEW PRICES IN NEW PRICESYnew=A Lnew=B Enew=C

Po Pn Pnr

A=Ynew

a (Qnp—QnJ*Pn

Po Pn Pnr

B=Lnew

a (Qnp—QneJ *Pn

C = Enew

a (Qne — QnJ *

FPN PRmIUCTIVIIV CeIPO4ENT OLD & NEW REPORT

BUSINESS A1988 as. 1989

Values are In IOLLAWI

CAPACITY UTILIZATION —:EFFICIENCYENTITY NEW PUICE OLD PRICE REPRICING NEW PRICE OLD POUCE OEPVICING

YARIUNCE VARIANCE VURIARCE VARIANCE VARIANCE VARIARCE

B + C U

Figure E18.Fl - CAPACITY UTILIZATION VARIANCES IN CHAPTER E18

Column El8 A Column EI8 B Column E18 C

CAP UTILZATION CAP UTILZATION CAP UTILZATIONVARIANCE VARIANCE VARIANCEIN NEW PRICES IN OLD PRICES REPRICING TERMLnmw=A Lold=B Lrep=C

E18 — I


Chapter Ei8 EXAMPLE OF PRODUCTIVITY COMPONENT OLD AND NEW

Qnp

Qne

Qn

Qo

This chapter presents the axioms which define the Productivity Oldand New Report and an example. The purpose of this report is tobeth capacity utilization and efficiency variances in new prices oldprice component and a repricing component.

Column E17 D

PERCENTAGE CHANGE INCAPACITY UTILIZATIONIN NEW PRICESttnew

Column E17 E

PERCENTAGE CHANGE INEFFICIENCYIN NEW PRICESATnew

Po Pn Pnr

Atnew e A/BA=Lnew

efl7np—QneJ*Pn

B = VALUEnew + Enew

eQne*Pn

Po Pn Pnr

ATold C/DC=Enew

s[Qne—QnJ*Pn

0 = VALUEnew

eqn*Pn

A

:0

- E + F'

FVNCTIUNS

601.01 600.00 : 61.10

661.11 610.11 60.11

1411.11 1000.00 400.01 711.11— - 516.11— —

1411.11 1111.19 401.11 760.00— 500.00—--- 1400:00 400:00 100.00

Lnew bid brep Enew Eoid Erep

Column E17 D

PERCENTAGE CHANGE IN CAPACITY UTILIZATION IN NEW PRICES

Atnew a Lnew / (VALUEnew + Enew j$ 0 / [$12540,O + $660,O = 0 for cost resource

$1400,O / [$ 3500,0 + $700,O—] = 50,0000% for capital resource

$1400,O / [$16040,O + $ 40,0—] = 8,7500% for Total Resources

Column E17 E

PERCENTAGE CHANGE IN EFFICIENCY IN NEW PRICES

aTnew is presented in chapter Eli figure Eil.Fl and column Eli D.

FOOTNOTE Column E17

ATnew

0

a

NOT SHOWN

AEold

Column E17

L?new

E

eFor each resource

For Total Resources Ainew(I) > = c ATold(I) A?new(I) > =

NOT

ATold

< Is?old(I)

A = Lnew

(Qnp — Qne] * Pn

Eli — 3

Po Pn Pnr Po Pn Pnr

B = LoIS

(Qnp — Qne] * Po

C = Lrep

(Qnp — Qne]*(Pn —

Column E18 B

CAPACITY UTILIZATION VARIANCE IN OLD PRICES

Lold a (Qnp — QneJ * P0

[600,0 — 600] * 20,0

12,0 — 8] * 250,0

Column E18 C

CAPACITY UTILIZATION VARIANCE REPRICING TERM

Lrep a (Qnp — QneJ * I Pn — Pa I

[600,0 — 600,0] * [ 22,0 — 20,0] = $0 for cost resource

12,0 — 8,0] * [300,0 — 250,0] = $400,000 for capital resource

$400,000 for Total ResourcesColumn E18 D

EFFICIENCY ViRIANCE IN NEW PRICES

Enew is presented in chapter E9 figure E9.F2 and column E9 G.

EFFICIENCY IN OLD PRICES

a [Qne — Qn] *Po

[600,0 -. 570,0] * 20,0

8,0 •- 10,0] * 250,0

Iolumn E18 F

EFFICIENCY VARIANCE REPRICING TERM

a [Qne — Qn 3 * [ — Pa 3

[600,0 — 570,0] * [ 22,0 — 20,0] = $ 60,000 for cost resource

1 8,0 — 10,0] * [350,0 — 250,0] = $200,000- for capital

$140,000- for Total

E18 — 3

Column E18 A


Lnew is presented in chapter E9 figure E9.F3 and column E9 I.

Figure E18.F2 - EFFICIENCY VARIANCES IN CHAPTER FiB

= $0= $1000,000

$ 1000,000

Column E18 D Column E18 E Column E18 F

EFFICIENCY EFFICIENCY EFFICIENCYVARIANCE VARIANCE VARIANCEIN NEW PRICES IN OLD PRICES REPRICING TERMEnew = A Eold = B Erep C

for cost resource


for Total Resources

Pa Pn Pnr Po Pn Pnr

A=Enew B=Eold

a [Qne — Qn] * Pn a [Qne — Qn] * Po

C = Erep

a [Qne — Qn]*[Pn — Po]

Eo id

= $600,000 for cost resource

= $500,000- for capital resource


E18 — 2

PART F - RESOURCE VARIABILITY (REVA)

This distinction is essential because long term control analysis employsproductivity measures which assume full resource variability. it isnecessary to recognize the existence of a step function that''ntity to product quantity. REV/i is used to introduce the step function

productivity analysis and to uncover the variable component of. resourceto productivity change.

REV/i is defined as a real number. It can therefore assume zero orositive. values shown below. The following figure also shows that REVA isble to assume any sign regardless of the sign of change in

to a restriction when = 0 which is presented in F1.F3through F1.F5 below.

Figure F1.FI - REV/i AND

Fl — 1

This part of the book presents the following chapter.

Chapter Fl VARIOUS CASES OF REVA

As discussed in part B of the book, REV/i (REsource VAriability ratio) is a

specified dimensionless quantity which is used to specify Qne is inturn used to decompose change in productivity into the from-change in capacity utilization and change in efficiency. The of thelatter breakdown is to separate short term from long term control

+VE +— -i-0 ++

REVA ZERO 0— 00 0+

—yE —— —O —+

—yE ZERO +VE

ld(U)CHANGE IN PRODUCTION

Figure F1.F2 - SUMMARY OF REVA VALUES

— [35—251/25

[6 — 8]/8

0,4

0,25—

1,6—

CASE I

RESOURCE QTY > 0PRODUCT QTY < •0REVA <0

@1

10

8

6

15 25 35Q

REVA =

__________

LY/Y

— [35—251/25

- [8 - 8J/ 8

Qu

10 . NEW

/8 .

6

15 35

Q

RE VA =lxY /

—

[10— 811 8

0,4

0,25

= 1,6

CASE 3

% CH RESOURCE QTY% CH PRODUCT QTY

REVA

Negative

SIGN OF CHANGE IN PRODUCTION

Zero Positive

SIGNCHANGE

INQne

Positive

Zero

Negative

Figure F1.F3 - 3 REVA STEP FUNCTIONS UNDER INCREASING RESOURCE USAGE

Quo = 8 Qun = 6

Qo = 25 Qne = 35

CASE 1

Quo = 8 Qun = 8

Qo = 25 Qne = 35

CASE 2

Quo = 8 Qun = 10Qo = 25 Qne = 35

CASE 3

Quo = 8 Qun = 6

Qo = 25 Qne = 25

CASE 4

Quo = 8 Qun = 8

Qo = 25 Qne = 25

CASE 5

Quo = 8 Qun = 10Qo = 25 Qne = 25

CASE 6

Quo = 8 Qun = 6

Qo = 25 Qne = 15

CASE 7

Quo = 8 Qun = B

Qo = 25 Qne = 15

CASE 8

Quo = 8 Qun = 10Qo = 25 Qne 15

CASE 9

Qu

10

8 OLD

\\

6 NEW

15 25 35Q

REVA= —/ Y

OLD—NEW

% CH% CH

0,4

0

= NOT DEFINED

CASE 2

% CH RESOURCE QTY > 0% CH PRODUCT QTY = 0

REVA = NOT DEFINED

The above figure summarizes the product and resource quantity data for 9

cases of the step function which REVA seeks to address. The step functionsare developed in figures F1.F3 through F1.F5 below.

Fl — 2

In all 3 step functions resource usage is targeted to growdeclining, constant or increasing production.

Case 2 revealsdefined wheneverproduction. Thebook.

the flaw in the current specification since REVA notcapacity is increased under conditions ofspecification will be revised in the next edition the

Fl — 3

25

Q

AX/XREVA

/ V

In all 3 step functions resource usage is targeted to stay constant despite

declining, constant or increasing production.

Case 5 reveals the flaw in the current specification since REVA is

defined whenever capacity stays constant under conditions of constant

production. The specification will be revised in the next edition of the

book.

Fl — 4

In all 3 step functions resource usage is targeted to declineining, constant or increasing production.

8 reveals the flaw in the current specification since REVA notrifled whenever capacity is reduced under conditions of constant

specification will be revised in the next edition of the book.

Fl — 5

Figure F1.F4 - 3 REVA STEP FUNCTIONS UNDER CONSTANT RESOURCE USAGE

Qu Qu

10 . .. 10

8

6

Qu

10

OLD

NEW

Figure F1.F5 - 3 REVA STEP FUNCTIONS UNDER DECLINING

Qu

10

15

RESOURCE USAGE

8 OLD

//

NEW6

8 . OLD=NEW

6

35 15 25

Q

AX/XREVA =

AY / V

— [25 — 251/25

[8-. 81/80

0

NOT DEFINED

CASE 5

% CU RESOURCE QTY = 0% CH PRODUCT QTY = 0

REVA = NOT DEFINED

25 35Q

NEW

8 . OLD

6

15 25 35

Q

M/XREVA =

AY / V

[25—25]/25

- [10— 8J/ 8

0

0,25

=0CASE 6

% CU RESOURCE QTY = 0% CH PRODUCT QTY > 0

REVA =0

— [25—25]/25

— [6 — 81/8

0

0,25—

= 0

CASE 4

% CH RESOURCE QTY = 0% CU PRODUCT QTY < 0

REVA =0

Qu

10

8 NEW—OLD

6

15 25 35Q

AX/XREVA =

__________

LIV/Y

— [15—251/25

- [8 - 8]/ 8

0,4—

0

= NOT DEFINED

CASE 8

% CH RESOURCE QTY < 0% Cl-I PRODUCT QTY = 0

REVA = NOT DEFINED

15

REVA -—/ V

— [15—25]/25

[6 — 8

0,4—

0,25—

= 1,6

CASE 7

CU RESOURCE QTY < 0CH PRODUCT QTY < 0

REVA >0

Qu

10 NEW

\ \-8 . OLD

6

15

REVA =

_______

—

[10- 8)73

0,4—

— 0,25

= 1,6—

CASE 9

% CU RESOURCE QTY 0% CH PRODUCT QTY 0

REVA

PART G — PROXY DATA


Chapter GI PROXY PRICES AND QUANTITIES WHEN NONE ARE AVAILABLE

Chapter G2 SCORING MATRICES FOR PROXY PRODUCT QUANTITY

Chapter Gl PROXY PRICES AND QUANTITIES WHEN. NONE ARE

Proxy prices for product and resources

The value axiom is the fundamental identity on which this work rests, Sincevalue is defined as the product of quantity and pricw, it is simplyto find two of the three functions and the model will derive thirdfunction. Although the data to populate the model exist, they are ofteninaccessible on grounds of cost of capture.

Readers would then be advised to use the value data, which areavailable, and to resort to price proxies for product and variabledata and to quantity proxies for fixed resources. Public priceproxies are provided by the price series published by government

a monthly basis. Use of published statistical wouldrequire the reader to assign individual series to specific product ähd costentities. Fixed capital proxies are normally easy to make if one a

a base period and then enquires from mapgementwhat is the relative capacity in a later period.

Proxy product quantities

If the accounting system allocates resources but not products to givencost center, it is necessary to define "proxy products" formeasurement and control. A familiar illustration is the shared resot*Ie caseof common costs categories. For example, corporate resources which fle notattributed to the individual businesses which carry their own costswould fall into this category.

When an operation contains no specified product, the model requires that theuser indicate which, of the set of operations that do have productsmust be used for proxy products in that particular operation.

Scalars for proxy product and resource quantities

Another need for oroxy data involving the use of scalars arises inapplications which compare operations in which technologies, aredissimilar in process or in order of scale, make identical Forexample, an electrical engineer enrolled for an MSc degree usingdeterministic productivity accounting to compare two different powertechnologies which make a homogeneous electricity of the same persecond. Similar research is being conducted by a mining engineer; alsoenrolled for an MSc degree, to compare two different mining technologii4 whichmake identical product. A simpler need for scalars arises incomparisons to avoid the analysis being swamped by a spuriousutilization effect caused by a spurious REVA.

G1 — I

This chapter provides elementary example of a scoring matrix application to

specify a proxy product quantity for an operation where none is available.This is a specialized application for creating a proxy product quantity.

The product quantity "Q" is readily defined in the accounting systems of theprivate sector since it is used to determine selling prices for goods and

services produced (with respect to final product) and for controlling the

costs of production per unit of production (with respect to both intermediate

and final product). By contrast, the product quantity "Q" is not so readilydefined in accounting systems of either the teaching and research sectors or

of the informatics sectors of the economy since it is not systematically used

for pricing and production control. —

Scoring matrices generally provide performance measurement based on multiple

criteria. Scoring matrices can be developed in such a way that they become

highly participative instruments which enhance communication within the

organization whilst being eminently suitable for those activities for which

outputs, or product quantities, are not readily defined, e.g. white collarworkers, maintenance and other service functions.

Various techniques for obtaining co—operation and participation exist.Nominal Group Technique (NGT) is one of these, and it possesses the additionaladvantage of being a prolific idea generator.

In essence the implementation of scoring matrices requires:—

• The setting of criteria against which participants will be measured.

• The consolidation of these criteria into (say) 6 to 8 criteria per

matrix. In this process an experienced facilitator is a great asset. The

objective would be to cover as wide a range of criteria as possible, withthe participation and acquiescence of the staff whose performance is to

be measured.

• The allocation of weights to each criterion by the next level of

management in accordance with their perception of the importance of each

of the criteria to the furtherance of the objectives and strategic goals

of the organization.

These criteria create an awareness at management level of how staff members

see their own functions in the organization. The specification of weights

similarly conveys to these staff members the relative importance management

attaches to each of these tasks.

Care must be taken during this stage that the criteria are expressed in

physically measurable output quantities.

Another important step in the process is to identify levels for excellent,

standard and mediocre (or unacceptable) performance for each critorion. Scoresare applied as 10 for excellent, 3 for standard (or present level) and 0 for

unacceptable (or mediocre) performance with intermediate scores interpolated

between these. The interpolated scores are often linear but need not

necessarily be so.

In our simple example student results are represented by three criteriashowing the number of students who are required to pass the final year, the

second year and the first year during the first and second semesters.

G3 — 1

OBJECTIVES and AlLOCATED SCORESMEASURED SCORE

ATRAIHED

4

2

ALLOCATED WEIGHTED

SCORE

100

40

Final year passes

Sec,,d year passes

—10

30A

404

—9

292

374

—H

264

349

—7

246

322

—6

228

296

—5

210

270

—4

192a

244

—3

174

218

—2

156

IH2a

—I

13W

166

—0

128

14W

tIITPUT

287

194

First year passes 550 513 476 439 402 365 328 291 254 217* 184 232 1 15

PaRes published 160 144 126 lID 96 86 64 48a 32 16 H 49 3 8 24

Assrs censuitatiss 247 220 196 178 114 132* 11W 66 66 44 22 137 5 0 HO

Lubsratsry Hears 300 276 252 220 204 180 156 132a 108 84 HH 135 3 45

PubliccentacE, 55 00 45 40 35 30 25 20 15 10 Ha H 0 9 •

Tetal eeigete4 284

The criteria for the lecturers performance are identified as the pumber ofpages published in prescribed journals, hours used to councel studafls, hoursspent in the laboratories and the number of public relation contactj.

The actual measured output quantities are then compared to thi agreededperformance scales and the appropri4te scores are determined. arethen multiplied by the allocated weights to obtained the weighted sflres whichare then added together to give the total weighted score for each

Finalyearpannen

OBJECTIVES and ALLOCATED SCCAES— — — — — — — — — — — HEASUHEO

EtITFUT

220

SCORE

ATTAINED

5

WIGHTWEIGHTED

SCORE

US

16

300

9

U?

6

U4

7

246

6

228

5

flDa

4 3

lU

2

166

1

138

H

120

Secnnd year passe,

First year passe,

Page, published

Huur,c,n,ulEaEi,e

Laberatery Hears

Public cuntactn

420

594

160

242

300

55

374

513

144

220

276

DV

348

476

128

198

152

45

322

439

212

176

216

40

'296

402

96

154

1V4

35

270

385

80

132

186

30

244

329*

64

110*

166*

25

218

291

48*

88

132

20

192

254

32

66

108

IS

166*

217

16

64

84

IHa

140

IWO

0

20

6W

5

175

329

50

111

162

12

1

4

3

4

4

1

uA

Al

5

22

60

24

48

HO

5

A comparison of the total weighted scores show that there has a 20.4%Improvement in the second semester compared to the first semester in output.To obtain a productivity analysis this change in output must now comparedto the resources consumed in the first and second semesters. The productquantity is obtained from the output matrix, (i.e. Qo = 284 and = 342).There is no product value and we therefore take the total value of theresources and use this as a proxy product value, where we have the costof the capital resourcos and not their asset values. This a

total cost recovery since the total value of production is equal the totalcost of the resources.

Chapter G3 SCORING MATRICES FOR PROXY PRODUCT QUANTITY Figure 63.F1 FIHST SEHESTE6

Figure 03.F2 SECOND SEHESOEH

lutal weighte4icere 342

L

G3 — 2

4

PART H — TRADEOFF ANALYSIS


Chapter HI TRADITIONAL PRODUCTIVITY INDEX NUMBERS AND WORKAPPROACHES

Chapter H2 TRADITIONAL INFLATION ACCOUNTING APPROACH

Chapter H3 TRADITIONAL STANDARD COST ACCOUNTING APPROACH ANIiEXPENSE TO REVENUE RATIO APPROACH

Chapter H4 DETERMINISTIC PRODUCTIVITY ACCOUNTING APPROACH

Chapter H5 COMPARISON OF TRADITIONAL STANDARD COSTING ANDPRODUCTIVITY ACCOUNTING APPROACHES

Chapter Hi TRADITIONAL PRODUCTIVITY INDEX NUMBERS AND WONK STUDYAPPROACHES

This chapter reviews the limitations of traditional productivity indexnumbers and work study approaches with regard to tradeoff analysH Tradeoffanalysis is needed to ascertain whether or not substitution of o*e resource

• (or group of resources) for another resource (or group of reflurces) isbeneficial.

Systematic tradeoff appraises the direction of the tradeoff as Wi11 as thesign of the traeoff. Tradeoff direction indicates whethof resource

• substitutions are directionally proper, and tradeoff sign whetherresources substitutions increased or reduced profits. Chapter a

tradeoff matrix to illustrate how tradeoff sign and tradeoffsign areassessed.

Change in traditional productivity index numbers, which we have asAVold(I), give a signal on the direction of productivity However,they give neither a bottom line impact needed to determine the trjdeoff signnor any insight into tradeoff direction.

Traditional work study measures suffer from identical weaknessek. and arefurther handicapped by the fact they typically focus on labor to exclusionef other resources.

Hi — I

The weaknesses of inflation accounting are cited below:—

• The productivity variance is measured in old prices and contains no

repricing term;

• It offers no breakdown of productivity variance into capacity utilizationvariance and efficiency variance;

• It offers no resource breakdown of its productivity variance;

• The productivity variance is contaminated by the deflator which is

spurious because it is applied to both new revenue and new cost and

thereby creates a zero price recovery variance;

• It offers no resource breakdown of its "inflation" variance; and

i The "inflation" varianco suppresses the price recovery term which is

set at zero.

The above weaknesses are to some degree visible in the inflation accountingvariance analysis of Business B given in in figure H2.F1 below.

ENTITY

REHENOE

OLD OLD OLD

RALOE QOANTITT PRICENEN NEW NEN

OALOE QUANTITY PRICE QUANTITY PRICE

S UnIts 9/1JnIE

11001 III III

$ OnlEs 8/OnIE

10010 150 Ill

S S

50,000 00,000

RESOURCE (VARIABLE) 8000 400 DO 10540 570 00 40,100 10,000

RESOURCE (FISED)

TOTAL RESOURCE COST

PRom

DIII 8 210

10000

3100 II 350

10048

01,000 41.101

0 1908

50083008

1908P 1100 P

I

500—I

J 1140-3400—

LUND TERNPROUOCT = HOLUNE 4-. PRICE

PROFIT VARIANCE VARIANCE VARIANCE

LORO TERNTRADEOFF DIRECTIOU NOT KORAN AS INFLATICNI ACCOUNTINO OFFERS NEITHER A PROUUCTIHITT

VARIANCE PER RESOURCE NOR AN EFFICIENCY RARIANCE PER RESOURCEN4ICN ARE ESSENTIAL TO ASSESS LORD TERN TRASEOFF BIAECTIOUAND SHOUT TERN TRAOEOFF DIRECTION RESPECTIAELY

LOUD TERNTRADEOFF SOON FAVORABLE AS THE NET HOLUNE RARIANCE FOR PNOUACT AND RESOURCE IS

POSITINE

LONG TERM PRODUCT PROFIT VARIANCE

$1960 — 0 = $1960

Chapter H? TRADITIONAL INFLATION ACCOUNTING APPROACH

This chapter reviews the limitations of traditional inflation accounting

approaches with regard to tradeoff analysis. This chapter conatins a page

which sets forth an inflation accounting variance analysis of Business B.

Inflation accounting typically applies a common deflator (i.e. price) to newrevenue and to new cost to create an inflation—adjusted new profit. The

difference between the inflation—adjusted new profit and the old profitconstitutes a productivity variance, while the difference between the nRW

profit and the inflation—adjusted new profit constitutes the "inflation"variance.

The strength of inflation accounting is that it recognizes that new profitcontains an inflation component which should be factored out to reveal real

new profit.

Figure H2.F1 INFLATION ACCOUNTING VARIANCE ANALYSIS OF BUSINESS B

VOLUME VARIANCE

Resource "A" [Qo — Qn] * Po = [400 — 570] * 20 = $3400—

Resource "B" = [8 — 10] * 250 = $500—

TOTAL $1100

Product Qun * [Pun

PRICE

— Puo] =

VARIANCE

150 * [120 — 100] = $3000

Resource "A" Qn * [P0 — Pn] = 570 * [20— 22] = $1140—

Resource "B" = 10 * [250 — 350] = $1000—

H2—Y H2—2

Chapter H3 TRADITIONAL STANDARD COST ACCOUNTING ANUEXPENSE TO REVENUE APPROACHES

This chapter reviews the limitations of traditional standard cost accountingand expense to revenue approaches with regard to tradeoff Thischapter conatins a page which sets forth a standard cost varianceanalysis of Business B.

Standard Cost Accounting

Standard costing employs proper deflators to create the vanances (seeFigure 1.39D). The strengths of standard costing are:--

• The deflators flow from internal prices which allow a dependablemeasurement of productivity and price recovery;

• The productivity variance is broken down into capacity utillntion andefficiency variances; and

• - The efficiency variance per resource is provided.

The weaknesses of standard costing are:—

• The efficiency variance is measured in old prices and norepricing term;

• The capacity utilization variance is measured in old prices containsno repricing term;

• The capacity utilization variances is measured for total and isnot accompanied by a breakdown showing the contribution per

• The "cost pass—through" variance is distorted because it is sum ofthe price :-ecovery variance and the productivity repricing valance; and

• The cost pass—through variance is measured for total resources and is notaccompanied by a breakdown showing the contribution per

Figure H2.F2 INFLATION ACCOUNTING PARTITION OF VARIANCES

QnpDI D2 D3

Product—lvi tyvariance

Qne -I- -Cl C2 C3

TOTALRESOURCES Infl ati on

ONLY

Qn +Bl B2 B3

Van ance

Qo +Al A2 A3

OLD TOTAL

value RESOURCES

Vo

Po Pn Pnr

This figure shows that inflation accounting does not provide the

contribution by resource to productivity variance in old prices and to the

inflation variance. Although it does provide the contribution by resource te

total resource volume variance and to total resource price variance, such

information is inadequate for tradeoff analysis.

H2—3 H3 — I

-4

Figure H3.F1 STANDARD COST ACCOUNTING VARIANCE ANALYSIS OF BUSINESS B

ENTITY

1988 ACTUAL 1989

OLD OLD OLD

VALUE QUANTITY PRICE

5 Units 1/Unit

HEN HEN


9 UniEs 5/UnIEQUANTITY PRICE

S S

REVENUE 10008 108 108 18008 ISO 100

570 DO

SD,RO0 10,000

48.50010,000RESOURCE 'U' (VARIABLE)

RESOURCE 'I' (FIXED)

TOTAL RESOURCE COST

OSOR 400 DR

0000 U DOD 3908 ID 3D0 09,000 40,000

10000 IUR4O

PRUFIT 8 1988

3000

600

BUD

500- Hen

1000-

1140-

—4— EFFICIENCY —4—PRICE

RARIANCE VARIANCE

SHOUT TERMTRADEOFF DIRECTION is FAVOURILE AS RESOURCE 'A' IS TARGETED 10 ACHIEVE A MOUE FAVOUABLE

EFFICIENCY RARIANCE THAN RESOURCE 'B' IN RESPONSE TO TUE FACTRESOURCE 'U' IS TARGETED TO ACHIEVE A LESS FAVOUABLE RESOURCE

PRICE VARIANCE TUAR 'RESOURCE B'

SHOUT TERNTRADEOFF SIGH Is FUROUABLE AS TOTAL RESOURCE EFFICIENCY VARIANCE IS POSITIVE

LONG TERM PRODUCT PROFIT VARIANCE$1960 — 0 = $1960

CAPACITY UTILIZATION VARIANCE in old prices

[$10000 — $8000] 100 * [150 — 100] = $10000

EFFICIENCY VARIANCE in old prices

Resource "A" [Qne — Qo] * Po = [600 — 570] * 20 = $600

Resource "B" = [8—10] *250= $500—

$100

Figure H3.F2 STANDARD COST ACCOUNTING PARTITION OF VARIANCES

Qnp

Qne

'5"

Qo

STANDARD COSTING

Po Pn Pnr

This figure shows that standard cost accounting does not provide thecontribution by resource to productivity variance in old prices to thecost passthrough variance. Although it does provide the contribflion by

resource to efficiency variance in old prices and to total resourcø: volumevariance and to total resource price variance, such information isfor comprehensive tradeoff analysis. Use of such inadequate data giVjjs riseto incorrect tradeoff analysis as shown in chapter H5.

Traditional Expense to Revenue Ratios

Change in traditional expense to revenue ratios give a signal on thecombined effect of productivity change and of price recovery changa. Thiscreates confusion. Furthermore, they give neither a bottom impactneeded to determine the tradeoff sign nor any insight into tradeoff direction.

Dl 02 D3

TOTAL CostRESOURCES pass—through

ONLY variance+Cl C2 C3

PER TOTALRESOURCE RESOURCES

ONLY

Bi B2 - B3

Al AZ - A3

OLDvalue

Vo

PRICE VARIANCE

Product Qun * [Pun — Puo] = 150 * [120— 100] = $3000

Resource "A" Qn * [P0 — Pn] = 570 * [20—22] = $1140—

Resource "B" = 10 * [250 — 350] = $1000—

$860

H3-2H3 —

-4

I3

Figure H4.Fl DETERMINISTIC PRODUCTIVITY ACCOUNTINGVARIANCE ANALYSIS OF BUSINESS B

E N I I I Y

1988 ACTUAL 1989 BUDGET PERCENT CVANOE

OLD OLD OLD


$ Units N/Unit

NEW MEW MEW


$ Units S/UnitQUANTITY PRICE

0 0

REVENUE 10000 IDO 100 18000 150 120 50,000 20,000

RESOURCE (VONIABLE)

RESOURCE 9 (FIlED)

IRTAL RESOURCE COST

8000 400 20

2000 8 050

12540 570 22

3500 10 350

42,500 10,000

25,000 40,000

10000 16040

PROFIT 0 1960

19601860

1400 14001200FAN I

660 800OTA Rs

I

0 — — — — 1i___I±i —

—

ON B B

FAR • 40

COO 600— 200— 200—

BLE 700- -

CAPACITYSHOUT TERM UTILIZATION TERN

LONG TERM CAPACITY PRICE FOR LONG IE60IRECOVERY —4-- PRICE RECOVERYPRORUCI = BTILIZAIIOM —4— EFFICIENCY —4—

PROFIT VOUIUNCE VARIANCE VARIANCE VARIANCE VARIANCE

SHOUT TERMTRADEOFF DIRECTION is UNFAVOUABLE AS RESOURCE B IS TARGETED TO ACHIEVE A LESS FANcITABLE EFFICIENCY

VARIANCE 116AM RESOURCE A DESPITE THE FACT RESOURCE B IS TURGETEDTO ACHIEVE A LESS FAVOUARLE SVOUT TERM PRICE RECOVERY VARIANCE 11600RESOURCE A

SHOUT TERMTRADEOFF SIGN Is OMFVVCOARLE AS TOTAL RESOURCE EFFICIENCY VARIANCE IS NEGATIVE

The specification of all the above variances is specified in part E ofbook. There is also discussion of the short term and long termanalysis using deterministic productivity accounting in chapter H5.

Figure H4.F2 DETERMINISTIC PRODUCTIVITY ACCOUNTINGPARTITION OF VARIANCES

17,ie

4PER

RESOURCE

8PER

RESOURCE

12PER

RESOURCE

çn

Qo

3

PER

RESOURCE

7PER

RESOURCE

11PER

RESOURCE

2

PER

RESOURCE

6

PERRESOURCE

10PER

RESOURCE

1

OLD

valueVo

5

PER

RESOURCE

9

PER

RESOURCE

This figure thatall the resource decompositionschapter A2.

'5.,,,

Po Pn Pnr

deterministic productivity accounting offersprescribed for an ideal measurement systom in

H4 — 2

I

H4 — I

k

Standard costing provides the following analysis. Scrutiny of onthe number line for resource price variance with respect to actual (jsage inthe new interval reveals that the cost resource makes the least t1avorablecontribution to resource price variance. It therefore appears on onthe resource price variance number line shown above. This position suggeststhat the cost resource should be targeted for the most favorable cohfributionto efftciency improvement which would place this resource on the righj on theefficiency variattce in old prices number line shown above. Suchmay be attended by a targeted efficiency loss from the capital resouEce whichmust less than offset the favorable contribution from the costGiven such signal, it is noted from the above matrix for short terqj analysisof the direction and sign of tradeoff that resources were in afavorable directon. Furthermore, the sum of the efficiency variances shows apositive (and hence favorable) tradeoff, because they are measured in oldprices rather than new prices. -

The above analysis is not dependable for short term analysis. It- flawed measure of efficiency variance with a flawed measure of resourcevariance. The efficiency variance is flawed because it is meaAijred in.J prices in lieu of new prices, while the resource price variance flawedbecause it applies resource price change to the new resource usage which cancontain an efficiency change component and hence distortion.

FIGURE W5.FI STANDARD COSTINGbOUT TERN ANALYSIS SFDIRECTIcN AND SIGN SF TUADEGFFRUING EFFICIENCY AND REIaJRCE PRICE VARIANCES

qep

Qow

Re

Qo

Chapter H5 COMPARISON OF TRADITIONAL STANDARD COSTING ANOPRODUCTIVITY ACCOUNTING APPROACHES

EFFICIENCU VARIANCE Is flawed becaosw It uses

Ps test,ad of Fe

ADJU5IEII RESOURCE PRICE VARIANCE Is flawed becasue YR uses

Qe Iestead of Roe

CAP UTILIZTII UIVARIANCEIN OLD PRICES(Rep—New] Fe

Dl 13

EFFICIENCY CIVARIANCEIN OLD PRICES(Qew-Qo I Fe

CD CI

63

A3

RESCARCE UIVGLUNE VARIANCE

(Re — Re] * Fe

AlRESEeRCERID VALUE

ADJUSTED Dl

PRODUCT

PRICE VARIANCEQuo (Fun — Fus)

AlRES000CEPRICE VARIANCEQe .a (Fe — Fe]

STANDARD EDITING SNOUT TERM TRADEGFF ANALYSISUSING EFFICIENCY VARIANCE IN VII PRICES P341 RESOURCE PRICE VARIANCE

COST RESeIRCE

Fe Fe Per

FIGURE NS.FD DETERMINISTIC AlT? ACCOUNTING

SAOUT TERN ANALYSIS OFDIRECTION AND SIGN OF TRADEOFFUSING EFFICIENCY AND RESOUACE PRICE VARIANCES

FIGARE AS.F3 DETERMINISTIC PR000CTIVITY ACCOUNTINGSNOUT TERN ANALYSIS OFDIUECIION AND SIGN OF IRAGCGFFUSING EFFICIENCY AND PRICE RECOVERY VARIANCES

CssE CapItalResource Resource$1140- $1000-

YEDOURCE PRICE VARIANCE NARUER LINESown

\ /UtaRsuaf patrtng mea,s short \ /,Own tradeoff dtrwctluse /to FAAARAULE / \

EFFICIENCY RARIANCE IN GIl PRICES NANRER LINE" "

Estd1500— SOlDEfflcteecy GradwoFf stge to psstttyw DUOS Cwptcel CesE(I.e. FAAOUAULE) Resource ResourceRep --

Quo

Re

Ye

RepDl

QewCl

SACNT TERNRESOURCE

PRICE

Re VARIANCE(UtOUNUALIOED AlFOU NEA PGRIOUPRODUCTION

AND OlD FERIOU

Rs EFFICIENCY)AS

Row w (Pu — P0)

Fe Fe

FIGURE AN.F4 DETERNINIGTIC PRODUCTIVITY ACCOUNTINGLONG TERN ANALYSIS OFDIRECTION AND SIGN OF 1RADEOFFUSING PRODUCTIVITY AND REGOURCE PRICE YOUIAACEG

Dl' Dl

Cl C3

EFFICIENCY VARIANCE

IN Nflt PRICES(Qew — Re] 5 Fe

Ut II

Al AD

OLD YALGE

SAOUT TERNPRICE

RECOVERY

VARIANCE(VeRNALIZED UT

FOU NEW PERIODPR005CTIONAND OLD PERIODEFFICIENCY)

AS

Roe o (Per — Fe)

NAYNIS ON TRADEOFF DIRECTIOU TRADEOFF SIGN

FAOOUARLE )F(

TRADEOFF NEUTRAL (NbUIRECY)OU

UNFAYOUAILE (tip

IN F

TRADEOFFSIGN

Fe Pc Pu

FIGURE R5.F6 OETERNINISTIC FROUUCTIOITA ACCOUNTINGLONG TERN ANALYSIS OFDIRECTION AND SIGN OF TRADEOFFUSING PRODUCTIVITY AND PRICE RECRAORY VARIANCES

Rep

Quo

Re

Re

Dl' Dl Dl

FROUUCTIAITA VARIANCE LONG TERN

IN NEA PRICES RESOUACE

4 PRICE

CI Cl VARIANCE CD

(NOUNUALIOED

(Rep — Qe] a Fe tOU NEW PERIODFROUSCTIENAND OIl FERIOU

UI ID FROUACIIAITA) Il

Rep a )Ps — Fe]

Al Al - Al

Fe Pope Fe

Rep

Qee

Ye

Ye

TERNPROUACTIVITY VARIANCEIN NEW FRICEG

4Cl

(Rep — To] a Fe

Ut

Cl

ID

PRICERECAYERY

VARIANCE Cl(NOUNALIOESFOU NEW PERIODPRODUCTION

AND RID PERIODFVODUCTIAIIT) Dl

Qep a (For — Fe]

AlOLD VALUE

Al A3

Fe F,

115 — 1 -,

Per

115 — 2

Pu20 22

Cost CapitalResource Resource$1200- $000-

Cohort

\ /

/\/ \

Esew

1700— 0660Capital CostResource Resource

Deterministic productivity accounting provides the following analysis.Scrutiny of positions on the number line for short term resource price

variance (with respect to usage in the new interval normalized for new

interval production and old interval efficiency) reveals that the cost

resource cakes the least favorable contribution to resource prfce variance. Ittherefore appears on the left on the short term resource price variance number

line shown above. This position suggests that the cost resource should be

targeted for the most favorable contribution to efficiency improvement which

would place this resource on the right on the efficiency variance in new

prices number line shown above. Such improvement may be attended by a targetedefficiency loss from the capital resource which must less than offset the

favorable contribution from the cost resource.

Given such signal, it is noted from the above matrix for short term analysisof the direction and sign of tradeoff that resources were substituted in a

favorable direction. Furthermore, the sum of the efficiency variances shows a

negative (and hence unfavorable) tradeoff, because they are measured in new

prices rather than old prices. It is noted that the above analysis coincides

with standard costing with respect to tradeoff direction but diverges from

standard costing with respect to the tradeoff sign.

The above analysis is the most dependable for short term analysis if the

absence of a product price necessitates recourse to resource price variance inlieu of price recovery variance. It contrasts a flawless measure of

efficiency variance with a flawless measure of resource price variance. The

efficiency variance is flawless because it is measured in new prices in lieu

of old prices, while the resource price variance is flawless because itapplies resource price change to the new resource usage normalized for new

interval production and old interval efficiency which is by definition free ofany efficiency distortion.

Resource Resource

SHRAT TERM PRICE RECOVERY AARIANCE POORER LINE$400- $1200

Rshurt FARmADLE (F)

Rertical pairing meansshort tern tredeof F directIon

, TRADEOFF

DIRECTItWiNEUTRAL (W$

is UMFARRAAWEE

DFFICItNCR VARIANCE IN NEW PRICES NUTIOER LINE

Efficiency tradeoff sign is negative 040(i e. UTTFAARAADLE)

$700-CapitalResoisrcn

1660CostResource

Esee

•

.ONFARtNARLE (U) 1 0

N F

-

TRADEOFF

Deterministic productivity accounting provides the following analysis.Scrutiny of positions on the number line for short term price recoveryvariance (with respect to usage in the new interval normalized for newinterval producdon and old interval efficiency) reveals that capitalresource makes the least favorable contribution to price recovery variance. Ittherefore appears on the left on the short term price recovery numberline shown above. This position suggests that the capital resource betargeted for the most favorable contribution to efficiency whichwould place this resource on the right on the efficiency in newprices number line shown above. Such improvement may be attended by a targetedefficiency loss from the cost resource which must less than oUset thefavorable contr)bution from the capital resource.

Given such signal, it is noted from the above matrix for short term analysisef the direction and sign of tradeoff that resources were substituted in anonfavorable direction. Furthermore, the sum of the efficiency variandO showsa negative (and hence unfavorable) tradeoff, because they are in new

- rather than old prices. It is noted that the abovestandard costing with respect to both the analysis of - resource

titution direction and the sign of the efficiency tradeoff.

The above analysis is the most dependable for short term analysis wj1ere theof a product price permits recourse to price recovery vanjmnce in

of resource price variance. It contrasts a flawless meflure ofciency variance with a flawless measure of price recovery varia4è. Theliciency variance is flawless because it is measured in new pricet--In lieuold prices, while the price recovery variance is flawless befluse it

plies price recovery change to •the new resource usage normalized for new.ul production and old interval efficiency which is by definitiq4-free of

v efficiency thstortion.

COST RESRARCE

DETERNINISTIC PRmUCTIRITT ACCmWTIAG SORAT TERN TRADEOFF AWALVEIRUSING EFFICIENCR RRRIANCE iN NEW PRICES RHO TERN RESRARCE PRICE R&VIANCE

EFFICIENCI Qne —I 600 —

CAPITAL RESRARCE

RARIANCE

is ) a Po70 3

a 2160

570 Qs

400 Re

SHRAT TERNRESRARCE

PRICERARIANCE

• (ADJUSTER -

FtR CONSTARTEFFSCRENCT)

RseoIPa —

WOAe(20 — 02]

$1200—

DETERNINISTIC PR000CTIRITT ACCmWT100 SHORT TERN TRADEOFF ANALYSISROING EFFICIENCY RARIARCE IN NEW PRICES OAR RHORT TERN PRICE RECORERY RARIANCE

COOT REStWJRCE CAPITAL RESOJRCE

Pu Pis

20 22

070 Qn

400 Ru

Ps200

EFFICOENCYRARIANCE SHORT TERMEQne—QnJsP, PRICE

WOO — 070 1 0 Dl RECORERO$660 RelIANCE

• (ADJUSTER -

Fm CONSTANTEFFICIENCY)

Qnea(Pnr —

600a(24 — 22] -

$1000

Ps Ps350 200

SRORT TERM RE506RCE PRICE VARIANCE WONDER LINE

Ria$osaT pairing meansshort tern tradeoff directionis FURtIRAILE

EFPICIERCT RAOIAWCE IN NEW PRICES NANRER LINE

Efficiency tradeoff sign is negatiee 140(I.e. UNFAVORAILE)

Pn

350

TWIRlS tNT TRADEOFF RIRECTION AND TRADEOFF SISN

/

'u Pn PerDO Dl 24

FARTRTARLE (F) S

TRASEOFF NEUTRAL (N)DIRCCTIIRT

ONFARORARLE (0)

ON F

IRADEOY F

SION

Pa Ps For250 350 - 300

Hb — 3H5 — 4

LUNG TERMRESOURCE

PRICERARIANCE(ADJUSTED -FUN CONSTANT

PROUUCTIRITT(

Deterministic productivity accounting provides the following analysis.Scrutiny of positions on the number line for long term resource price yariance(with respect to usage in the new interval normalized for new intervalproduction and old interval productivity) reveals that the cost resource and

capital resource coincide on the same point on the number line. This positionsuggests that either the cost resource and/or the capital resource should be

targeted for productivity improvement on the productivity variance in new

prices number line shown above. Such productivity improvement in eitherresource may be attended by a targeted productivity loss in the other resourcewhich must less than offset the favorable contribution from the firstresource.

Given such signal, it is noted from the above matrix for long term analysisof the direction and sign of tradeoff that resources were substituted in a

favorable direction. Furthermore, the sum of the productivity variances shows

a positive (and hence favorable) tradeoff because they are measured in new

prices rather than old prices. It is noted that the above analysis cannot be

compared with standard costing since standard costing offers neither of the

variances shown above.

The above analysis is the most dependable for long term analysis if theabsence of a product price necessitates recourse to resource price variance in

lieu of price recovery variance. It contrasts a flawless measure ofproductivity variance with a flawless measure of resource price variance. The

productivity variance is flawless because it is measured in new prices in lieuof old prices, while the resource price variance is flawless because itapplies resource price change to the new resource usage normalized for new

interval production and old interval productivity which is by definition freeof any productivity distortion.

Deterministic productivity accounting provides the following analysis.Scrutiny of positions on the number line for long term price recover1 vari?nce(with respect to usage in the new interval normalized for intervalproduction and old interval productivity) reveals that the capital resourcemakes the least favorable contribution to price recovery vart4nce. Ittherefore appears on the left on the long term price recovery numberline shown above. This position suggests that the. capital betargeted for the most favorable contribution to productivity improv ent whichwould place this resource on the right on the productivity in newprices number line shown above. Such improvement may be attended by targetedproductivity loss from the cost resource which must less than oSfset thefavorable contribution from the capital resource.

Given such signal, it is noted from the above matrix for long terra analysisof the direction and sign of tradeoff that resources were substituted in afavorable direction. Furthermore, the sum of the productivity varianães showsa positive (and hence favorable) tradeoff. They are measured in pricesrather than old prices. It is noted that the above analysis lannot becompared with standard costing because standard costing offers of thevariances shown above.

The above analysis is the most dependable for long term analysis theexistence of a product price permits recourse to price recovery inlieu of resource price variance. It contrasts a flawless ofproductivity variance with a flawless measure of price recovery varljpce. Theproductivity variance is flawless because it is measured in new pricfl in lieuof old prices, while the price recovery variance is flawless itapplies price recovery change to the new resource usage normalized. newinterval production and old interval productivity which is by definilion freeof any productivity distortion.

DETERMINISTIC PROUWCTI WIT? ACCOUNTING LONG TERM TRADEOPF ANALYSISRSING PROEOCIIVIIV VARIANCE IN MEW PRICES AND LUNG TERM RESOURCE PRICE VaRIANCE

CN$1 RESOURCE

PROUUCTI RITE

RONIANCE

(Qnp-tIaP,[ MOD — 57W 1 * 22

1660

600 gee

5lSWn

NeD i(o

W,pa(Po — P,,1

DETERMINISTIC PRONUCTIRITO ACCOUNTING LONG TERN TRADEWFF ANALTIISUSING PROURCTIRIOT RaDIANCE IN NEW PRICES AND LONG TEeN PRICE REC6RERT CARIANCE

CN$1 RESOURCECAPITAL RESOURCE

— 600'(lW — 22)

51200—

Po Po 7, Pc

2W 22 20 22

Coot and CapitalResourCe

51200—

LONG TERR WESOURCE PRICE VARIANCE WONDER LINE Ziong

Identical pairing mean,long Rena tradeoff directionI, NEUTRAL

PROUOCTIVITV VARIANCE IN NEA PRICES NUNRER LINE Inee1660 5700

ProduCtielty tradeoff sign iG po,itive 11365 Coot Capitol(i.e. FAUOUARLE( Resource Resource

PRmIUCIIRITT

RARIANCE

ERop-tIePo(12 — ID I ' 350

1700

UUO0n—. 12

PRXmCIIRITV LONG TERNPRICE

VARIANCE RECURERT

RARIANCENOD Rne . —)-- - (AUJORTED 0 Wee

(Rep — We J e Pc IOU CCNSTARTPROUUCTIAITV)

I dUO — 570 2 • 221660

SPORe - lOQe

gepalP,r — Pc]

WOOQe —

__________

. IQeUOOa( 24 — 22]

11200

Po Pc Per20 22 24

Capital CentRe,ource ResourcegROW— 51200—

LONG TERN PRICE RECOAERY AARIANCE NURSER LIRE Rlseg

pairing meano \ /long ten tradeoff direction /is FAVOUAOLE / \

PROEUCTIUITV VARIANCE IN OUR PRICES NUMBER LINE/

Veee1600 1700

Preductieity tradeoff sign io pesitiee 51360 Cost Capital(i.e. FAVOUASLE( Re,eurce Reseurce

LONG TERNtRICERECOVERYVARIANCE(ADJAUTED

CONSTANT

kPOCCACTIAITY

— Pn(

— 350]

- — gURU—

Pc? Per350 - 300

RWTRIA ON TRADEOFF DIRECTION AND TRADEOFF lIEN

FAVOUAOLE (F(

TRADEOFF REUTRAL (B] A

DIRECTIONURFAROUADLE (U)

UN F

TRADEOFF

SIGN

Pe

250

NUTRIA ON IRADEOFF MID TRADEOFF SIGR

- FAVOUARLE ifl1

TRADEOFF NEUTRALDIRECTION

_______

ANFARnERDLE

U N F

TRADEOFFSIGN

H5—5- -- H5—6

PART I — NET PRESENT VALUEFigure H5.F7 - TRADEOFF MATRIX CASES

TRADEOFF ADIRECTION

FavorableThis part of the book presents the following 2 chapters.Neutral \

Unfavorable — — —U Sum < 0

Chapter II DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSIONTRADEOFFTO NET PRESENT VALUE ANALYSISSIGN

BChapter 12 DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSION

TO BENEFIT TO COST RATIOSFavorableNeutral — —Unfavorable — -

u ii P Sum = 0Chapter Il DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSION TQC

NET PRESENT VALUE ANALYSIS

HipFavorable —

— This chapter is intended for the advanced reader who an

Neutral — —

— understanding of the deterministic productivity accounting extension the

Unfavorable0 < SumU N P

net presept value analysis which flows from the application of cashD Eflow techniques. Such extension is intended to decode measures of

Favorable value of discounted cash flows by making patent the underlying contt1butionsNeutral of productivity and price recovery which would otherwise remain TheUnfavorable 1H IL analysis.following text assumes the reader is conversant with orthodox c4jh flowUNF Sum<OSum<O

F GThe extension is developed through the following 8 steps with toFavorable Business B. For simplicity, it is assumed that the fixed capital

NeutralUnfavorable '[II - employed is non-depreciable and commands a residual value equal to bookvalue, and that taxes are disregarded.

Sum = 0UN FH I

DETERMINISTIC PRaISCIIAITS ACCOUNTING EXTENSICM TN QQTN0005 CASH FLOW ANALYSIS

Favorable STEP I — NOUMUL HWE OF DATA DISPLAY ANN DATA ENT1IY SHOWN FCN NOSINESS NI

NeutralUnfavorable I YaToes are Is DOLLARS. PrIces are dlsceunEed by UN

OcSumO<SumJ

YearNJ

Yearl Year2U N FINSES ENTITY VERA VALUE QUANTITY PRICE VALUE QUANTITY PRICE AALYE QUANTITY FVCE

J K

REVENUE:

Favorable UI Shirts hiISUAS INS IOU 1850U 150Neutral

_______

Unfavorable [H II 25460

NI Nat,rIal hI0000 400 20 12540 570

INTRINSIC PNAFIT2000

UNF Sum<OSum<OL N CAPITAL RESOURCES:

01 EqutpmenL hI 40000 8 SAlON 70000 10IFavorable

NeutralUnfavorable HJI

5uJicUNF Sum = 0N 0 Stepl

Favorable This step presents the standard form of input data which would beNeutralUnfavorable provides replacement cost of capital. Prices are disounted by 0% are

for analysis by the deterministic productivity accounting algorithm. 14 also

O < Sum D C Som left undiscounted).UNF

ci Ii — 1115—7

L

DETERMINISTIC PROSOCTIVITY ACCOUNTING EUTENSICNI 16 CAViOSOX CASH Flow ANALYSIS

STEP D — COURECTED NOSE OP DATA DISPLAY SHOW POU ROSINESS RI

Values are in DOLLAUD. Prices are discounted by IS

INDEX ENTITY

Tear 0 Year 1 Year 2

REVA VALUE QUARTITY PRICE VALUE QUARTITT PRICE VALUE QUANTITY PRICE

REVERIE:US Shirts bI

.

10000 100 III IR001 150 120

COST RESOURCES:

Ml Raterial bI 0000 401 20 12540 570 22

IIRTRSRSIC PROFIT 2110 5400

CAPITAL RESOURCES:Dl Equipment bI outlay

LESS Residual Value40000 N 5000 70000 II 7USD

40000 R S000 70000 10 7000

TOTAL CAPITOL RESOURCES 40000 30000 70000—

RETURN CR INOESTRERT (Oil

Step 2

This step modifies the data to recognize that fixed capital resources must

be provided prior to the commencement of production. It also providesresidual values of capital. Prices remain undiscounted.

DETERMINISTIC PROUHCTI VITO ACCOUNTING EXTENSIOS TO OSTHOSOU CASH PLON ARALYSIS

STEP 3 — COURECTCD NOSE OF DATA DISPLAY SHOW FOU ROSINESS RI

Values are In DOLLARS. Prices are discounted by 25%

INDEX ENTITY

Tear 0 Year I Tear 0

REVA VALUE QUORTITY PRICE AALOO QUANTITY PRICE VALUE QUANTITY PRICE

RERENUE:Ni Shirts hI WOO 100 NA 11020 150 76,0

COST RESOURCES:RI Raterial hI OAOX 600 SN 0A25,6 570 24,00

IINRVIN5IC PROFIT 2000 3RVR,4

CAPITAL RESOURCES:DI Equipment hi Outlay

LESS Residual Value40000 N SOVV 50000 10 5000

40000 N 5000 50000 10 5600

TOTAL CAPiTAL RESOURCES 40000 06000 50000—

I

Step 3

DETERRIVISTIC P0000CTiVITY ACCOUNTIRO EUTENSIOSTO OUTV0000 COON FLOU AVALYUIS

STEP 4 — COSRECTED NOSE OF DATA ENTRY SHOW POU ROSINESs RD (ai

Values are In DOLLARS. Prices are diocoonted by 250

VEVA VALUE QUANTITY PRICE VALUE QOARTITY PRICE I RALUE QUANTItY PUICE(

00 11020 250 760.!

MW 400 16 570 LAIR!

El Equipment hI Outlay40000 6 NOSY 56000 10

06000 -

I TOTAL CAPITAL REOCIJOCES:

:0:::6

OS IN RESIN

mi 00010050 RD ROSINESS N 67Th PRICED DISCOUNTED DV 25%

Step 4

I-f jJ t I

This step discounted prices (and their corresponding intothe years shown in step 1 to achieve the standard form of input data whichwould be supplied for analysis by the deterministic productivitya limitation in the 1988 rejgase ofdeterministic productivity accounting which specifies the value

a future release of deterministic productivity willspecify the value axiom as

VALUE = QUANTITY * PRICE * QUALITY * DISCOUNT * EXCHANGEFACTOR FACTOR RATE

Given the modifications to the input data in steps (1) through (4)a steps(5) through (8) illustrate the mechanics of the deterministicaccounting extension to orthodox cash flow analysis.

This step applies a 25% discount rate to the prices shown in step 2.

— 2

-I

II — 3

IL

OWT00000RREAKARAN SF CASH FLAW

NET PRESENT VALUE

DETERMINISTIC PRCCIACTIYITY ACCOWNTINGBREAKDOWN OF CASH FLAW

NET PRESENT VALUE

AISCOWRTRATE

Revenue

LESS Cast

PraFiA

Capital

CASH FLOW

YearA

CASHFLAW

0%

4HAAA—

40000—

DISCERNTRATE

Cast

Capital

CASH FLOW

Current Current FriarYear Year Year CRRHGE YECENCIL PWAOACT PRICE

CAPITAL PRAFIT OLD IN —IATIOW —IYITY RECOVERY

FLAW FLOW PROFiT PROFIT VARIANCE RARIARCE YARIAHCE

A I C A E F A

Cvii E-vF+0

45uSD—

YearA

CASH

FLAW

ASH

AtH

4OAAS—

45500— 4ASAA—

OWTHOWAS

aREAKSAHN OF CASH FLOWNET PRESENT VALUE

DETERMINISTIC PROWACTIRSTY ACCOWNTIWOBREAKAOIRI SF CASH FLOW

NET PRESENT VALUE

DISCOWWTRATE

Revenue

LESS Caat

Fraf it

Capital

CASH FLOW

YearH

CASHFLOW

DNA

400A0—

40000—

DISCOWRT

RATE

Ceat

Capital

CASH FLOW

Current Current FriarYear Year Year CHANGE RECOWCIL P0055CY PRICE

CAPITAL PeAFIT ALA IN —IAYIOW —IHITT RECAYERY

FLOW FLOW PASFIT PROFIT HARIANCE VARIANCE YAROANCE

A I C 0 E F G

C+D E+FeG

AlIAS—

YearA

CASHFLAW

DUO

H

A+D

40000—

4ISAO— RAOEA—

Step 5

This step shows analysis of the Year 0 cash flow first with undiscountedprices (i.e., prices disounted by 0%), and then with prices discounted by 25%.The bottom line of the orthodox cash flow analysis is equal to the bottom

right hand cell of the matrix which expresses the deterministic productivityaccounting breakdown of the cash flow. Year 0 values in undiscounted prices

appear in Step 2 above while values in discounted prices appear in Step 3

above, Year 0 data are confined to the intitial capital outflow.

Attention is drawn to the following identities:

OWTAOWOA

BRE000ARWI OF CASH FLOW

NET FRESENY HALRE

DETERMINISTIC PRtOACTIYITY ACCOWNTIN0BREAKDAWN OF CASH FLOW

NET PRESENY VALUE

DISCOWNT

RATE

Revenue

Year1

CASHFLOW

DO

11111

DISCOHNTRATE

Current Current FriarYear Year Year CHAHGE RECOWCIL

CAPITAL PROFIT ALD IN —IATIOWFLOW FLOW PROFIT FROFIT YOWIANCE

A B C 5 0

Cvii EvFeG

FIOWACT

—IOSTYYARSANCE

F

FRICERECAAERYVARIANCE

I

YearI

CASA

FLOW

OW

A

0-va

LESS Cast RAIN Cast

PraFit 2050

Capital

CASH FLOW

30000—

2OWAA—

Capital

CASH FLOW

30000— DIII 2000 DaAIY—

3000W— 1100 1100 20000—

00THRREAKSSNN

HEY FRES

0000IF CASH FLOWWT OALAE

DETERMINISTIC FROWACTIOITT ACCOWNTINGBREAKDOWN RF CASH FLOW

NEY PRESENT RALUE

Year - Current Curraht Friar Year•

I Tear Year Year CRANOE RECOWCIL FROWACT PRICE I

CASH CAPITAL PROFIT OLD 1R —IATIOW —IKITY RECOISRY CASH

FLOW FLOW FLOW PROFIT PROFIT VOWIANCE HOWIANCE VOWIANCE FLOW

DISCOWNT SDSCOWHT

RATE 150 RATE ORG

Revenue 000WA I C S E

E+F+0F H

AvG

LESS Cast

Frafit

640W

1600

CaaO B

1

Capital

CASH FLOW

14010—

22400-

CvpiOii

CASH FLOW

14111— SAIl 1601 12450—

D4050— IAOO 1600 DD4AI—

Step 6

This step shows aralysis of the Year 1 cash flow first with undiscozwltedprices (i.e., prices Jisounted by 0%), and then with prices discounted bfls%.The bottom line of the orthodox cash flow analysis is equal to theright hand cell of the matrix which expresses the deterministic productjwityaccounting breakdown of the cash flow. Year 1 values in undiscounted ptlcesappear in Step 2 above while values in discounted prices appear in Stag 3

above. Year 1 data relate to revenue, cost and capital data.


- RETERMIBISTIC PROWUCTIHITY ACCOWNTINO ESTERSIOW TO OWTHOWAO CASW FLOW ARALYSIS

STEP S — ANALYSIS OF IRSINESS B SN TEAR A. Yalaea are 1' DOLLARS.

DETERNINSDTIC FROWOCTIRIIT ACCOWWTINI ESTENOSOW TA OW1WOWOS CASH FLOW ARALYSIS

STEP 6 — OWALYSIS OF BASINESS B IN YEAR I. Values are in DOLLARS.

OrthodoxBreakdown of Cash FlowNet Present Value

COLUNN : Year 0 CASH FLOWROW Profit

COLUMN : Year 0 CASH FLOWROW : Capital

COLUMN Year 0 CASH FLOWROW CASH FLOW

Oeterministic Productivity AccntgBreakdown of Cash FlowNet Present Value

Current Year PROFIT FLOW— CASH FLOW

Current Year CAPITAL FLOW— CASH FLOW

Year 0 CASH FLOW— CASH FLOW

COLUMN

ROW

OrthodoxBreakdown of Cash FlowMet Present Value

Year I CASH FLOWProfit

— 4

COLUMN : Year 1 CASH FLOW- ROW Capital

COLUMN

ROW

Oetermlnlstlc ProductivityBreakdown of Cash FlowMet Present Value




Year 1 CASH FLOWCASH FLOW

II — 5

DETERMINISTIC PRAROCTIVITO HCCCGNTIHG ESTENSIOW TO OWSHAROU CASH nON ANALYSIS

STEP 7 — ANALYSIS OF NOSINESS B IN YEAR 2. values are In DOLLARS.

DETERMINISTIC PV000CIIYITT HCCOWNTIHGNR00000IHI or CASH FLOW

NET PRESENT VALHE

Current Current PrIorYear

Year Year Year CHANGE PROWOCT PRICE 2

CAPITAL PROFIT OLD SW —IATI&i —lAITY RECOYERY CASH

FLOW PLON PROFIT PROFIT HHRIARCE YARIARCE VARIANCE PLOH

ARTOAROSDETERNINISIIC POSHOCTIRITH ACCOUNTIWS

BREAKDOWN HF CASH PLeABREAKDOWN OF CAIN FLOW

NET PRESEWY YALHENET PRESENT HALSE

Year

ID 2

I CASH

CASH

I FLOHFLRH

DISCOWOT I DISCOWNO

PATE I 25% RATE

25%

I A N C B EA

Revenue 111520C-sO E+F+G

0+0

LESS Cest 8025,6 Cost 1100,4 1100,4 402,4 7H8 1500,4

PrnFlt 3404,4

Capital 44001

___________________________________________________________

CASH FLOW HHDR4.4

CWOTOCKIOO

BREAKDOWN OF CHOW FLOW

WET PRESENT YHLHE

Year

CASHFLOW

DISC RANT

lATE NA

Renanue 10000

LESS Cnst 12540

ProF It SNNN

CaplRal 70000

CASH FLOW 7SWAO

DETERMINISTIC PRRAOCTOA1IT ACCOWNTIWS EXTENSION TO 001110000 CAIN FLOW ANALYSIS

STEP 8 — ANALYSIS OF BUSINESS N VOW SON OF ALL YEARS. Values are In DOLLARS.

DISCOUNT

RATE0%

A B C I E - F G W

CeO E+F+RA+N

Cost 1800 1060 660 1200 1800

CapItal 70000 3600 2000 1000 1500 700 600— 73600

CASH FLOW 70000 N4NO 2000 3400 1500 1360 608 7S400

torrent Current PrIorYear Tear Year CHRNSE RECOWCSL PROWACT PRICE

CAPITAL PROFIT OLI IN —DATIOW —lAITY RECOYERY

FLOW PLOW PROFIT PROFIT VARIANCE YORIORCE VARIANCE

F C

OWTROWOU

NREAKOOWN OF CASH FtNET PRESENT RALNE

— DETERMINISTIC PROWOCTIVITY ACCOWNTIWO30 DREOKDOAN OF CASH FLOW

NET PRESENT NALOE

AllYearsCASW

FLOW

DISCOWNTDATE AR

Rooenoe 20000

LESS Cost 20540

ProFit 7460

CapItal 0

CAIN FLOW 7460=-

All All All HID Years All Teara All Tears All YearsTears Years Years CHANGE RECOWCIL PRAROCT PRICE YCosCAPITAL PROFIT OLO IN —IHTIOW —1051'! RECOVERY

FLOW FLOW PROFIT PROFIT VARIANCE VARIANCE VARIANCEDISCOUNTRATE

A 8 C D E F 6 irC+D E+FaG

Cost 5000 1800 - 660 1200

I SHOA 4000 1600 1500 700 600—

CHOW FLOW I 7460 4000 3460 1500 5360 600 744k=—

OWTOOWOO

BREAKDOWN OF CASH FLOVNET POESENT RALHt

- - DETERNINIOTIC PROWOCTI PITT ACCOUNTINGBREAKDOWN OF CAIN FLOW

NET PRESENT VALUE —

DIOCOWNT

RATE

Revanoe

LESS Cost

ProfIt

Capital

CASH FLOW

AllYearsCASH

FLOW

25%

10520

14425,6

5004,4

58200,0-.

54105W..

,

DISCOWNT

RATE

Cost

Capital

CASH FLOW

.

—All All All All Years All Tears All Years All YearsTears Years Years CHARGE RECOWCIL POOWOCT PRICECAPITAL PROFIT OLD IN —IWIIOW —IRITT RECROERY

FLOW FLOW PROFIT PROFIT VARIANCE RARIANCE RARIANCE

A N C D E F K

Cell E+F+G

5100,4 1110,4 422,4 768

11200— 3004 3200 704 640 448 304—

CA01+

,--

0.

-

10200— 5004,4 3200 5004,4 N4H 870,4 380

CapItal 44000 2304 1600 704 640 440 304— 47104

CASH FLOW 5448003484.4 1000 1804,4 640 870,4 304 40294,4

Step 7

This step shows analysis of the Year 2 cash flow first with undiscounted

prices (i.e., prices disounted by 0%), and then with prices discounted by 25%.

The bottom line of the orthodox cash flow analysis is equal to the bottom

right hand cell of the matrix which expresses the deterministic productivity

accounting breakdown of the cash flow. Year 2 valUes in undiscounted prices

appear in Step 2 above while values in discounted prices appear in Step 3

above. Year 2 data relate to revenue, cost and capital data.


- Step 8

This step shows analysis of the sum of the cash flows for all years (i.e.,Years 0, 1 and 2) first with undiscounted prices (i.e., prices by0%), and then with prices discounted by 25%. The bottom line of the jrthodox

- cash flow analysis is equal to the bottom right hand cell of the matr-}j whichexpresses the deterministic productivity accounting breakdown of tbe cashflow. For all years the values in undiscounted prices appear in Step 4 abovewhile values in discounted prices appear in Step 3 above. The data Lor thesum of all years relate to revenue, cost and capital data.

OrthodoxBreakdown of Cash FlowNet Present Value

COLUMN Year 2 CASH FLOWROW Profit

COLUMN Year 2 CASH FLOWROW : Capital

COLUMN Year 2 CASH FLOWROW CASH FLOW

Deterministic productivity AccntgBreakdown of Cash FlowNet Present Value




OrthodoiBreakdown of Cash FlowNet Prusent Value

- COLUMN

ROW

Deterministic Productlvltg AccntgBreakdown of Cash FlowNet Present Value

COLUMN : (Sum of) All Years CASH FLOW All Years PROFIT FLOW -

ROW Profit — CASH FLOW

Ii — 6

(Sum of) All Years CASH FLOWCapital

COLUMN (Sum of) All Years CASH FLOWROW CASH FLOW

Ii — 7

All Years CAPITAL FLOW— CASH FLOW

All Years.CASH FLOW— CASH FLOW

Chapter 12 DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSION TOBENEFIT TO COST RATIO

This chapter Is intended for the advanced reader who requires an

understanding of the deterministic productivity accounting extension to thebenefit/cost ratio which flows from the application of discounted cash flowtechniques. Such extension is intended to decode benefit/cost ratios by

making patent the underlying contributions of productivity and price recoverywhich would otherwise remain latent. The following text assumes the reader Asconversant with orthodox cash flow analysis and the associated benefit/costratio which arises from dividing total dollar benefit over the forecast periodby total dollar investment cost over the forecast period.

The extension is developed through the following 2 steps with respect toBusiness B as presented in the preceding chapter. For brevity, such steps areconfined to the case of a 0% discount factor, although the logic applies toany discount factor.

DETERMINISTIC PRONUCTI VIII ACCOUNTING EXTENSImI TO OWThWAO BENEFIT COST ANALYSIS

STEP I — ANALTSIS OF BUSINESS B FOB SUM OF ALl. YEARS. Values are In DOLLARS.

OWTSOOIOO

IREA000IVI OFBENEFIT AND COST

SETESNINISTIC P0000CTI VIII ACCOUNTINGBRE00500N OF

BENEFIT AND COST

DISCeVITRATE

AllYearsCAlMFLOW

0%

DISCOUNT

RATE

All an all All Yeara All TearsYears Years Tears CAYNGE RECOWCIL

CAPITAL PROFIT OLD IN —IASSOW

FLOW FLOW PROFIT PROFIT VARIANCE

All Years All YearsPROWUCT PRICE—lAITY RECOVERT

VARIANCE VARIANCE

AllYearsCASO

FLOW

5%

Veeeeue D000V

A B C S E

CeO [WoOF 0 V

Aol

LESS Cest 26540 Cast 1000 IONS 005 1100 INNS

PraY It 740S .

Cap InFlow

BENEFIT

Cap OutFlow

COST

ENEFIT-COST= CASH FLOW

10000

77400

70000

7V555

7460

Capital

CASN FLOW

70000 BUSS 400S 1600 1000 700 000— 75600

10000 7400 4000 340S SBUS 130S 005 77600

70000 70000

70000 70005

7400 400S 3460 1500 1301 005 7460

Step I

This step re—arranges the data displayed in the precedingtable into the definition of benefit and cost shown above.row relates to the residual value of capital defined in theprevious chapter.

It is noted that the above row described as BENEFIT - COST is equal to therow described as CASH FLOW in the preceding chapter.

DETEVNINISTVC PROWOCTIVITY ACCOUNTING ESTENSIOW TO OWI1IOWOX BENEFIT/COST RATIO

STEP 2 — ANALYSIS OF BUSINESS B FOW SUN OF ALL YEARS.

BREAKDOWN OF

BENEFIT/COST RATIO

POOWOCTIVSTT ACCOUNTINGDRE0000IN OF

BENEFIT/COST RATIO

AllYearsCASA

FLOWOSSCmINTRATE OW

tonEr—Ibet—lenLa

Bene?/CsotRatio

Nenenue 0.400

LESS Cost 0,203

ProFIt 0,107

SSCOWNT

YAlE

Cost

All All All 011 Years 011 YearsYears Years Tears CHANGE OECOWCILCAPITAL PROFIT OLD IN —IATSOWFLOW FLOW PROFIT PROFIT VOWIANCE

Contr Cootr Centr Contr CanEr-Ibut —Ibat —Ibat —Ibat —IbaE—lan —Ion —Ion —Ian —Ianto On ta to to

Dccc? Ieee? Bane? Bone? lene?/Cost /Coot /CoaE /Cost /CesORatio RatIo Ratio RatIo Ratio

A B C 0 E

CoO EoF+G

0,027 0,026

All Tears All YsursPRODUCT PRICE—IVITT RECOVERYVARIANCE VARIANCE

-

CanEr CanEr—IbuE —lUst—Ion —Ionto to

lone? Ieee?/Cost /CastRatIo RatIo

F 6

0,000 0,017

All-TearsCASH

FLOW

NO

Centr—Ibut—Ianto

lone?/CostDatla

V

A+B

0,027

-

Cap InFloaq 1,000

BENEFIT/COST RATIO 1,107

CapItal

BEIIEFIT/COST RATIO

1,000 0,000 0,050 0,023 0,021 0.010 0,006— I,OOW

1,000 6,107 0,050 0,641 0,021 - 0,011 0,000 1,107

Step 2

This step divides all Step I rows comprizing BENEFIT by the Step 1 rowcomprizing COST which amounts to $70000. It therefore provides two ofthe contributions to the Benefit/Cost ratio of 1,107 provided above.

The first view is called the orthodox breakdown of the benefit/cost rflio Hbecause it flows from orthodox cash flow analysis. The second view is cOledthe deterministic productivity accounting breakdown of the benefit/cost i'4tiobecause it flows from the deterministic productivity accounting tocash flow analysis. The latter view does make patent thecontributions of productivity and price recovery which would otherwise rel$ainlatent.

Hence the benefit/cost ratio can be supported by the profit,quantity and price grids already specified. This would permit an analyst toto distinguish between 2 projects having identical initial inve$tiheiTt—-—Rons,project life spans, payback periods and benefit/cost ratios. The anajystwould be permitted to assign preference to, say, a project appearing in

the profit grid relative to a project appearing inSCRAMBLE segment of the profit grid.

Benefit/cost ratios based upon difference cash flows (i.e., the differodcebetween two mutually exclusive options) also lend themselves to ?lheproductivity extension presented in this chapter.

12—112 — 2

chapter Step 8 topThe Capital Inflowfirst page of tho

PART J — UNIT LIFE CYCLE COST


Chapter Ji DETERMINISTIC PRODUCTIVITY ACCOUNTINGTO UNIT LIFE CYCLE COST ANALYSIS

This chapter is intended for the advanced reader whounderstanding of the deterministic productivity accounting to unitlife cycle analysis which flows from the application of discounted flowtechniques. Such extension is intended to decode measures of presentvalue of discounted cash flows by making patent the underlying contributionsof productivity and resource price which would otherwise remain 4tent. Thefollowing text assumes the reader is conversant with orthodox unit cyclecost analysis.

The extension is developed through the following 14 steps withis assumed that the fixed capital resource

employed is non—depreciable and commands a residual value equal bookvalue, and that taxes are disregarded.

DETERMINISTIC PRODUCTIVITY ACCOUNTING EXTENSION TO ONTHODOS LIFE CYCLE COST ANALYSIS

STEP I — NORItAL MODE OF DATA DISPLAY AND DATA ENTRY SNUbRI FOD BUSINESS B

Values are DOLLARS. Prices are discounted by 0%

Year 0 Year I Year 2 YEARS

INDEX ENTITY

REVENUE:

UI Product bi

VERA VALUE QUANTITY

•

PRICE VALVE QUANTI

100

TV PRICE VALUE QUARTITY

INN

PRICE ICC

250

COST RESOURCES:

NI Material bI 1,0 OOUO 400 20 12540 57N 22 82.160

CAPITAL RESOURCES:El Equipsaent bI

LESS Residual Vaoe

RET Capital Flow --ICASN FLOW I--

40000 N 5000 10000 1040000 8

100070000 10

I

7000 70i0$.r280,000280,000—

40000

40000

30000

30000

70U00—

57460—

T

I 82,160 I

Step 1

This step presents the standard form of input data which would suppliedfor analysis by the deterministic productivity accounting algorithm. It alsoprovides replacement cost of capital. Prices are disounted by 0% (i.e., areleft undiscounted).

This step recognizes that fixed capital resources must be provided prior tothe commencement of production. It also provides residual values capital.Prices remain undiscounted.

Resource values for all years are summed to create the ALL VALUEcolumn representing Life Cycle Cost (LCC). Product quantities are forall years to create the ALL YEARS QUANTITY column. The former isdivided by the latter column to create the Unit Life Cycle Cost column.

Although the ULCC has a positive sign, the LCC has a positive in steps1, 2, 8 and 9 but has a negative sign in all other steps to express factLCC cash flows cash outflows.

— 1

DETERMINISTIC PROSUCTI VITO ACCOUNTING EOTENSIcN1 TO DATROSOS LIFE CYCLE COST ANALYSIS

STEP 2 — CmOECTEI NOSE OF DATA DISPLAY S1I0AR FDA ROSINESS

Yalses are in DOLLARS. Prices are discoa,ted by 25%

INRER ENTITY RERA VALUE

Tear 0

QUANTITY PRICE

Sear

VALUE ROANT

1

ITT PRICE

Year 2


ALL YEARS

VALUE QUANJARIT LCC

REVENUE:Dl Predact hi III ISO 250

EOST RESOURCES:NI Material hi 1,0 6400 400 16 0025,6 570

)

14,00)14425,61 57,7S2j

ElCAPITAL RESOURCES: I

EqaipmeaL hiI

LESS Residaal Yalsa

NET Capital Flow

40000

40000

8 5000 56000 1032000 8

24UVA

50004000

.

44800 10

44800—

4400

I

NOV0076800

p

102A0 f

I

384,000I

307,200

—

Step 2

This step discounts by 25% the prices givenprovides a discounted measure of unit life cycleundisounted unit life cycle cost given in Step 1upfront investment is undiscounted.

Data in such form are unusable for measuring capital productivity throughoutthe economic life of capital because the values and quantities of capital arerecorded only in years when capital flows occur. It is therefore necessaryto specify an annual cost of capital for each year in which the capital isused to facilitate the measurement of capital productivity in every year ofits economic life. This chapter therefore employs two methods of determiningan annual cost of capital

The first method of determining the annual cost of capital employs thenominal 5% annual cost of capital already shown for Business B in thepreceding chapter which sets out the deterministic productivity accountiVgextension to orthodox cash flow analysis. The steps entailed in suchapproach appear in steps 3 through 7 whose description therefore contains thewords "using no annuity payment for cost of capital".

The second method of determining the annual cost of capital employs the 25%discount rate already shown for Business B in the preceding chapter which setsout the deterministic productivity accounting extension to orthodox cash flowanalysis. The steps entailed in such approach appear in steps 8 through 14whose description therefore contains the words "using a variable annuitypayment for the cost of capital". The second method employs an enhancementto the normal concept of a level annuity payment by introducing in theequations which follow the concept of a variable annuity payment whose profilematches that of the changing total asset exposure throughout the economic lifeof the assets.

Furthermore, it is noted that although the undiscounted net present valuesof the capital flows and the variable annuity payment are unequal, their netpresent values based on a 25% discount rate are, by design, identical. Thebenefit of this methodology is that it eliminates lumpy caØital flows(including residual values) and thereby facilitates capital productivitymeasurement throughout the economic life of the asset without perturbing thenet present value of capital flows based on the 25% discount rate.

OUTNOSOY

BREAKDOWN OF L C CNET PRESENT VALUE

DETERMINISTIC POOSUCTIVITYDVEA0000N OF I C C

NET PRESENT VALVE

ACCmNTINS

DISCOUNTRATE

Year0

CASH

FLOW

IXDISCOUNTRATE

Carre,t Carre,t PrierYear Taar Year CHANGECAPITAL TOTAL TOTAL IN TOTALFLOW COST COST COST

RECONCIL

—IAT1S81

VARIANCE

PROSOCT

—lAITYVARIANCE

RESOURCE

PRICEVARIANCE

Year0

CASH

FLOW

A D C ICaR [WaG

E F 0

0%

N

Cost Researcea Ccet

AtO

Capital Cast Capital 40000—

Capital Flow

LCC

40000-

40000— LCC

40000—

40000—40000—

OUTVmIOSOREAKO VON HF L C C

NET PRESENT VALUE

— DETERMINISTIC PROSOCTIVITYDREAKO VAN OF L C C

NET PRESENT VALUE

ACCOUNTING

YearV

CASH

FLOA

Carreot Carreet PriorYear Year Year CHANGECAPITAL TOTAL TOTAL IN TOTALFLOW COST COST COST

RECOWCIL—IATIONVARIANCE

PRVOSCT

—lAITYVARIANCE

RESOURCE

PRICEVANIANCE

TearU

CASHFLOWDISCOUNT

RATE 25%DISCOUNT

A 8. C 0CaR [eFaG

E P 0

255

U

Coot Reeaarceo Cast

Capital Coat CapRal 40000—

Capital Flow

ICC40000—

0%000- LCC

40000—

fl140000-

Step 3 refers to Year 0 and assumes an annual cost of capital and avalue at the end of the economic life of the asset (i.e., it uses no annuitypayment to redeem capital).

Attention is drawn to the following identities:,

DETERMINISTIC P0000CTIVITY ACCOUNTING ESIENSIm4 TO milimloo LIFE CYCLE COST )L C C) ANALYSIS

USING 00 ANNUITY PATNENT FOU COST OF CAPITAL

sTEP 3 — ANALYSIS OF BUSINESS B IN YEAH H. Valaaa are I, GOLLARD.

in Step 1. It thereforecost which is higher than thebecause in Step 2 the Year 0

COLUMN OrthodoxBreakdown of Life Cycle CostNet Present ValueYear 0 CASH FLOW

ROW Capital Cost + Capital FloW —

LCC —

No cost resource payments arise in Year 0.

JI — 3J1—2

i

Deterministic Productivity AccrqgBreakdown of Life Cycle CostNet Present ValueYear 0 CASH FLOW

CapitalLCC

DETERMINISTIC PRUROCTIVITT ACCOUNTING EATENSIOW TO OUThUROX LIFE CYCLE COST (L C C) ANALYSIS

USING NO ANNUITY PAYMENT FOU COST OF CAPITAL

STEP 4 — AJIALYSIS OF NOSINESS U IN YEAR I. Values are In DOLLARS.

OU10C000NREA0001NIOF LCC

NET PRESENT VALUE

OETERNINISTIC PNCOUCTI VITA ACCOUNTINGNREA000hNOF LCC

NET PRESENT VALUE

DISCOUNTRATE

Cent Rennurcen

Capital Cant

Capital Flow

L C C

YearI

CASN

FLOW

0%

0011—

2000—

30000—

40000—

DISCOUNTRATE

Cost

CapItal

1 C C

Current Current PrierTear Teur Year CAANGE RECOWCIL PROSUCT RESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IAIICN —I VITA PRICE

FLOW COST COST COST VARIANCE VARIANCE VARIANCE

A I C S E P 0

CuD EFaG

0000— 0001— 0000—

30001- 2000— 2000— 20A0—

YearL

CATSV

FLOW

0%

A

0-el

0050—

32000—

30000— 10000— 10000— 10000— 40000—

OUTYOSOO

NREAE200N OF L C CNET PRESENT VALUE

DETERMINISTIC PR000CTIYITT ACCOUNTINGNREAEOO¾N OF L C C

NET PRESENT VALVE

DISCOUNTRATE

Coot Resources

Capital Coot

Capital Flow

ICC

YearI

CASR

FLOW

25%

0000—

IANO—

24000—

32000—

DISCOUNT

RATE

Cost

Capital

LCC

Current Current PrierTear Your Tear CNANGE RECOUCIL POOUUCT RESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IATIOW —IYITT PRICE

PLON COST COST COST VARIANCE VARIANCE VARIANCE

.

A U C I E F G

CuD E+EoD

0400— 6400-. 0400—

20000— 1000— 1000— 1000—

Tear1

CASV

FLOA

25%

N

A+l

6400—

25601-

24000— 0000— 0000— 0000— 32000—

Step 4 refers to Year I and assumes an annual cost of capital and a residualvalue at the end of the economic life of the asset (i.e.0 it uses no annuitypayment to redeem capital).


COLUMN Orthodox Deterministic Productivity AccntgBreakdown of Life Cycle Cost Breakdown of Life Cycle CostNet Present Value Net Present ValueYear 1 CASH FLOW Year 1 CASH FLOW

ROW Cost ResourcesCapital Cost + CapitalLCC

Flow—

a—

CostCapitalLCC

-

CHANGE RECOWCIL PROUOCT RESOURCE M 2IN TOTAL —IATIOW —IVITY PRICE t CASVCOST COST VARIAACE RARIANCE VARIANCEf FLOW

[NoE F 0 --to

4000— 660 1200— U,N40_1000- 700 2200— 500

7000020040— 20000— 6040— 5000— I3NO 2400—

Capital -

LCC

Current Current PriorTear Tear Year CHANGE VECOWCIL PREOUCT UESEEJVCECAPITAL TOTAL TOTAL IA TOTAL —IATIOW —lAITY PRICE toyiFLOW COST COST COST VARIANCE AAJ1IANCE VARIANCE

0-'

410*0

3Nfl,4

Step 5 refers to Year 2 and assumes an annual cost of capital and residualvalue at the end of the economic life of the asset (i.e.n it uses nà annuitypayment to redeem capital).

DETEOtNIOTIC PVOUUCTI 0211 ACCOUNTING EATENSIOW TO OUOUOUOV LIFE CTCLE COST (I C C) ANALTSfl

USING HO ANNOIIT PAVUENT FUR COST GF CAPITAL

STEP S — ANALYSIS OF NOSINESS I IN TEAS 2. Values are In DOLLARS.

00100000DETEONINI5TIC FROUOCTJR2TT ACCOUNTINGNREA020NN OF L C C

RVEA000IVI OF L C CNET PRESENT VALVENET PRESENT VALUE

N C SC-au Eu-P 4

12540- 0000- 4540-

7000N 3500— 2V00— 1500—

DETERNINISTIC POOUOCTIVITT ACCOUNTINGROEAKDOAN OF L C C

NET PRESENT VALUE -

LCC

A I C 2CuD Eu-FoG

NO2N.N— 6400— IO2N,6— 3200—

44000 2240,0— 1000— 640,0— 000—

E F 0

422,4 1252

440 200-

44RVA 10205,0— 0000— 2265.0— 4000— 070,0 064

Ji — 4

Attention is drawn to the following identities:COLUMN : Orthodox Deterministic AccntgBreakdown of Life Cycle Cost Breakdown of Life CycleNet Present Value Met Present Value

Year 2 CASH FLOW Year 2 CASH FLOW

ROW Cost Resources— Cost

Capital Cost + Capital Flow — CapitalLCC— LCC

Ji — 5

COLUMN OrthodoxBreakdown of Life Cycle CostNet Present ValueSum of All Years CASH FLOW

ROW Cost ResourcesCapital Cost + Capital FlowLCC

Oeterministic Productivity AccntgBreakdown of Life Cycle CostNet Present ValueSum of All Years CASH FLOW

= Cost— Capital= LCC

COLUMN OrthodoxBreakdown Gf Life Cycle CostNet Present ValueSumof All Years ULCC

ROW Cost ResourcesCapital Cost + Capital FlowULCC

— Cost— Capital• ULCC

DETERMINISTIC PROUOCII VITO ACCOUNTING ENTENSIOW TO OUIOOUOA LIFE CYCLE COOT )L C C) ANALYOIO

00260 NO A000ITY PAYMENT FOR COST OF CAPITAL

STEP 6 — ANALYSIS OF 20510ES5 N PEN SON OF ALL TEARS. Aalaes ore In DOLLARS.

DETERNINISTOC PROUOCTIRITT ACCOUNTING ETTENSIIAI TO OWTNOUOO OMIT LIFE CYCLE COST 10 L C C) ANALYSIS

05105 NO ANNOITT PAYMENT FEll COST OP CAPITAL

STEP 7 — NIALYSIS OP ROSINESS N rm SON OP ALL TEARS. Values are in DOLLARS / OMIT OF PNOSOCT.

01100100NOE0000VNI OF I C C

NET PRESENT YALNE

DETERMINISTIC PROUOCTIYITY ACCOUNTINGOREA000NAI OF I C C

NET PRESENT YALOE

AllTearsCASN

FLOW

DISCOUIITRATE OS

Cast Resources 20540—

Capital Cast 5500-.

Capital Plsw A

C C 26040—

DISCCAJNT

RATE

Cast

Capital

L C C

AlT All All All Years All Years All Tears All TearsTears Tears OLD COARSE RECOICIL PROUYCT RESOURCECAPITAL TOTAL TOTAL IN TOTAL —IASIOU —lAITY PRICEFLOW COST COOl COST YARIANCE VARIANCE YARIANCE

.

A N C 0 E P 0CeO E+F+O

20040— 0000— 12540- 22000— ROY 1200—

N 5000— 2000— 3500— 3000— 700 1200—

AllYearsCASA

FLOA

AX

A

A+O

20540—

5000—

S 20A4O— 10200— 10040— 16000— 1300 SAYS— 26040—

OUTAOUOA

NREAEDSAI4 OF L C CNET PRESENT YALOE

SETEANINISTIC PROSOCTI VITA ACCOUNTINGOREA000IsII SF L C C

NET PRESENT AALOE

AllTearsCASHFLYA

DISCOUI4TRATE DOS

Cast Ressor 14425,0—

Capital Cost 3840.0—

Capital Floo 18200.0—

C C 37465.6—

DISCOUNTRATE

Cost

Capioal

•

L C C

All All All All Years All Tears All Years All TearsYears Years OLS CHANGE SECONCIL PRTOISCT RESTYRCECAPITAL TOTAL TOTAL IN TOTAL —IATIOU —lAITY PRICEPLAN COST COST COST YARIANCE YARIAACE YANITNCE

A S C 0 E F S

C+S E+P+G

24420,6— 0400— 8025,6— NaRY— 422,4 1152

10100- 3840,0— 1000— 2240,0— 2400— 448 250—

AllTearsCASOFESA

25%

.0keN

11420,6—

23040,0—

19000— 28205,6— 8000— 20265,6— 22000— 870,4 804 17060,6—

OWTAOUOS

DREA050V.N OF N I C CNET PRESENT VALUE

DETERNIMISTIC PROUOCTIYITY ACCOUNTINDNREAEDOIsN OF N L C C

NET PRESENT RALNE

DISCOUNT

RATE

Cost Researceo

Capital Cost

Capital Plow

O L C C

AllTears

ULCC

DX

82,26

02,80

N

104,20

DISCOUNT

SATE

Coot

Capital

0 L C C

All All All All Tears All Years All Tears All TearsYears Years OLD COANSE RECONCIL PYOSUCT RESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IATIOU —lAITY PRICE

PLOW COST COST COST VARIANCE VARIANCE AARIANCE

A B C B E P 5Cell E+FeS

8D,SN 32,00 SO;iN 48.09 2,64— 4,00

8 22,00 8,00 24,80 12,00 2,00— 4,00

AllTears

•

YLCC

OS

N

A+l

80,26

22,00

0 104,16 40,00 04,26 60,00 5,44— 0,60 204.16

OUTOOUOS

DREA506VIIOF NLCCNET PRESENT RALSE

— DETERMINISTIC PROUUCTIRITT ACCOUNTING IONEA050ANOF OLCC

NET PRESENT AALOE A

DISCOUNTRATE

Coat Resoor

Capital Cost

Capital Flow

O L C C

AllYears

OLCC

55%

S1,PODA

15.34

76.8

149,8424

DISCOUNTNATE

lost

Ca2ital

AL C C

All All All All Years All Tears All Tears All TearsTears Years OLD CHANGE RECOICIL PROUUCT AESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IATIOW —lAITY PRICE

FLOW CAST COST COST VARIANCE VARIANCE VARIANCE

A C C 0 E - F S

EaFoG

51,7024 25,6 32,1024 30,4 2,6096— 4,600-

70,0 15,36 6,4 8,86 9.6 1,1920— 1,150

AllTears

-

YLCC

05%

H

YoU

51,1054

92.26

141,860476,8 73,0624 32 42,0624 45 3,4826— 3,456—

Step 6 refers to the sum of all years and assumes an annual cost of capitaland a residual value at the end of the economic life of the asset (i.e., ituses no annuity payment to redeem capital).


Step 7 refers to the sum of all years and assumes an annual cost of capitaland a residual value at the end of the economic life of the asset.measure is the unit 1 fe cycle cost.


Ji — 6

Oeterministic ProductivityBreakdown of Life Cycle Cost-Net Present ValueSumof All Years ULCC

j

Steps 8 through 14 provide the alternative approach to life cycle costanalysis in which the cost of capital employs a variable annuity payment.

J1 — 7

The following equations indicate the response of deterministic productivityaccounting to the orthodox approach to life cycle cost analysis which excludesan annuity payment to redeem capital. The equations utilize the Net PresentValue of the net capital flow shown above in step 2 to generate variableannuity payments for each year of the cycle. In this context the term

variable means that the discount factors would not be linear with respect totime If plotted against a log scale V—axis for the discount factor and an

arithmetic scale X—axis for the sequence of years for which the discountfactor is defined.

$40000- =—

$40000

$70000=

______

* [1 + 0,25] ** —2$40000

= 1,12

Variable Year 1 Year 2Annuityfactor

= variable +discount factor

variablediscount factor

= 0,8 + 1,12

BETEOMINISTIC ACCOUNTING EXTENSION TO 80100000 LIFt CYCLE COST ARALYSIU

STEP B CTRRECTED BOUE OF DATA ENTRY ROTaTOR FSR BUIIIIESS B

Values are in DOLLARS. Prices Ire discounted by 05

INDEX ENTITY

Year B

REYA YYLOE QOYNTITY PRICE

Year I

RALBE QUANTITY PRICE

Tear

VAIRE QOANTI

2 ALL YEARS

TV PRICE IYALOE IQOANIONIT ICC

- COST RESOURCES:Ni Material bi

CAPITAL REXTROCES:El Eqaipoeet HI

LESS Residual Value

BET Capital Ploa

iCYSR P100 -

1,8 8000 400

10000 B

20

1200

12140 570

17100 10

1:22 120140fff"

I

.

10000

18000

17000

30040

— 110,000

1192,160

Step 8

This step applies the variable annuity payment calculated on jhe previouspage. It is noted that in this step the prices are nijinal (i.e.undiscounted) and that the net present value and unit life cycleetosts for thecapital resource vary from those shown in step 1.

BETERRIBISTIC PRODUCTIVITY ACCOUNTIMO TO CNITOTROX LOPE CYCLE COST ANALYSIS

STCP B — CCOTRECTEB NOSE OP DATA ERTRY SHOWN POW ROSINESS B

Values are i' DOLLARS. Prices are discounted by 25%

Tear 0 Tear I Veer 2 ALL TEARS

IRDEI ENTITY RE0A VALUE QSORTITY PRICE VALUE QUANTITY PRICE VALUE RUANTITA PRICE IAUANIONIT LCC

REAETOUE:

01 Product HI 100 ISO 250

COST RESOURCES:RI BuLeriai HI 1,0 0400 400 16 8025,0 570 IU,08(ft420,b S7,7O24

CAPITAL RESOURCES:El Equipment HI 8000 B 1000 11210 10 1120 IØ200 70,0000

LESS Residoal Ralue

BET Capital Flow 0000 11200 76,0000

ICAS0 PLOW 04400 18225,6 14A25,Bl 113A,50241

Step 9

This step applies the variable annuity payment calculated on Qie previouspage. It is noted that in this step the prices are discounted byiS% and thatthe net present value and unit life cycle costs for the capital areequal to those shown in step 2. Yet the capital data in fore aresuitable for capital productivity measurement throughout the ecorlEllic life ofthe asset, whereas the capital data in the fore of step 2 are u4t&oitable forcapital productivity measurement.

REVENUE:81 Product HI 000 ISO 2501

Year °t°van ablediscount factor

Year t Asset Closing Value

Year 1

variable -discount factor

Year 1 Asset Closing Value

Year I Asset Closing Value

Year I Asset Closing Value

Year 2

variablediscount factor

= 0,8



* [1 + Discount rate] ** —t

* [1 + Discount rate] ** —i

* [1 + Discount rate] ** —2

1,92

Net Present Value Year t Asset Closing ValueYear tVariableAnnuityPayment

Year 1 $10000 =

Year 2 $17500 =

Variable Annuity Factor Year 1 Asset Closing Value

$19200 $40000

________

*1,92 $40000

$19200 $70000

1,92 $40000

________

*

J1—8 ji—g

Current Current PriorTear Year Tear CHANGE RECONCIL PROUSCT RESOURCE 0

CAPITAL TOTAL TOTAL

FLOW COST COST

IN TOTALCOST

—lOTIONOARIANCE

—SHill PRICERARIANCE YARIANCE PLOW

OS

E F 0 0A 0 C

CoO EOF0O 0+0

DETERWINISYIC PROUACTINITY ACCOUNTIWO0000050WN OF I C C

NET PRESENT TALOE

Curront Current Prior Your

leer Yeor Year CHANGE RECONCIL PROUOCT RESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IATSON —lAITY PRICE CASH

PLOW COST COST COST 000IANCE YORIANCE OARIARCE FLOW

RETERRINSITIE PROUOCTITITT ACCEAJNIINO EOTENSIeI TO ORTNOUOX LIFE CYCLE COOT IL C C) ANALTOIS

00100 A YOWl WILE WNNAITY PAYMENT FUR COST OF CAPITAL

STEP 10 - ANALYSIS OF ROSINESS S IN YEAR N. Na)ues are in OOLLARS.

ORTOOROO

NREAEOOYW1 OF L C CNET PRESENT NOIRE

ORE0050)Wi OF L C CNET PRESENT OOLOE

Tear

CR50FLOW

OU

40000-

00000-

RETE001NISTIC PRWOCTIYITY ACCOUNTINGEOTENOIOW TO ORTWOUOA LIFE CYCLE COST )L C C) 000LYSSO

055WO A NORIORLE ARWOITY POAREWTFOR Cool OF CAPITOL

STEP IS — OCOLYSSS OF ROSINESS I IN YEAR I.NaiaeO are in 5011000-

RISCOUNYRATE

Coot

Capital

LCC

DISCOUNTRATE

Coot Re000r000

Capital Coot

Capital Flew

LEO

OUTNOUOO

0RE0000NN OP L C CRRE0000WW OF L C C

NET PRESENT NOLOEWET PRESENT AOLAE

Current Current PriorYear Year Year CHANGE RECONCIL

CAPITAL TOTAL TOTAL IN TOTAL —lOTION

PLOW COST COST COST YARIANCEI

IA

PROUACT RESOURCE

—INITY POICE

YARIONCE WORIAWCE

0 C Ii

COO E+F+O

0000—

UOOROUOO

ORE0000AN OF L C CRET PREOEWT AALOE

0

10000—

OUSO— 0000—

10000— 10000—

50000-

Year

COON

FLOW

210DISCOUNT DISCOUNT

HATE RATE- 050

A 0 C 0 0 F 0 N

CuD E+F+O 0+0

Cost Resources CosE

Capital Cost CapiEal

Capital Flow 40000—

_____________________________________________________________

LCC 40000— LCC

__________________________________________

This step refers to Year 0 and assumes an annual cost of capital without anyresidual value at the end of the economic life of the asset. It employs the

variable annuity payment specified between steps 7 and 8.

No values are shown in the above deterministic productivity accounting

matrix. This is proper since the variable annuity payment used for definiugcost of capital distributes the payments across all years other than year 0.

No other identities regarding capital resources arise until step 13 with

respect to a linkage between orthodox analysis and the deterministicproductivity accounting analysis of life cycle costs.

Ji — 10'

This step refers to Year 1 and assumes an annual cost of capital withood+ any

residual value at the end of the economic life of the asset. It emplofl the

variable annuity payment specified between steps 7 and 8.


COLUMN OrthodoxBreakdown of Life Cycle CostNet present ValueYear 1 CASH FLOW

ROW : Cost Resources

Oetermlnlstlc 4çcntg

Breakdown of Life Cycle Cost-Net present Value -

Year 1 CASH FLOW

= Cost

No otherregarding capital resources arise until step 13.

Ji — 11

ENSTOE000

RREAE000NOF ICCNET PRESENT VALUE

DETERMINISTIC P000UCTI VITYIREAEDOI,00F ICC

NE! PRESENT VALUE

ACC01JNTING

DISCEWNYRAYE

Year2

CASh

FLOW

0%

DISCcOINTRATE

Current Current PrIorYear Year Tear CHANGE

CAPIYAL TOYAL YHYAL IN TOTALFLEW COSY COST COST

OECE4ICIL—IAYI01IAAUIANCE

PUEWOCT

—lAITYVARIANCE

RES01ITCEPRICEVARIANCE

Year2

CASH

FLOW

0%

-A N C S

CuD E+FoDE F U N

A+I

Cost Reuuurces 12540— Cost 12545— 0000— 4540— 4000— 660 1200— 12540—

Capital Cent Capital 17500— 10000— 7500— 5000— 3500 0005— 57100—

Capital Flow

C C

70000

57400 L C C 30040— 10000— 10040— 0000— 4160 7200— 30040—

OWTHWOO

IOtAKDO1,R1 OF L C CNET PRESENT VALAE

DETERMINISTIC P0000CTI VITOORE VE004,T4 OF L C C

NET PRESENT VOLOE

ACCOSNTINS

OISCWNTRATE

Year2

CASH

FLOW

250DISC060TRATE

Current Current PriorVeer Vear Year CHANGE

CAPITAL TOTAL TOTAL IN TOTALFLOW COST COST COST

RECONCIL—1011014VARIANCE

PREOUCT RESEAIRCE

—10110 PRICEVARIANCE VARIANCE

Year2

CASH

050

0 0 C 0

CuD E+F+O

E F 0 N

0+0

Cost Resour 0625,6— Coot 6025,0— 6400— 1625,0— 3200— 422.4 1102 6025,6—

Capital Coot Capital 11200,0— 8000— 3200,0— 4000— 2040 0400— 11200,0—

Capital Flow

ICC

44800,0

36774,4 L C C 01225,6— 14600— 4825,0— 7200— 2602,0 200-- 1R225,6—

This step refers to Year 2 and assumes an annual cost of capital withoutresidual value at the end of the economic life of the asset. It employsvariable annuity payment specified between steps 7 and 8.


AllYearsCASH

FLOW

RISCC*JNT

RATE 0%

DETERNINISTIC P0000CYI AlIT ACCEONTING ESTENSICN TO EMTiI0000 LIFE CYCLE COST (I C C) ANALYSIS

USING A VARIANLE ANNOITT PAYMENT FEW COST OF CAPITAL

STEP 02 — ANALVSIS OF NOSINESS N IN YEAR 2. Romeo are In DOLLARS.

REIERNINISTIC pREWACIIYITY ACCEOINTIMG EOTENSIGI TO EWT00600 LIFE CYCLE COST )L C C) ANALYSIS

-ASING A RAOIARLE ANNUITY PAYRE6T PENS COST OF CAPITAL

STEP 13 — ANALYSIS OF ROSINESS N FEll 506 OF ALL TEARS. Names are lo ROLLNSO5.

EWT5000S — DETERMINISTIC PRSI1OCTIVITY ACCEAJRYINO

RRE00000IM or L C C ORE0000I6O OF L C C

NET PRESENT VALOENET PRESENT VALOE

Coot Resources 20540—

Capital Coot

Capital FToa

LCC 20540—

All All All All Years All Years Oil Years AlT Years All

Tears Years OLD CHANGE RECEUICIL P0000CT RESEOIOCE Years

CAPITAL TOTAL YOTAL IN TOTAL —IATIENI —lAiTY PRICE CASH

FLOW COST COST COST VARIANCE VARIANCE VARIANCE FLEW

DO SC. WIT

HAIc0%

A R C U F F 0 0

CoO E+F+OAul

20540— 0600— 02540— 12001— 660 1200— 20540—

Camital 27500— 10000— 57500— 15000— 3500 6000— 27500—

C C 40040— 16000— 30040— 27000— 4160 1200— 40060—

-

anythe

ROW

COLUMN : OrthodoxBreakdown of Life Cycle CostNet Present ValueYear 2 CASH FLOW

Cost Resources — Cost

Deterministic Productivity AccntgBreakdown of Life Cycle CostNet Present ValueYear 2 CASH FLOW

This step refers to the sum of all years and assumes an annual cos% of

capital without any residual value at the end of the economic life of the

asset. It employs the variable annuity payment specified between steps and

8.


No other identities regarding capital resources arise until step 13.

Ji — 12

COLUMN OrthodoxBreakdown of Life Cycle CostNet Preseat ValueSum of All Years CASH FLOW

ROW : Cost ResourcesCapital Cost + Capital FlowLCC

Ji — 13

Deterministic ProductivityBreakdown of Life Cycle CosçNet Present Value -

Sum of All Years CASH FLOW -

— Cost— Capital when discounted by 45%— L C C when discounted by

DETERMINISTIC PNODUCTIAITT ACCWNTIAG EXTENSIOW 10 ENTITWAA UNIT LIFE CYCLE COST (U L C C( ANALYSIS

RUING A TAAIAAL( ANNUITY PATMENT PEA CURT UP CAPITAL

STEP 14 — APENLYSIS UP RASINESS N PEA SAN UP ALL TEARS. Tallies are In DOLLARS / UNIT UP PRODUCT.

EATNODOG

NNEA000AN UP 0 1 C CNET PRESENT TAINt

DITERNINISTIC PNOUUCTIAITT ACCOUNTINGNNEAUOUENI OP U L C C

NET PRESENT AALUE

DISCOUNTRAID

Cost Neanarcen

Capital Cast

Capital Flew

N L C C

AllTears

61CC

0%

NO.16

R2,IN

OISCODNTNATE

CnnE

Capital

N I C C

All All All All Yearn All Years All Yearn All TearsYearn Tears ALl CAANRE NECONCIL PRODUCT NESOURCE

CAPITAL TOTAL TOTAL IN TOTAL —IATIEN1 —lAITY PRICE

PLOW COST COST COST AANIANCE TATIANCE AANIANCE

A I C 2 E P 0

Call EaPAG

NO.10 32,00 50,16 lOUT 2,64— 6,NO

11000 48,00 70,00 ROOT 14,00— 04,00

AllYears

ULCC

OS

A

YeN

60,10

hOOT

190,10 70,00 100,10 IAN,00 16,60— ON,NA INO,16

ODTNODOO

NNEACOORN UP A L C CRET PRESENT TALUE

DETENNINISTIC PN000CTIAITT ACCOUNTINGNNEAKOOAN UP A L C C

NET PNERENT AALOE

OISCEAINTTOTE

ConS Nennar

Capital Cost

Capital Ploe

N I C C

AllTears

NLCC

250

57,7604

76,1

I.34,5N04

DISCOUNT

NATE

Cost

Capital

N L C C

All All All All Tears All Years All Tears All TearsTears Tears OLD CNANGE DECORCIL PRODUCT NOSOROCE

CAPITAL TOTAL TOTAL IA TOTAL —IAIIOR —lAITY PRICE

PLOW CURT COST COST AANIARCE AANIANCO AANIANCE

A I C 0 E P 0

CeO (eP+O

57,7026 05,6 32,1024 38,4 l,NAAO— A,AON—

PRO TO 44,1 46 N,AATU— 1.76

134,0004 hR 76,9024 86.6 10,6416— 1,112

AllTears

ULCC

210

A

A+N+C

RT;7020

IR.N

134,1004

PART K — PRODUCT NORMALIZATIONS


Chapter Ki AXIOMS TO NORMALIZE NEW PRODUCT QUANTITY AND NEW PRODUCT PRICE

The Input Quantity and Price Report examines by way of the measure Qnp the

effect of productivity change on new resource quantity, by way of theQne the effect of effiiency change on new resource quantity, and by way Ifthe measure Pnr the effect of price recovery change on new resource price.

Such report reveals that deterministic productivity accounting alsoan alternative view of the impacts of productivity change, efficiencyand price recovery change. It reveals by way of the measure Qunp the effjttof productivity change on new product quantity, by way of the measure Qune floe

i effect of efficiency change on new product quantity, and by way of thePunr the effect of price recovery change on new product price.

The following rule on mutual exclusivity is noted:

Qunp Qnp

Qune Qne

Punr Pnr

We first introduce the function in order to specify Qune on the

following page.

SUM (Qne — Qo] * Po

SUM Qo * Po (Ki Al.!)

J1—14 1(1—1

PRODUCTMORMALIZATIOMS

RESOURCE

and MORMALIZATIOMS are mutually exclusive.

This step refers to the sum of all years and assumes an annual cost ofcapital without any residual value at the end of the economic life of the

asset. It employs the variable annuity payment specified between steps 7 and8. The measure is the unit life cycle cost.


COLUMN : OrthodoxBreakdown of Life Cycle CostNet Present ValueSum of All Years U L C C

ROW : Cost ResourcesCapital Cost + Capital Flow —

ULCC —

Deterministic Productivity AccntgBreakdown of Life Cycle CostMet Present ValueSum of All Years U L C C

CostCapitalULCC

when discounted by 25%when discounted by 25%

This step uncovers the cost—reducing contribution of productivity growth

which is embedded in, but undisclosed by, the othodox measure of Unit LifeCycle Cost shown in the bottom right hand cell of the diagram in step 2.

SUM fQne — Qn + Qn — QoJ * Po

SUM Qo * Po(Ki Al7?)

SUM fone—QnJ*Po +(Qn_QoJ*PO

SUM Qo*Po (K1 Al.3)EFFo1d + VOLold for total resources

VALUEo7d for total resources(Ki A1,4)

= change in total resource quantity prescribed by old

$100 + $3 900=

$10 000

= 0,4 = 40,000%

Column (E2.5}

New product quantity adjusted for constant efficiency.

Qune = Quo * (1 +

150 * [1 ÷ 0,4 ] = 210,00 for product Ui

80 * [1 + 0,4 ] = 112,00 for product U2

Column (E2.7}

New product quantity adjusted for constant productivity.

Qunp = Quo * + 14o7d(I) ]

208,5 = 150,0 * [ 1 + 0,39 ] for product Ui

111,2 = 80,0 * [ 1 + 0,39 ] for product U2

Column (E2.13)

New product price adjusted for constant price recovery.

Punr = Puo * (1 + ls2new(I)

46,1584 = 40,0000 * [ 1 + 0,15396 1 for product Ui

51,6980 = 50,0000 * 1 1 + 0,15396 ] for product U2

The normalized new product quantity and new product price data specified

above are provided for illustration purposes. It is more customary to use

resource normalizations than product normalizations since resource levels can

typically be more readily varied by management than can product levels.

At the time of writing, the above product normalizations have not been

implemented in the 1988 software release. They will first be implemented in

the Input Quantity and Price Report, and thereafter will in due course appear

in an extension to the product volume and product price variances which appear

in the Input Variance Report. This report is not shown in this book, but is

specified in the scientific work on difference calculus on which this book is

based.

The following two pages show a graphical derivation of Qunp, Qnp, Punr and

Pnr which are defined in this chapter.

Although no graphical derivation is provided for Qune, it can be inferred

from the step function for REVA shown in Part I of the book.

KI — 2

• This page specifies'the measures Qnp for a resource and Qunp for product,

They are mutually exclusive and are used to ascertain the effect

productivity change on resource quantity used and on product quantity

Qnp represents new resource quantity normalized for constant

it prescribes a new level of resource quantity, given a new level of produfl

quantity, assuming that old productivity level is maintained in the

interval. Step 7 shows that Qn, representing new resource quantity,

subtracted from Qnp to measure the effect of productivity change on

quantity used.

Qunp represents new product quantity normalized for constant productivity.

it prescribes a new level of product quantity, given a new level of resourO

quantity, assuming that old productivity level is maintained in the nui

interval. Step 7 shows that Qunp is subtracted from Qun, representing nn

product quantity, to measure the effect of productivity change on

made.

Figure K1.F1 GRAPHICAL DERIVATION OF Qnp and Qunp

STEPZS1EPXCONSTANT (OLD)

:E"L,Qo RESORDCE

0' 0'

CONNECT OLD PROROCT Q0ANTFn ANDDRAW DIASEWAL CONNECTION AXIS INTER—

CONNECT NEW PROROCT Q0ANTITY TO DIA0m4AL

I OLD REDORDCE QOONTITY TO ESTABLISHCEPT TO OLE POOROCTI WIlT LEVEL TO SOON

AND EXTEND This INTERSECTION SOON TO

OLD PRcDOCT1YITY LEVELALE pOOROCTI VIII AT ANY

RESORRCE QUANTITY AXIS FOR DEW REDCURCL I

LEVELQUANTITY 0050NINO CONSTANT PRORUCTI Vii!

sTEP 4STEP S

STEP 6 1

:: EENPOOROCTIVITY

Qo 0, Q'o Qo QnQo nQop

CONNECT DEN RESORRCE QUANTITY TO rOEDRAW Quop HORIZONTAL AS SHOWN FOR MEN

PROROCTINIIY CAANGE RECTANGLE SHOWS

HORIZONTAL CONNECTING MEN PROROCTPHORUCT QUANTITY ASSONINS CONSTANT

EFFECT OF PRORUCTINITY CHANGE OR

QUANIITT TO THE DIAGONAL TO ESTASLTSS PVOROCTSYITTSESOROCE QUANTITY OR OR PRORACT

DEN PROROCTIVITT LEVEL --

STEP 1sTEP 0

STEP S

Qo

Qo Qo Qo Qop

POOROCTIVITT CONNSE IMPACTS ON

Q, < Qop For Qop C I, W

EIThER PRORUCT QSHNTITT AS Qo' — QuopPOOROCTIVITY

OR NESOROCE OOANTITT AS Qop — Qo

GAIN LOSS

PROROCTENIIY IMPACT ON POORACT QOANTIITPRCOOCIIYITY IMPACT OR RE OROCE QUANUIY

HENCE Quo/Qo = Qunp/Qn = Qun/Qnp >=< Qun/Qn

K1—3

I

This page specifies the measures Pnr for a resource and Punr for product.

They are mutually exclusive and are used to ascertain the effect of price

recovery change on resource price paid and on product price realized,

respectively.

Pnr represents new resource price normalized for constant price recovery andprescribes a new level of resource price given a new level of product price

assuming that old price recovery level is maintained in the new interval . Step

7 shows that Pn, representing new resource price, is subtracted from Pnr to

measure the effect of price recovery change on resource price paid.

Punr represents new product price normalized for constant price recovery andprescribes a new level of product price given a new level of resource price

assuming that old price recovery level is maintained in the new interval. Step7 shows that Punr is subtracted from Pun, representing new product price, to

measure the effect of price recovery change on product price realized.

Figure K1.F2 GRAPHICAL DERIVATION OF Pnr and Punr

STEP I STEP I STEP 3

APPENDIX A - SPECIMEN EXPERT SYSTEM REPORTS

computer inplementations of deterministic productivity accounting shvgld

provide for two independent reporting tracks. They are:

— detailed numeric reports, given by Part E in the book, to provide

with detailed information which underpins the results summarized by griA$.

— expert system reports, given by this appendix in the book, which proiiide

management with "big picture" data. They refer to results for tflalresources and introduce the commentary specified for each grid.

Expert systems flow the concept of artificial intelligence and are deslgjied

to make the knowledge of the expert available to the non—expert. Sfvce

solution of the model would place a given operation into grids :for

productivity disclosure as described in the chapter A3 discussion of the

productivity management journey, the expert system provides the gridsto the segments in which the operation

Hence the software would provide the user with a summarized of

concepts which are stated more fully in this book.

This appendix provides some diagrams to illustrate the concept of

intermediate and final operations. Thereafter it complements the

analysis of Business A by introducing Inhouse Supplier A whose prpduct

becomes the cost resource of Business A. The Input compact

Inhouse Supplier A is provided on page APPENDIX A — 5. Although $her

detailed numeric reports are not provided for Inhouse supplier A, its

reports are provided as explained below. The expert report for the Operjtion

consolidation (of Business A and Inhouse Supplier A) is supported

numeric reports for the consolidation of Business A and Inhouse Supplier in

order to indicate the origin of the numbers with respect to

supplier A. These reports are given on pages APPENDIX A — 6

APPENDIX A - 7.

— the Expert Operation Profit Overview Report (dealing with both long term

product profit and short term product profit changes) is providpd on

pages APPENDIX A - B through APPENDIX A - 12 for Business A.

— the Expert Operation Profit Long Term Report (dealing with longterm

product profit change) is provided on pages pages APPENDIX A — 13

APPENDIX A - Cor Inhouse Supplier A.

— the Expert Oprvation Profit Long Term Report (dealing with long term

product profit change) is provided on pages pages APPENDIX A — 17

APPENDIX A — 20 for the Operation Consolidation (i.e., theof Business A and Inhouse Supplier A operations).

Intermediate, Hybrid and Final Operations

Intermediate operations produce solely for inhouse customers and are iahouse

suppliers.

Final operations produce solely for external customers and are

APPENDIX A - I

CONSTANT (OLD)PRICE RECAREAR

I/

I I

DRAW DIAGONAL CONNECTING AXIS INTER-CEPT TA OLD PRICE RECORERT LEREL TOSWAN OLD PRICE RECORERO AT ANT PRONACT

PRICE LEREL

STEP S

:4 - - -

Pa Pn Pnr

ROAN Punr AOUIZONTAL AS SHOW Fm NEWpR000CT PRICE ASSONING CONSTANTPRICE RECORERA

Pun //

Pun /

II \/Pa Par

CONNECT NEW PRONACT PRICE TO DIAGONALAND EXTEND TRIS INTERAECTION DOW TARESOURCE PRICE WAIT FON NEW RESOURCEPRICE ADAANINO CONSTANT PRICE RECAVERA

STEP N

Pan PRICE REC00000

I CNANOE

Puar— — — —

NECTRRDLE

Pua / I

/1/

Pa In Pnr

PRICE OECOAEOT CRANOE RECTANGLE SROATEFFECT OF PRICE RECAAERT CHANGE ONRESOURCE PRICE ON ON PROUACT PRICE

PRONACT

OLD

Pun PRICE RECDRERT

Pa REIOUDCE

CONNECT OLD FRONOCT PRICE ANDOLD RESOURCE PRICE 10 ESTANLIINDLD PNICE RECORERT LEVEL

SIEP 4

NEW PRICE RECDRERT

1/iPa Pn Pnr

CONNECT NEW RESOURCE PRICE TO IREHONIZONTAL CONRECTINO NEW POOUACTPRICE TO THE DIAOONAL 10 ESIADLISNNEW PRICE RECARERA LEREL

STEP 7

Pun

I /Panr — — — —,

Pun / I

/ I

Pa Pn Pnr

PRICE RECARERA COUNAE IMPACTS ONEIThER PROUOCT PRICE AX Pun — Punr

CO RESOURCE PRICE AS Par — Pn

4

In this appendix the following expert system reports are provided:

SIEP NSTEP

Pun PunrPun DPRICE RRER-OECDYEOVPuar

Pun A PuarPun

PRICE ANDER—RECARERA

Pa Pa Par

Pun

rmlI / i

Pa Pa

Pa < Par Far Par < Pa farPRICE ORER PRICE ORDER

RECOTERO RECATERA

PRICE RECORERO IMPACT ON PROUOCT PRICE PRICE RECORERA IMPACT ON ESOURCE PAICD

HENCE Puo/Po = Punr/Pn = Pbn/Pnr >=< Pun/Pn

Kl — 4

Hybrid operations produce for both inhouse customers and external customers.The hybrid operation may draw upon both cost and capital resources from

outside of the business as a whole. Part of Its products then feed otherinhouse supplier operations, who may themselves also draw from exteriorsources for additional cost and capital resources to produce final products

(i.e., products that are invoiced to external customers and thereby generate

revenue).

A typical example of this would be a production unit that produces

components that are used within the business for insertion into products thatare sold by the business to the exterior market. Some of the components may besold direct to the exterior market.

The FPM software does not yet cater for a hybrid operation. Hybrid

operations must be divided into a purely intermediate component and a finalcomponent.

The various combinations of final, intermediate and hybrid operations are

illustrated on the following two pages.

APPENDIX A — 2

U = symbol for product

N = symbol for cost resource

K = symbol for capital asset resource

APPENDIX A — 3

INTERMEDIATE OPERATIONS

HYBRID OPERATIONS1900/00/01

PPM. INPUT CEIIPACT REPEOTADJUSTER PEI1 ZERO INTERVAL

WIDTH CHANGE

INVERSE SUPPLIER AIRAN vs. 1909

VeTOeR eve In DOLLARS

INREXIENTITY

Old (Reference)Interval —>c——— New InteresT

adjosted ———> C———— PRrCRIIECHANGE In

REVO VALUE QUANTITY PRICE VALUE QIJANTIB PRICE VALUE QUANTITY $JCE

A S C E E F El A

INCENE:

Y

03 PredatE w3

TRIAL INCCI4E

0000.9 4RR.0 20.000 12540.0 570.0 22.000 SR.75R 42.500 11,200

00000

I

.

COST IIE0000CES:

02 Naterlal a3 .00 5000.0 150.0 50.000 12R0.I 100.0 52.000 45.000 4R.E00

I -- TOTALETPE9GES - --

720045.600 40.000 ftoo I

TO Equipment s3 .20 2400.0 50.0 40.000 3500.0 15.0 52.000 62.500 50.000

.

30052.500 50:000 j333

;rTr;RorflI1NTOINSIC PROFIT

3000 05200 0

75 333 40 607 545

E2 EquIpment o3 .20 20000.0 50.0 400.000 39000.0 75.0 520.000 95.000 50.000 20.000

TOTAL CAPITAL RESEORCER20000.0

30000.0 j 95.000 50.000 'hOOD)

N = symbol for cost resource

APPENDIX A — 4

IAPPENDIX A — 5

-

NN

INTERNEDIATEFINAL

r ERATION

U

OPERATIONOP

4 KK

U = symbol for product

K = symbol for capital asset resource

1988/09/01FPN INPUT VALIDATION 'U' REPORT

CONSOLIDAIION OF 2 OPERATIONS

1989 vs. 1909


(iNDEX) ENTITY A I C D

INCOME:

UI Product ci 0000.00 100.00 40.00000 0000.00

02 ProducE a2 4000.00 90.00 50.00000 1100.00

03 Product a3 8000.00 400.00 20.00000 12540.00

INCOME 18000.00 30540.00

COST RESOURCES:

NI Maoerlal a 9000.00 400.00 00.00000 12540.00 570.00 22.00000

82 Material a3 5000.00 100.00 50.00000 7200.00 140.00 02.00000

IITOTUL OPERATING EXPENSES I

13000.0019820.00

CAPITAL RESOURCES:

TI Equipment a 0000.00 8.00 050.00000 3500.00 10.00 300.00000

TO Equipment a3 - 0000.00 50.00 40.00000 3900.00 70.00 01.09900

I)TOTUL CAPITAL RESOURCES I

4400.00 7400.00

ITOTAL RESOURCES I17400.00 27020.00

I10FF TARGET PROFIT I

600.00 3320.00 = -—

141018010 PROFIT 5000.00 10720.00

CAPITAL RESOURCES:

01 Eqalpoent a 40000.00 0.00 5000.00000 70000.00

02 Equipment u3 00000.00 50.00 400.00000 30000.00

I110101. CAPIIAL RESEOJRCEI 00000.00 109000.00

I044 INVESTMENT (5) 8.33 9.03

APPENDIX A — 6

1900/09/UI

0988/09/01

MEW OLD NEW OLD MEW 091009010

OLD (REFERENCE) INTERNALNEW (REVIEW) INTERVAL

UPERATIGII INTERVAL INTERVAL IMIERVUL INTERVAL 18I00051C INTRINSIC PR'#IT

VALUE QUANTITY PRICE VALUE QUANTITY PRICE1=_======?

FRONT PROFIT

i 1

0 EAC 7:8-0

(148GIISE SUPPLIER A I6000.0 12540.0 5000.0 700.0 3000.0 5200.0 2268.0 I

0:90

7280 3000 sooo

570.00 22.00000'

SUM OF FINAL OPERATIONS I00000.0 18000.0 8080.0 12540.0 2000.0 0400.0

(OPERATION CONSOLIDATION )

18000.0 30540.0 13000.0 19020.0 0000.0 10700.0 I

(LESS INTERMEDIATE = (8000.0 12540.0 5000.0 7280.0 3000.0 0080.0 I

(AUJUUIED CONSULIOUTIEM )100000 08000.0 -- 8000.0 - 12540.0 2000.0 5060.0 3440

1008/09/007PM PROFIT RECDNCILIATOE*I REPORT --

0988 vu. 0989

Values are in OOLL005

PROFIT INTERVAL INTERVAL UET000 UN TARGET 184 19

00 00 7000 00000OPERATION

RECONCILIATION PROFIT GAP PROFIT 90010 REVENUE RVI INVES — NT

75:02

VARIANCE VARIANCE VARIANCE VARIANCE VARIANCE 0*T4CE

L0 +

(INV005E SUPPLIER U I0800.50

340.50 780.00- I

(GUM OF INTERMEDIATE UPERU(02.00.50

340.50 780.00- 22goo I

(BUSINESS 8 I1500.00

10MO0 I

(000 OF FINAL OPERATIONS I0500.00

I

(070001188 CONSOLIDATION I= 3340.50

-- 340.00 780.00- I

(LE TEOIIEOIA'IE 1340.00340.50 .00

—

FF8 PROFIT BACKGROUND REPORT

198045. 0189

Values are In UOLLMS

FF8 PROFIT PERFUR1'GINCE OVERVIEN REPORT

1988 vs. 1089

APPENDIX:-7 —fl

.

!

0=8+ CC 0 + E P = 0 v

io.5 410.5;5.o_SOO.51413.i:10330_4149W4°I

2200,0 1840.5 419.5 00.0— 480.5 1413.1— 0833.0- 419.9 'fl6U.Q(

H

(00807 INTERMEDIATE

(BUSINESS A 3460.C 1000.0 1900.0 1360.0 600.0 700.0 40.0— 800.0 I

UP FINAL OPERATIONS I 3460.0 1500.0 0080.0 1300.0 600.0 760.0 40.0- 800.0

(SUN

(OPERATION CONSOLIDATION (5724.0 3340.0 2379.5 0290.0 0086.5 053.1- 1873.0- 1210.9 24100.0

1[i[cINT500EO10T

1

The old interval profit of $2 000.00 was derived from a total revenue of$10 000.00 and a total cost of $8 000.00 . The new interval profit of$5 460.00 was derived from a total revenue of $18 000.00 and a total cost

of $12 540.00. Thus the INTRINSIC PROFIT VARIANCE before adjustments is$3 460.00 which amounts to 173.000% of the old interval profit. These

results are summarized in the profit background report.

The above INTRINSIC PROFIT VARIANCE may now be dividedcontributions, all of which are shown in the profitperformance reports.

The LONG TERM PRODUCT PROFIT variance of $1 960.00 , contributes 98.000% tothe 173.000% change in profit. This variance is of fundamental importancesince it is the sum of the productivity and price recovery variances which areimportant for resource allocation decisions. The above monetary value shows

the favorable financial effect of decline in the ratio of expense to revenue

between old and new intervals. The old interval ratio of 100.000%

($10 000.00 divided by $10 000.00) declined to the new interval ratio of89.111% ( $16 040.00 divided by $18 000.00).

The product profit variance is the change in profit that takes cognizance ofboth cost resources and capital resources. It employs a cost of capitalbased on the target return—on—investments of the capital in the old and new

intervals.

\2 2/\+ 1

3 -s-/

3—\ ++ I—i

0 X 0 X

— \+6 4+! —

4 —\ /— 6

5 \ /5TERM SHORT TEEM PROOUCTIVTY LONG TERM SHORT TERM PRICE

GRID PROFIT G11D GRID QUANTITY GRD QUANTITY GRD GRID

=VplusX =YplusX =YplusX =YminusX =YminusX =Y-X+ + +

PRDDUCTIVITV EFFICIENCY CAP UTIL CHANGE IN RES Q AT CONST CHANGE

VARIANCE VARIANCE PRODUCTIVITY jEFFICIENCY

- .———— + +

TERM SHORT T[RM EFFICIENCY CHANGE IN CHANGE IN CHANGE

REC PRICE REC VARIANCE RESOURCE Q RESOURCE Q RESOURC

-+. + + -4

CENTER CENTER CENTER CENTER CENTR

<—— AWAKEN WIN LIFTOFF LIFTOFF TRAILORBIT c——

PURSUE

FINETUNESCUTTLESALVAGESCRAMBLEC——

GAMBLE c——

SQUANDR

LOSERECOUP

EXCEL

ORBITDISCHARG DISCHARG

OVEREACT OVEREACT

HOARD HOARD

DESTRUCT DESTRUCT

GOUGE

SHAVEPARE

SLASH

-

I N LONG TERM PRODUCT

F- +

PROFIT I$1 960.00

I8.479%

-PRODUCTIVITY IMPROVEMENT

LONG TERN PRICE OVCR—RECOVERY (UNSAFE)

Your business appears in the AWAKEN segment of the long term profitbecause the favorable product profit variance of $1 960.00 , arises fronj a

favorable productivity variance of $1 360.00 , and a favorable but

long term price recovery variance of $600.00 . The productivityflows from a B.479% gain in productivity with respect to all resources,the price recovery variance flows from a 3.448% price over—recovery with

respect to all resources.

++

CONSUMER PAYS SUBSIDY TO PRODUCER IN THE LONG TERM OF I$600.00

+

SUPPLIER HARMED IN THE LONG TERM BY AN AMOUNT OF I$1 360.00

+-t

The combination of increasing product profit and umbrella pricingprices are changing favorably relative to resource price changes)

trigger the entry of new competitors. However, even if competitive

-completely eliminates the price umbrella, this business would reflect

APPENDIX A — 9

1988/09/01 FPM EXPERT OPERATION PROFIT OVERVIEW REPORT

1988 vs. 1989BUSINESS A

NEW INTERVAL $18 000.00 — $12 540.00 = $5 460.00+ I I

OLD INTERVAL $10 000.00 — $8 000.00 = $2 000.00

INTRINSIC P/OFIT VARIANCE $3 460.00

into the followingreconciliation and

INTRINSIC PROFIT VARIANCE $3 460.00

RECONCILIATION VARIANCE $1 500.00

+— LONG TERM PRODUCT PROFIT VARIANCE $1 960.00

— LONG TERM PRICE RECOVERY VARIANCE $600.00

CAPACITY UTILIZATION TERM ($200.00)

+— SHORT TERM PRICE RECOVERY VARIANCE $800.00

+— PRODUCTIVITY VARIANCE $1 360.00

CAPACITY UTILIZATION VARIANCE $1 400.00

+— EFFICIENCY VARIANCE ($40.00)

LONG TERM PROFIT GRID ANALYSIS

$600.00 3.448%

APPENDIX A — 8

but still positive, change in product profit on account of productivity gain.This situation harms the suppliers of resources in the long term by an amountof $1 360.00 because of the decreasing resource content per unit of product.It also harms the consumer in the long term because he pays a subsidy of

$600.00 to the producer.

SHORT TERM PROFIT GRID ANALYSIS

Your business appears in. the SCRAMBLE segment of the short term profit gridbecause the favorable short term product profit variance of $760.00arises from an unfavorable efficiency variance of ($40.00) , and a

favorable but unsafe short term price recovery variance of $800.00 . Theefficiency variance flows from a (.249%) decline in efficienct with respectto all resources, and the price recovery variance flows from a 5.000% priceover—recovery with respect to all resources.

+ +

CONSUMER PAYS SUBSIDY TO PRODUCER IN THE SHORT TERM OF $800.00+

SUPPLIER FAVORED IN THE SHORT TERM BY AN AMOUNT OF ($40.00)

Short term product profit is increasing because the umbrella pricing gain(product prices are changing favorably relative to resource price changes)exceeds (and hence camouflages) efficiency loss. The threat of new competitorsis real because of both umbrella pricing and increasing product profit.Furthermore, efficiency loss narrows the efficiency gap between this businessand the low efficiency levels of newcomers to the market. A verticalturnaround from efficiency loss to gain is needed, since competitive erosionof the price umbrella could transform this business from increasing todecreasing short term product profit. There is no efficiency pie to sharebetween producer and consumer. Instead there is a efficiency deficit. Thissituation favors the suppliers of resources in the short term by an amount of

($40.00) because of the increasing resource content per unit of product. Italso harms the consumer in the short term because he pays a subsidy of

$800.00 to the producer.

PRODUCTIVITY GRID ANALYSIS

GAMBLE SEGMENT VARIANCE % CHANGE

PRODUCTIVITY IMPROVEMENT $1 360.00 8.479%

CAPACITY UTILIZATION GAIN $1 400.00 8.750%

EFFICIENCY DECLINE ($40.00) (.249%)

Your business appears the GAMBLE segment of the productivity grid becausethe favorable productivity variance of $1 36O.D0 , arises from a favorablicapacity utilization variance of $1 400.00 , and an unfavorable efficiencjvariance of ($40.00) . The capacity utilization vatiance flows from

8.750% gain in capacity utilization with respect to all resources, and thpefficiency variance flows from a (.249%) decline in efficiency with respectto all resources.

+ ÷

POTENTIAL GAIN TO CONSUMER OF $1 360.00+

PRODUCER FAVORED BY AN AMOUNT OF. I

$1 400.00+

SUPPLIER FAVORED IN THE SHORT TERM BY AN AMOUNT OF j($40.00)

In this situation the producer gambles through reducing efficiency and erodinghis cost advantage which flows from increased capacity utilization. This,balance, harms the supplisrs of resources because his loss from theresource content per unit of product which arises from increased capacitijutilization exceeds his benefit from the increasing resource content per unitof product which arises from reduced efficiency.

LONG TERM QUANTITY GRID ANALYSIS

Your business appears in the ORBIT segment of the long term quantity grI4because the favorable productivity variance of $1 360.00 , arises from

50.000% growth in production and a 39.000% increase in resourceThis is the ideal segment as it favors the suppliers of resources because dtthe increasing demand for resources. It can arise in the later (i.e.phase of increasing demand for product. Productivity growth reduces productcost, so that in the long term this situation will enhance competitivenessthe viability of the producer.

SHORT TERM QUANTITY GRID ANALYSIS

LIFTOFF SEGMENT I

EFFICIENCY DECLINE OF I($40.00)

+

INCREASE IN RESOURCE QUANTITY AT CONSTANT EFFICIENCY I40.000%

+

INCREASE IN RESOURCE QUANTITY 39.000%

Your business appears in the LIFTOFF segment of the short term quantitybecause the unfavorable efficiency variance of ($40.00) , arises from

40.000% growth in resource usage at constant efficiency is less than

APPENDIX A — 11

SCRAMBLE SEGMENTI

VARIANCE % CHANGE+ +

IMCREASE IN SHORT TERM PRODUCT PROFITI

$760.001

+ +

EFFICIENCY DECLINEI

($40.00) (.249%)+ +

SHORT TERM PRICE OVER—RECOVERY (UNSAFE)I

$800.00I

5.000%

ORBIT SEGMENT

PRODUCTIVITY IMPROVEMENT OF I$1 360.00

- +

INCREASE IN PRODUCT QUANTITY 50.000%- +

INCREASE IN RESOURCE QUANTITY 39.000%

APPENDIX A — 10

39.000% increase in resource usage. This situation favors the suppliers ofresources because of the increasing demand for resources. It can arise in the

early (i.e. weak) phase of increasing demand for product, and is typicallyconstrued by management as a transient stage which precedes migration to theORBIT segment. Efficiency decline increases product cost so that in the shortterm this situation will undermine competitiveness and the viability of the

producer.

PRICE GRID ANALYSIS

SPURT SEGMENT

+PRICE OVER—RECOVERY OF $600.00

+

INCREASE IN PRODUCT PRICE 20.000%+

INCREASE IN RESOURCE PRICE I16.000%

+

Your business appears in the SPURT segment of theprice grid because thefavorable price recovery variance (price over—recovery) of $600.00 is due

to a 20.000% increase in the total price of products which is reduced by a

16.000% increase in the total price of resources.

This situation harms the consumer because he pays a subsidy to the producer.The consumer is required to pay more than the resource price increase which

the producer pays his supplier. This situation can arise in the later (i.e.strong) phase of increasing demand for product. Price over—recovery increasesshort term profitability, yet if it is maintained in the long term it will beperceived as a price umbrella which could trigger competitive pricing behaviorwhich will undermine profitability and the viability of the producer- in the

event of no productivity growth.

APPENDIX A — 12

1988/09/01 FPM, EXPERT OPERATION PROFIT LONG TERM REPORT

1988 vs. 1989

INHOUSE SUPPLIER A

The old interval profit of $3 000.00 was derived from a total revenue of

$8 000.00 and a total cost of $5 000.00 . The new interval profit of

$5 260.00 was derived from a total revenue of $12 540.00 and a total çpst

of $7 280.00 . Thus the INTRINSIC PROFIT VARIANCE before adjustments Is

$2 260.00 which amounts to 75.333% of the old interval profit. These

results are summarized in the profit background report.

The above INTRINSIC PROFIT VARIANCE may now be divided into the followingcontributions, all of which are shown in the profitperformance reports.

The LONG TERM PRODUCT PROFIT variance of $419.50 contributes to

the 75.333% change in profit. This variance is of fundamental

since it is the sum of the productivity and price recovery variancesimportant for resource allocation decisions. The above monetary value shows

the favorable financial effect of decline in the ratio of expense to re$nue

between old and new intervals. The old interval ratio of 92J0O%

$7 400.00 divided by $8 000.00 ) declined to the new interval of89.155% ($11 180.00 divided by $12 540.00).

The product profit variance is the change in profit that takes cognizance of

both cost resources and capital resources. It employs a cost of c4italbased on the target return—on—investments of the capital in the oldintervals. -

APPENDIX A — 13

TOTAL REVENUE TOTAL COST PROFIT

—-F

NEW INTERVAL $12 540.00 — $7 280.00 = $5 260.00

+ I I

OLD INTERVAL $8 000.00 — $5 000.00 = $3 000.00

INTRINSIC PROFIT VARIANCE I$2 260.00

+INTRINSIC PROFIT VARIANCE $2 260.00

RECONCILIATION VARIANCE $1 840.50

+— LONG TERM PRODUCT PROFIT VARIANCE $419.50

LONG TERM PRICE RECOVERY VARIANCE $484.50

+— PRODUCTIVITY VARIANCE ($65.00)+

V\2\+ 1

3—\ ÷

— \+64 -\

5 \

Y

2 /3 +1

+ /—l—O —x

—

/— 6/5LONG TERMPROFIT GRID=YplusX

PRODUCTIVITYGRID=YplusX

LONG TERMQUANTITY GRID=YminusX

PRICEGRID=YminusX

PRODUCTIVITYVARIANCE

CAP UTILVARIANCE

CHANGE INPRODUCT QUANTITY

CHANGE INPRODUCT PPRICE

LONG TERNPRICE RECOVERY

EFFICIENCYVARIANCE

CHANGE INRESOURCE QUANT

CHANGE INRESOURCE PRICE

0 CENTER

1 AWAKEN

2 PURSUE

3 FINETUNE4 SCUTTLE5 SALVAGE6 SCRANBLE <——

CENTERWINGANBLESQUANDER c——

LOSE

RECOUP

EXCEL

CENTERLIFTOFF <——

ORBITDISCHARGEOVERREACTHOARD

DESTRUCT

CENTERTRAILSPURT c——

GOUGE

SHAVEPARE

SLASH

LONG TERN PROFIT GRID ANALYSIS

I$419.50 I

- + +

PRODUCTIVITY DECLINE I($65.00) (.581%)

- + +

LONG TERM PRICE OVER—RECOVERY (UNSAFE) I$484.50

I4.359%

- +

Your business appears in the SCRAMBLE segment of the long term profit gridbecause the favorable product profit variance of $419.50 , arises from an

unfavorable productivity variance of ($65.00) , and a favorable but unsafe

long term price recovery variance of $484.50 . The productivity varianceflows from a (.581%) decline in productivity with respect to all resources,and the price recovery variance flows from a 4.359% price over—recoverywith respect to all resources.

CONSUMER PAYS SUBSIDY TO PRODUCER IN THE LONG TERN OF I$484.50

+

SUPPLIER FAVORED IN THE LONG TERN BY AN ANOUNT OF ($65.00)+

Product profit is increasing because the umbrella pricing gain (product pricesare changing favorably relative to resource price changes) exceeds (and hencecamouflages) productivity loss. The threat of new competitors is real because

APPENDIX A — 14

of both umbrella, pricing and increasing product profit. Furtherrisre,productivity loss narrows the productivity gap between this business and.Jthelow productivity levels of newcomers to the market. A vertical turnaround fromproductivity loss to gain is needed, since competitive erosion of the

umbrella could transform this business from increasing toproduct profit. There is no productivity pie to share betweenconsumer. Instead there is a productivity deficit. This situation favors

the long term by an amount of ($65.00) ofthe increasing resource content per unit of product. It also harms?theconsumer in the long term because he pays a subsdiy of $484.50 to 'theproducer.


SQUANDER SEGMENT VARIANCE % CHANGE

- + +

PRODUCTIVITY DECLINE ($65.00)I

(.581%)

+ +

CAPACITY UTILIZATION GAIN I$1 768.00

I18.915%

+ +

EFFICIENCY' LOSS I($1 833.00) I

(16.395%)

Your business appears in the SQUANDER segment of the productivity grid becausethe unfavorable productivity variance of ($65.00) , arises from acapacity utilization variance of $1 768.00 , and an unfavorable effictjncyvariance of ($1 83300). The capacity utilization variance flows a

18.915% gain in capacity utilization with respect to all resources,a (16.395%) decline in efficiency with

to all resources.

POTENTIAL LOSS TO+

PRODUCER FAVORED BY AN ANOUNT OF I$1 768.00

+

SHORT TERN BY AN AMOUNT OF ($1 833.00)SUPPLIER FAVORED+

In this case the producer squanders the cost advantage conferred byutilization gain through more than offsetting reductions in efficiency.benefits the supplier of resources because of his loss arising from incrnsedcapacity utilization is more than offset by his gain arising from

efficiency.

LONG TERN QUANTITY GRID ANALYSIS -

V LIFTOFF SEGMENT

PRODUCTIVITY DECLINE OF I($65.00)

+

INCREASE IN PRODUCT QUANTITY 42.500%+

INCREASE IN RESOURCE QUANTITY I43.243%

Your business appears in the LIFTOFF segment of the long term quantity grid

APPENDIX A — 15

I

-flu

because the unfavorable productivity variance of ($65.00) , arises from a

42.500% growth in production which is less than the 43.243% ingrease inresource usage, This situation favors the suppliers of resources because .of

the increasing demand for resources. It can arise in the early (i.e. weak)

phase of increasing demand for product; and is typically construed bymanagement as a transient stage which precedes migration to the ORBIT segment.Productivity decline increases product cost so that in the long term thissituation will undermine competitiveness and the viability of the producer.

PRICE GRID ANALYSIS

SPURT SEGNENT

PRICE OVER—RECOVERY OF $484.50+

INCREASE IN PRODUCT PRICE j 10.000%+

INCREASE IN RESOURCE PRICE 5.405%

Your business appears in the SPURT segment of the price grid because thefavorable price recovery variance (price over—recovery) of $484.50 is due



This situation harms the consumer because he pays a subsidy to the producer.The consumer is required to pay more than the resource price increase which

the producer pays his supplier. This situation can arise in the later (i.e.strong) phase of increasing demand for product. Price over—recovery increasesshort term profitability, yet if it is maintained in the long term it will beperceived as a price umbrella which could trigger competitive pr.icing behaviorwhich will undermine profitability and the viability of the producer in the

event of no productivity growth.

The old interval profit of $5 000.00 was derived from a total revanue of$18 000.00 and a total cost of $13 000.00. The new interval prjfit of$10 720.00 was derived from a total revenue of $30 540.00 and a totk$ cost

of $19 820.00. Thus the INTRINSIC PROFIT VARIANCE before is$5 720.00 which amounts to 114.400% of the old interval These

results are summadzed in the profit background report.

The above INTRINSIC PROFIT VARIANCE may now be divided into thecontributions, all of which are shown in the profit reconciliat%an and

performance reports.

The LONG TERN PRODUCT PROFIT variance of $2 379.50 , contributes tothe 114.400% change in profit. This variance is of fundamentalsince it is the sum of the productivity and price recovery variances wkjch areimportant for resource allocation decisions. The above monetary value showsthe favorable financial effect of decline in the ratio of expense tobetween old and new intervals. The old interval ratio of 96.667%

( $17 400.00 divided by $18 000.00) declined to the new interval r*tio of89.129% ($27 220.00 divided by $30 540.00). -

The product profit variance is the change in profit that takes ofboth cost resources and capital resources. It employs a cost of lapitalbased on the target return—on—investments of the capital in the old new

intervals.

1988/09/01 FPN EXPERT OPERATION PROFIT LONG TERN REPORT

1988 vs. 1989

OPERATION CONSOLIDATION

-NEW INTERVAL

!$30 540.00 $19 820.00

- I

OLD INTEIIVAL $18 000.00 — $13 000.00 = $5 000.00

$10 720.00

IRIIIRI $5 720.00

RECONCILIATION VARIANCE $3 340.50 -

+— LONG TERM PRODUCT PROFIT VARIANCE $2 379.50

LONG TERN PRICE RECOVERY VARIANCE $1 084.50

+— PRODUCTIVITY VARIANCE $1 295.00

APPENDIX A — 16APPENDIX A — 17

V\2\+ 1

3—\ +0 X

— \+64 —\

5 \

V

2 /3

+0 X

—

I— 6/5PRODUCTIVITY

GRID GRIDX = Y plus X

F— —

LONG TERMQUANTITY GRID= Y minus X

PRICEGRID= Yminus X

—

CAP UTIL CHANGE IN CHANGE IN

VARIANCE PRODUCT QUANTITY PRODUCT PPRICE- F- + -

EFFICIENCY CHANGE IN CHANGE IN

RECOVERY VARIANCE RESOURCE QUANT RESOURCE PRICE

CENTER

<—— WINGAMBLE C——

SQUANDER

LOSERECOUPEXCEL

CENTERLIFTOFFORBIT C——

DISCHARGEOVERREACTHOARD

DESTRUCT

CENTERTRAILSPURT <——

GOUGE

SHAVEPARESLASH

LONG TERM PROFIT GRID ANALYSIS

INCREASE IN LONG TERN PRODUCT PROFIT j $2 379.50

I$1 295.00 4.758%

+ +

LONG TERM PRICE OVER—RECOVERY (UNSAFE) I$1 084.50 I

3.803%

Your business appears in the AWAKEN segment of the long term profit gridbecause the favorable product profit variance of $2 379.50 , arises from a

favorable productivity variance of $1 295.00 , and a favorable but unsafe

long term price recovery variance of $1 084.50 . The productivity varianceflows from a 4.758% gain in productivity with respect to all resources, andthe price recovery variance flows from a 3.803% price over—recovery withrespect to all resources.

$1084.50

The combination of increasing product profit and umbrella pricing (productprices are changing favorably relative to resource price changes) could

trigger the entry of new competitors. However, even if competitive entry- completely eliminates the price umbrella, this business would reflect lower,

APPENDIX A —18

but still positive, change in product profit on account of productivity gain.This situation harms the of resources in the long term by an amount

of $1 295.00 because of the decreasing resource content per unit of product.It also harms the consumer in the long term because he pays a subsidy of$1 084.50 to the producer.


GAMBLE SEGNENT

PRODUCTIVITY IMPROVEMENT

CAPACITY UTILIZATION GAIN

EFFICIENCY DECLINE

VARIANCE % CHANGE+

$1 295.00 I4.758%

+

$3 168.00 12.499%+

($1 873.00) I(6.881%)

Your business appears in the GAMBLE segment of the productivity grid because

the favorable productivity '!ariance of $1 295.00 , arises from a favorablecapacity utilization varlanre of $3 168.00 , and an unfavorable efficiencyvariance of ($1 873.00). The capacity utilization variance flows from a

12.499% gain in capacity utilization with respect to all resources, and theefficiency variance flows from a (6.881%) decline in efficiency with respectto all resources.

POTENTIAL GAIN TO CON&INER OF I

+

PRODUCER FAVORED BY AMOUNT OF ' $3 168.00

SUPPLIER FAVORED IN THE SHORT TERN BY AN AMOUNT OF ($1 873.00)+

+

In this situation the producer gambles through reducing efficiency and erodinghis cost advantage which flows from increased capacity utilization. This, on

balance, harms the suppliers of resources because his loss from the decreasingresource content per unit of product which arises from increased capacityutilization exceeds his benefit from the increasing resource content per unitof product which arises from reduced efficiency.

LONG TERM QUANTITY GRID ANALYSIS

PRODUCTIVITY IMPROVEMENT OFI

$1 295.00+

INCREASE IN PRODUCT QUANTITY I46.810%

+

INCREASE IN RESOURCE QUANTITY 40.805%+

Your business appears in the ORBIT segment of the long term quantity gridbecause the favorable productivity variance of $1 295.00 , arises from a

46.810% growth in production and a 40.805% increase in resource usage.

This is the ideal segment as it favors the suppliers of resources because ofthe increasing demand for resources. It can arise in the later (i.e. strong)phase of increasing demand for product. Productivity growth reduces product

APPENDIX A — 19

cost, so that in the long term this situation will enhance competitiveness andthe viability of the producer.

APPENDIX B — BIBLIOGRAPHY

The following references list the published references to the work ofJames van Loggerenberg.

The following text cites fifteen references which proceed from item in1988 back to item Al in 1974.

Your business appears in the SPURT segment of the price grid because thefavorable price recovery variance (price over—recovery) of $1 084.50 is due



This situation harms the consumer because he pays a subsidy to the producer.The consumer is required to pay more than the resource price increase whichthe producer pays his supplier. This situation can arise in the later (i.e.strong) phase of increasing demand for product. Price over—recovery increasesshort term profitability, yet if it is maintained in the long term it will beperceived as a price umbrella which could trigger competitive pricing behaviorwhich will undermine profitability and the viability of the producer in theevent of no productivity growth.

Three notations have been developed to reach audiences with differingof mathematical appreciation.

Notation 1 is the simplest articulation of the concept and is containe4 initem A14 in the bibliography. It is non—technical and provideswith a description of the analytical tool and how it is used toallocation of resources and hence profitability. This notation isin courses in third year engineering, third year business economics ingraduate schools of bjsiness.

Notation 2 is algebraically more demanding than notation 1. It employ; an

index set 3 arguments to specify difference equations whichfrom ordinary differences of degree one and order one to partial differodcesof degree one and higher order. Notation 2 is contained in items A9in the bibliography. It is used in courses in fourth year engineering.

Notation 3 is algebraically more demanding than notation 2. It a

more generalized index set, comprizing 3 arguments and severalto specify difference equations which range from ordinary differencer ofdegree one and order one to partial differences of higher degree and htgherorder. This notation is contained in items AlS and All in the Itis used in postgraduate courses in engineering and specifies thegeneralized deterministic mathematical structure which underpins the

A15 van Loggerenberg, Bazil J."Difference calculus for deterministic productivity accountingfor engineers to decode financial signals"Productivity Measurement Associates, Monograph, (forthcoming in

ISBN 0 620 10527 5

This is the latest exposition of all concepts using notation 3.and replaces the specification published in reference All below.

A14 van Loggerenberg, Bazil J.,"Productivity dncoding of financial signals:a primer for manngers ondeterministic productivity accounting".Productivity Measurement Associates, Monograph, 1988.

ISBN 0 951 3828 0 2 (UK edition)

It

ISBN 0 620 10540 2 (RSA

This is the latest exposition of major concepts using notation 1.

I

APPENDIX A — 20APPENDIX B —

PRICE GRID ANALYSIS

SPURT SEGMENT

PRICE OVER—RECOVERY OF $1 084.50+

INCREASE IN PRODUCT PRICE 15.747%+

INCREASE IN RESOURCE PRICEI

11.494%

LIST A — Published Works of Author

1988),

A13 van Loggerenberg, Basil J."A deterministic analysis of change in international unitlabor cost: import implications for U.S. industry"Managerial and Decision Economics

Vol. 8, 339—342 (1987)

This article is aimed at quantitative readers and presents a deterministicapproach to measure the relationship between productivity and unit labor costchange. The article employs the abridged notation cited under item E9 below.

A12 van Loggerenberg, Basil J."Deterministic productivity accounting for engineersto decode financial signals"S.A. Journal of Industrial Engineering

December 1987, Vol 1, No 2, (33 — 39)

This article provides engineers with an overview of the principal consepts.

All van Loggerenberg, Bazil J."Difference calculus for deterministic productivity accountingin the firm and in the economy"Productivity Measurement Inc., Monograph, 1986.

ISBN 0 620 09917 8 (1st edition)

This volume is aimed at mathematicians and presents the fully generalizednotation developed by the author to provide a comprehensive mathematicalspecification for deterministic productivity accounting. It updates itemA7 which is cited below. -

AlO van Loggerenberg, Basil J and Parsons, John"Tax rebates for productivity winners"The 5th World Productivity Congress,

Djarkata, Indonesia 1986, organised byThe World Confederation of Productivity Science.

This article aims at policy analysts and proposes a framework in whichfiscal policy can reward winners in the corporate productivity race. Thearticle is non—algebraic and addresses the issues raised by such a policyproposal.

A9 van toggerenberg, Basil J."The deterministic nexus between productivityand price change"South African Journal of Science

January 1986, vol 82 (34 — 45) ISSN 0038 2353

This article is aimed at mathematiciansd!terministic alternative to the customary

employed by econometrics to measure the relationship between productivity aqdprice change. The article presents an abridged version of thegeneralized notation specified in the PMI monograph cited in reference A)below.

A8 Visser, Jan H. and van Loggerenberg, Basil J."Product ivity and its proper measurement"South African Journal of Science

January 1986, vol 82 (21 — 23) ISSN 0038 2353

This article is aimed at scientists and brings to theirthe notion of productivity and its proper measurement in view Qtthe interest on the part of the authorities in linking the fundingteaching and research activities to productivity performance.

A7 van Loggerenberg, Basil J."A Mathematical Specification for Deterministic ProductivityAccounting in the Film and in the Economy",Productivity Measurement Inc., Monograph, November 1985,

ISBN 0 620 08958 X (1st edition)

This volume is aimed at mathematicians and presents the fully generalise4notation developed by the author to provide a comprehensive mathematica)specification for deterministic productivity accounting.

A6 van Loggerenberg, Basil J."Measuring business productivity",(Paper presented to theAmerican Institute for Decision Sciences

November 1983 Conference at San Antonio, Texas)

This article is aimed at business accountants and specifies geometricidentities to define variables. It reviews cost accounting measures andextends them with the additional measures introduced by the REALST model.

AS van Loggerenberg, Basil J."Deterministic growth accounting",DRI Statistician, December 1982

This article shows how a deterministic decomposition methodologycomprising a system of partial difference identities can be used tdvalidate stochastic models. The application entails testing part ofInput—Output model of DRI (Data Resources Inc.) which is the largest firmengaged in econometric modelling in the United States.

A4 van Loggerenberg, Basil J. and Cucchiaro, Stephen J."Productivity measurement and the bottom line",National Productivity , Winter 1981—82: 87—99.

This non—technical article is aimed at management and focusses on thephilosophy of the approach and on business applications.

APPENDIX B — 2

and presents a

stochastic approach

APPENDIX B — 3

A3 van Loggerenberg, Bazil J."Measuring telecommunications productivity"Telephony, 200(23): 28—31, 46, June 8, 1981.

This article contains a non—algebraic but technical, discussion of the workcovered by this approach.

A2 van Loggerenberg, Bazil J."Productivity targeting", inProductivity Measurement (An international review of

concepts, techniques, programmes and current issues)edited by David Bailey and Tony Hubert — 1980,ISBN 0—566—02230—3

This article is aimed at a technical audience but is non—algebraic incontent.

81 Sink, D.S."Organizational system performance: iscritical component?"Annual lIE Conrerence Proceedings, 1983

October 1974, Geneva)

This article is aimed at national accountants and statisticians. Itcontains an algebraic exposition of the imputation procedure employed bystatisticians to react to price change of a quality nature (including thoseinduced by technological change), and demonstrates flaws in suchprocedures.

LIST B — Citations In engineering literature

87 Parsons, John"Productivity Accounting and the Accountant"Pacific Rim International Productivity Conference,

American Institute of Industrial EngineersHawaii, February 1986.

B6 Sink, D.S.,"Productivity management: planning, measurement andevaluation, control and improvement",John Wiley & Son Inc., Monograph, 1985

ISBN 0—471—89176—2

LIST C — Citations in economics literature

C4 du Plooy, Roelf M.Productivity in South African Industry,South African Journal of Economics

Vol. 56 (1) , 82—93, (1988)

C3 Kendrick, John W."Improving Company Productivity"John Hopkins University Press, 1984

ISBN 0—8018—2992—5

C2 Guy, C.E., Brown, G.F., and O'Hara, D.J.,"A determinsitic profit attribution model— the postal service, a case study"

Managerial and Decision Economics 1983, 4(3) 208—213

CI Parsons, John"Profitability analysis in inter—firm comparison:A new approach", in

Productivity Measurement (An international review of

B5 Sink, D.S., Tuttle, T.C. and Devries, S.J.,"Productivity measurement and evaluation: what is available?"National Productivity Review, Summer 1984

concepts, techniques, programmes and current issues)edited by David Bailey and Tony Hubert — 1980,ISBN 0—566—02230—3

APPENDIX B — 4 APPENDIX B — 5

B4 Sink, D.S. and Devries, S.J.,"An in—depth study and review of the state—of—the—art andpractice productivity measurement techniques",Annual International lIE Conference Proceedings, 1984

B3 Swaim, J.C. and Sink, D.S.,"Productivity measurement in the service sector: ahotel/motel application of the multi—factor productivitymeasurementAnnual International lIE Conference Proceedings, 1984

Al van Loggerenberg, Bazil J.'Distortions in the existing price series"(Paper distributed to theUnited Nations Conference of Statisticians

B2 Swaim, J.C. ar,d Sink, D.S.,"Current in in firm orproductivity and evaluation",lIE Conference Proceedings, Fall, 1983

corporate level

a

LIST D — Citations in accounting literature

Dl Gordon, Paul N., and Parsons, John'Productivity: its impact on profits"Corporate Accounting Spring 1985, 3(2) 82—84

APPENDIX B — 6

PRODUCTIVITY DECODING OF FINANCIAL SIGNALS

Documents

Transcript of PRODUCTIVITY DECODING OF FINANCIAL SIGNALS