04 Cost Benefit Analysis 2019 - จุฬาลงกรณ์มหาวิทยาลัย

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4 Cost-Benefit Analysis

Public Finance, 8th EditionRosen and Gayer, Chapter 8

Adapted by Chairat Aemkulwat for Theory of Public Expenditures

2943410

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OutlineI. Introduction

II. Present value

III. Private sector project evaluation

IV. Discount rate for government projects

V. Valuing public benefits and costs

VI. Cost-benefit “games”

VII. Distributional considerations

VIII. Uncertainty

ชยรตน เอ+ยมกลวฒน Theory of Public Expenditures 2943410

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I. Introduction

• การวเคราะหตนทน-ผลประโยชนหมายถง เคร;องมอท;ใชในทางปฏบต สาหรบเปนแนวทางในการตดสนใจการใชจายหรอการลงทนภาครฐ– Cost-benefit analysis is a set of practical

procedures for guiding public expenditure decisions.

I. Introduction

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II. Present Value• Project evaluation usually requires

comparing costs and benefits from different time periods

• Dollars or baht across time periods are not immediately comparable, because of

1) inflation and 2) returns in the market.

II. Present Value

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Present Value:Present Dollars into the Future• Suppose you invest $1000 today in the bank . .

R0 = $1000

R1 = $1000*(1+.01) = $1010

R2 = $1010*(1+.01) = $1020.10

R2 = $1000*(1+.01)2 = $1020.10

RT = R0*(1+r)T

II. Present Value

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Present Value:Present Dollars into the Future

• Define– R = initial investment amount– r = rate of return on investment– T = years of investment

• The future value (FV) of the investment is:

( )FV R r T= +1

II. Present Value

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Present Value:Future Dollars into the Present

• Suppose someone promises to pay you $100 one year from now.

• What is the maximum amount you should be willing to pay today for such a promise?

• เรากาลงสญเสยผลประโยชนท6เราควรไดจากการปลอยก – You are forgoing the interest that you could earn on

the money that is being loaned.

II. Present Value

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• มลคาปจจบนของเงนกอนในอนาคต คอ จานวนเงนกอนสงสดท7เรายนดจายวนน< เพ7อสทธในการไดรบเงนกอนในอนาคต– The present value of a future amount of

money is the maximum amount you would be willing to pay today for the right to receive the money in the future.

II. Present Value

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Present Value:Present Dollars into the Future

• Define– R = amount to be received in future– r = rate of return on investment– T = years of investment

• The present value (PV) of the investment is:

( )PV R

r T=+1

II. Present Value

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Projecting Future Dollars into the Present

R0 = RT/(1+r)T PV =

discount ratediscount factor

In previous equation, r is often referred to as the discount rate,

and (1+r)-T or 1/(1+r)T is the discount factor.

FV = RT = R0*(1+r)T

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• Finally, consider a promise to pay a stream of money, $R0 today, $R1 one year from now, and so on, for T years.

( ) ( ) ( )PV R R

rRr

RrTT= +

++

++ +

+0

1 221 1 1...

II. Present Value

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Present Value:

Future Dollars into the Present

• Present value is an enormously important

concept

• A $1,000,000 payment 20 years from now

is only worth today:

– $376,889 if r=.05

– $148,644 if r=.10

II. Present Value

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Present Value:Inflation

• Nominal amounts are valued according to the level of prices in the year the return occurs.

• Real amounts are valued according to the level of prices in one particular year.

• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.

II. Present Value

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Present Value:Inflation

II. Present Value

( ) ( ) ( )1 2

0 2(1 ) (1 ) (1 )...

(1 ) 1 (1 ) 1 (1 ) 1T

TR R RPV R

r r rp p p

p p p- - -

= + + + +- + - + - +

• Inflation affects both the payout stream and the discount factor, and these two cancel each other out.

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11.4

4.9 4.3

10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9 5.4 5.6 5.8

4.6 5.5

9.5

13.3 12.2

11.2

8.6 8.1 8.3 8.0 8.1

5.7

(2.8)

(7.6)

4.6 4.5 3.4

6.1 7.2

6.3

4.2 5.0 5.4

1.7

(0.7)

7.5

0.8

7.2

2.7

1.0

3.0 3.3 3.9

(10.0)

(5.0)

0.0

5.0

10.0

15.0

20.0

1970

1971

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GROWTH RATES 1970-2017 Thailand Korea, Rep.

Source: Tradingeconomicscom

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11.4

4.9 4.3

10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9 5.4 5.6 5.8 4.6

5.5

9.5

13.3 12.2

11.2

8.6 8.1 8.3 8.0 8.1

5.7

(2.8)

(7.6)

4.6 4.5 3.4

6.1 7.2

6.3

4.2 5.0 5.4

1.7

(0.7)

7.5

0.8

7.2

2.7 1.0

3.0 3.3 3.9

(10.0)

(5.0)

0.0

5.0

10.0

15.0

20.0

25.0

1970

1971

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GROWTH RATE 1970-2019 Thailand China


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11.4

4.9 4.3

10.2

4.5 5.0

9.3 9.8 10.3

5.4 5.2 5.9

5.4 5.6 5.8 4.6

5.5

9.5

13.3 12.2

11.2

8.6 8.1 8.3 8.0 8.1

5.7

(2.8)

(7.6)

4.6 4.5 3.4

6.1 7.2

6.3

4.2 5.0 5.4

1.7

(0.7)

7.5

0.8

7.2

2.7

1.0

3.0 3.3 3.9

(10.0)

(5.0)

0.0

5.0

10.0

15.0 19

7019

7119

7219

7319

7419

7519

7619

7719

7819

7919

8019

8119

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0020

0120

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0420

0520

0620

0720

0820

0920

1020

1120

1220

1320

1420

1520

1620

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Growth Rate 1970-2017 Thailand Malaysia


Thailand vs Malaysia Compared

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2556 2557 2558 2559 2560 2561 THB

2013 2014 2015 2016 2017 2018

Malaysia 4.7 6.0 5.1 4.2 5.9 4.7

Thailand 2.7 1.0 3.0 3.3 3.9 4.1

Differnce 5.0 2.1 0.9 2.0 0.6

Economic Value

GDP at 2018 price 13,932,560 14,069,720 14,494,612 14,970,404 15,601,188 16,314,417

i=0% 706,625 300,233 140,831 309,548 97,887 1,555,122

i=2% 764,873 318,610 146,520 315,739 97,887 1,643,628

i=5% 858,907 347,557 155,266 325,025 97,887 1,784,641

4 3 2 1 0

Source: www.bot.or.th EC_EI_027-2

http://www.bot.or.th/

Thailand 2014 2015 2016 2017 2018

Nominal GDP 13,230 13,747 14,534 15,452 16,314

Real GDP at constant price 9,232 9,511 9,823 10,237 10,708

GDP Deflator 143.3 144.5 148.0 150.9 152.4

Economic growth 1.0% 3.0% 3.3% 4.2% 4.6%

GDP deflator (base = 2018) 106.34 105.44 103.01 100.97 100.00

Real GDP(2018 price) 14,070 14,495 14,970 15,601 16,314 21

Thailand GDP Data 2013-1018

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III. Private Sector Project Evaluation

• Suppose there are two projects, X and Y.

• Each entails certain benefits and costs, denoted as BX, CX, BY, and CY.

• Need to ask:– Is the project admissible?– Is the project preferable?

III. Present Sector Project Evaluation

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Private Sector Project Evaluation

• Admissible: Are the benefits greater than the costs?

• Preferable: Are the net benefits the highest?

• โครงการสวนใหญเก0ยวของกบกระแสผลประโยชนและตนทนหลายชวงเวลา– Most projects involve a stream of benefits and costs

over time.


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• Define:

Bti =

Cti =

Benefits from project i at time t

Costs from project i at time t• Then the present value of project i is:

( ) ( )( )

( )( )

PV B CB C

rB C

ri i i

i iTi

Ti

T= - +-

++ +

-

+0 0

1 1

1 1...


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• The present value criteria for project evaluation are that:– A project is admissible only if its present

value is positive.

– When two projects are mutually exclusive, the preferred project is the one with the highest present value.


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• Two different projects (R&D or Advertising).

• The discount rate plays a key role in deciding

what project to choose, because the cash

inflows occur at different times.

• The lower the discount rate, the more

valuable the back-loaded project (โครงการท)มผลประโยชนสงในชวงทายๆ - advertising).


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TTT

rCB

rCB

rCBCBPV

)1(...

)1(1 23322

11 +-

++++

++-

+-=

Annual Net Return

Year R&D Advertising0 - $1,000 - $1,0001 600 02 0 03 550 1,200

AdmissiblePreferablePresent Value Criteria

PV

R = R&D Advertising

0 $150 $200

0.01 128 165

0.03 86 98

0.05 46 37

0.07 10 -21

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• Several other criteria are often used for project evaluation, but can give misleading answers– Internal rate of return (IRR)– Benefit-cost ratio (B/C)


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• The internal rate of return, ρ, is defined as the ρthat solves the equation:

( ) ( )( )

( )( )

01 10 01 1= - +-+

+ +-

+B C

B C B CT TTr r

...

• The IRR is the discount rate that would make the present value of the project equal to zero.– Admissible if ρ>r.

– The flawed analysis would choose an admissible project with the higher internal rate of return, ignoring scale.


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Internal Rate of Return

0)1(

...)1(1 23322

11 -+-

++++

++-

+-= TTT CBCBCBCBPV

rrr

Project Year 0 Year 1 ρ Profit PV

X -$100 $110 10% $4 3.77

Y -$1,000 $1,080 8% $20 18.87

Assume the firm can borrow and lend freely at a

6 percent rate of return

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Private Sector Project Evaluation• The benefit-cost ratio divides the discounted

stream of benefits by the discounted stream of costs. In this case:

B=stream of benefits and C=stream of costs:

( ) ( )B B B

rBrT

T= ++

+ ++

01

1 1...

( ) ( )C C C

rCrTT= +

++ +

+0

1

1 1...


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• Admissibility using the benefit-cost ratiorequires:

BC> 1

• This ratio is virtually useless for comparing across admissible projects, however.

• Ratio can be manipulated by counting benefits as “negative costs” and vice-versa.


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Project 1: Project waste Dump

B=250; C=100

Project 2: Wastes sent to Saturn

B=200; C=100

• Neglect seepage-induced crop damage of $40– Reduction of dump benefits. B=210; B/C=2.1

– An increase in cost C=140; B/C = 1.79


2.0 1B BC C= >


2.5 1B BC C= >

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Problems with the Benefit-cost RatioMethod B C B/C

I $250 $100 2.5

II $200 $100 2.0

I: Subtract $40 mistake

from B

$210 $100 2.1

I: Add $40 mistake to C

$250 $140 1.79

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IV Discount Rate for Government Projects

• Government decision making involves present value calculations.

• Costs, benefits, and discount rates are somewhat different from private sector.

IV. Present Sector Project Evaluation

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Discount Rate for Government Projects• Less consensus on appropriate discount rate in

public sector. One possibility are rates based on returns in private sector.– Assumes all of the money that is raised would have

been invested in a private sector project.– In reality, funding comes from a variety of sources –

investment and consumption.– Funding that come from consumption should be

discounted at the after-tax discount rate.– Hard in reality to determine what proportions of

funding come from consumption or investment.


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Discount Rate for Government Projects• Another possibility is the social rate of

discount – which measures the valuation society place on consumption that is sacrificed in the present.

• Differs from market returns because it:– Accounts for concern about future generations– Involves paternalism– May solve some market inefficiency such as positive

externalities


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Discount Rate for Government Projects

• In reality, federal agencies are required to use a real rate of return of 7%, on the assumption that this measures the before-tax rate of return in the private sector.

• Some use 2% real return instead, thought to measure the after-tax rate of return.


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2556 2557 2558 2559 2560 2561 THB

2013 2014 2015 2016 2017 2018

Malaysia 4.7 6.0 5.1 4.2 5.9 4.7

Thailand 2.7 1.0 3.0 3.3 3.9 4.1

Differnce 5.0 2.1 0.9 2.0 0.6

Economic Value

GDP at 2018 price 13,932,560 14,069,720 14,494,612 14,970,404 15,601,188 16,314,417

i=0% 706,625 300,233 140,831 309,548 97,887 1,555,122

i=2% 764,873 318,610 146,520 315,739 97,887 1,643,628

i=5% 858,907 347,557 155,266 325,025 97,887 1,784,641

4 3 2 1 0

Source: www.bot.or.th EC_EI_027-2

http://www.bot.or.th/

42

V. Valuing Public Benefits and Costs

• Recall that the discount rate, benefits, and costs are needed to compute the present value of a project.

• For private company:– Benefits = revenues received– Costs = firm’s payments for inputs


43

Valuing Public Benefits and Costs

• For public sector, market prices may not reflect social benefits and costs.– Externalities, for example

• Several ways of measuring benefits and costs– Market prices– Adjusted market prices– Consumer surplus– Inferences from economic behavior– Valuing intangibles


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• Market prices– In a properly functioning competitive

economy, the price of a good simultaneously reflects its marginal social cost of production and its marginal value to consumers.

– Ignores market imperfections– Easy to gather


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• Adjusted market prices– If markets are imperfect, prices generally do

not reflect true marginal social cost.– Shadow price of a commodity is its true,

underlying marginal social cost, which can sometimes be estimated.

– Examples where insights can be gleaned include monopoly price, taxes, and unemployment.


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• Consumer surplus– Public sector projects can be large and

change market prices.– Figure 8.1 measures the change in consumer

surplus from a government irrigation project that lowers the cost of agricultural production.


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Pounds of avocadosper year

Pric

e pe

r pou

nd

of a

voca

dos

Da

Sad

A0

Sa’

$1.35

$2.89b

c g

A1

e

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• In this figure, the change in consumer surplus is area bcgd.

• Provided the government planner can accurately measure the demand curve, the project’s benefit can be measured with this change.


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• Inferences from Economic Behavior

• Many times a good in question is not explicitly traded, so no market price exists.

• Examples:– Value of time– Value of life


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• Value of time

• In cost-benefit analysis, need to estimate the value of time to take advantage of theory of leisure-income choice.

– After-tax wage is often used

– But hours of work not always a “choice,” and not all uses of time away from job equivalent.


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• Researchers have examined value of time by travel commuting choices.– Trains are more expensive, but less time-

consuming, than buses. The same is true about non-stop airline flights versus those with a layover.

– Estimates are that value of time approximately half of the before-tax wage.


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• Value of life

• The mindset that “life is priceless” presents obvious difficulties for cost-benefit analysis.

• If the benefits of a saved life are infinite, any project that leads to even a single life saved has an infinitely high present value.


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• Economists use two methods to assign finite

values to human life:

– Lost earnings: Net present value of individual’s

after-tax earnings over lifetime.

• Taken literally, no loss for aged, infirm, or severely

handicapped

– Probability of death: Most projects affect probabilityof death (e.g., cancer research). People are willing to

accept increases in the probability of death for a finite amount of money.


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• Examples:

– Purchasing a more expensive, safer car with a lower probability of death versus a less expensive, less safe car.

– Occupational choice: Riskier jobs have higher wages, all else equal

– Willingness to pay for safety devices like smoke alarms.


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• Estimates suggest value of a life between $4,000,000-$9,000,000

• Can contrast this versus the cost per life saved:– Emergency floor lights on airplanes cost

about $900,000 per life saved


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• Valuing intangibles– National prestige, others

• Can be used to subvert entire cost-benefit analysis

• Could use difference between costs and benefits to make an argument on how large intangibles would have to be to make the project admissible


จรง/ไมจรง ตองพสจน

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ใช Cost-Benefit Analysis ดกวาไหม

Cost Benefit Analysis หรอ ม.44 (1)

• ม.44 "ปดประตหลายช0นในการตรวจสอบ"

• สวนมมมองของนกวชาการดานกฎหมายมหาชน คณะนตศาสตร จฬาฯ รศ.ดร.ณรงคเดช สรโฆษต หนไมพนความกงวลเรGองการใช "อานาจพเศษ" ตามมาตรา 44 ของรฐธรรมนญฉบบชGวคราว ซG งถกรบรองโดยรฐธรรมนญป 2560 ออกคาสGงเรงรดโครงการนY เขาชYใหเหนวา แมในคาสGงหวหนา คสช. จะอางถงการดาเนนการตองเปนไปตาม "ขอตกลงคณธรรม" หากผเกGยวของไมปฏบตตามขอตกลงนY ใหดาเนนการตามกฎหมาย แตปรากฎวาคาสGงหวหนาคสช. ฉบบเดยวกน กลบยกเวนการบงคบใชกฎหมายรวม 7 ฉบบ

60Source: https://www.bbc.com/thai/thailand-40369155

Cost Benefit Analysis หรอ ม.44 (2)

• ม.44 "ปดประตหลายช0นในการตรวจสอบ"

• "กฎหมายท, คสช.ใหยกเวน เปนกฎหมายมงขจดการทจรตท@งส@น ความหมายคอเจาหนาท,รฐไทยทาผด ยงโดนลงโทษตามกฎหมาย แตถาคนเสนอราคาทาผด หลดหมด ถอเปนการยกเวนการบงคบใชกฎหมายท,ไมควรยกเวน นอกจากน@ยงมความไมชดเจน หากรฐวสาหกจจนตองการใหบรษทใดบรษทหน,งของไทยมารบงานตอ จะสามารถเขามาไดโดยอตโนมตหรอไม" รศ.ดร.ณรงคเดชโยนคาถามข@นกลางวงเสวนา

61Source: https://www.bbc.com/thai/thailand-40369155

Cost/Benefit Analsis หรอ ม 44 (3)

• เขาบอกดวยวา คาส4งตามมาตรา 44 ไมเพยงตรวจสอบไมได เพราะถกรบรองโดยรฐธรรมนญ และแนวบรรทดฐานการพจารณาคดของศาลในประเดนท4เก4ยวของกบมาตรา 44 ยงใหความคมครองการรถไฟแหงประเทศไทย (รฟท.) ในการส4งการ การปฏบต ถอเปนการ "ปดประตหลายชQนในการตรวจสอบ"

• "ตอใหการออกคาส4งนQ เร4มตนดวยเจตนาด อยากสลายขอตดขด อยากพฒนาประเทศ ซ4 งทางกฎหมายมคาพดวาทาอยางไรกไดใหถงเปาหมาย แตแมเปาหมายด แตวธการไมถก กจะไปอยางน4นหรอ" รศ.ดร.ณรงคเดชระบ

62

63

VI. Cost-Benefit “Games”• Chain-Reaction game

– Include secondary benefits to make a proposal appear more favorable, without also including the secondary costs

• Labor game– Wages are viewed as benefits rather than

costs of the project

VI. Cost-Benefit “Games”

64

Cost-Benefit “Games”• Double counting game

– Benefits are erroneously counted twice

• 1) the increase in value of land

• 2) the present value of the stream of net income obtained from farming

VI. Cost-Benefit “Games”

65

VII. Distributional Considerations

• Hicks-Kaldor Criterion – a project should be undertaken if it has positive net present value, regardless of distributional consequences

• The Hicks-Kaldor criterion bases project selection on whether there is a potential Pareto improvement

VII. Distribution Considerations

66

Distributional Considerations

• Others view some groups in population as “more deserving” and argue this should be taken into account in project selection

• Government costlessly corrects any undesirable distributional aspects

VII. Distribution Considerations

68

Ans.

d. The subway project has a higher present value. If a dollar to the “poor” is valued the same as a dollar to the “middle class,” choose the subway project.

e. Let l = distributional weight. set– 220,000 = -68,750 + l[(62,500/1.25) + (62,500/1.252)]– l = 3.21– This distribution weight means that $1 of income to a poor person must be viewed as more

important than $3.21 to the middle class for the legal services to be done.

69

VIII. Uncertainty

• The results of many projects are uncertain (e.g., AIDS vaccine research or defense research).

• In risky projects, benefits or costs must be converted into certainty equivalents– the amount of certain income the individual would trade for a set of uncertain outcomes generated by project.

VIII. Uncertainty

70

Uncertainty

• Requires information on distribution of returns and risk aversion.

• Figure 8.2 shows a risky project (E,E+y) and a certain project (C) that give the same expected utility.

VIII. Uncertainty

71

Figure 11.2

Calculating the Certainty Equivalent Value

VIII. Uncertainty

72

Uncertainty – Certainty equivalent• ลกตานา – บณฑตศกษาท1จฬาลงกรณมหาวทยาลย คาดวาจะทาใหรายไดสงเพ1มขHน y บาท– Probability of ½

• Expected Income รายไดเฉล1ยของลกตานา = E+y/2 หรอจด

• Expected Utility = ½ U(E) + ½ U(E+y) หรอ จด C• Risk premium =• The project’s expected value be reduced by a risk premium

that depends on the shape of the utility function.

VIII. Uncertainty

I

I C-

73

Recap of Cost-Benefit Analysis• Present value

• Private sector project evaluation

• Discount rate for government projects

• Valuing public benefits and costs

• Cost-benefit “games”

• Distributional considerations

• Uncertainty

ชยรตน เอ+ยมกลวฒน Theory of Public Expenditures 2943410

04 Cost Benefit Analysis 2019 - จุฬาลงกรณ์มหาวิทยาลัย

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