Use of Warranties on Highway Projects: A Real Option Perspective

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Use of Warranties on Highway Projects: A Real OptionPerspective

Qingbin Cui1; Mehmet Emre Bayraktar2; Makarand Hastak3; and Issam Minkarah4

Abstract: Since the introduction of warranty provisions in federal highway jobs, more and more state departments of trans~DOTs! have considered the use of such provisions to protect their initial investment. This paper describes the pros and cons ocontracting in highway construction based on a survey of warranty practices in the United States. In particular, the need for sto buy a warranty for a well-built project is questioned. As an alternative, this paper introduces the warranty option, which givesthe right to buy a warranty only if it becomes necessary at the end of construction. This option is exercised if the performanwarrants it. This paper describes the mechanics of the warranty option and its advantages over the conventional warranty. A bidmodel is also developed for thewarranty optionapproach.

DOI: 10.1061/~ASCE!0742-597X~2004!20:3~118!

CE Database subject headings: Highway construction; Construction industry; Warranties; Quality control; State government

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Introduction

Since the adoption of warranty provisions on federal highjobs, more and more state departments of transportation~DOT!have considered the use of warranty provisions to protectinitial investment and to encourage innovations and qualityprovement. Eleven states participated in the warranty experunder Special Experiment Project Number 14, referred to as14, which was created by the Federal Highway Administra~FHWA! to study the effects of innovative contracting techniq~Hancher 1994!. By 1999, more than 21 states had applied wranty provisions and finished about 240 warranted highwaystruction projects~Russell et al. 1999!. By the end of 2002, morthan 25 states had adopted warranty provisions in highwaystruction, but only a limited number of these projects have sused up their warranty periods.

The warranty approach in highway construction contrsharply with traditional highway contracting practices. Understandard contracting option, the state DOTs provide a detdesign and decide on the construction processes and materbe used. Contractors perform the construction and bear no re

1Graduate Student, Div. of Construction Engineering and Manment, School of Civil Engineering, Purdue Univ., West LafayeIN 47907-2051. E-mail: [email protected]

2Graduate Student, Div. of Construction Engineering and Manment, School of Civil Engineering, Purdue Univ., West LafayeIN 47907-2051. E-mail: [email protected]

3Assistant Professor, Div. of Construction Engineering and Manment, School of Civil Engineering, Purdue Univ., West LafayeIN 47907-2051. E-mail: [email protected]

4Professor Emeritus, Dept. of Civil and Environmental EngineeUniv. of Cincinnati, Cincinnati, OH 45221-0071. E-mail: minkarucmail.uc.edu

Note. Discussion open until December 1, 2004. Separate discumust be submitted for individual papers. To extend the closing daone month, a written request must be filed with the ASCE ManaEditor. The manuscript for this paper was submitted for review andsible publication on May 8, 2003; approved on November 25, 2003.paper is part of theJournal of Management in Engineering, Vol. 20, No.
3, July 1, 2004. ©ASCE, ISSN 0742-597X/2004/3-118–125/$18.00.
118 / JOURNAL OF MANAGEMENT IN ENGINEERING © ASCE / JULY 2004

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sibility for future repairs once the project is accepted. Strinquality control and inspection are necessary to make surecontractors are complying with the specifications and the deThe warranty approach, usually used with performance-bspecifications, changes almost every step in the standard coing system. The changes go beyond the manner in which prare bid, awarded, and constructed. Most important, contraare bound by the warranty and are required to come back toand maintain the highway whenever certain threshold valueexceeded. In return for the shift in responsibility, contractorsgiven the freedom to select construction materials, methodsmix designs.

This paper describes the pros and cons of warranty practithe United States and questions the need for state DOTs towarranty for a project that is well executed. Instead, the pintroduces a possible solution, thewarranty option, which is aright but not an obligation to buy a warranty only if the narises at the end of construction.

Warranty Contracting

Warranty use on federal highway projects was prohibited untpassage of the Intermodal Surface Transportation Efficiencin 1991 because warranty provisions could indirectly resufederal aid participation in maintenance costs, which at thatwere a federal aid nonparticipating item~FHWA 2000!. Under thewarranty Interim Final Rule published April 19, 1996, the FHallowed warranty provisions to be applied only to items conered to be within the control of contractors. Ordinary weartear, damage caused by others, and routine maintenance remthe responsibility of the state DOTs~AASHTO 2001!.

A warranty in highway construction, like warranties for mafactured products, is a guarantee that holds the contractocountable for the repair and replacement of deficiencies undor her control for a given period of time. Warranty provisionswidely used in highway construction contracts throughout Eubut are still regarded as an innovative concept in the United S~Hancher 1994; Anderson and Russell 2001!.

In the United States, North Carolina first used the warr
approach on a pavement marking project in 1987~Russell et al.

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1999!. Soon after, warranty provisions were adopted by ostate DOTs and implemented on all kinds of highway projeincluding pavements, bridge decking, bridge painting, prevemaintenance jobs, intelligent traffic systems, and so on. Theranty approach requires more general specifications thanstandard contracting. Rather than defining how to construproject, a warranty specification would describe the performof the project. Some of the identical elements in a warraspecification include warranty terms, performance criteria~indi-cators! and threshold values, bonding requirement, conflict rlution team, control methods, and remedial actions, as wemeasurement and payment~Anderson and Russell 2001!.

Most state DOTs consider calendar time as the uniqueranty term that governs a warranty period. A few states~NewMexico, Colorado, and so on! use two-dimension warranterms—calendar time and traffic load—whichever comes~Abbey 1999; Ashenbrener and DeDios 2001!. Contractors arrequired to guarantee that the warranted project works wellspecified period without exceeding threshold values. If the prfails during the warranty period, contractors would come bacrepair or replace the item at no cost to the state agency. Onwarranty period expires, the contractor is relieved from theranty. In the time and usage scenario, the warranty expiresthe time is met or the usage exceeds the design value, whiccomes first. This is similar to the 5-year or 50,000-m warranthe automobile industry. The warranty could expire earlierthe specified period if the real traffic load exceeds the devalue.

In a warranted project, the contractor provides a guarantethe performance of the project. In return, he or she is alloweselect construction materials, processes, and methods, whimpossible in the standard system. In a design/build warrproject, the contractor would provide a detailed design forwhole project. Instead of a tight quality control program, warraprovisions require that state DOTs only evaluate and accepwarranted item based on performance criteria. Indicators sucracking, rutting, bleeding/flushing, raveling, and roughnesswidely used by many states in evaluating asphalt paveprojects, while scaling, spalling, and cracking are the indicaused in decking projects. State DOTs set up threshold valuethese performance criteria in accordance with average histdata from similar projects. The threshold value could be adjua little higher or lower based on performance expectationswarranted project.

Most states require contractors to follow a standard remaction whenever a threshold value is exceeded. The contracrequired to obtain a warranty bond from a surety companyguarantee against default during the warranty period. It couldsingle-term warranty bond or a renewable performance bondface value of the bond is set as either a total sum or a perceof the contract price to cover the worst-case scenario for manance costs when the warranted item fails. Since disagreemay arise with regard to the possible causes for failure of swarranted items in the project, there is a need for an indepeentity empowered to resolve these disputes and assign resbilities. This task is entrusted to the conflict resolution tewhich is formed from representatives of the state DOT, thetractor, and a third party.

Warranty contracting is primarily classified as a workmanand material warranty or as a performance warranty~Aschenbrener and DeDios 2001!. A workmanship and material warranholds a contractor responsible for correcting deficiencies ca
by bad workmanship and material but exempts the contractor
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from deficiencies caused by design and other reasons beyocontractor’s control. The state DOTs are still responsible foficiencies that are design related. The workmanship and mawarranty is compatible with the low-bid system and usually hshort-term period, from a few months to 7 years. The contracgiven the responsibility for material selection and undertakerisk for bad workmanship and early failure of the selected mrial.

In the performance warranty approach, the contractor is gflexibility to design and even modify contract details, in addito material selection and workmanship. Thus he or she assthe responsibility for correcting defects caused by workmanand material as well as design. The contractor may also chorehabilitation strategy or undertake preventive maintenanceing the warranty period. To provide adequate protection fromsign defects, the performance warranty usually has a longeriod, from 5 to 20 years, which under certain conditions maybe a biddable item~Russell et al. 1999!.

Warranty Practices: Pros and Cons

Among the states that have applied warranty provisions inway construction, Michigan, Ohio, Wisconsin, and New Mexare considered the current frontrunners in highway warrantyImplementation of warranty provisions in construction contris considered an innovative contracting practice that is expto provide many benefits. However, many challenges are aated with its use nationally, and research on its evaluatiohighway construction is limited.

A questionnaire survey and follow-up interviews were cducted to compare warranty projects to nonwarranty projectsregard to cost, time, quality, bonding, risk, and dispute. Thevey covers the warranty experience in 14 states: California, Crado, Florida, Indiana, Michigan, Minnesota, Mississippi, OOregon, Pennsylvania, South Carolina, Texas, West VirginiaWiconsin. Fig. 1 shows the annual sales of warranty projecthese 14 states. Based on the survey results, the followingtions describe the advantages and disadvantages of warranvisions.

Advantages of Warranty Provisions

State DOTs and contractors both believe that warranty provilead to higher quality on site. The survey confirms this bealthough only a slight improvement in quality was observe

Fig. 1. Annual sale of warranty projects in 14 states surveye

most states.

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One important result obtained from the use of performabased specifications in highway construction projects is the dopment of contractor-funded internal innovations. As judgedcontractors, quality-conscious construction, better workmanand more design input are the most attractive features of warprojects. A few contractors differentiate themselves from tcompetitors by providing new materials and innovative techngies that will need less maintenance and fewer repairs infuture. State DOTs are still protected by the warranty provisin the event of early failures of these innovative, unproven pucts and techniques. In this sense, state DOTs therefore archasing not only labor, equipment, and materials from thetractor, but also innovation and expertise.

Warranty requirements release state DOTs from stringenspection. Under a performance-based specification, contraare responsible for the design of the construction process aas the selection of the materials used in the project. Therethere is no need for state agencies to follow standard inspeprocedures on warranted projects. In addition, contractors asponsible for the performance of the finished project duringwarranty period. Early failures caused by a contractor’s badformance will be corrected at the contractor’s expense.

Another advantage of warranty requirements is that liabilitransferred from state DOTs to contractors. In standard coning, the contractor’s responsibility for the project ceases oncproject is handed over to the state. If early failures occur,DOTs would have to make the repairs with public funding. Wranties provide an assurance to state DOTs that the contractocorrect failures that occur during the warranty period. The risearly failures within the contractor’s control is thus transfefrom state DOTs to contractors.

Disadvantages of Warranty Provisions

Warranty provisions increase the initial bid price, especiallylong-term warranty projects, because of the risk of potentiaability. The more the risk, the more the bid price increases.typical 5 to 7 year warranty pavement project, the bid pricecreases by 5 to 15% on average; however, if the warranty teless than 3 years, the price increase is barely noticeableincrease in the initial price varies with the type of warranproject. In Ohio, an average increase in the bid price of 90%pavement-marking projects led to a phase-out in the use ofranty provisions on such projects. Although warranty provisare expected to yield savings in project delivery and maintencosts, the survey does not support the view that warranties rlife-cycle costs by spreading the initial investment over the ewarranty period. Most states do not have sufficient informatiothe change in maintenance costs due to warranty provisHowever, the data obtained from the survey indicate that 8 sthat have used warranty provisions have experienced a slighing ~under 10%! in maintenance costs for warranty projects.potential change in maintenance costs after the warranty exis expected to be minimal as compared to nonwarranty proWith regard to the project life cycle cost, 6 out of 12 respondstated that they expected a little increase due to warranty psions. Only the state of Wisconsin expects a substantial savthe project life-cycle cost. Considering that the probability oearly failure is quite low, state DOTs are paying extra monewarranty projects to get contractors to do what they are suppto do anyway, that is, provide a quality product that meet
performance requirements.

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Surety companies are uncomfortable with issuing a long-warranty bond, and small contractors find it difficult to gewarranty bond. Even some large contractors have difficultyting a warranty bond if the warranty term goes beyond 7 oyears. Companies that do not have problems in getting warbonds might later find that warranty projects could hinder tfrom bidding new contracts by using up the companies’ boncapacity.

A warranty is only as good as the contractor and the scompany involved. The concern is whether the contractor ansurety company still remain in business for the duration ofwarranty period and whether the companies will honor theranty bond if a project failure occurs.

The use of warranties may not always improve overall quaIn a low-bid contracting environment, with or without warrantthe tendency will be for the contractor to try to cut costs wherpossible while barely meeting quality requirements.

The warranty approach has raised some concerns regardicompetition. Although warranty provisions do not cause anservable change in the number of bidders, some smaller cotors may already have dropped out of the bidding due toinability to obtain a warranty bond for the project. This somewsupports the concern that smaller companies might get elimifrom warranty projects since they have more difficulty obtainand carrying long-term bonds compared to larger companie

The potential for an increase in litigation can also be expedue to the difficulty in identifying the real reason for a failureproject failure could be caused by many factors beyond thetrol of a contractor, such as subsurface conditions, weathetraffic load. Although litigation has not increased in current wranty practice, many state agencies have expressed concethis may happen in the future.

Warranty Provisions: Best Value to State Agencies?Many uncertainties are involved in highway construction, incing variables such as quality, cost, and time. The warrantyproach provides state DOTs with a method to lock in thesecertainties through a warranty agreement at the time the cois awarded. This is an early decision, before state DOTs havopportunity to observe the performance of the contractor onThe assumption behind this approach is that the warrantychase decision could not be delayed, or at least a delay wouadd value to the project. However, this assumption is not altrue. Since the warranty period starts after the project is accethe warranty buy-in decision could always be delayed till theof construction. Is this delay of the decision valuable? The anis definitely yes. Because of the uncertainty involved, delathis decision until the end of the project makes it possible foowner to gather more information that could be used to impthe decision.

A warranty does not add value to a well-performed prosince the project is expected to finish the warranty period witmajor problems. This situation is shown in Fig. 2~a!, whereproject quality is described using a normal distribution. Proquality, which is affected by construction performance, is untain before the start of construction. It might go above the avelevel, called favorable uncertainty, or stay at an average levthese cases the project is expected to perform well durinwarranty period. A warranty buy-in decision under this scenwill then become a bonus for contractors to do what theysupposed to do. On the other hand, construction quality cou
below the average level or even below the acceptable level, which

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would result in a project that will not perform well during twarranty period. This constitutes a performance risk, whichranty provisions try to eliminate. But under the current warraapproach, a warranty is bought before the start of constructhereby eliminating the contribution of performance to the dsion.

With regard to cost, the warranty approach is reasonableif the present value of the failure cost during the warranty peis higher than the price of the warranty@Fig. 2~b!#. The warrantyprice in this figure is a little higher than the present valueaverage failure cost to account for a contractor’s profit anreduction in the state delivery cost. The failure cost here refemaintenance and other related costs when a failure occurs wthe warranty period. User costs could be estimated and facinto the failure cost. However, the failure cost is not knownfore the contract is sold. The state DOT estimates the failurebased on typical projects rather than real information fromproject under construction. The discounted failure cost couldbelow the warranty price or even below the average failureThese situations are favorable for the state DOT and makwarranty an unnecessary investment. In a bad scenariopresent value of the failure cost could be higher than the warprice. In such a situation the warranty provision would benefistate DOT and save on potential maintenance costs. Howevwarranty approach also eliminates the possibility of a goodnario, as discussed earlier. In the conventional warranty appthe state DOT pays for the warranty in both cases, favorabunfavorable.

Under the conventional warranty approach, the state DOTprotection for early failures, but a potential favorable uncertais not considered. The state DOT has no flexibility to buy aranty based on observed performance during construction.information is not considered in the buy-in warranty decisThus, the best value is not achieved. Since the warrantyafter the construction is completed, a possible solution is to dthe warranty purchase decision until the end of constructiothis scenario, the contractor is required to provide a price fowarranty while bidding a project. The state DOT will then decon the need for a warranty after construction is completewould buy a warranty only for projects with a high probabilityfailure. This method is based on an important analogy to finaoptions, which will be presented in the following section.

Financial Options and Real Options

An option is a right, but not an obligation, to take an action infuture. In financial markets, the most common types of optare a call option and a put option. A call option gives the owthe right to buy a stock at a predetermined exercise pricespecified maturity date. The option is exercised only whenprice of the stock on that date exceeds the exercise price.

Fig. 2. Uncertainty in warranted project

stock price on the maturity date is below the exercise price, the

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option can be ignored. A put option can be viewed as the oppof a call option. A put option gives its owner the right to sellstock at a fixed exercise price. Stock prices are notorious forvolatility. The stock price on the maturity date might be abovbelow the exercise price. An option gives its owner an oppnity to exercise it and make a profit if a favorable uncertaunfolds. On the maturity date, the value of an option dependthe difference between the stock price and the exerciseBefore an option expires, the value of an option is a functiofive variables: the current price of the stock, the exercise pthe time to maturity date, the variability of the stock, andrisk-free rate. The most famous quantitative model, the BScholes Model, was developed by Fischer Black, Myron Schand Robert Merton, whose Nobel prize-winning work putvalue on a call option by duplicating the call over an infinitesitime horizon~Hull 1997!.

Many corporate decisions can be thought of as options ounderlying value of the risky asset. Those options are calledoptions. Like financial options, the value of real options depon five variables: the value of the underlying risky asset,exercise price, the time to expiration of the option, the variaof the value of the underlying risky asset, and the risk-freeThe value of underlying risky assets is the stream of cash floa discounted value generated from the risky asset. The exprice is the money invested in getting the risky asset. The fumental insight of the real option theory is to view opportunitieoptions—rights but not obligations to take actions in the futurdeferral option is a call option in most projects where one haright to delay the start of a project. This opportunity to delayinvestment allows the owner to start the project if it is advageous to do so.

When one exercises a deferral option by making an irreible investment, he or she effectively gives up the possibilitwaiting for new information that might affect the desirability atiming of the investment. The net present value rule assumnoncontingency scenario in which one can start and compproject. No opportunity to delay or abandon the investmeanticipated if market conditions turn sour. The real option memakes a more useful comparison. Several possibilities, suinvest today or wait for one year or longer, are examined to ma right and timely decision. The option value is an opportucost that should be included in the capital investment. An opis valuable when there is uncertainty. The more uncertainunderlying asset is, the more valuable the option~Trigeorgis1996; Amram and Kulatilaka 1999!.

Warranty Option: Possible Alternative to WarrantyApproach

Similar to a financial option, a warranty option is a right butan obligation to buy a warranty. It is a contingent decisionopportunity to delay the warranty buy-in decision until the sDOT sees how events unfold. On the expiration date, if evturn out to be favorable, the state DOT will make one decisiogive up the warranty option. But if events turn out to be unfaable, the state DOT will buy a warranty protection. This methat the payoff to a warranty option is nonlinear—it changesthe decision. Fixed~noncontingent! decisions have linear payobecause no matter what happens, the same decision is madwarranty option has the potential to benefit state DOTs by pring managerial flexibility.

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chase decision is delayed until the end of construction. Fpresents the workflow in the warranty option approach.project is bid the same way as in a traditional low-bid systemcontactors are required to submit the price of the warrantytheir bids. The state agency does not need to make the decisthe purchase of the warranty during the bidding phase. To eate the bids under the warranty option approach, the total prithe warranty should not be included in the bid since the statemight not exercise the option at the end of construction. Onlyof the warranty price, called the value of the warranty optshould be considered when evaluating the bids. The valuewarranty option is then deducted from the bid to determinelowest bidder. After the project is completed, all information gered during construction is considered to evaluate performThe potential failure cost will be predicted, discounted, and cpared to the warranty price to make a decision on exercisinwarranty option. Thus, information on project constructiongathered and used to improve the decision process. If the qof construction is considered to be good and the warranty prhigher than expected discounted failure costs, the state DOTnot exercise the warranty option. But if a high probabilityfailure is predicted, the state DOT can exercise the optionbind the contractor into project maintenance. If contractorsallowed to provide multiple warranty terms, a derivative warraterm option is created.

Comparison of Warranty Option versusConventional Warranty

The current warranty approach ignores the value of waiting,the decision is made before actual performance during contion unfolds. Instead of making a decision beforehand, theranty option delays the decision until the end of construcwhen more information is available and future performance

Fig. 3. Workflow of warranty option contracting

be better predicted. Warranty option contracting is superior to


conventional warranty contracting from the point of view of bding, flexibility, risk, bonding, and incentive~Table 1!. The optionconcept has the potential to provide a great benefit to thestruction industry. These benefits are discussed below.• Bidding: As compared to conventional warranty contract

the warranty option delays the decision on the purchasewarranty until the end of construction. Thus, the initialprice will not increase much. Since the price of the warrannot included in the evaluation of the bids, contractorssubmit bids that are not too dissimilar to regular nonwarracontracts.

• Flexibility: Instead of buying a warranty before construcbegins, the warranty option makes it possible to delaydecision. More information is gathered as the project isstructed. The new information could be used to make a mmore accurate prediction of the future performance ofproject. Compared to current warranty practice, the warroption allows state DOTs to buy warranties only for thprojects that have a high probability of failure within the wranty period. This managerial flexibility benefits state DOby allowing them to buy the right warranties for the riprojects.

• Risk: The warranty option changes risk allocation amproject participants. Under current warranty contracting,tractors and surety companies are exposed to defaulwithin the period of the term of the warranty. The risk isrelated to the performance of the project. The warranty opwill lower the risk for a high-quality contractor but increathe risk for a poor-quality contractor because the statemight give up the option if a well-performed project isserved.

• Bonding: A long-term warranty puts surety companiesrisky situation if contractors default. Surety companies arecomfortable issuing long-term warranty bonds. Underranty option contracting, the warranty liability mightwaived if the contractor provides high-quality work. Althoumany surety companies evaluate the worst-case scenarioissuing a warranty bond, the reduced risk involved in warroption contracting could make them lower the cost of theranty. Covering smaller construction films that provide hquality work is no more risky than for the same companiethe conventional warranty environment.

• Incentive: The warranty option gives contractors an additiincentive to produce higher-quality work since the DOTsnot exercise the purchase of the warranty after the projeover. After all, many of them have limited bonding capac

• Warranted projects: The warranty option gives the state Dright to delay the warranty decision until the completionconstruction. Thus, state DOTs would be able to cover mprojects, which would greatly benefit them if they were un

Table 1. Comparison of Conventional Warranty versus WarrOption

Category Conventional warranty Warranty opt

Bid price High LowFlexibility for DOTs Low HighRisk for contractor and surety High LowBonding Difficult Possibly easyIncentive High HighWarranted projects Less More

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Evaluation of Warranty Option

Since the state DOT has managerial flexibility to exercise orup a warranty option, the total warranty price should not be aup in the evaluation of the bids. On the other hand, the warprice does affect project cost if the state DOT decides to exethe option. Therefore, a model is needed for calculating the vof the warranty option so as to include it in the bids. This papresents a quantitative model for calculating the value of theranty option.

The value of managerial flexibility is believed greatest w~1! high volatility is expected in the future;~2! there is more roomfor flexibility; and ~3! net present value~NPV! is near zero~Co-peland and Antikarov 2001!. As discussed earlier, the warraoption, like a stock option, has five key components: valuunderlying asset, exercise price, time to expiration, volatility,risk-free rate. The explanations of these components with reto the warranty option are listed in Table 2. The value ofunderlying asset is defined as the present value of the expfailure cost during the warranty period. The warranty price inbid is the exercise price when the state DOT decides to buwarranty. The failure cost varies according to the contracperformance on the site and the materials used during contion. If the contractor uses good-quality material on the proand is generally quality conscious, the project will likely llonger without a failure. Therefore, future maintenance onproject will be less expensive. This suggests that the presentof the failure cost within the warranty period~the value of theunderlying asset! will be less. At the end of construction, twarranty option is valued as the difference between the prvalue of the failure cost within the warranty period and the liprice of the warranty in the bid. The payoff of the warranty opat the expiration date is then

WOT5MAX ~CT2P,0! (1)

whereT5time of end of construction;WOT5value of warrantyoption at timeT; CT5estimated present value of failure costime T based on information on construction performance;P5warranty exercise price in bid. If the present value offailure cost were greater than the warranty exercise price ibid, the state DOT would buy the warranty at the predetermprice P. The added value of the warranty option at that twould beCT2P. If the present value of the expected failure cwere less than the warranty exercise price, the warranty owould be worthless; the state DOT would have no reason toa warranty at such a price. With the value of the warranty opknown at the time of completion of the project~or time T!, thefollowing assumptions are needed for calculating the value owarranty option at the time of bidding~time 0!.1. The risk-free interest rate is known and constant throug

Table 2. Key Elements of Warranty Option

Underlying asset 5 Warranty

Value of underlying asset 5 Expected failure cost within warranperiod ~present value!

Exercise price 5 Warranty price in bidTime to expiration 5 Construction periodVolatality 5 Construction performance uncertaiRisk-free rate 5 Interest rate of U.S. treasury bond

the construction period;

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2. No structural maintenance funded by the state DOT ocduring the warranty period; and

3. In a continuous time frame over period@0,T#, whereT.0,the perception of project quality~measured via the predictfailure cost! follows a stochastic differential equation:

dC5mCdt1sCdZ (2)wherem ands are the mean and standard deviation of percenchanges in the failure costC, anddZ follows a standard Wienprocess in the probability space. The Wiener process descrparticular type of stochastic process where only the presentof the process~the current quality level! is relevant for predictinthe future. The past history of the process is irrelevant becauhistorical behavior has been impounded into the current qulevel. In other words, the current quality state contains all inmation needed to predict future deterioration. This assumptifairly standard in finance~Hull 1997! and construction researon deterioration modeling~Livneh 1996!. This assumption makit possible to duplicate a warranty option over an infinitestime period.

Modeling project quality in this fashion allows the use of sdard option-pricing models. With the assumptions discuabove, the warranty option could be evaluated by the clBlack-Scholes equation~Hull 1997!

WO05C0N~d1!2Pe2rtN~d2! (3)

where

d15@ ln~C0 /P!1~r 11/2s2!t#/As2t (4)

d25d12As2t (5)

N~d!5E2`

d 1

A2pe2x2/2dx (6)

The equations indicate that the value of the warranty optiothe time of biddingWO0 is determined by five parameters lisin Table 2:C05engineer-estimated present value of failurewithin warranty period at time 0~time of bidding!; P5exerciseprice of warranty option predetermined in bid;s5annualizedcompounded standard deviation of percentage changes in pvalue of failure cost within warranty period (C); r 5risk-freeinterest rate based on treasury bond or treasury bill withtime period as construction period; andt5time to expiration owhole construction period. In addition,N(d)5probability that astandardized, normally distributed, random variable will bethan or equal tod.

The model can be divided into two parts. The first calculthe expected benefit from acquiring the warranty option, ansecond gives the present value of paying the exercise priceexpiration day. The value of the warranty option is then calcuby taking the difference between these two parts~Hull 1997!. Thevolatility of the failure costs is an unobservable variable thcould be very challenging to estimate. However, the state Dcould estimate this variable from historical data.

Warranty Option Approach: Hypothetical Case

By calculating and using the value of the warranty option atime of bidding, state DOTs can evaluate bids with differentranty exercise prices. The following example illustrates howwarranty option for a hypothetical pavement project can be in
porated in bid evaluations during the bidding stage.

ave-mentnty isto be, theo bed an

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con-f theat itthen onoretheetterption

ce tolures

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Assume that a state DOT plans to build a new asphalt pment. The state is considering a 7-year warranty for the paveto guarantee quality and pavement performance. The warraexpected to be about 9% of the total contact price, estimatedabout $9 million. Under the conventional warranty approachcost of the warranty becomes a part of the bid that will have tpaid by the DOT irrespective of the quality of construction anassessment of the probability of failure during the warrantyriod. If the project is well built, the pavement will quite possilast through the 7-year warranty period without any major fathat is expensive to repair. The taxpayer’s money could bemore effectively by the state DOT if this decision is delayed uthe quality of construction is known. In the proposed warraoption method, the project can still be bid under the traditilowest-bid system. To keep the choice of the warranty openstate asks contractors to provide warranty exercise prices inbids.

Four bids are received for the pavement project~Table 3!.Contractor A does not qualify because a warranty option isoffered. With different expectations of project failure risk,remaining contractors B, C, and D provide different quotes fo7-year warranty. These quotes now have to be incorporatedbids by calculating the value of the warranty options using~1! through~5!. The warranty option is valuable to the DOT sinit gives the state an opportunity to save on warranty costs. Tfore, this value should be credited to the bid~deducted from thbid amount when evaluating the bids, as shown in the exabelow!. From historical data, the state DOT assumes that thedard deviation of construction performance is about 10%.time to expiration of the warranty option is the same as the

Table 3. Bid Evaluation in Warranty Option Contracting: Exam~in Millions of Dollars!

Contractor A B C D

Construction contract~$! 94 95 98 97Warranty price~$! NA 8 7 5

d1 @Eq. ~4)] NA 1.58 2.91 6.28

d2 @Eq. ~5)] NA 1.48 2.81 6.81

Value of warranty option~$! NA 1.30 2.24 4.17Bid value ~$! 94 93.70 95.76 92.83

Best value

Note: Assumption: ~1! Engineer’s estimate of warranty pri5$9,000,000;~2! risk-free interest rate53.5%; ~3! standard deviation operformance510%; and~4! construction period51 year.

Evaluation of bid of contractor B is

d15FlnS9,000,000

8,000,000D1~3.5%11/2•10%2!•1GY A10%2•1

5~0.117810.04!/0.151.578 d25d12As2t51.478

WO05C0N~d1!2Pe2rtN~d2!

5~$9,000,000•0.9427!2~$8,000,000•e20.035•0.9304!

5$1,297,146

Bid value of contractor B5~Construction contract!2~Value of warranty option!

5~$95,000,0002$1,297,146!5$93,702,854

struction period, assumed to be 1 year. With a risk-free rate of


3.5%, the value of the warranty option can be calculated usinabove evaluation equations.

The value of the warranty option is considered a credit forevaluations, which means the warranty option is a deductiblein the bids. Although contractor B submitted the lowest bidconstruction, the warranty option gives him or her only $1.3lion credit. Contractor D quoted a much lower warranty exerprice that generated a $4.2 million bid value. The final correbids for contractors B, C, and D are $93.7 million, $95.8 milland $92.8 million, respectively. Therefore contractor D is thecessful bidder, giving the state the best value for the projec

Conclusions

The warranty option concept suggests a new development instruction research. The warranty option, as a derivative oconventional warranty approach, is a better concept in thgives state DOTs managerial flexibility. While maintaininglowest-bidder approach to contracting, it delays the decisiobuying the warranty until the end of construction when minformation is available on the quality of the end product, andneed for a warranty to cover future maintenance can be bassessed. A decision is made on exercising the warranty oonly after comparing the cost of possible future maintenanthe cost of purchasing the warranty. The costs of future faican then be assessed from information gathered during thestruction of the project rather than using average values fromprojects.

Acknowledgments

This research was supported by the Ohio Department of Tportation ~ODOT!, whose support is gratefully acknowledgThe opinions and findings expressed here, however, are thothe writers alone and not necessarily the views or positionODOT.

References

AASHTO. ~2001!. Primer on contracting for the twenty-first century, 4thEd., Washington, D.C.

Abbey, D.~1999!. ‘‘Review of statewide transportation improvement pand related topics.’’Technique Rep., State Highway and Transportion Dept., Santa Fe, N.M.

Amram, M., and Kulatilaka, N.~1999!. Real options: Managing strateginvestment in an uncertain world, Harvard Business School PreWatertown, Mass.

Anderson, S. D., and Russell, J. S.~2001!. NCHRP Rep. 451 guidelinfor warranty, multi-parameter, and best value contracting, Transportation Research Board, National Academy Press, Washington, D

Aschenbrener, T., and DeDios, R.~2001!. ‘‘Materials and workmanshiwarranties for hot bituminous pavement.’’Technique Rep. NCDOTS-DTD-2001-18. Colorado DOT.

Copeland, T., and Antikarov, V.~2001!. Real options: A practitionerguide, TEXERE Publishing Limited, London.

Federal Highway Administration~FHWA!. ~2000!. ‘‘Warranty clauses ifederal-aid highway contracts.’’FHWA Briefing, December 7, Washington, D.C.

Hancher, D. E.~1994!. NCHRP synthesis 19: Use of warranties in road

emy

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.’’

mith,

in

construction, Transportation Research Board, National AcadPress, Washington, D.C.

Hull, J. C. ~1997!. Options, futures, and other derivatives, Prentice-HallUpper Saddle River, N.J.

Livneh, M. ~1996!. ‘‘Deterioration modeling for life cycle cost analysis
Transportation Research Record 1524, Transportation Research
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Board, Washington, D.C.Russell, J. S., Hanna, A. S., Anderson, S. D., Wiseley, P. W., and S

R. J. ~1999!. ‘‘The warranty alternative.’’Civ. Eng.,69~5!, 60–63.Trigeorgis L.~1996!. Real options: Managerial flexibility and strategy

resource allocation, MIT Press, Cambridge, Mass.


Use of Warranties on Highway Projects: A Real Option Perspective

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