Engineering, Construction and Architectural ManagementAn optimal target cost contract with a risk neutral ownerS. Mahdi Hosseinian David G. Carmichael

Article information:To cite this document:S. Mahdi Hosseinian David G. Carmichael , (2014),"An optimal target cost contract with a risk neutralowner", Engineering, Construction and Architectural Management, Vol. 21 Iss 5 pp. 586 - 604Permanent link to this document:http://dx.doi.org/10.1108/ECAM-01-2013-0003

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An optimal target cost contractwith a risk neutral owner

S. Mahdi HosseinianSchool of Civil and Environmental Engineering,The University of New South Wales, Sydney,

Australia and Bu-Ali Sina University, Hamedan, Iran, and

David G. CarmichaelSchool of Civil and Environmental Engineering,

The University of New South Wales, Sydney, Australia

Abstract

Purpose Target cost contracts are commonly used to share the monetary outcome of work or aproject. However, discussion is ongoing, as to what constitutes optimal sharing. The purpose of thispaper is to examine optimal sharing and derives a result for defined risk assumptions on the owner(risk neutral) and contractor (risk-averse ranging to risk neutral).Design/methodology/approach The derivation is based on solving a constrained maximizationproblem using ideas from principal-agent theory. Practitioners were engaged in a designed exercise inorder to validate the approach and propositions. The influence of the contractors level of risk aversion,the cost uncertainty and the contractors effort effectiveness are examined.Findings The paper shows that, at the optimum, the sharing ratio between contractor and ownerneeds to reduce and the fixed fee needs to increase when the contractor becomes more risk-averse, thelevel of the cost uncertainty increases, or the effectiveness of the contractor effort decreases.Practical implications The papers findings provide practitioners with a useful benchmark foroutcome sharing in target contracts.Originality/value Existing work on outcome sharing in target contracts is limited to being qualitativeand anecdotal in nature. This paper extends existing knowledge by providing a quantitative treatment ofoptimal sharing.

Keywords Construction, Contracts

Paper type Research paper

IntroductionTarget cost contracts attempt to establish cooperative behaviour between the contractingparties by sharing any project gains/losses or reward/risk, and to motivate the parties towork towards the same project cost goal or target (Carmichael, 2000; Lahdenpera, 2010;Love et al., 2011). A desire for cost savings, enhanced teamwork and the eliminationof adversarial behaviour lead an owner to use a target cost contract (Chan et al., 2011a),with a desired result of a successful project (Carmichael, 2000; Turner and Simister, 2001;Broome and Perry, 2002).

However, concerns exist about the design of appropriate outcome sharingarrangements (Ward and Chapman 1994; Badenfelt, 2008), which are seen as centralto achieving project goals (Rahman and Kumaraswamy, 2002; El-Sayegh, 2008;Lahdenpera, 2010). In construction projects with large risk (Lahdenpera, 2010),inappropriate sharing arrangements may create an atmosphere of hostility that canreduce a contractors performance (Bresnen and Marshall, 2000), generate disputes(Rahman and Kumaraswamy, 2005) and promote a reluctance to tender for future work(Zaghloul and Hartman, 2003; Chan et al., 2011b). Previous research has highlightedthat a sharing arrangement should be tailored to particular project circumstances, and

The current issue and full text archive of this journal is available atwww.emeraldinsight.com/0969-9988.htm

Engineering, Construction andArchitectural ManagementVol. 21 No. 5, 2014pp. 586-604r Emerald Group Publishing Limited0969-9988DOI 10.1108/ECAM-01-2013-0003

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should fairly distribute risks and rewards between the parties, though how fair andunfair are defined is not stated. (Bower et al., 2002; Love et al., 2011; Badenfelt, 2008).

A number of researchers have examined outcome sharing. However, the underlyingjustification for any recommendations made is not always clear. Badenfelt (2008) notesthat outcome sharing in projects is often established in an arbitrary way and not basedon scientific evidence or mathematical modelling. Hughes et al. (2012) and Badenfelt(2008) recommend that future studies develop appropriate sharing arrangements. Tanget al. (2008), Broome and Perry (2002) and Uher and Toakley (1999) share a similarperception about the lack of research in outcome sharing arrangements tailored tothe construction industry. Despite a current trend towards the use of target contracts(Chan et al., 2011b), only a few studies have looked at optimal sharing arrangements.This paper fills part of this gap in knowledge, by investigating the outcome sharingproblem in contracts with defined risk assumptions on the owner and contractor.

The term outcome, in this paper, refers to a projects monetary outcome expressedrelative to a target that is desired by the owner, for example, with respect to costunderruns/overruns. The term risk neutral is used here in the sense of Clemenand Reilly (2001) and Kraus (1996) to refer to those who do not care about risk, andcan disregard risk associated with different alternatives in decision making. The termrisk-averse is used here in the sense of Clemen and Reilly (2001) to refer to those whoavoid risk, are afraid of risk, or are sensitive to risk. The term risk is used here inthe sense of Al-Bahar and Crandall (1990) and Carmichael (2004) to mean exposureto the chance of occurrence of events adversely or favourably affecting the projectas a consequence of uncertainty.

The derivation presented here is based on solving a constrained maximizationproblem using ideas from principal-agent theory. The paper looks at the influence onthe optimal outcome sharing of the contractors level of risk aversion, cost uncertaintyand the contractors effort effectiveness.

The paper is original and will be of interest to academics and practitioners (owners,contractors and design consultants) interested in the design of target contracts. Itproposes a solution to the problem of optimal sharing of a projects outcome between arisk-neutral owner and a contractor (risk-averse ranging to risk neutral). As well, thepaper casts new light on establishing optimal sharing arrangements in the constructionindustry and it provides those who design target contracts with recommendations onoutcome sharing. By exploring optimal sharing, both theoretically and empirically, thepaper contributes an enhanced understanding of the nature of optimal outcome sharingwithin projects, over that currently existing. The paper also contributes to principal-agent theory by expanding its applicability to construction contracts, and beyond itstraditional home of sales, advertising and the like (Lal and Srinivasan, 1993; Zhao, 2005).

The paper is organized as follows. First, existing approaches to outcome sharingand the background to principal-agent theory are given. Discussion on optimaloutcome sharing arrangements is then given. Applying the results to constructionprojects leads to the development of the papers propositions, which are assessed basedon a designed exercise.

Literature reviewA number of publications address sharing arrangements in construction contracts. Forexample, Al-Subhi Al-Harbi (1998) uses utility theory to explain how owners andcontractors determine the best sharing arrangement. Badenfelt (2008), via interviewswith construction clients and contractors, finds that any outcome sharing arrangement

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is affected by perceptions of fairness, knowledge of target cost contracts and long-termrelationships. Chan et al. (2011b) suggest, based on a survey, that risks associatedwith tender documentation and project design should be borne by owners, whileconstruction-related risks should be borne by contractors. Hosseinian and Carmichael(2013a, b, c, d), respectively: explore outcome sharing in alliances; suggest that a risk-neutral contractor should receive/bear all project outcome underrun/overrun; explorehow outcome sharing in target contracts should be determined in projects with aconsortium of contractors; and treat projects with multiple outcomes sharing.

Broome and Perry (2002) suggest that any outcome against a target be divided inpre-agreed and specified portions. Wong (2006) suggests similarly. Bubshait (2003),based on a questionnaire survey, finds support for the use of outcome sharing. Tanget al. (2008), also based on a questionnaire survey, recommend that future studies developincentives to match project features. Hauck et al. (2004) examine outcome sharing onone project where it was used. Bower et al. (2002) conclude that sharing arrangementsmust align the needs of the contracting parties through appropriate sharing.

Ross (2003) proposes a model for outcome sharing in alliance projects. He suggests thatany cost overrun/underrun be shared 50:50, while underrun sharing should be adjusted,up or down, based on performance in non-cost areas (such as schedule and quality). Sakal(2005) and Love et al. (2011) further discuss the Ross (2003) model. Perry and Barnes(2000) suggest that the contractors share of outcome should not be less than 50 per cent.Similarly, McGeorge and Palmer (2002) suggest that the allocation of sharing shouldbe 50 per cent to the owner and 50 per cent to the other parties to the project; divided inproportion to each of the other parties contributions. Ward and Chapman (1994) arguefor contractors to nominate a sharing value as the part of their tender. Sappington (1991)discusses of an iterative approach to establishing the sharing arrangement.

Despite an extensive body of publications on target contracts, a review of theliterature reveals that few studies have examined the influence of factors affectingthe choice of outcome sharing (Al-Subhi Al-Harbi, 1998; Broome and Perry, 2002;Badenfelt, 2008). No literature appears to have focused on the optimal outcome sharingin contracts with a risk-neutral owner. This paper addresses this knowledge gap usingideas from principal-agent theory (Holmstrom and Milgrom, 1987), where the owneris the principal and the contractor is the agent. This theory provides a useful insightinto the sharing of outcome (Eisenhardt, 1989); however, there are no studies on theoptimal sharing of outcome in target contracts with a risk-neutral owner based onthe framework of principal-agent theory. Some background to this theory follows.

Principal-agent theoryPrincipal-agent theory has been widely used in the literature in economics, finance,accounting, organizational behaviour and political science (Eisenhardt, 1989).It addresses work relationships and issues related to outcome, uncertainty and risk( Jensen and Meckling, 1976; Holmstrom, 1979; Shavell, 1979; Eisenhardt, 1989;Baiman, 1990). In general terms, a principal engages an agent to do work on behalf ofthe principal. The agent is assumed to be a self-interested, rational actor and risk-averse (Eisenhardt, 1989; Petersen, 1993). Information asymmetry, whereby the agentis better informed than the principal, may exist (Eisenhardt, 1989). Opportunisticbehaviour could be anticipated in such situations. The agent performs effort thatleads to an outcome. The principal is not able to perfectly monitor the agents effort.Because effort is at cost to the agent, the agent may not give the effort that the principaldesires (Eisenhardt, 1989). The theory suggests that outcome-based contracts can be

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effective in curbing agent opportunism (Shavell, 1979; Weitzman, 1980; Holmstrom andMilgrom, 1987). Such contracts align the agents interests with those of the principal,but at the price of transferring risk to the agent.

Based on principal-agent theory thinking, the following section looks at a constrainedmaximization problem expressed in terms of a projects outcome, the contractors fee, andthe utilities of the owner and contractor. The solution of the optimization problem leadsto the optimal outcome sharing result for target contracts.

Theoretical developmentConsider an owner contemplating engaging a contractor. The owner is not able to fullymonitor the contractors effort, but the owner is able to measure the monetary outcomeof the work. The problem examined is how this outcome should be shared between theowner and the contractor.

The works monetary outcome, x, is affected by the contractors effort, e, and eventswhich are outside of the contractors influence, denoted by e . e is assumed to benormally distributed with a mean of zero and variance s2 (Holmstrom and Milgrom,1987). For convenience, x is assumed to be a linear function of the contractors effort:

x ke e 1

where k is a coefficient converting units of effort to money, and represents theeffectiveness of the contractors effort. Coughlan and Sen (1989) demonstrate thislinearity assumption does not involve much loss of generality.

Consider the contractors fee, Fee, defined as the sum of a fixed component, F, and ashare of the works monetary outcome:

Fee F nx 2

Here n is a sharing ratio distributing the outcome between the contractor and the owner,defined as the proportion going to the contractor, and taking values in the range 0-1.

The owner is assumed to be risk-neutral and its utility (or payoff), in monetaryunits, is the difference between the works monetary outcome received and the fee paid.Using Equations (1) and (2), the owners expected utility is given by:

EUo Ex Fee 1 nkeF 3

The contractor is assumed to be risk-averse (including risk neutral as an extreme), withutility defined in terms of the difference between the fee received and the cost, C, of theeffort. A risk-averse decision maker (contractor) has a concave utility function, whichcan be modelled, for example, by exponential, power and linear-exponential functions(Kirkwood, 2004). The most commonly used function is the exponential form(Holmstrom and Milgrom, 1987; Clemen and Reilly, 2001; Kirkwood, 2004), and it isadopted in this study. Kirkwood (2004) shows that the exponential utility function isaccurate for many decision situations. For a risk-averse-contractor, this gives:

UcFee C 1 exprFee C 4where r is the level of contractor risk aversion.

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The contractor wishes, through choice of effort e, to maximize its expected utilityor its certainty equivalent. A certainty equivalent is a fee that is the same in thecontractors mind to a corresponding situation that involves uncertainty, and equalsexpected fee minus the cost of its effort, C(e), minus a risk premium:

Certainty equivalent Expected fee Ce Risk premium 5

Risk premium is defined as the cost compensating the contractor for the risk borne(Clemen and Reilly, 2001) and is given by:

Risk Premium n2rs2

26

The expected fee to the contractor can be obtained by substituting Equation (1) intoEquation (2), while noting that E[e] 0:

EFee F nke 7

Following Holmstrom and Milgrom (1987, 1991), the contractors cost function C(e) isassumed to increase with e at an increasing rate. The simplest functional form thatmeets this requirement can be written as:

Ce b2e2 8

Here b is a constant coefficient reflecting the influence of contractor effort on cost; itconverts units of effort2 to monetary units.

Using Equations (6), (7) and (8) in Equation (5), the certainty equivalent correspondingto the contractors expected utility is given by:

CE F nke b2e2 n

2rs2

29

OptimizationThe owners problem is to offer a contract with a fee defined as in Equation (2), in orderto maximize its expected utility:

Maxn;F

1 n keF 10

This contract needs to include a minimum fee, MinFee, required by the contractor tomotivate the contractor to agree to the contractual arrangement:

F nke b2e2 n

2rs2

2XMinFee 11

The contractor selects the effort level that maximizes its certainty equivalent. As aconsequence, the effort level the owner favours needs to maximize the contractorscertainty equivalent:

Maxe

F nke b2e2 n

2rs2

212

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Maximizing expression (12) with respect to e yields the optimal level of effort:

e kbn 13

The optimal value of F is such that expression (11) holds as an equality, that is:

F MinFee nke b2e2 n

2rs2

214

Substituting Equations (13) and (14) into (10), the owners problem can be restated as:

Maxn

k2

bnMinFee k

2

2bn2 n

2rs2

215

Differentiating expression (15) with respect to n and setting to zero, the optimal sharingratio is obtained by:

n 11 rs2b=k2 16

Substituting Equations (13) and (16) into (14) provides the optimal fixed fee:

F MinFee 12

rs2 k2

b

n2 17

Optimal target cost contractConsider the above in the context of target cost contracts. Cost plus contracts based ona target cost may have a fee calculated according to:

Fee F n Tc Ac 18

where F is a fixed component of the fee tendered or agreed; n is a sharing ratiodistributing the outcome between the contractor and the owner, defined as the proportiongoing to the contractor, and taking values in the range 0-1; Tc is a target cost estimate ofthe work (excluding contractors fee); andAc is the actual (final) cost of the work (excludingcontractors fee). Similar target formulae apply based on target durations and quality.

For the example target cost contract presented by Equation (18), when comparingthis with Equation (2), the outcome may be interpreted as cost underruns/overruns.Hence, the optimal target cost contract determines the contractors fee according to:

Fee F nTc Ac 19

where n* and F* are obtained from Equations (16) and (17), respectively. Similaroptimal target formulae can be developed based on target durations and target quality.

In practice, a risk cap may be set by some contracts so that a small return margin orzero loss is guaranteed to the contractor; however, this can lead to extra cost to theowner (Carmichael, 2000).

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The cost of the risk borne by the contractor (risk premium) is directly affected bythe contractors risk attitude, level of uncertainty and contractor effectiveness, based onEquations (16) and (17):

. The sharing ratio needs to increase and the fixed fee needs to reduce as acontractor becomes less risk-averse. As the level of risk aversion continues toincrease, the risk premium becomes too large, forcing the owner to reducethe sharing ratio and to increase the fixed fee in order to retain the contractor.

. As actual cost uncertainty increases, it becomes increasingly expensive totransfer the risk associated with cost underruns/overruns to the contractor.According to Equation (16), the sharing ratio needs to reduce for increasing costuncertainty in order to manage the risk premium. For high cost uncertainty, theowner needs to bear a high proportion of the risk. This risk is not important toa risk-neutral owner, as assumed here. For high cost uncertainty, the fixed feeneeds to increase to motivate the contractor to accept the contract, as shown byEquation (17); the opposite occurs when the cost uncertainty is low.

. The sharing ratio needs to increase and the fixed fee needs to reduce as theeffectiveness, k, of the contractors effort towards the actual cost increases;the opposite occurs when the contractors effort effectiveness decreases.

The results presented here are applicable provided the following assumptions hold:

. The contractor is risk-averse ranging to risk neutral (Holmstrom and Milgrom,1987; Al-Subhi Al-Harbi, 1998), and the owner is risk-neutral (e.g. a public sectorowner) (Holmstrom and Milgrom, 1987; Al-Subhi Al-Harbi, 1998).

. Potential contractors have appropriate skills. Practices such as prequalificationor rigorous tender evaluation could be expected to ensure minimum goodstandards amongst all potential contractors.

. The works final cost is normally distributed. The central limit theorem supportsthis assumption where the works final cost is comprised of the sum of manycomponent costs (Ang and Tang, 1975).

In practice, establishing agreement on targets may be difficult (Carmichael, 2000;Badenfelt, 2008). Where incentives are based on targets, it is in the nature ofcontractors to overstate the target, while it is in the nature of owners to understate thetarget. To deal with these issues the target cost and target duration estimates can beagreed by the parties, or established by a third independent party. Hughes et al. (2012)stress the need for an open and transparent relationship, necessary to avoid targetcosts being set too high.

PropositionsBased on the papers theoretical development, the following propositions are examinedempirically:

P1. With increasing level of contractor risk aversion: (P1a) the sharing ratio needsto reduce, and (P1b) the fixed fee needs to increase.

P2. With increasing uncertainty in the actual cost: (P2a) the sharing ratio needs toreduce, and (P2b) the fixed fee needs to increase.

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P3. With increasing effectiveness of the contractors effort towards the actualcost: (P3a) the sharing ratio needs to increase, and (P3b) the fixed fee needs todecrease.

Empirical study outlineTo support the above findings an empirical outcome sharing study was carried out. Thiswas based on a designed interview of a sample of 60 construction contractors.The contractors involved in the empirical study were from mid-sized companies,typically pursuing projects in the range of $5M-$15M. The participants were instructedto act as corporate decision makers, not as private individuals dealing with their ownfunds, and to make decisions based on usual practice, workload and economic conditions(Hosseinian and Carmichael, 2013b). This was so because the economic situation mayhave affected their responses (Willenbrock, 1973). Before starting the interviews proper,a pilot study was conducted with a number of experienced contractors, in order to finetune and validate the study.

Contractor sampleThe backgrounds of the participants are shown in Table I. Approximately 43.3 per centof the interviewees were project managers, 26.7 per cent were contract managers,21.7 per cent were executive directors and 8.3 per cent were construction managers.The number of projects in which the participants have been involved is considerable asshown in Table I; approximately 43 per cent of the contractors were engaged in morethan 26 projects, and 47 per cent of the contractors between 5 and 25 projects.Approximately 46 per cent of the contractors had more than 21 years of experience inthe construction industry, and 33 per cent of the contractors between 11 and 20 years asillustrated in Table I. Because the experience of the participants in the constructionindustry is quite extensive, induction based on their responses could be regarded asvery persuasive.

Interview partsThe interview questions were based on this papers theoretical findings, and consistedof three parts: first, contractor risk attitudes and levels of risk aversion; second, theinfluence on the sharing ratio, n, and the fixed fee, F, of level of contractor riskaversion; and third, the influence on the sharing ratio and the fixed fee of actual costuncertainty and contractor effort effectiveness towards the actual cost.

(i). Contractor risk attitudes and levels of risk aversion. The participants utilityfunctions and levels of risk aversion were established using the method of certaintyequivalence (Clemen and Reilly, 2001). This involved offering each contractor a seriesof hypothetical, uncertain contracts (choice 1) with a 50-50 chance of either gainingb1Tc or gaining/losing b2Tc; where Tc is the target cost estimate of the work. Given

Age (years) o30 30-35 35-40 40-45 45-50 50-55 55-60 460% 1.7 6.7 20.0 16.7 20.0 16.7 10.0 8.3Experience (years) o5 5-10 11-15 16-20 21-25 26-30 31-35 435% 3.3 16.7 21.7 11.7 20.0 8.3 10.0 8.3Number of projects o5 5-15 16-25 26-35 36-45 46-55 455% 10.0 26.7 20.0 16.7 11.7 6.7 8.3Position Project manager Contract manager Executive director Construction manager% 43.3 26.7 21.7 8.3

Table I.Age, experience,

involvement in projects,and positions of the

participants in the study

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b1 and b2, the participants were required to evaluate the values of their certaintyequivalents (CEs) (choice 2) such that they would be indifferent between (choice 1) and(choice 2). The contractors utility function is then inferred from the choices made.To frame the size of the work and complexity, contractors were asked to make theirdecisions in scenarios similar to that in which they would usually operate. A target costof $10 M, representing the approximate mid-point value of the projects for the sampleof contractors, was used.

The level of risk aversion was obtained by asking the contractors to consider ahypothetical contract that has equal chances of gaining aTc or losing half of thatamount. a is a constant, which varies between 0 and 1. The value of a is adjustedduring the study. The largest value of aTc is approximately equal to the decisionmakers risk tolerance. The inverse of the risk tolerance equals the level of risk aversion(Clemen and Reilly, 2001).

(ii) Effect of risk aversion on sharing ratio and fixed fee. For a fee, defined as inEquation (18), the contractors were asked to choose the preferred value of n. To keepthe fixed fee, F, constant, the participants were asked to decide on the value of n, whereF equals 0.1Tc. The target cost, Tc, was kept the same as in part (i). The contractorswere told to consider the level of uncertainty in the actual cost of the project similar tothe uncertainty in the projects that they usually carry out.

To examine the impact of the level of risk aversion on the fixed component of thecontractors fee (for a fee defined as in Equation 1), the sample contractors were askedto choose a minimum amount for F as their tendered fee, such they would not agree tothe contractual arrangement for any lesser amount. Keeping the sharing ratio, n,constant at 0.5, the contractors were asked to decide on the value of tendered F. Thetarget cost, Tc, was kept the same. In order to limit the contractors response, thecontractors were required to select the preferred value of tendered F between 0.05Tc to0.15Tc. This mentioned range covers the fee amount that the contractors commonlyreceive from their usual projects, although fees outside this range can occur, dependingon the industry sector and the type, size and complexity of the project.

(iii) Effect of cost uncertainty on sharing ratio and fixed fee. For a fee defined as inEquation (18), the contractors were asked to choose the value of n and the tenderedF for five different scenarios. Each scenario provided the contractors with differentlevels of uncertainty in the actual cost of the work due to events outside of thecontractors influence, as shown in Table II. As an example, in Scenario 3 thecontractors were told that the optimistic, most likely and pessimistic actual cost valuesequalled 0.90Tc, Tc and 1.10Tc, respectively. The contractors were asked to considerthe level of uncertainty in the projects that they regularly carry out as the usualuncertainty mentioned in Table II. In this table the actual cost variances are calculatedusing the PERT-style approximation based on optimistic (a) and pessimistic (c) values,

Project costScenario Uncertainty level Optimistic Pessimistic Most likely s2/Tc2

1 No 1.00Tc 1.00Tc Tc 0.00002 Very low 0.95Tc 1.05Tc 0.00033 Low 0.90Tc 1.10Tc 0.00114 Usual 0.85Tc 1.15Tc 0.00255 High 0.75Tc 1.25Tc 0.0070

Table II.Cost variances fordifferent scenarios due toevents outside of thecontractors influence

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namely, [(ca)/6]2 (Carmichael, 2006). Similarly to above, keeping the fixed fee, F,constant, the contractors were asked to select the value of n, where F equals 0.1Tc.Keeping the sharing ratio, n, constant at 0.5, the contractors were asked to decide onthe value of tendered F. The target cost, Tc, value of $10 M was kept the same.

(iv) Influence of the effectiveness of the contractors effort towards the actual cost, onsharing ratio and fixed fee. For a fee defined as in Equation (18), the contractorswere asked to choose the value of n and the tendered fee, F, for a scenario wherethe effectiveness of the contractors effort towards the actual cost increases.The contractors chose the value of n and the tendered fee when the effectivenessof their effort towards the actual cost was more than that of their usual projects.The contractors were asked to make their decisions based on projects where earlyinvolvement of the contractor is required. Here projects with early involvement of thecontractor represent projects where the contractors effort effectiveness towardsthe actual cost increases. Similarly to above, keeping the fixed fee, F, constant, thecontractors were asked to select the value of n where F equals 0.1Tc. Keepingthe sharing ratio, n, constant at 0.5, the contractors were asked to decide on the valueof the tendered fee, F. The target cost, Tc, value of $10 M was kept the same.

Empirical study resultsContractor risk attitudes and levels of risk aversionAccording to the shape of the (contractor) utility function, three different risk attitudesfollow. A risk-averse decision maker has a concave (opening down) utility function.A risk-neutral and a risk-seeker decision maker have, respectively, a linear anda concave (opening down) utility function (Clemen and Reilly, 2001). Of the 60practitioners, 48 (80 per cent) were found to be risk-averse, 12 (20 per cent) risk-neutraland none to be risk-seekers. The following study focuses on the risk-averse contractors.

The results of the study are summarized in Table III. The associated utilityfunctions, using an exponential form, are shown in Figure 1.

Level of risk aversion Tc

Low HighC1-C2 C3-C8 C9-C16 C17-C26 C27-C32 C33-C36 C37-C40 C41-C44 C45-C46 C47-C485 6.7 8.3 10 12.5 14.3 16.7 20 25 33.3

Table III.Ranking risk attitudes of

the sample of contractors;Ci refers to contractor i

C1 and C2C3 to C8C9 to C16C17 to C26C27 to C32C33 to C36C37 to C40C41 to C44C45 and C46C47 and C48

Utilit

y

1

0.8

0.6

0.4

0.2

0

Fee (proportion of Tc)0 0.05 0.1 0.15 0.2 0.25

Figure 1.Utility functions for

contractors

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Effect of risk aversion on sharing ratio and fixed feeFigure 2 (bottom data set) shows the influence of risk aversion on the sharing ratio, asidentified by the contractors. This figure indicates that a contractor with a low level ofrisk aversion prefers a high sharing ratio. This supports the validity of the theoreticalresult (Equation 16), and P1a.

Figure 2 (top data set) shows the influence of risk aversion on the fixed feecomponent, as identified by the contractors. This figure indicates that a contractorwith a high level of risk aversion prefers a high fixed fee. This supports the validity ofthe theoretical result (Equation (17)) and P1b.

In Figure 2, the sharing ratio and the fixed fee represent opposing trends as a functionof level of risk aversion. Taken as a whole, the figure shows that a high sharing ratio anda low fixed fee need to be offered to a low risk-averse contractor. In contrast, a lowsharing ratio and a high fixed fee need to be offered to a high risk-averse contractor.

Effect of cost uncertainty on sharing ratio and fixed feeFigure 3 shows the relationship between actual cost uncertainty and the valueof n selected by the contractors.

According. to Figure 3, an increase in the level of actual cost uncertainty leadsto a decrease in the value of n, reflecting the contractors concern. This supports P2a.

Figure 4 plots the relationship between the fixed fee identified by the contractorsand cost uncertainty. Figure 4 shows an opposing trend to Figure 3.

Shar

ing

ratio

1.0

0.8

0.6

0.4

0.2

0.0Sharing ratio Fixed fee

Level of risk aversion Tc

Fixe

d fe

e /

Tc

0.00

0.03

0.06

0.09

0.12

0.15

0 5 10 15 20 25 30 35

Figure 2.The relation between fixedfee (F) and sharing ratio(n) as a function of level ofrisk aversion; data andbest-fit curves

r = 5.0/Tcr = 6.7/Tcr = 8.3/Tcr = 10.0/Tcr = 12.5/Tcr = 14.3/Tcr = 16.7/Tcr = 20.0/Tcr = 25.0/Tcr = 33.3/Tc

Shar

ing

ratio

1.0

0.8

0.6

0.4

0.2

0.0

Actual cost variance / Tc20.000 0.002 0.004 0.006 0.008

Figure 3.Influence of uncertainty inthe actual cost of the workon sharing ratio

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Figure 4 shows that an increase in the fixed fee follows from an increase in the level ofcost uncertainty, reflecting the contractors concern about uncertainty in the actual costof the work. This supports P2b.

Influence of the effectiveness of the contractors effort towards the actual cost, on sharingratio and fixed feeFigure 5 shows the average value of the sharing ratio selected by the contractors wherethe effectiveness of the contractors effort towards the actual cost increases, calledhigher effectiveness in Figure 5. It compares these results with those obtained forprojects that the contractors usually carry out without any need for early involvementof the contractor, called usual effectiveness in Figure 5.

Figure 5 supports the validity of the theoretical results in terms of the relationshipbetween the sharing ratio and the effectiveness of the contractors effort towards theactual cost (Equation (2)). It shows that an increase in the value of the sharing ratio, n,follows from an increase in the effectiveness of the contractors effort towards theactual cost. This supports P3a.

Figure 6 shows the equivalent results for the fixed fee selected by the contractors.It supports the validity of the theoretical results in terms of the relationship between thetendered fixed fee, F, and the effectiveness of the contractors effort towards the actual cost(Equation (3)). It shows that a decrease in the value of the fixed fee follows from an increasein the effectiveness of the contractors effort towards the actual cost. This supports P3b.

r = 33.3/Tcr = 25.0/Tcr = 20.0/Tcr = 16.7/Tcr = 14.3/Tcr = 12.5/Tcr = 10.0/Tcr = 8.3/Tcr = 6.7/Tcr = 5.0/Tc

Fixe

d fe

e /

Tc

0.160.140.120.100.080.060.040.020.00

Actual cost variance / Tc20.000 0.002 0.004 0.006 0.008

Figure 4.Influence of actual

cost uncertainty onthe fixed fee

Higher effectiveness

Usual effectiveness

Shar

ing

ratio

0.90.80.70.60.50.40.30.20.10.0

Level of risk aversion Tc0 5 10 15 20 30 3525

Figure 5.Influence of the

effectiveness of thecontractors effort towards

the actual cost, on thesharing ratio

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RecommendationsThe data derived from the participants can be used to develop a set of recommendationsfor outcome sharing. In the cumulative frequency plot of the Table IV data, the level ofrisk aversion of the sample contractors has been classified into three groups low,medium and high. The results that follow are relatively insensitive to the choice ofboundaries between these classifications. By calculating the average sharing ratiospresented in Figure 3, for the risk aversion classification, recommended values of sharingratios can be obtained Table IV for three levels of cost uncertainty (low, usual and high)as defined in Table II.

In Table IV the sharing ratio varies from 0.75 to 0.20. The highest sharing rationeeds to be used in work with low cost uncertainty where a low risk-averse contractoris engaged. By contrast, the lowest sharing ratio needs to be offered to a high risk-averse contractor in high cost uncertainty work.

Where there is little or no information about both the cost uncertainty and thecontractors level of risk aversion, the average value of the sharing ratio is recommended.This average equals 0.45, which is obtained from data presented in Table IV.

Using the data presented in Figure 4, for a sharing ratio of 0.5, the averages of thefixed fee selected by the sample contractors for different levels of cost uncertainty andcontractor risk attitude are summarized in Table V. The lowest fixed fee corresponds to alow risk-averse contractor, with low cost uncertainty in the work; the highest fixed feecorresponds to a high risk-averse contractor, with high cost uncertainty in the work.

Based on data presented in Figure 5, Table VI presents the recommend values ofsharing ratios for projects with early and usual contractor involvement. The highestsharing ratio (n 0.8) needs to be used in work with early involvement of thecontractor where a low risk-averse contractor is engaged. By contrast, the lowestsharing ratio (n 0.25) needs to be offered to a high risk-averse contractor in non-earlycontractor involvement.

Usual effectiveness

Higher effectivenessFixe

d fe

e /

Tc

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.00

Level of risk aversion Tc0 10 20 30 40

Figure 6.Influence of theeffectivenessof the contractors efforttowards the actual cost,on the fixed fee

Level of risk aversionCost uncertainty Low Medium High

Low 0.75 0.60 0.40Usual 0.55 0.45 0.25High 0.40 0.35 0.20

Table IV.Recommended values ofsharing ratios for differentlevels of uncertainty andcontractor risk attitude

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Based on the data presented in Figure 6, using a sharing ratio of 0.5, Table VII presentsthe averages of the fixed fee selected by the sample contractors for early contractorinvolvement and usual contractor involvement. According to Table VII, the lowest fixedfee needs to be used for a low risk-averse contractor with early involvement. By contrast,the highest fixed fee needs to be offered to a high risk-averse contractor with no earlycontractor involvement.

DiscussionThe above findings highlight the influence on the optimal outcome sharing of thecontractors level of risk aversion, cost uncertainty and the contractors effort effectiveness,and how they should be acknowledged in any outcome sharing arrangement. Al-SubhiAl-Harbi (1998) suggests that the contractor needs to be open about its risk attitude and,in particular, its level of risk aversion. This will assist the owner and contractor inreaching agreement on the optimal outcome sharing. In practice, it may be difficult toassess the contractors level of risk aversion, because of commercially and politicallysensitive issues. In the situation where there is little or no information about thecontractors level of risk aversion, practitioners will find Tables IV-VII useful for selectingan appropriate outcome sharing. Ignoring the optimal outcome sharing may translate intoan unattractive risk for contractors, resulting in a conflict of interest between thecontracting parties and perhaps putting the projects success at stake. Barnes (1983)claims that owners in such situations have problems getting their work completed to asatisfactory standard without substantial additional costs.

It is acknowledged that there may exist parameters affecting the selection of theoptimal sharing ratio and fixed fee other than those considered in this paper, and thiscould be the subject of future research. Considering together all parameters that mayaffect an optimal outcome sharing would lead to a complicated analysis, the results of

Risk aversionCost uncertainty Low Medium High

Low 0.08 0.09 0.12Usual 0.10 0.11 0.13High 0.11 0.12 0.14

Table V.Average values of

Fixed fee/Tc

Risk aversionContractor involvement Low Medium High

Early 0.80 0.65 0.40Usual 0.55 0.45 0.25

Table VI.Recommended values ofsharing ratios for early

and usual contractorinvolvement vs differentlevels of contractor risk

attitude

Risk aversionContractor involvement Low Medium High

Early 0.08 0.09 0.12Usual 0.10 0.11 0.13

Table VII.Comparison between

average values of Fixedfee/Tc for work with early

and usual contractorinvolvement

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which may be difficult for practitioners to use. Petersen (1993) argues that fewowners or contractors would contemplate taking the advice offered by verycomplicated models. Although some assumptions are considered in deriving anoptimal outcome sharing, the insight gained from the results does address the problemof the selection of the optimal sharing ratio and fixed fee. Weitzman (1980) arguesthat economic models may operate in accordance with some simplification of reality,but these models usually lead to significant insights into the nature of the problemsthat they address.

This paper does not attempt to describe the way in which owners and contractorsmake decisions in selecting a sharing arrangement. Rather, the paper indicates whata rational decision maker would do. In construction projects with a high level ofuncertainty, the papers findings have a valuable role to play for decision makers(owners, contractors) who are familiar with the concept of utility, expected utility andoptimization. Accordingly, the papers derived results give useful insight into theoutcome sharing problem. Knowing the factors that influence the optimal formof sharing ratio and fixed fee can facilitate the process of negotiation between theowner and the contractor to reach an agreement on the form of the optimal targetarrangement. The authors do not regard the derived results as a perfect solution to theoutcome sharing problem. Instead, it is more sensible to think of the derived results asproviding a better understanding of the sharing problem in construction.

ConclusionsThis paper derives a result for the optimal outcome sharing in target cost contractsunder defined risk assumptions on the contractor (risk-averse ranging to risk neutral)and the owner (risk neutral), and fills a knowledge gap in the literature. The paperproposes an original solution to the problem of establishing optimal parameters intarget relationships; thereby, contributing to knowledge on target cost contracts. It isfound that the sharing ratio needs to reduce and the fixed fee needs to increase forincreasing contractor level of risk aversion. It is also found that the sharing ratio needsto reduce and the fixed fee needs to increase for increasing actual cost uncertainty andreducing contractor effort effectiveness towards the actual cost. The optimizationresults presented in this paper may be used by contracting parties in the design of theircontracts, or as optimal benchmarks by which contracts designed differently, may becompared. Although this paper refers primarily to construction projects, the solutionspresented here apply equally to related project types.

LimitationsThe results presented in this paper are applicable provided the following assumptions,discussed in the body of the paper, hold: the contractor is risk-averse and the owner isrisk-neutral; potential contractors have appropriate skills, and a projects final cost isnormally distributed.

The. theoretical results and the papers propositions were supported throughconducting an empirical study based on interviewing a sample of risk-aversecontractors. The study was based on a group of medium-sized contractors in thecommercial and building fields, and hence the support for the theoretical resultsis limited to similar situations, until further data are assembled. Similarly, therecommended values of the sharing ratio and the fixed fee are based on the datacollected from a group of medium-sized contractors, and hence their validity is limitedto similar situations.

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Sharma, A. (1997), Professional as agent: knowledge asymmetry in agency exchange, Academyof Management Review, Vol. 22 No. 3, pp. 758-799.

About the authors

Dr S. Mahdi Hosseinian is a Graduate of the Shiraz University (BSc) and Isfahan University ofTechnology (MSc), where he achieved maximum marks among his cohorts. This paper formspart of his PhD research at The University of New South Wales. Before joining The University ofNew South Wales, he worked at the Buali Sina University.

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David G. Carmichael is a Professor of Civil Engineering at the University of New SouthWales. He is a graduate of the Universities of Sydney and Canterbury. He publishes, teaches,and consults widely in most aspects of project management, systems, and problem solving.He is known for his leftfield thinking on project and risk management (Project ManagementFramework, A. A. Balkema, Rotterdam, 2004), and project planning (Project Planning, andControl, Taylor and Francis, London, 2006). Professor David G. Carmichael is the correspondingauthor and can be contacted at: D.Carmichael@unsw.edu.au

To purchase reprints of this article please e-mail: reprints@emeraldinsight.comOr visit our web site for further details: www.emeraldinsight.com/reprints

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