Sunk costs and sunk benefits: A re-examination of re-investment decisions

The British Accounting Review 44 (2012) 144–156

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Sunk costs and sunk benefits: A re-examination of re-investment decisions Darren Duxbury* Leeds University Business School, The University of Leeds, Leeds LS2 9JT, UK

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 October 2010 Received in revised form 2 November 2011 Accepted 16 November 2011

Prior experimental studies supporting the prospect theory explanation of the sunk-cost effect manipulate the framing of the initial investment, describing it either in neutral terms or as a prior loss. This paper subjects the prospect theory explanation to further examination, but takes an alternative experimental approach based on the differential risk taking behaviour predicted by prospect theory’s S-shaped value function. The experiments manipulate whether an initial investment produces a sunk cost (prior loss) or a sunk benefit (prior gain) and investigate the impact of this on the likelihood of authorising an incremental investment held constant across treatment conditions. To ensure the results are robust to the type of incremental investment, two experiments are conducted across which the outcomes of the incremental investment are manipulated to produce poor or good investment opportunities. In all cases the results fail to support a higher likelihood of authorising the incremental investment following a sunk cost than a sunk benefit. In isolation, therefore, prospect theory is unable to explain fully the sunk-cost effect. Ó 2012 Elsevier Ltd. All rights reserved.

JEL classification: C91 Keywords: Escalation of commitment Prospect theory Sunk benefit Sunk cost

1. Introduction The conventional wisdom in management accounting follows the principles of economic rationality, which dictate that individuals should evaluate financial decisions based solely on an incremental analysis and so consider only future costs and benefits. Behavioural research in accounting, however, provides convincing evidence that individuals’ decisions are influenced by prior outcomes. Numerous studies, for example, document escalation of commitment; the tendency to commit additional funds to a failing project in an attempt to recoup prior sunk costs (e.g. Arkes & Blumer, 1985; Cheng, Schulz, Luckett, & Booth, 2003; Chow, Harrison, Lindquist, & Wu, 1997; Denison, 2009; Garland, 1990; Ghosh, 1997; Kanodia, Bushman, & Dickhaut, 1989; Staw, 1976; Thaler, 1980).1 While various explanations of the sunk-cost effect have been proposed (see Wilson & Zhang, 1997, for a review), many authors (e.g. Arkes & Blumer, 1985; Garland, 1990; Whyte, 1993) draw on Kahneman and Tversky’s (1979) prospect theory in which prior outcomes impact on subsequent decisions, with increased risk seeking behaviour in the presence of prior losses (i.e. sunk costs) and risk aversion in the presence of prior gains (what might be referred to as sunk benefits).

* Tel.: þ44 113 343 4508; fax: þ44 113 343 4459. E-mail address: [email protected]. 1 It is necessary at this stage make clear the distinction between “escalation of commitment” and the “sunk-cost effect”. Following Navarro and Fantino (2008), escalation commonly refers to the persistence in a course of action, usually in the face of failure. Studies of escalation have identified several determinants of this persistence, including self-justification, but have not manipulated sunk costs. In contrast the sunk-cost effect relates to the specific impact of sunk costs on decision making, and necessitates the manipulation of sunk cost as an independent variable to determine its role in investment decision making. Thus escalation is seen as a broader phenomenon than the sunk-cost effect. This paper manipulates sunk cost and so belongs to the latter camp, though the two terms are used interchangeably where no confusion will ensue. 0890-8389/$ – see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.bar.2012.07.004

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Given that escalation of commitment is routinely related to a failing course of action, the escalation and sunk-cost effect literatures have tended to focus on the prospect theory explanation of behaviour in the presence of prior losses, ignoring its prediction relating to behaviour in the presence of prior gains. Whyte (1986, p. 319), however, an early proponent of the prospect theory explanation of the escalation of commitment or sunk-cost effect, recognises the testable implication stemming from prospect theory’s prediction in the presence of prior gains; notably that “escalating commitment in the context of success will occur, but the level of commitment evidenced in the future will tend to be less than is warranted by an objective analysis of the situation.” More specifically, if prospect theory is at the root of the sunk-cost effect, then changes in risk taking behaviour following prior outcomes should make re-investment more likely following sunk costs (prior losses) than would be observed following sunk benefits (prior gains). This paper examines this testable implication, thus subjecting the prospect theory explanation of the sunk-cost effect to further experimental examination. In the experiments reported here participants are presented with either a sunk cost or a sunk benefit investment scenario and then asked to make an identical, incremental investment decision, the outcome of which feeds directly into the monetary incentive mechanism used to determine payment for participation in the experiment. Holding the incremental investment constant, economic theory would predict no difference in the tendency to authorise the incremental investment across the sunk cost/benefit treatment, while if prospect theory is at the root of the sunk-cost effect there should be an increased tendency for those participants experiencing the sunk-cost condition to accept the incremental investment than those experiencing the sunk benefit condition. To ensure the results are robust to the nature of the incremental investment two versions of the experiment are run. In Experiment One the incremental investment represents a poor investment (i.e. it has a negative expected value), while in Experiment Two it represents a good investment (i.e. positive expected value). Contrary to the predictions of both economic theory and prospect theory, the results from Experiment One indicate that individuals are less likely to authorise incremental investments in the presence of a sunk cost than a sunk benefit when the incremental investment represents a poor investment opportunity. In Experiment Two, when the incremental investment represents a good investment, contrary to prospect theory there is no effect of the sunk cost/benefit treatment on the tendency to authorise the incremental investment, which is in line with economic theory. In isolation, therefore, prospect theory is unable to explain fully the sunk-cost effect, thus supporting Wilson and Zhang (1997) who conclude that, while many of the explanations of escalation have explanatory power, none alone can explain fully the phenomenon. The structure of the paper is as follows. The next section provides a brief review of related literature, explains in more detail the prospect theory explanation of the sunk-cost effect and states in general terms the hypotheses to be examined. Section 3 discusses the experimental method employed, along with the background of the participants and a manipulation check. Section 4 highlights unique features of the design and presents the results from Experiment One, while Section 5 does the same for Experiment Two. Section 6 presents additional analyses intended to provide further insight concerning the factors that influence participants’ decisions to authorise the incremental investment. The final section draws conclusions. 2. Related literature and the prospect theory explanation The principles of economic rationality dictate that individuals should evaluate decisions based solely on an incremental analysis and so consider only future costs and benefits. Thus prior outcomes should not impact upon their decisions. However, prior studies document that individuals’ decisions, whether consumption or investment related, are influenced by prior outcomes (e.g. Thaler & Johnson, 1990). One area that has received widespread investigation is the sunk-cost effect; the tendency to commit additional funds to a project in an attempt to recoup prior sunk costs. Numerous academic studies, with their roots in the early work by Staw (1976) on the escalation of commitment, have documented empirically the effect of sunk costs on individuals’ decisions to commit incremental investments (e.g. Garland, 1990; Thaler, 1980). Routinely cited examples of the sunk-cost effect at large in practice range from the prolonging of the Vietnam War, the collapse of Barings bank due to the investment behaviour of Nick Leeson, continued financial commitment to the supersonic airliner Concorde and NASA’s space shuttle program. The sunk-cost effect is believed to have played an integral part in the irrational decision to continue investing (whether in terms of time, money or life) in projects that should have been abandoned on a rational economic basis (i.e. projects that represented poor investment opportunities). Various explanations of the sunk-cost effect have been proposed in the literature, including the desire to avoid waste (e.g. Arkes & Blumer, 1985), personal responsibility and the need for self-justification (e.g. Schulz & Cheng, 2002; Staw, 1976), reputation and information asymmetries (e.g. Kanodia et al., 1989) and mental accounting effects (e.g. Soman & Cheema, 2001; Thaler, 1980). Another popular approach in the literature is to draw on the implications of Kahneman and Tversky’s (1979) prospect theory to explain the sunk-cost effect (e.g. Arkes & Blumer, 1985; Garland, 1990; Northcraft & Neale, 1986; Whyte, 1993). In recognition of the high cost implications of falling foul of the sunk-cost effect, recent studies have begun to investigate ways in which the effect can be mitigated (e.g. Cheng et al., 2003; Ghosh, 1997; McCain, 1986; Tan & Yates, 1995, 2002). Such endeavours would be more productive, however, if a clear understanding of why individuals succumb to the sunk-cost effect was available in the first place. The wide range of possible explanations cited above, indicates that a general consensus does not exist. This paper contributes to our understanding of the sunk-cost effect by taking one explanation, prospect theory, and subjecting it to further experimental scrutiny. Whyte (1986) provides a comprehensive discussion of the prospect theory explanation of the sunk-cost effect, thus the following discussion is purposefully brief. The S-shaped value function of prospect theory is concave in the domain of gains

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and convex in the domain of losses, and steeper in the loss domain than the gain domain, which Kahneman and Tversky (1979) term the reflection effect. Thus, the absolute value of a marginal gain is less than the absolute value of an equivalent marginal loss. The implication of the reflection effect is that individuals will display more risk seeking behaviour in the domain of losses than they would in the domain of gains. The concave/convex shape of the value function implies that the value placed on a prospect or gamble is not constant, but is dependent upon the reference point from which it is evaluated. Thus, the marginal value placed on a given gain/loss declines the further an individual’s reference point is from the origin. For example, a marginal loss of £X is felt more keenly if the reference point is zero than if the same marginal loss of £X was evaluated from the position of a prior loss. Kahneman and Tversky (1979) call this the reference effect. Jointly the reflection and reference effects imply that if a sunk cost is coded as a prior loss, an individual may be predisposed to accept risky gambles that they would not have accepted in the absence of the sunk cost. In an early examination of prospect theory in a management accounting setting Harwood, Pate, and Schneider (1991) employ a modified version of the classic framing manipulation used by Kahneman and Tversky (1979) to investigate the impact of framing of decision alternatives on budgeting decisions. While they report evidence of a framing effect, they do not investigate escalation or sunk-cost effects specifically. Following the framing manipulation approach of Harwood et al. (1991), Whyte (1993) and Sharp and Salter (1997) subject the prospect theory explanation of escalation to experimental examination. Both studies manipulate the description of the initial investment, framing it either neutrally or as a prior loss. While the initial investment is constant across the framing manipulation, when framed as a loss there is an increased tendency to observe escalation or sunk-cost effects in the experiments of Whyte (1993) and Sharp and Salter (1997). Given the focus in these studies is on the notion of escalation, which is commonly studied in the context of an initially failing project, both studies consider only one dimension of prior outcomes, namely losses. Prospect theory, however, describes decisions under risk more generally, predicting that prior gains, in addition to losses, will influence subsequent behaviour. It is this broader view of decision making under risk that this paper exploits in a re-examination of the prospect theory explanation of the sunk-cost effect. This paper adopts an alternative experimental approach to the framing manipulations used in prior studies. Prospect theory’s S-shaped value function depicts risk seeking behaviour for losses and risk aversion for gains. While prospect theory can be used to explain why individuals are willing to invest additional funds in a failing project, even when the incremental investment is on less than favourable terms (i.e. poor investment opportunity), it would also predict that in the presence of prior gains an individual may be predisposed to more readily dismiss risky gambles they would accept otherwise, thus resulting in underinvestment in the presence of prior success (a proposition acknowledged by Whyte, 1986, p. 319). Thus a prospect theory explanation of the sunkcost effect leads to the testable implication, ceteris paribus, that an increased tendency for re-investment should be observed after a sunk cost than a sunk benefit. This paper exploits prospect theory’s disparate predictions about individuals’ risk preferences in the loss domain versus gain domain to investigate experimentally its ability to explain the sunk-cost effect in isolation. The paper examines the following null and alternate hypotheses expressed in general terms. Ho: The presence of a sunk cost versus a sunk benefit does not significantly impact upon the decision to authorise additional funds to an incremental investment. Ha: The presence of a sunk cost versus a sunk benefit significantly increases the decision to authorise additional funds to an incremental investment. Premised on the principle of economic rationale, in which prior outcomes are irrelevant to future decisions, the null hypothesis (Ho) states that the decision to authorise an incremental investment is expected to be unaffected by the presence of a prior sunk cost (prior loss) or sunk benefit (prior gain). In contrast, the alternate hypothesis (Ha) draws on prospect theory to predict, ceteris paribus, that authorisation of an incremental investment is more likely following a sunk cost than following a sunk benefit. The following section discusses the experimental method employed. 3. Experimental method 3.1. General experimental design Participants are presented with a decision scenario in which they adopt the role of a project manager in a medium sized firm (see the Appendix for an example of the experimental instrument). A 2  2 between-subjects design is employed as summarised in Table 1, which also displays the experimental parameters employed, and explained below. In the first part of the decision scenario participants are informed about the cash flows associated with an existing project they had previously authorised.2 The two-level SUNK treatment manipulates whether the participants were presented with an existing investment that produced a sunk cost or sunk benefit. In the second part of the decision scenario, the reinvestment decision, the expected cash flows associated with an incremental investment to prolong the existing project are displayed and participants are asked to indicate on a scale of 1–7 how likely they would be to authorise the incremental investment (where 1 ¼ ‘definitely authorise’ and 7 ¼ ‘definitely not authorise’). In this incremental investment stage

2 Prior studies (e.g. Arkes & Blumer, 1985; Staw, 1976) document the importance of responsibility for the sunk cost, thus the decision scenario informs participants they are responsible for investment decisions in the organisation, including the existing project.

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Table 1 Design and parameters: Experiment one and two. Experiment one (poor project)

Experiment two (good project)

Sunk cost

Sunk benefit

Sunk cost

Sunk benefit

Good outcome low probability Existing project Initial investment Cash inflow Net cash flow

£m’s 3 2 1

£m’s 3 4 1

£m’s 3 2 1

£m’s 3 4 1

Incremental Investment Immediate cash outflow Good outcome inflow (prob. ¼ 0.2) Bad outcome inflow (prob. ¼ 0.8) Net cash flow (expected value)

2 5 0 1

2 5 0 1

2 15 0 1

2 15 0 1

Good outcome high probability Existing project Initial investment Cash inflow Net cash flow

£m’s 3 2 1

£m’s 3 4 1

£m’s 3 2 1

£m’s 3 4 1

Incremental investment Immediate cash outflow Good outcome inflow (prob. ¼ 0.8) Bad outcome inflow (prob. ¼ 0.2) Net cash flow (expected value)

2 5 15 1

2 5 15 1

2 7.5 15 1

2 7.5 15 1

The table reports the experimental designs and parameters employed in Experiment one and two. Each experiment employs a 2 (sunk cost/benefit)  2 (low/ high probability of good outcome from incremental investment) design. In Experiment One the incremental investment has a negative expected value and so represents a poor opportunity, while in Experiment Two it has a positive expected value and so represents a good opportunity.

a monetary incentive mechanism is employed with one in every 25 participants chosen randomly to play out their decision for cash at a rate of £10 for every £1m earned by the incremental investment. The decision facing participants can essentially be viewed as a choice between a certain payout and a lottery. Those individuals choosing not to authorise the incremental investment (i.e. they responded with a score of 5–7) effectively choose the certain payout of £20 (i.e. the payout equivalent of the £2m cash outflow not invested). Those individuals choosing to authorise the incremental investment (i.e. they responded with a score of 1–3) effectively choose the lottery, with the outcome (good or bad) from the incremental investment determined at random and the individual receives the net cash flow from the incremental investment. For example, consider the versions of the experimental instrument faced by an individual where the good outcome was £15m (probability 0.2) and the bad outcome was £0m (probability 0.8). If the good outcome of £15m was chosen at random based on the associated probability of 0.2, then the individual would receive payment of £130 (¼£15m–£2m, at a rate of £10 per £1m) and zero if the bad outcome was randomly chosen. For ethical reasons if the calculated net cash payment for an individual turned out to be negative the money owed could not be taken from the participant. Instead, if the cash payment was negative (as would be the case if the bad outcome was selected at random in the example above), the individual would undertake departmental clerical work until the negative cash payment was paid off at a rate of 1 h for every £5. While participants could not lose their own money, therefore, the forgone wage rate of £5 per hour represents a real opportunity cost.3,4 An important feature of the experimental design is that the net cash flows from the existing project (i.e. sunk cost or sunk benefit) do not form part of the monetary incentive mechanism and thus should be irrelevant to the choice between the gamble and the certain payout. This was an intentional feature of the experimental design to ensure full comparability of monetary incentives across the SUNK treatment conditions and to remove the potential for house money effects associated with windfall gains (Thaler & Johnson, 1990) to distort the results. Soman and Cheema (2001) demonstrate that windfall gains weaken the sunk-cost effect, thus if real monetary incentives based on the existing project cash flows are employed, such that participants receive windfall gains (sunk benefits) or losses (sunk costs), there is the potential for the house money effect to overwhelm any sunk-cost effect.5

3

Participants knew and agreed to this in advance. The situation occurred once across the two experiments. If selected, an individual with a score of 4 would have been required to make a definitive decision, but this situation never occurred. 5 An alternative approach to the one adopted here would be to initially endow participants with a real cash lump-sum. In the sunk benefit treatment an additional amount would be added to represent the gain on the existing project, while in the sunk cost treatment some of the cash lump-sum would be confiscated to represent a loss on the existing project. On first consideration such an approach would appear to build in real, prior gains and losses, rather than using hypothetical ones. However, unless the amount confiscated exceeded the initial cash endowment (which would be problematic from an ethical perspective), even those participants in the sunk cost condition would effectively find themselves in a real, net windfall gain situation and so could potentially promote house money type behaviour. 4

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The two-level PROB treatment is a secondary factor to manipulate the probability of the incremental investment producing a good outcome (i.e. the higher of the two possible cash flows) such that the probability is either 0.8 (high) or 0.2 (low). The expected value of the incremental investment is held constant across the PROB treatment conditions. The PROB treatment is included to ensure that the results with respect to the main SUNK treatment factor are robust to whether there is a high or low probability of the incremental investment being a success.6 The experimental parameters employed are displayed in Table 1.

3.2. Participants In order to provide as clean a test as possible of the prospect theory explanation of the sunk-cost effect, it was deemed desirable to draw participants from as homogeneous a participant-pool as possible to ensure that differences in behaviour across treatment conditions were due solely to the experimental manipulations under investigation and not due to differences between participants. For this reason it was thought that students would represent an ideal participant-pool, hence participants in both experiments were undergraduate students at a UK Business School. All participants had undertaken modules in management accounting and as such had been exposed to investment appraisal techniques such NPV, IRR, ARR and Payback. In addition they had undertaken modules in statistics and so were familiar with probabilities and features of distributions including measures of central tendency (mean), dispersion (standard deviation/variance) and symmetry (skew). Given this common background, all participants were well placed to engage with the decision and to evaluate the risks associated with the investment scenario they faced, thus ensuring the internal validity of the experiments. The participantpools were approximately evenly split by gender and ages ranged from 19 to 21 years. It is perhaps prudent at this stage to revisit the long standing debate on the use of students as surrogates for practitioners in accounting experiments. Proponents of the view that students serve as poor surrogates for practitioners point to evidence from a variety of studies (e.g. Bouwman, 1984; Frederick, 1991; McAulay, King, & Carr, 1998) demonstrating differences between the decision-making processes of ‘experts’ (practitioners) and ‘novices’ (students). A common feature of such studies is the elicitation of attitudes or judgements concerning complex, ill-defined scenarios (e.g. case studies with no definitive solution), where prior experience and expertise are fundamental to the attitude forming process. In contrast, there is evidence to suggest that students can meaningfully serve as surrogates for practitioners in scenarios concerning decision-making tasks where there exists a transparent connection between the decision (choice) and the outcome, whether it be certain or probabilistic in nature (e.g. Ashton & Kramer, 1980; Remus, 1986). In summary, while students may not be good surrogates for practitioners in complex, ill-defined, attitude based tasks, it seems in simple, choice-outcome decisions with well-defined incentive mechanisms, of the kind studied in this paper, that students can be used as surrogates for professionals without any obvious loss of external validity. More recently, in a task close in nature to the focus of the current study, Liyanarachchi and Milne (2005) demonstrate that students can be viewed as acceptable surrogates for accounting practitioners in an investment decision task, for both short-term and long-term decisions. Their findings provide further evidence to support the view that the results reported in this paper are robust to the use of students as participants. It is important also to note the purpose of this paper, which is to test theoretical predictions via the manipulation of experimental treatment conditions. In this context interpretation of the results reported below is not hindered by the decision to use student participants. Indeed, an argument could be made that the use of accounting practitioners, who may have varying degrees of prior exposure to sunk-cost situations and may bring with them pre-conceived ideas from outside of the laboratory, would weaken the level of control achievable in the experiments.7 Furthermore, Libby, Bloomfield, and Nelson (2002) argue that accounting practitioners willing to participate in experimental research represent a valuable and scarce resource, only to be used when the research question under consideration necessitates it. That is not the case here and so the decision was made to use students in the current study, so as to conserve the practitioner participant-pool for other studies with research agendas for which practitioners are deemed essential.

3.3. Manipulation check While the hypothetical nature of the sunk costs and sunk benefits in the first part of the decision scenario is a necessary component of the experimental design, as discussed above, the success of the treatment manipulation remains to be demonstrated. By way of manipulation check, 40 individuals different to those participating in the main experiments reported below were shown information relating to the existing investment employed in the main experiments. In a task asking participants to spontaneously report words to describe the existing investment, 17/20 individuals in the sunk-cost condition reported words relating to “loss” and 16/20 individuals in the sunk benefit condition reported words relating to “gain”, thus establishing the effectiveness of the SUNK treatment manipulation.

6 Prior studies (e.g. Arkes & Hutzel, 2000; Harbaugh, Krause, & Vesterlund, 2002) suggest that this may be important in the context of the current experiments. 7 It is conceivable that random assignment to treatment conditions could not be relied upon to ensure experimental control had accounting practitioners been used as participants in the experiments.

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4. Experiment one 4.1. Experimental design The convention in prior studies of escalation of commitment and sunk-cost effects is for the incremental investment to represent a poor and risky investment opportunity that is unlikely to lead to a good outcome (e.g. Garland, 1990; Staw, 1981), hence the notion that individuals are “throwing good money after bad” (Garland, 1990). In Experiment One this conventional feature of prior studies is retained and the incremental investment represents a poor investment opportunity in the sense that the expected value is negative. The experimental design and parameters are displayed in Table 1. Note that in all four cells of the design the expected value of the incremental investment is held constant. 4.2. Hypotheses The following formal hypotheses are tested in Experiment One and also in Experiment Two. The null hypothesis reflects the rational economic perspective, while the alternative hypothesis states the predicted behaviour based on prospect theory. Ho: There is no difference in mean authorisation score across the sunk cost and sunk benefit treatment conditions. Ha: The mean authorisation score in the sunk-cost condition is lower than that in the sunk benefit condition.

4.3. Analysis and results Fig. 1 summarises the percentage of responses across the authorisation score categories and Table 2 reports the authorisation score frequencies and descriptive statistics for the decision to authorise the incremental investment in Experiment One and Experiment Two. While participants in Experiment One are closely split between willing/unwilling to authorise projects with negative incremental expected value (willing ¼ 44.5% scores  3, unwilling ¼ 52.5% scores  5), the majority display a clear preference one way or the other with only 4 participants unable to decide (score ¼ 4). The data provides clear evidence, therefore, that the participants engaged with the decision scenarios and felt able to make a decision about authorising the incremental project or not. Table 3 reports the mean responses by treatment condition for the 137 participants in Experiment One, along with the results from a between-subjects ANOVA. The SUNK and PROB treatments produce significant main effects, but the interaction effect is insignificant. Contrary to both economic theory and prospect theory, the results indicate a higher likelihood of authorising (i.e. lower score) the incremental investment following a sunk benefit (3.89) than a sunk cost (4.46). Thus Ho and Ha are both rejected in favour of lower mean authorisation scores in the presence of a sunk benefit, supporting a higher likelihood to authorise in this treatment condition. The results also indicate that the higher the probability of the ‘good’ outcome, the higher the likelihood of authorising the incremental investment (3.59 and 4.78, respectively), despite the expected value being held constant.8 In all four cells of the experiment the expected value of the incremental investment is negative, thus authorising the incremental investment clearly constitutes risk seeking behaviour. Contrary to the predictions of prospect theory the results support the view that individuals exhibited, relatively speaking, increased risk seeking behaviour in the presence of a sunk benefit rather than in the presence of a sunk cost. Thus, when the incremental investment represents a poor opportunity (i.e. negative expected value), as is the norm in the escalation of commitment literature, the predictions of prospect theory are not upheld.9 This result is robust to changes in the probability that the incremental investment delivers a ‘good’ outcome. This probability, however, impacts on individuals’ relative tendency to risk seeking behaviour in its own right. When the probability of a ‘good’ outcome is high (i.e. 0.8) there is an increased tendency to risk seeking behaviour in the absence of changes in expected value. The behaviour across the PROB treatment conditions is at odds with standard assumptions in finance theory where expected return (expected value of outcomes) is traded-off against risk (variance of outcomes). The variance of the outcomes in the high (0.8) treatment condition is higher than in the low (0.2) treatment condition, without any increase in expected value to offset this.

8 The data do not meet some of the distributional assumptions for ANOVA. The Shapiro–Wilk test indicates non-normality and Levene’s test suggests that homogeneity of variance may not hold (p ¼ 0.078). While it is commonly accepted that ANOVA is robust to violations of these assumptions when cell numbers are similar (see Lindman, 1974), as is the case here, additional analyses are conducted to confirm this. First, given the insignificant SUNK  PROB interaction in Table 3, one-way ANOVAs are run separately for the SUNK and PROB treatment factors with the Brown–Forsythe and Welch corrections to the F test requested to check for robustness to violations of homogeneity of variance. Results from these analyses are consistent with those reported in Table 3. Second, the above one-way analyses are replicated using the non-parametric medians test and one-way Kruskal–Wallis test, with both tests confirming the original results are robust to departures from normality. Third, the dependent variable is converted to a binary, yes/no authorisation variable (scores of 1–3 coded “yes” and scores 5–7 coded “no”, with scores of 4 omitted). The coefficients and significance levels from a binary logistic regression again confirm the robustness of the original ANOVA results, with both the SUNK and PROB treatment factors being significant. It is concluded, therefore, that the results in Table 3 are robust to departures from the distributional assumptions for ANOVA. 9 The finding of behaviour contrary to prospect theory predictions echoes the results in Moreno, Kida, and Smith (2002) who report increased risk seeking for gains and risk aversion for losses in the presence of affect and conclude that “we should not automatically assume that accounting decision makers will conform to the prospect theory predictions.” (p. 1346).

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Experiment One

Percentage response

70% 60% 50% 40% 30% 20% 10% 0% 1

2

3

4

5

6

7

Authorisation score PROBLOW:SUNK COST

PROBLOW:SUNK BENEFIT

PROBHIGH:SUNK COST

PROBHIGH:SUNK BENEFIT

Experiment Two

Percentage response

70% 60% 50% 40% 30% 20% 10% 0% 1

2

3

4

5

6

7

Authorisation score PROBLOW:SUNK COST

PROBLOW:SUNK BENEFIT

PROBHIGH:SUNK COST

PROBHIGH:SUNK BENEFIT

Fig. 1. Percentage of responses across authorisation score – Experiment one and Experiment two. The figure reports the percentage of responses across the authorisation score categories for each treatment condition.

5. Experiment two 5.1. Experimental design While the results from Experiment One fail to support the prospect theory explanation of the sunk-cost effect, the theory makes predictions under more general conditions than those in Experiment One. Specifically, the prospect theory prediction

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Table 2 Frequency of authorisation score and descriptive statistics – Experiment one and Experiment two. Experiment one (poor project)

Experiment two (good project)

PROB LOW with Score 1 2 3 4 5 6 7 n Mean Median Mode Variance

SUNK COST Frequency 3 1 5 – 9 13 5 36 4.94 5.5 6 3.14

SUNK BENEFIT Frequency 1 3 6 1 11 9 2 33 4.61 5.0 5 2.50

SUNK COST Frequency 1 3 19 5 15 10 2 55 4.24 4.0 3 2.04

SUNK BENEFIT Frequency 2 5 13 4 16 9 2 51 4.22 5.0 5 2.37

PROB HIGH with Score 1 2 3 4 5 6 7 n Mean Median Mode Variance

SUNK COST Frequency 1 9 8 1 8 4 4 35 3.97 3.0 2 3.32

SUNK BENEFIT Frequency 3 8 13 2 3 4 – 33 3.18 3.0 3 2.15

SUNK COST Frequency 1 16 24 4 7 1 – 53 3.06 3.0 3 1.17

SUNK BENEFIT Frequency 2 9 36 3 8 4 – 62 3.29 3.0 3 1.36

The table reports the frequency of the authorisation scores and descriptive statistics for the likelihood of authorisation. The scores are from a 7-point Likert scale anchored on 1 ¼ ‘definitely authorise’ and 7 ¼ ‘definitely not authorise’.

of risk seeking following losses and risk aversion following gains holds irrespective of the nature of the incremental investment, be it a good or bad opportunity. Experiment Two was intended, therefore, to give prospect theory a second chance at predicting incremental investment behaviour and to determine whether the results reported for Experiment One are robust to the type of incremental investment (i.e. whether it represented a ‘poor’ or ‘good’ project). The design replicates that of Experiment One with only one exception; the expected value of the incremental project is positive, thus classing it as a good investment opportunity. Where possible the experimental parameters replicate those in Experiment One, however, some changes are necessary to produce the positive expected value (see Table 1). The monetary incentive mechanism is identical across the two experiments. 5.2. Analysis and results Experiment Two investigates the same hypotheses as those examined in Experiment One (see Section 4.2 above). Table 4 reports the mean responses by treatment condition for the 221 participants in this experiment, along with the results from the between-subjects ANOVA. A significant main effect is reported for the PROB treatment, but insignificant SUNK treatment and interaction effects. As with Experiment One, the higher the probability of the ‘good’ outcome, the higher the likelihood of authorising the incremental investment (3.18 and 4.23, respectively). There is no statistical difference, however, in the likelihood of authorising the incremental investment across the SUNK cost and benefit treatment conditions (3.71 and 3.66,

Table 3 Mean likelihood of authorisation and between-subjects ANOVA results: Experiment one – poor incremental investment. SUNK COST

SUNK BENEFIT

Overall mean

F test

Sig. level

PROB LOW PROB HIGH Overall mean

4.94 3.97 4.46

4.61 3.18 3.89

4.78 3.59

(1, 133) ¼ 17.584

p ¼ 0.000

F test Sig. level

(1, 133) ¼ 3.893 p ¼ 0.051

SUNK*PROB interaction (1, 133) ¼ 0.6223

p > 0.4

The table reports the results from a 2  2 between-subjects ANOVA of the mean likelihood of authorisation of the incremental investment when it represents a poor opportunity. The scores are from a 7-point Likert scale anchored on 1 ¼ ‘definitely authorise’ and 7 ¼ ‘definitely not authorise’. Participant numbers across the four cells are approximately equal, ranging from 33 to 36, with a total of 137 participants. All significance levels are two-tailed.

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Table 4 Mean likelihood of authorisation and between-subjects ANOVA results: Experiment two – good incremental investment. SUNK COST

SUNK BENEFIT

Overall mean

F test

Sig. level

PROB LOW PROB HIGH Overall mean

4.24 3.06 3.71

4.22 3.29 3.66

4.23 3.18

(1, 217) ¼ 35.501

p ¼ 0.000

F test Sig. level

(1, 217) ¼ 0.364 p > 0.5

SUNK*PROB interaction (1, 217) ¼ 0.518

p > 0.4

The table reports the results from a 2  2 between-subjects ANOVA of the mean likelihood of authorisation of the incremental investment when it represents a good opportunity. The scores are from a 7-point Likert scale anchored on 1 ¼ ‘definitely authorise’ and 7 ¼ ‘definitely not authorise’. Participant numbers across the four cells are approximately equal, ranging from 51 to 62, with a total of 221 participants. All significance levels are two-tailed.

respectively). The rejection of Ha once more challenges the prospect theory explanation of the sunk-cost effect, while the failure to reject Ho provides support for economic theory.10 In all four cells of the experiment the expected value of the incremental investment is positive, but the probabilistic nature of the outcome still means that authorising the incremental investment constitutes a risky proposal. Consequently, prospect theory still predicts greater risk seeking behaviour in the presence of a sunk cost than a sunk benefit. Thus, while the evidence from Experiment Two is not as damning as that from Experiment One, it still fails to support the prospect theory explanation of the sunk-cost effect. When the incremental investment represents a good opportunity (i.e. positive expected value), as is the case in Experiment Two, decisions are in line with economic theory in the sense that participants are not influenced by the sunk outcome, thus appearing more rational. As with Experiment One, the results support the conclusion that when the probability of a ‘good’ outcome is high (i.e. 0.8) there is an increased tendency to risk seeking behaviour (i.e. authorising the incremental investment) in the absence of changes in expected value. 6. Further insight This section reports the results of additional analyses that combine to provide further insight into how participants evaluate the risk inherent in the decision to authorise the incremental project.11 Across the two experiments, the incremental investment differs on a number of dimensions including expected value, maximum loss and probability of the good/bad outcomes (i.e. probability of gain/loss, respectively). The academic backgrounds of the participants ensure that they are well placed to evaluate the risks associated with acceptance of the incremental project. 6.1. The potential to misperceive zero outcome cash flows How participants react when the bad outcome inflow is zero, as is the case in the PROB LOW condition across both experiments, can provide further insight into their decision-making processes. If participants discount the initial cash outflow of the incremental project (2 in all cases) they may misperceive12 the bad outcome inflow of zero as a “no loss” position and so view the incremental project as riskless, in which case one would expect a higher likelihood of authorising when the bad outcome is zero (0) than when the bad outcome is negative (15). However, across both experiments, the number of participants authorising the incremental investment when the bad outcome is 0 and 15 are 65/175 ¼ 35.4% and 130/ 183 ¼ 71.0%, respectively. Furthermore, the mean authorisation score of 4.45 when the bad outcome is 0 (in the PROB LOW condition) is significantly (p ¼ 0.000) higher than the mean score of 3.33 when the bad outcome is 15 (in the PROB HIGH condition). Participants are less likely to authorise the incremental investment when the bad outcome is 0 than when it is 15, indicating that they perceive the risk associated with the incremental investment when the bad outcome is 0 and do not misconstrue the investment to be riskless. 6.2. The role of expected value and probability of loss It is possible that participants focus exclusively on expected value when making their decisions, thus ignoring other indicators of risk. If this is the case then participants on the whole would be unwilling to authorise the incremental project in Experiment One due to its negative expected value. As can be seen from the distribution of authorisation scores reported in Table 2, however, 44.5% of participants are willing to authorise the incremental project in Experiment One, hence expected value alone is not driving their decisions. Staying with Experiment One, the tendency to authorise the incremental

10 The results of identical robustness checks to those reported for Experiment One, confirm that the results in Table 4 are robust to departures from the distributional assumptions for ANOVA. 11 The referee raised many interesting observations that motivated the inclusion of this section in the paper. 12 Misperceive because the worst situation is not a “no loss” position, but a negative net outcome of 0–2 ¼ 2 (the 0 cash inflow from the incremental project minus the 2 initial cash outflow if a decision to authorise is taken).

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investment is influenced greatly by the probability of the outcomes, with the likelihood of authorising significantly higher under the PROB HIGH condition (42/68 ¼ 61.7%) than the PROB LOW condition (19/69 ¼ 27.5%), indicating that participants react to the risk associated with the probability of good/bad outcomes, when the expected value of the incremental project is negative. The same is true also of the incremental project with a positive expected value in Experiment Two. The strong and significant main effects for probability of outcome (PROB treatment factor) reported in both Tables 3 and 4 support strongly the view that participants evaluate risk in ways other than just looking at expected value, in particular they look to the probability of good/bad outcomes (i.e. probability of gain/loss) with respect to the incremental project. The finding that 71.0% of participants are willing to authorise the incremental investment when the bad outcome condition is 15 (see Section 6.1 above), despite the potential for a much higher loss, provides clear insight into the cognitive process adopted. In this condition the probability of obtaining the good outcome is 0.8 (PROB HIGH), hence the probability of loss is low at 0.2. This is further evidence, therefore, that participants, at least in part, perceive probability of loss as an indication of the risk associated with authorising the incremental project. This finding is in line with a long established literature in psychology relating risk perception to the probability of loss (e.g. Payne, 1975; Shapira, 1995; Slovic & Lichtenstein, 1968; Yates & Stone, 1992). 6.3. The ability to distinguish good from bad projects Turning to a comparison across Experiment One and Experiment Two, reveals similar mean authorisation scores across the SUNK BENEFIT conditions of Experiment One (bad incremental project) and Experiment Two (good incremental project). While the mean scores for the bad (3.89) and good (3.71) incremental projects are in the expected direction (higher likelihood to authorise the good project with a positive expected value), there is no significant difference between these mean scores. A possible interpretation of this result is that participants do not recognize that the good incremental project in Experiment Two has a higher expected value than the bad incremental project in Experiment One. However, adding in the data from the SUNK COST conditions of Experiment One and Experiment Two, to allow a full analysis of the effect of good versus bad incremental project, produces mean scores of 4.19 and 3.68, respectively. This result is statistically significant (p ¼ 0.005) and indicates that participants recognize that the good incremental project represents a lower risk than the bad incremental project. Further comparing across Experiment One and Experiment Two, the mean authorisation scores are very similar across the SUNK BENEFIT condition in Experiment One and the SUNK COST condition in Experiment Two, suggesting that the two conditions are perceived to be similar in risk. While both conditions produce a net expected value of 0 (þ1  1 and 1 þ 1, respectively) when taking into account the sunk outcome, suggesting that sunk outcomes are incorporated in the evaluation of perceived risk, the incremental project in Experiment One (negative expected value) is inferior to that in Experiment Two (positive expected value), which suggests that the likelihood of authorising should be higher in Experiment Two than Experiment One. Indeed the number of participants authorising the incremental investment when it represents a bad prospect with negative expected value (Experiment One) and when it represents a good prospect with positive expected value (Experiment Two) are 34/64 ¼ 53.1% and 75/110 ¼ 68.2%, respectively. These frequencies are statistically different (p ¼ 0.048) indicating that, even when the net expected value is 0 taking into account the sunk outcome, participants were more likely to authorise a good incremental project (Experiment Two) than a bad one (Experiment One). In summary, the additional analyses reported above provide strong evidence to support the view that participants are able to evaluate the risks present in the decision to authorise the incremental investment, provide insight into the cognitive processes participants adopt when making their decisions, indicating that probability of loss and expected value are strongly linked to perceived risk.13 7. Conclusions This paper provides an alternative evaluation of the prospect theory explanation of the sunk-cost effect. Two experiments are conducted in which participants make incremental investment decisions in the presence of either a sunk cost or a sunk benefit. The two experiments differ with respect to the type of incremental investment available to participants. In common with the approach in prior studies, the incremental investment in Experiment One represents a ‘poor’ proposal with a negative expected value, thus authorising the investment constitutes risk seeking behaviour. However, contrary to the predictions of both prospect theory and economic theory, the results indicate that individuals exhibit, relatively speaking, an increase in risk seeking behaviour after a sunk benefit rather than after a sunk cost. This result is robust to changes in the probability that the incremental investment delivers a positive net cash flow. The incremental investment in Experiment Two represents a ‘good’ proposal as it has a positive expected value, but the probabilistic nature of the outcome means that authorising the incremental investment is still risky. No effect of the sunk cost/benefit treatment is found, thus observed

13 Further evidence in this regard is provided by the results of a binary logistic regression (not reported here due to space considerations) of the yes/no decision to authorise against project type (negative versus positive expected value), sunk outcome (cost versus benefit) and probability of good outcome (high versus low). The results confirm that projects with negative expected value and low probability of a good outcome (i.e. high probability of loss) were less likely to be authorised.

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behaviour in the presence of a good investment opportunity appears to be in line with economic theory and conventional accounting wisdom. However, while the evidence is not as damning as that from Experiment One, it still fails to support the prospect theory explanation of the sunk-cost effect. In addition to the main result discussed above, there are a number of other interesting features of the results across the two experiments that warrant comment. First, while individuals appear to be affected by the sunk cost/benefit manipulation when evaluating a poor investment, they appear not to be affected when evaluating a good investment and so appear to make more rational choices. Thus in times of adversity, when investment opportunities are poor and good investment decisions are particularly important, individuals appear to make less rational decisions than in times of prosperity, when investment opportunities are good and poor investment decisions are not so costly. Second, Sitkin and Weingart (1995) argue that perception of decision risk is negatively related to risk taking behaviour, thus the lower the perceived risk the higher the risk taken. Following this reasoning, it is possible to gain insight about what individuals perceived as risk in the investment scenarios they faced. For both experiments there was a significantly higher likelihood of authorising the incremental investment in the high probability of a good outcome condition than the low probability of a good outcome condition. In both experiments, the high probability condition generated a potential loss that was larger than that in the low probability condition (£17m including initial outlay, compared to £2m) and also produced a higher variance of outcomes than the low probability condition, but in contrast was associated with a lower probability of loss (0.2 compared to 0.8 in the low probability condition). The results suggest, therefore, that individuals perceived risk to be associated with probability of loss, not size of loss or variance of outcomes. Third, Zeelenberg and van Dijk (1997) investigate the sunk-cost effect and demonstrate that feedback on forgone outcomes, with the associated potential to induce anticipated regret, can modify behaviour. By focussing on probability of loss it is conceivable that individuals in the experiments reported here were concerned with the probability of ending up worse off than they would have been for certain had they chosen not to authorise (a cash prize value of £20); a situation that would have clearly prompted regret. Individuals were four times more likely to end up worse off if they authorised than if they did not authorise in the low probability of a good outcome condition than the high probability condition (probability of loss of 0.8 and 0.2, respectively). A potential limitation of the experimental method employed may be that participants did not actually experience the prior outcome, sunk cost or sunk benefit, for real and so it could be questioned whether participants’ reference points were influenced by the treatment manipulation. The results of a manipulation check reported earlier, however, suggest that the treatment manipulation would have the desired effect on participants’ reference points. In addition, Experiment One reports a significant effect of the sunk cost/benefit treatment, thus providing clear evidence that the hypothetical nature of the manipulation did not prevent it from impacting upon participants’ reference points, though the change in behaviour was not in the direction predicted by prospect theory. Finally, it is worth noting that many studies, including of course Kahneman and Tversky (1979), report behaviour consistent with prospect theory based upon hypothetical decision scenarios, thus there is no a priori reason to question whether participants’ frames of reference, and hence behaviour, could be manipulated by a hypothetical sunk cost (loss) or sunk benefit (gain). To conclude, if a decision maker falls prey to the sunk-cost effect when deciding whether to commit additional resources to a failing project, they are making decisions on less than rational economic grounds and scarce resources can potentially be allocated inefficiently. Understanding why individuals fall prey to the sunk-cost effect is, therefore, important and will help in the development of robust techniques aimed at mitigating the effect. Contrary to the predictions of prospect theory, this paper provides evidence that individuals are not more likely to authorise incremental investments in the presence of a sunk cost than a sunk benefit. In isolation, therefore, prospect theory is unable to explain fully the sunk-cost effect. This view is corroborated by Friedman, Pommerenke, Lukose, Milam, and Huberman (2007) for whom the sunk-cost effect proves elusive and whose data provide little evidence of loss aversion. While the findings reported here fail to support the prospect theory explanation, it is not to say that it does not have a role to play. Predictions of changing risky behaviour across gains and losses based on the S-shape value function are not supported, however, the sunk-cost effect could be seen as a special case relating to losses only. It may be that prospect theory behaviour under losses coupled with the desire to avoid waste, which cannot meaningfully be extended to decision scenarios involving sunk benefits, are joint drivers of the sunk-cost effect, though this remains to be investigated.14 Future research seeking to mitigate the sunk-cost effect should look to other possible explanations of the effect, such as the way in which individuals form and use mental accounts. The results in Soman (2001) indicate that when the prior investment is in the form of time individuals do not fall prey to the sunk-cost effect in the same way as when the investment is monetary. Soman (2001) provides evidence to suggest this result is due to the way in which individuals mentally account for time, which Duxbury, Keasey, Zhang, and Chow (2005) show differs from how they mentally account for money. Thus, mental accounting effects, perhaps coupled with prospect theory, may play an important role in the tendency for individuals to succumb to the sunk-cost effect and represent an important avenue for future research, both in terms of causes of the sunk-cost effect and ways in which to mitigate its impact on investment and consumption behaviour.

14 It is not immediately apparent how the influence of the prospect theory value function on behaviour in the loss domain can be separated from the influence of a desire to avoid waste. 29.

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Acknowledgements I am grateful to Kevin Keasey, an anonymous referee and the joint editors for detailed comments and advice on earlier drafts of this paper. Appendix. Example of the decision scenario You are the project manager of a medium sized engineering firm and are responsible for making investment decisions. You are considering whether to authorise the investment of additional company funds into an existing project that you previously authorised. The additional investment would prolong the project, which would end otherwise. The expected incremental cash flows associated with the additional investment are shown below. Note that there are two possible outcomes if you decide to undertake the additional investment.

Further information The original project required an initial investment of £3m (cash outflow) and generated a cash inflow of £2m. Cash flow information for additional investment

Immediate cash outflow Estimated future cash inflows

£ Million

Probability

2 5 0

20% 80%

On a rating of 1–7 how likely would you be to authorise investment in this project (where 1 ¼ definitely authorise and 7 ¼ definitely not authorise)? Please indicate on the scale below by circling the number corresponding to your decision.

1

2

3

4

5

6

7

Definitely authorise

Highly likely to authorise

Likely to authorise

Undecided whether to authorise or not

Unlikely to authorise

Highly unlikely to authorise

Definitely not authorise

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