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Purpose

The study investigates the effects of Prospect Theory’s loss aversion within the context of project financing.

Design/methodology/approach

The study makes use of a balanced paired comparison best/worst scaling (PCBWS) experimental design method. It has not been used in prior Prospect Theory studies and provides increased internal validity compared to other ranking methods by eliminating transitive assumptions.

Findings

The results show that within the context of project-financed investments, the difference between the predictions of Expected Utility Theory (EUT) and Prospect Theory can be explained by Prospect Theory’s loss aversion. As anticipated, loss aversion decreases as expected utility increases.

Originality/value

(1) This paper investigates Prospect Theory’s loss aversion within the context of a very specific, but very large, market that has not yet been studied in Prospect Theory literature – the $200+ bn annual global market for project finance. (2) It finds experimental confirmation of Prospect Theory’s loss aversion using a quantitative method (PCBWS) not used in prior Prospect Theory research. Furthermore, PCBWS eliminates transitive assumptions to increase validity.

Prospect Theory has been well-studied during the past four decades and is well-accepted in numerous contexts for helping to explain observed decision-making under uncertainty (Finger et al., 2024; Kahneman and Tversky, 1979; Kairies-Schwarz et al., 2017; Tversky and Kahneman, 1992; Wen et al., 2019). Absent in the literature, however, is an investigation of Prospect Theory within a project-financing context.

The methods of analysis used in the study of Prospect Theory have grown from the elementary coin flip, lottery and Ellsberg jar experiments to more recent experiments that employ complicated computer simulation methods such as Monte Carlo techniques (Fortin and Hlouskova, 2024; Gaspar and Silva, 2023). Absent in the literature is an investigation of Prospect Theory using a quantitative paired comparison best/worst scaling (PCBWS) experimental design analysis, which has precedent in economics and finance literature involving willingness-to-pay analyses (Louviere and Islam, 2008; Rausch et al., 2021; Samarzija, 2019; Tanaka et al., 2022). This analytical method provides specific advantages when used in Prospect Theory analyses involving financial decisions (see Section 3.1).

The experimental results of this paper are consistent with the results of other Prospect Theory studies discussed herein and, in that regard, simply provide further confirmation of the theory. However, it does so by filling the following unique gaps in the literature:

  1. It finds that Prospect Theory’s loss aversion helps to explain decision-making behavior within a very specific, but very large, market that has not yet been studied in Prospect Theory literature and

  2. It finds experimental confirmation of Prospect Theory’s loss aversion using a quantitative method, PCBWS, not used in prior Prospect Theory research, and which increases validity by eliminating transitive assumptions.

There are compelling academic and practitioner reasons for studying the effect of Prospect Theory within a project-financing context. First, much of the world’s economy now depends on project financing. During the past 40 years, project financing has replaced traditional balance-sheet financing as the means to obtain funding for the construction of most electric power projects around the world, including every electric power project within deregulated electricity markets (Buscaino et al., 2012; Kaminker, 2017; Mora et al., 2019). It is also common within other capital-intensive investment markets such as commercial real estate and the oil and gas industries. Project financing has grown into a $200+ bn per year global financing market (Fight, 2006; Yescombe, 2002).

Moreover, the size of each project financing is considerable. The average size of a project-financed loan in 2022 was $361 m (Refinitiv, 2024). The financial risks to a company and the risks to a manager’s career associated with making an incorrect decision for investments of this magnitude can be significant, and this can lead to risk-averse behavior that may not maximize the value of a firm (Bleichrodt and L’Haridon, 2023; Farinha and Maia, 2021; Kahneman and Tversky, 1979; Loubergé and Outreville, 2001; Schmidt and Zank, 2005; Sorensen, 2018; Tversky and Kahneman, 1991).

There are existing Prospect Theory studies involving financial investment decisions, but they were performed within the context of traditional balance-sheet financing, not project financing and the results of these existing studies cannot be extended to project financing because the investment community analyzes project financing very differently from balance-sheet financing (see Section 2.3).

The inability to extend the results of previous studies to project financing leaves a literature gap affecting a major portion of the world’s economy. Because of the magnitude of the global project-financing market, because of the significant size of a typical project-financing, because of the differences in how the investment community analyzes project-financing and because of the importance of project-financing in meeting the world’s energy growth, it is fitting and proper that financial decision-makers understand those factors which can affect their decision-making, especially since these project-financing decisions are typically made under uncertainty. The academic and practitioner implications are clearly significant, which elevates the importance of investigating this topic.

This paper is the first to explore the existence of Prospect Theory within a project-financing context. This first foray into the topic assists financial decision-makers with their decision-making under uncertainty (see Section 5.2) as well as provides foundational support for future research that, in turn, will lead to further insight and guidance into the topic (see Section 5.4).

EUT evolved as a means to assist in rational decision-making under uncertainty. “Pascal’s Wager” provides a popular example of EUT where, in 1670, mathematician Blaise Pascal quantified the alternate outcomes of eternal reward and punishment that could emerge from his choice to accept or not, the existence of God (Neiva, 2023).

From Pascal’s era onward, EUT was considered the accepted model of choice for rational decision-making under uncertainty (Just and Peterson, 2010; Marcarelli, 2023; Moscati, 2016). However, the results of numerous studies found differences between the predictions of EUT and the experimental measurements of human behavior under uncertainty (Barberis et al., 2016; Just and Peterson, 2010; Kalinowski, 2020; O’Donoghue and Somerville, 2018; Marcarelli, 2023; Moscati, 2016). These differences led decision theorists to develop alternative theories such as Prospect Theory (Kahneman and Tversky, 1979) and its successor, Cumulative Prospect Theory (Tversky and Kahneman, 1992). As detailed below, studies performed over the past four decades have shown that Prospect Theory and Cumulative Prospect Theory (hereafter referred to together in this paper as Prospect Theory) are often able to better explain experimental outcomes than EUT.

The study of Prospect Theory has grown during the past four decades from the elementary coin-flip, lottery and Ellsberg jar experiments which demonstrated the foundations of the theory, to more recent experiments with diverse commercial implications such as the marketing of medical insurance to consumers (Kairies-Schwarz et al., 2017), maximizing retirees’ consumption choices given uncertain lifetimes (Deng et al., 2022), deciding among customer compensation choices following an airline flight delay (Wen et al., 2019), optimizing consumer choice among various forms of transportation (Chremos and Malikopoulos, 2023), selecting roadway alternatives under uncertainty (Wei and Jian, 2022), determining the size of monetary discounts to overcome risk aversion in the selection of hotels (Han et al., 2024), understanding the farming practices of European farmers (Finger et al., 2024), optimizing consumer choice regarding the recharging of electric vehicles (Pelka et al., 2024), understanding the decision-making of electric generating companies in arriving at daily quoted prices within competitive electricity markets (Hu et al., 2021), the valuation of equities in the US and several international stock markets (Barberis et al., 2016), the selection of stock investment portfolios (Fortin and Hlouskova, 2024) and providing an explanation for the popularity of stock investment portfolio insurance (Gaspar and Silva, 2023). Indeed, a globally expansive domain. Absent in the literature, however, is an investigation of Prospect Theory and its key principle of loss aversion within the context of project-financed investments.

The concept that “losses loom larger than equivalent gains” (Tversky and Kahneman, 1991, p. 1,039), often referred to as “loss aversion” (Tversky and Kahneman, 1986, p. 258), is one of the core principles in behavioral economics and a central tenet of Prospect Theory (Farinha and Maia, 2021; Godoi et al., 2005). It has been observed in children as young as five years old as well as in non-human primates (Farinha and Maia, 2021). Loss aversion describes how people perceive a greater impact from an economic loss relative to that of an equal-size economic gain and is believed to be tied to the “human insecurity related to surviving” (Godoi et al., 2005, p. 49). This insecurity is addressed in the seminal work by Akerlof, which relates perceived uncertainty and the possibility of purchasing something that turns out to be a “lemon” (Akerlof, 1970, p. 489) to a reduction in the willingness-to-pay point. This reduction is expected to have an impact on the PCBWS binary choice of “invest” vs “do not invest” contained in this paper’s experiment.

Loss aversion is exacerbated under conditions of increasing risk and uncertainty (Farinha and Maia, 2021; Kahneman and Tversky, 1979; Tversky and Kahneman, 1991). For example, people are willing to accept a smaller gain when uncertainty is removed rather than the expectation of a larger gain with greater uncertainty (Kahneman and Tversky, 1979), which helps explain the popularity of certain investment strategies such as index funds.

Ownership of an item can increase the perceived value of the item, known as the endowment effect (Kahneman et al., 1991; Knetsch, 1989; List, 2004; Sorensen, 2018; Thaler, 1980), which then impacts loss aversion (Kahneman et al., 1991; List, 2004). For example, investors may place greater value on the money they hold (i.e. that which they are endowed with) than on trading that money for a financial investment. This is expected to have an impact on the PCBWS binary choice of “invest” vs “do not invest” contained in this paper’s experiment.

The size of the endowment can exacerbate the endowment effect (Bleichrodt and L’Haridon, 2023; Loubergé and Outreville, 2001; Schmidt and Zank, 2005; Sorensen, 2018). When faced with the potential of a substantial loss, such as a corporation’s investment in a new project, people tend to exhibit risk-averse behavior. In contrast, when the potential loss is perceived as small, such as the purchase of a lottery ticket, people have been found to be risk-seeking. In 2022, the average size of a project-financed loan was $361 million (Refinitiv, 2024), an amount that would likely be perceived by any decision-maker as substantial. This paper’s experiment is limited to a project-financing context, and as such, the size of a potential loss is expected to have an impact on the PCBWS binary choice of “invest” vs “do not invest”.

Loss aversion can also be affected if the choices under consideration lie within the domain of gains or within the domain of losses. For example, risk-averse behavior has been found when the experimental choices are constrained to lie within the domain of gains (i.e. the presented choices include a gain or lesser gain or no gain, but no loss) and risk-seeking behavior has been found when the experimental choices are constrained to lie within the domain of losses (i.e. the presented choices include a loss or a lesser loss or no loss, but no gain) (Erdogan, 2020; Kahneman and Tversky, 1979). However, this risk-seeking behavior within the domain of losses is not universal. Various studies (Farinha and Maia, 2021; Kairies-Schwarz et al., 2017; Loubergé and Outreville, 2001; O’Donoghue and Somerville, 2018) reported risk-averse behavior within the domain for losses due to the size of the endowment and the means of endowment, e.g. a windfall, such as gambling winnings vs the result of someone’s “hard-earned” income.

Furthermore, some experimental studies lie within both the domains for losses and gains (i.e. the choices presented are between the less risky choice of the status quo versus a riskier choice that presents the possibility of becoming either a gain or a loss), and these experiments are characterized in the literature as “mixed domain” (Kahneman and Tversky, 1979; Levy and Levy, 2002; Schoemaker, 1990; Thaler et al., 1997). In mixed domain experiments, the outcomes are consistently risk averse, and the kink in the value function at the zero point generates the risk aversion (Blavatskyy, 2021; O’Donoghue and Somerville, 2018; Tversky and Kahneman, 1986; Tversky and Kahneman, 1991). This is important because this paper utilizes a mixed-domain experiment involving a financial investment, and the literature regarding mixed-domain financial investments all exhibit risk-aversion (Barberis et al., 2016; Benartzi and Thaler, 1995; Deng et al., 2022; Fortin and Hlouskova, 2024; Gaspar and Silva, 2023; Levy and Levy, 2002; O’Donoghue and Somerville, 2018). Therefore, we would anticipate the results of our experiment to demonstrate risk-averse behavior within the context of project financing.

This paper provides an investigation of Prospect Theory’s loss aversion within the context of project financing to address the above-noted gap in the literature. Project financing is a separable capital investment owned by a special purpose company in which the lenders look only to the cash flow of the investment to service their loans (Buscaino et al., 2012; Fight, 2006; Klompjan and Wouters, 2002; Yescombe, 2002). Unlike balance-sheet financing, project financing provides an impenetrable, non-recourse “wall” between the investment and the balance sheet of the investing firm that prevents the lender from accessing the cash of the parent company and from relying on the parent company’s balance sheet (Fight, 2006; Klompjan and Wouters, 2002; Yescombe, 2002). The weighted average cost of capital (WACC) for a project-financed-investment is also calculated differently than for a balance-sheet financed investment because the debt and equity financings are limited to those of the specific project and not reflective of the parent company’s balance sheet (Dansky, 2024). With balance-sheet financing, the WACC of each investment is dependent on the WACC of those projects that “line up” in the investment opportunity schedule ahead of the investment (Brigham and Ehrhardt, 2017). This restriction does not hold for project-financing as the WACC of each investment is independent of each other, which prevents certain long-standing balance-sheet decision-making principles from being applied to project financing (Dansky, 2024). In summary, the investment community analyzes project financing very differently from balance-sheet financing, thus limiting prior Prospect Theory studies from being extended to project-financed investments.

The expected utility of an investment that makes use of project financing can be expressed as the ratio of the investment’s internal rate of return (IRR) to the investment’s WACC (Dansky, 2024). Simply put, this ratio of IRR:WACC represents the marginal benefits and marginal costs as viewed by the equity investor. Utility maximization is a foundational assumption of EUT, and investments with an IRR:WACC ratio greater than unity will increase the total utility of a utility-maximizing investor, while those investments with an IRR:WACC ratio less than unity will decrease the total utility of a utility-maximizing investor.

However, some financial decision-makers may be loss averse under Prospect Theory, and the degree of loss aversion is dependent on the expected utility of the alternative outcomes under consideration (Tversky and Kahneman, 1986). This phenomenon has been labeled the certainty effect (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986; Weber and Chapman, 2005), i.e. a person’s loss aversion is reduced the more certain they perceive the outcome will result in a gain rather than a loss. Thus, the higher the expected utility of the proposed investment, the greater the percentage of respondents willing to invest. Consistent with the certainty effect, this leads to the following hypothesis:

H.

Within the context of project-financed investments, loss aversion decreases as expected utility increases.

The actual percentage of those exhibiting loss aversion cannot be known in advance and is revealed through experiment (Tversky and Kahneman, 1986). This paper performs such an experiment by manipulating the expected utility of potential investments that are project-financed using a methodology (PCBWS) not used in prior Prospect Theory studies. The expected utility of each project-financed investment is expressed in this experiment as the IRR:WACC ratio, as per Dansky (2024). It is the only study to provide experimental support for this construct and was limited to project financing. Thus, the scope of this paper and its results remain limited to project financing since an experimental foundation for widening this paper’s results to other types of financing is not available.

If the proposed theoretical relationship is correct (i.e. some financial decision-makers may exhibit loss aversion within a project-financing context as a function of the investment’s expected utility), then it should be possible to observe behavior that aligns with this theoretical construct. Sufficient corporate data for quantitative analysis is not reasonably available. However, it is possible to design an experiment that replicates the decision-making environment, generates sufficient data for quantitative analysis and enables the quantification of this behavior. Such experimental methods are adept at describing the decision-making of individuals, and they broaden traditional economics research by allowing the study of individual human choices that are difficult to observe in natural environments, including an individual’s willingness to pay (Levin, 1999; Nermend and Latuszynska, 2016). Such is the case here.

The willingness-to-pay can be analyzed using various ranked preference methods (Bardsley et al., 2010; Hawkins et al., 2014; Lehmann, 2011; Marley and Louviere, 2005; Nermend and Latuszynska, 2016), including conjoint ranking (Gamel et al., 2016; Mahajan et al., 1982) and MaxDiff (Cohen and Orme, 2004; Rausch et al., 2021; Tanaka et al., 2022). Another method is paired comparison best–worst scaling (PCBWS), which dates to Fechner in 1860 and has been further developed over time (Kingsley and Brown, 2013). Sometimes referred to as the paired comparison method, it is “a straightforward way of presenting items for comparative judgment” (USDA, 2023, p. 1). PCBWS is often used to compare a benefit, as one dimension and price, as the other dimension, thus yielding estimates of monetary value or the willingness to pay (Kingsley and Brown, 2013; USDA, 2023).

There is a long list of precedents for the use of PCBWS in willingness-to-pay analyses (Louviere and Islam, 2008; Rausch et al., 2021; Samarzija, 2019; Tanaka et al., 2022). This relates directly to this paper’s analysis because the willingness to pay (or purchase or invest in) a financial investment that yields a future payment stream is a specific subset of the more general willingness of a purchaser to pay for any good or service that provides or is expected to provide, utility.

It is this willingness-to-pay logic that underpins the valuation of debt and equity securities (Brigham and Ehrhardt, 2017; Ross et al., 2016). Specifically, the willingness-to-pay point represents the maximum price that an investor would be willing to pay for an investment. According to EUT, a utility-maximizing investor should be willing to invest when IRR is greater than the cost of capital (i.e. IRR > WACC) and not willing to invest when IRR is less than the cost of capital (i.e. IRR < WACC). However, per Prospect Theory’s loss aversion, some investors will require an additional risk premium compared to valuations made pursuant to EUT and thus affect which projects will receive an investment.

PCBWS respondents are given a series of direct comparisons between two items and are asked to select their preference in each set (Kingsley and Brown, 2013; USDA, 2023). In each direct comparison, the respondent’s selected preference is the “best” in that set, and the unselected item is the “worst” in that set (Cohen and Orme, 2004; Massey et al., 2015). It is a binary choice.

Conjoint analyses and MaxDiff analyses can work well for decision sets that contain more than two dimensions of choice. This paper’s analysis, however, has only two dimensions, IRR and WACC, so there is no advantage in using them over PCBWS. In addition, a PCBWS experiment that contains all possible permutations is said to be balanced, and a balanced PCBWS introduces less error than an unbalanced PCBWS, less error than MaxDiff, and less error than conjoint analyses because all comparisons are direct and there are no inferred (transitive) comparisons (Kingsley and Brown, 2010). PCBWS, therefore, has a validity advantage whenever there are two dimensions of choice. Furthermore, the history of PCBWS in willingness-to-pay analyses suggests the use of PCBWS over other methods. Absent in the literature is any investigation of Prospect Theory using PCBWS.

Each respondent was presented with six scenarios that manipulated the IRR and WACC of a project-financed investment across conditions to measure the test subjects’ willingness to provide equity financing. The six scenarios formed a 2x3 experimental design which, along with the six choices of “do not invest,” required 21 direct comparisons to form a balanced PCBWS analysis. The direct comparisons against the “no investment” choice were included because the willingness-to-pay point under both EUT and Prospect Theory is the point of indifference (or equilibrium point) between investment and no investment.

The experiment was repeated with three groups of respondents using three different variations of the 2x3 manipulation matrix. See Table 1 for the three sets of manipulations (identified as Matrix A, Matrix B and Matrix C). This allowed for combinations where the IRR:WACC ratio was less than, greater than and equal to unity, which is important because the willingness-to-pay point under EUT is equal to unity.

Table 1

The manipulated experimental conditions

 

Experimental design analysis provides high internal validity, replicability and causality because only the manipulated variables are changed and, to the extent there may be confounding variables, they are spread evenly across all groups (Bougie and Sekaran, 2020; Levin, 1999). In this paper’s analysis, all external influences were held constant, and only the IRR and WACC were varied. All scenarios used the identical size investment since loss aversion may be affected by the size of the investment. Also, because Prospect Theory may be affected by the experience of the subjects (List, 2004), the survey instrument rejected any respondent without a minimum of five years of general financial investment experience.

Internal validity is increased as PCBWS provides greater discrimination by eliminating extreme response bias and middle response bias, and cognitive error is reduced due to binary choice (Lee et al., 2007; Marley and Louviere, 2005; Massey et al., 2015; Rausch et al., 2021). A balanced PCBWS increases internal validity because all comparisons are direct with no inferred comparisons (Kingsley and Brown, 2010). Reliable results can be obtained with smaller sample sizes (Bougie and Sekaran, 2020; Brown and Peterson, 2009), which can increase validity. In addition, the experiment was repeated with three groups of respondents using three different variations of the 2x3 manipulation matrix; this increased analysis validity through triangulation and parallel-form reliability (Bougie and Sekaran, 2020).

The tradeoff for this high internal validity is lower external validity. Experimental design scenarios require respondents to imagine how they would react to stimuli presented in a controlled format. Reactions of people to real-life stimuli may exhibit more variability because they are being made while subject to more variability and possibly subject to the influence of co-workers in a team setting. Thus, answers provided by respondents in a controlled environment may not reflect real-life decision-making (Portney, 1994). Losing real money may lead to a different experimental outcome than losing hypothetical money (Bleichrodt and L’Haridon, 2023).

Finally, this paper’s analysis increases external validity by experimentally duplicating as closely as practical the population of people that make real-life project-financing decisions. Project-finance decisions are only made by people within large corporations with specific financial expertise. Project financing is not available to small companies and the general public (Refinitiv, 2024). Thus, external validity is increased by limiting participants to experienced corporate investment employees having relevant academic degrees and who successfully passed all of the survey’s financial screener questions.

An online survey instrument was created using a commercially available platform. The use of online surveys for academic research is commonplace and well-accepted (Berinsky et al., 2014; Sharpe-Wessling et al., 2017; Strickland and Stoops, 2020); however, certain protections such as screening questions and attention checks are encouraged to ensure data validity (Berinsky et al., 2014; Danilova et al., 2022; Desimone et al., 2015; Toich et al., 2021; Verbree et al., 2020).

The survey instrument disqualified all respondents not holding an academic degree in finance or economics and at least five years of business investment work experience. This was followed by five screener questions to determine each respondent’s understanding of financial concepts. The use of screener questions is recommended to ensure that the respondents to a survey hold specific expertise (Danilova et al., 2022; Sharpe-Wessling et al., 2017; Strickland and Stoops, 2020). All five questions needed to be answered correctly.

Respondents were then presented with the survey instructions, which included specific instructions to focus the respondent on project financing, and this was followed by the PCBWS direct comparisons [1]. Attention checks were placed within the survey instrument as their use is considered best practice (Berinsky et al.,2014; Desimone et al., 2015; Toich et al., 2021; Verbree et al., 2020). An incorrect answer on any of the three attention checks resulted in disqualification.

An anonymous online link to each of the three versions of the survey was generated, and these links were distributed online by a market research firm to its survey panelists within the US. Data from the respondents was retrieved online and reviewed to confirm the absence of duplicate IP addresses. A total of 378 responses were collected between August 28 and September 11, 2023, which included 124 responses for Matrix A, 126 for Matrix B and 128 for Matrix C. Of these, 193 were rejected (64 rejections for Matrix A, 66 rejections for Matrix B and 63 rejections for Matrix C) due to failure to consent to voluntary participation, failure to meet the academic and work experience requirements, failure to correctly answer all five screener competency questions and the failure of the attention checks as well as for low-quality responses such as incomplete surveys, “long-stringing” and “Christmas tree” responses (DeSimone et al., 2015; DeSimone and Harms, 2017). One hundred and eighty five responses were retained as qualified completed surveys (60 for Matrix A, 60 for Matrix B and 65 for Matrix C), which satisfied the pre-established minimum of 60 qualified respondents for each matrix (Bougie and Sekaran, 2020; Brown and Peterson, 2009).

Of the 185 qualified responses, 41% self-reported a degree in Economics and 59% self-reported a degree in finance. For both economics and finance, the median level of academic attainment was a Masters (MA, MS and MBA) degree. For general business investment work experience, the median response was 11–15 years (60% of the responses), followed by 5–10 years (32%), and then by 16+ years (8%). The median response of 11–15 years of experience was consistent across all three of the data manipulation sets. Furthermore, all respondents indicated experience with project financing, with a median of 6–10 years. This median response of 6–10 years of project finance experience was also consistent across all three of the data manipulation sets.

The respondents also self-reported a high level of responsibility regarding investment decision-making. A significant majority (80.0%) responded that they are a “decision-maker” regarding potential investments, while 10.8% selected that they make recommendations for submittal to the decision-makers and 9.2% reported that they perform investment analyses for submittal to the decision-makers. This self-reported data suggests increased ecological validity because all the respondents had a degree in finance or economics, all had at least five years of professional investment experience, all had work experience with project financing, and a majority of the sample group consisted of experienced financial decision-makers.

The data from each respondent’s choice of “invest” vs “do not invest” was extracted from the full data set of direct comparisons (The remaining direct comparisons were reserved for an analysis outside the scope of this paper.). For each of the 18 “invest” vs “do not invest” comparisons (i.e. six from each of the three matrices), the percent of respondents selecting “invest” over “do not invest” was calculated and plotted against the IRR:WACC ratio of each investment. See Figure 1.

Figure 1
A table and scatter plot show how I R R, W A C C ratios relate to investment selection across three matrices.The figure contains a table on the left and a plot on the right. The table is positioned on the left and comprises 4 columns and 4 rows. From left to right, the column headers are as follows: Column1: No header; Column 2: “Investment hash”, Column 3: “I R R: W A C C Ratio”, and Column 4: “percent Selecting the Investment Over Not Investing”. The headers for the second through fourth rows are labeled from top to bottom as follows: “Matrix A”, “Matrix B”, and “Matrix C”. Rows 2 through 4 are each divided into 6 sub-rows. The entries in the table are as follows: Under “Matrix A”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.43, 1.00, 0.59, 2.14, 1.50, 0.88”, and the “percent Selecting the Investment Over Not Investing” column lists “93.3 percent, 81.7 percent, 0.0 percent, 100.0 percent, 93.3 percent, 0.0 percent”. Under “Matrix B”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.60, 2.00, 2.40, 0.40, 0.50, 0.60”, and the “percent Selecting the Investment Over Not Investing” column lists “98.3 percent, 100.0 percent, 100.0 percent, 0.0 percent, 0.0 percent, 0.0 percent”. Under “Matrix C”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.14, 1.43, 1.71, 0.73, 0.91, 1.09”, and the “percent Selecting the Investment Over Not Investing” column lists “89.2 percent, 92.3 percent, 100.0 percent, 0.0 percent, 18.5 percent, 67.7 percent”. The scatter plot positioned on the right is titled “percent of Respondents Selecting the Investment Over Not Investing versus the I R R: W A C C Ratio, Observed”. The vertical axis label reads “Percent x 100” and ranges from 0 to 1 in increments of 0.2 units. The horizontal axis label reads “I R R: W A C C Ratio” and ranges from “0.00” to “3.00” in increments of 0.50 units. Individual data points are plotted across the graph. Several points lie along the bottom near “Percent x 100” equals 0 between approximately “I R R: WACC Ratio” 0.40 and 1.00. One point appears below the 0.2 level around an “I R R: W A C C Ratio” slightly below 1.00. Above 0.6, multiple points rise as “I R R: W A C C Ratio” increases, with points near 0.7 to 0.9 between roughly 1.00 and 1.50, and several points reaching the top boundary at “1” between roughly 1.50 and 2.50. Note: All numerical values are approximated.

Percent selecting the investment, observed. Source: Authors’ own work

Figure 1
A table and scatter plot show how I R R, W A C C ratios relate to investment selection across three matrices.The figure contains a table on the left and a plot on the right. The table is positioned on the left and comprises 4 columns and 4 rows. From left to right, the column headers are as follows: Column1: No header; Column 2: “Investment hash”, Column 3: “I R R: W A C C Ratio”, and Column 4: “percent Selecting the Investment Over Not Investing”. The headers for the second through fourth rows are labeled from top to bottom as follows: “Matrix A”, “Matrix B”, and “Matrix C”. Rows 2 through 4 are each divided into 6 sub-rows. The entries in the table are as follows: Under “Matrix A”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.43, 1.00, 0.59, 2.14, 1.50, 0.88”, and the “percent Selecting the Investment Over Not Investing” column lists “93.3 percent, 81.7 percent, 0.0 percent, 100.0 percent, 93.3 percent, 0.0 percent”. Under “Matrix B”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.60, 2.00, 2.40, 0.40, 0.50, 0.60”, and the “percent Selecting the Investment Over Not Investing” column lists “98.3 percent, 100.0 percent, 100.0 percent, 0.0 percent, 0.0 percent, 0.0 percent”. Under “Matrix C”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.14, 1.43, 1.71, 0.73, 0.91, 1.09”, and the “percent Selecting the Investment Over Not Investing” column lists “89.2 percent, 92.3 percent, 100.0 percent, 0.0 percent, 18.5 percent, 67.7 percent”. The scatter plot positioned on the right is titled “percent of Respondents Selecting the Investment Over Not Investing versus the I R R: W A C C Ratio, Observed”. The vertical axis label reads “Percent x 100” and ranges from 0 to 1 in increments of 0.2 units. The horizontal axis label reads “I R R: W A C C Ratio” and ranges from “0.00” to “3.00” in increments of 0.50 units. Individual data points are plotted across the graph. Several points lie along the bottom near “Percent x 100” equals 0 between approximately “I R R: WACC Ratio” 0.40 and 1.00. One point appears below the 0.2 level around an “I R R: W A C C Ratio” slightly below 1.00. Above 0.6, multiple points rise as “I R R: W A C C Ratio” increases, with points near 0.7 to 0.9 between roughly 1.00 and 1.50, and several points reaching the top boundary at “1” between roughly 1.50 and 2.50. Note: All numerical values are approximated.

Percent selecting the investment, observed. Source: Authors’ own work

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Except for one datapoint outlier (investment #5 of Matrix C having an IRR:WACC Ratio of 0.91) [2], the observed data pattern in Figure 1 shows a zero preference for investing when IRR:WACC <1, a 100% preference for investing when IRR:WACC reached some “risk-less” point above IRR:WACC >1, and the effect of Prospect Theory’s loss aversion appearing in between. The data pattern shows an increase in the willingness to invest as a function of expected utility and is thus fully consistent with the certainty effect discussed in Section 2.2. The data shows that loss aversion decreased as expected utility (the IRR:WACC ratio) increased. The data also shows that once the IRR:WACC ratio increased to approximately 1.5, the expectation of profitable returns appears sufficient to overcome any loss aversion. The outcome of this experiment is consistent with the outcome of experiments carried out by Kahneman and Tversky (1979) and Tversky and Kahneman (1986) and replicated by others such as Kalinowski (2020).

The above data pattern exhibiting the certainty effect is pronouncedly different from the step function predicted by EUT with its singularity situated at IRR:WACC = 1 (see Figure 2). A comparison of the two figures shows that within the relevant range of IRR:WACC equal to and greater than unity, the experimental data exhibits a positive relationship between the willingness to invest and the expected utility of the investment [3]. Thus, as the expected reward (i.e. IRR) increased relative to the cost of capital (WACC), and/or the cost of capital decreased relative to the expected reward, the percentage of respondents willing to make the project-financed investment increased. This confirms our hypothesis:

Figure 2
A table and graph show I R R: W A C C ratios versus investment selection, illustrating E U T’s decision threshold at 1.00.The figure contains a table on the left and a plot on the right. The table is positioned on the left and comprises 4 columns and 4 rows. From left to right, the column headers are as follows: Column1: No header; Column 2: “Investment hash”, Column 3: “I R R: W A C C Ratio”, and Column 4: “percent Selecting the Investment Over Not Investing”. The headers for the second through fourth rows are labeled from top to bottom as follows: “Matrix A”, “Matrix B”, and “Matrix C”. Rows 2 through 4 are each divided into 6 sub-rows. The entries in the table are as follows: Under “Matrix A”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.43, 1.00, 0.59, 2.14, 1.50, 0.88”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100 percent, 0.0 percent, 100 percent, 100 percent, 0.0 percent”. Under “Matrix B”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.60, 2.00, 2.40, 0.40, 0.50, 0.60”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100.0 percent, 100.0 percent, 0.0 percent, 0.0 percent, 0.0 percent”. Under “Matrix C”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.14, 1.43, 1.71, 0.73, 0.91, 1.09”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100 percent, 100.0 percent, 0.0 percent, 0.0 percent, 100 percent”. The line graph positioned on the right is titled “percent of Respondents Selecting the Investment Over Not Investing versus the I R R: W A C C Ratio, E U T Predicted”. The vertical axis label reads “Percent x 100” and ranges from 0 to 1 in increments of 0.2 units. The horizontal axis label reads “I R R: W A C C Ratio” and ranges from “0.00” to “3.00” in increments of 0.50 units. A dashed step-shaped line is plotted that runs along the bottom near “0” from the left side until it reaches approximately “I R R: W A C C Ratio” 1.00, then rises vertically to “1”, and continues horizontally near the top at “1” from about “1.00” through “3.00”. Note: All numerical values are approximated.

Percent selecting the investment, EUT predicted. Source: Authors’ own work

Figure 2
A table and graph show I R R: W A C C ratios versus investment selection, illustrating E U T’s decision threshold at 1.00.The figure contains a table on the left and a plot on the right. The table is positioned on the left and comprises 4 columns and 4 rows. From left to right, the column headers are as follows: Column1: No header; Column 2: “Investment hash”, Column 3: “I R R: W A C C Ratio”, and Column 4: “percent Selecting the Investment Over Not Investing”. The headers for the second through fourth rows are labeled from top to bottom as follows: “Matrix A”, “Matrix B”, and “Matrix C”. Rows 2 through 4 are each divided into 6 sub-rows. The entries in the table are as follows: Under “Matrix A”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.43, 1.00, 0.59, 2.14, 1.50, 0.88”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100 percent, 0.0 percent, 100 percent, 100 percent, 0.0 percent”. Under “Matrix B”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.60, 2.00, 2.40, 0.40, 0.50, 0.60”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100.0 percent, 100.0 percent, 0.0 percent, 0.0 percent, 0.0 percent”. Under “Matrix C”, the “Investment hash” column lists “1, 2, 3, 4, 5, 6” with corresponding “I R R: W A C C Ratio” values “1.14, 1.43, 1.71, 0.73, 0.91, 1.09”, and the “percent Selecting the Investment Over Not Investing” column lists “100 percent, 100 percent, 100.0 percent, 0.0 percent, 0.0 percent, 100 percent”. The line graph positioned on the right is titled “percent of Respondents Selecting the Investment Over Not Investing versus the I R R: W A C C Ratio, E U T Predicted”. The vertical axis label reads “Percent x 100” and ranges from 0 to 1 in increments of 0.2 units. The horizontal axis label reads “I R R: W A C C Ratio” and ranges from “0.00” to “3.00” in increments of 0.50 units. A dashed step-shaped line is plotted that runs along the bottom near “0” from the left side until it reaches approximately “I R R: W A C C Ratio” 1.00, then rises vertically to “1”, and continues horizontally near the top at “1” from about “1.00” through “3.00”. Note: All numerical values are approximated.

Percent selecting the investment, EUT predicted. Source: Authors’ own work

Close modal
H.

Within the context of project-financed investments, loss aversion decreases as expected utility increases.

A balanced PCBWS analysis was performed to investigate the effects of Prospect Theory’s loss aversion within the context of project financing. The results of the experiment show the difference between the experimentally obtained outcome (Figure 1) and the outcome predicted by EUT (Figure 2). Specifically, the data pattern exhibits the certainty effect (i.e. loss aversion decreased as expected utility increased) and the certainty effect affirms the existence of Prospect Theory’s loss aversion.

In addition to reaffirming Prospect Theory’s loss aversion, this paper fills the following gaps in the literature:

  1. It finds that Prospect Theory’s loss aversion helps to explain the decision-making behavior within a very specific, but very large, market that has not yet been studied in Prospect Theory literature – the $200+ bn annual global market for project-finance and

  2. It finds experimental confirmation of Prospect Theory’s loss aversion using a quantitative method (PCBWS) not used in prior Prospect Theory papers and which eliminates transitive assumptions to increase validity.

This paper brings to the forefront that decision-makers may not be making project-finance decisions based on EUT, and as such, may not be maximizing their firm’s value. When project-finance decisions do not align with EUT predictions, senior-level managers may wish to investigate decision recommendations made by subordinates to determine whether rejection decisions are skewed due to risk aversion. Investment recommendations can be affected by a risk-averse analyst’s lack of effort to acquire additional information that could reduce the perceived risk due to the cost (manhours) of acquisition (Caplin and Dean, 2015), and thus, senior-level managers may wish to investigate whether subordinates have chosen to forego the additional information and, instead, simply seek higher returns to address their loss aversion, thus skipping investment opportunities that would add to the firm’s value.

This paper, being the first to investigate Prospect Theory within the context of project financing, makes significant contributions by identifying a gap in the literature affecting a $200+ bn/year commercial market and by opening up a new line of academic inquiry having practitioner implications. For example, Prospect Theory’s risk aversion has been shown in various studies to be affected by the age, experience and gender of the participants as well as by the size and type of endowment. Each has practitioner implications because two financial teams, disparate in their composition, may yield disparate recommendations when evaluating the same project investment due to Prospect Theory. Such knowledge would be of great value to senior-level managers who seek to maximize their firm’s value.

This paper made use of an experimental design analysis because sufficient corporate data for quantitative analysis is not reasonably available. Experimental design analyses provide high internal validity, replicability and causality. The balanced PCBWS also increased internal validity by eliminating transitive assumptions, and the experiment increased validity through triangulation and parallel-form reliability. However, experimental design scenarios require respondents to imagine how they would react to stimuli that have been presented in a controlled format. Such answers may not reflect real-life decision-making (Portney, 1994), and losing real money may lead to a different experimental outcome than losing hypothetical money (Bleichrodt and L’Haridon, 2023).

For online surveys, the use of screener questions is considered best practice to ensure that respondents hold specific expertise, and this study’s screener questions were tested to be effective at weeding out those respondents who did not possess a certain level of financial expertise. They were not intended to guarantee that a respondent holds a specific employment position. For this, our study relied on self-reported data.

PCBWS has not been used previously for Prospect Theory experiments. A balanced PCBWS analysis introduces less error than the methods found in various Prospect Theory experiments that manipulate more than one variable at a time and do not directly test for each permutation. For example, numerous lottery-type experiments simultaneously manipulated the odds of winning a reward and the size of the reward. It is recommended that an analysis of this advantage be conducted.

This paper made use of online surveys with screener questions to establish each respondent’s understanding of financial concepts. The analysis may be re-performed using participants whose credentials and experience can be verified through their place of employment, although we recognize the difficulty of obtaining the requisite data in a quantity sufficiently large to support a quantitative analysis.

The study made use of an experimental design analysis, however, answers provided by respondents in a controlled environment may not reflect real-life decision-making. This limitation can be partially offset by employing manipulated scenarios that exhibit high ecological validity. The manipulations selected for the analysis performed herein were varied at specific intervals to ensure that specific conditions were tested; they were not selected to reflect ecological validity. A follow-up study using real-life project finance data are recommended now that experimental evidence of Prospect Theory’s loss aversion within a project-financing context has been found.

Finally, there are large public/private infrastructure projects that make use of project financing. Public and private decision-makers operate within different environments, and their experiences differ. These differences may affect the framing of a decision under Prospect Theory (Kahneman et al., 1991), and this raises practical questions regarding the management of public/private infrastructure investments that are worthy of further research.

1.

The screener questions, instructions and set of direct comparisons can be obtained from the corresponding author.

2.

This type of inconsistency (the anomalous data point regarding Matrix C, investment #5) tends to occur in PCBWS analyses when choices are close in value (Brown and Peterson, 2009; Choi et al., 2013; Johanson and Gips, 1993; Kingsley and Brown, 2010). The Law of Comparative Judgment states that smaller degrees of “discriminal difference” increase the inconsistency of a test subject’s responses (Thurstone, 1994, p. 266). Such may be the case here, where the choice was between two investments having IRR:WACC ratios that were close together and the economic incentive for a respondent to complete a survey quickly was not aligned with completing the survey accurately.

3.

A similar outcome was found whether the expected utility of the investment was expressed as the ratio of IRR:WACC (as shown in Figure 1) or expressed as the difference of IRR-WACC. Economics literature presents the comparison of marginal benefits to marginal costs as either the ratio of one to the other (MB:MC) or the difference of one from the other (MB-MC). The analyses were performed both ways with generally similar results. Only the results of the ratio form are presented because Dansky (2024) was limited to finding experimental support for the MB:MC ratio as an expression of the expected utility of a project-financed investment.

Declarations: The authors declare there are no conflicts of interest concerning the research, authorship and/or publication of this article. The authors also declare there are no sources of funding concerning the research, authorship and/or publication of this article. The research protocol was reviewed and approved by the Florida Institute of Technology IRB (Date: May 18, 2023; IRB Number: 23-072), and voluntary informed consent was provided by each survey participant.

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