Commercial Arbitration: The art and science of but-for analysis
‘The greatest scientists are always artists as well.’
The quantification of damages requires more than just doing ‘the maths’. Damages quantification involves mathematics and reliable quantification certainly requires that mathematics is accurate. Yet reliable damages quantification requires more. It also requires detailed engagement with the legal claims under consideration and the design of an appropriate analytical framework.
The quantification of damages presents questions of causation and construction that extend beyond the maths. This necessarily combines elements of ‘art’, meaning thoughtful engagement with the legal claims under consideration, and ‘science’, meaning the careful use of established economic techniques to measure financial harm. However, it does not imply that damages quantification is just a matter of subjective opinion, nor that all damages opinions are equally legitimate.
Damages assessments can err through an overly mechanical approach without sufficient engagement with the facts and legal claims at issue and inadequate attention to causation. Causation is distinct from traditional ‘burden of proof’, which remains with the parties. Causation requires the careful construction of a counterfactual or ‘but-for’ world that eliminates only the conduct at issue but retains all relevant features of the actual world. The construction of the but-for world is necessarily hypothetical and must remain internally consistent. By definition, damages equal the difference between such a but-for construction and the actual scenario. By design, the difference should aim to isolate the financial harm due to conduct at issue from other unrelated financial developments.
Damages assessments can also err through a failure to apply appropriate quantification techniques or to apply them correctly. All quantification techniques make implicit assumptions and, as a result, particular techniques are well suited to certain factual situations but not to others. A failure to acknowledge or understand the underlying assumptions can lead to the application of techniques in inappropriate circumstances. Moreover, the application of common valuation approaches, such as the discounted cash flow (DCF) method, requires attention to the construction of cash flow forecasts and risk assessments. Best practice techniques are well established, and common application errors can and should be avoided.
With this in mind, we begin this article by discussing the ‘art’ of but-for construction and, in a second section, discuss the established ‘science’ of quantification. Finally, we consider the need to conduct plausibility and robustness checks on any estimate of damages. Such checks should be a central element in any economic analysis, particularly when assessing causation.
We discuss common plausibility checks and their limitations, and the potential existence of a ‘valuation smoking gun’. Claimants and respondents often reveal expectations and preferences in transaction or investment terms and other relevant documents. Lawyers and quantum experts should review the case record with more than liability in mind.
The ‘art’: engagement with the facts and legal claims
Fact patterns in commercial arbitration are often complicated, involving many acts and responses over an extended period. There might be numerous delays before a contract termination or breach, multiple changes in contract or investment terms or applicable regulations, or multiple responses by the other party. A joint venture might face failure not just due to a single act but through a series of interrelated actions (‘death by a thousand cuts’). Damages quantification necessarily starts with engagement with these fact patterns.
To illustrate, consider a scenario involving three ‘bad’ acts separated in time: a first bad act followed a year later by a second bad act, and in turn, by a third bad act after another year. Now consider a possible evolution of the affected project or company’s enterprise value (EV) over the relevant time frame. The first bad act might trigger a reduction in its EV. Independent market developments unrelated to the problematic conduct further reduce the EV during the year between the first and second bad acts. Like the first bad act, the second bad act then triggers a further decline in EV before independent market developments prompt a partial recovery of EV during the year between the second and third bad acts. The third bad act then occurs in year three and destroys the remaining EV.
What are the damages associated with the three bad acts? The framework for the damages analysis depends on applicable law, facts and the legal claims being advanced. For example, one possibility is that the three bad acts formed an interrelated series of conduct with an overall result: the ultimate destruction of the entire EV of the affected company or business. From this view, damages could equal the EV of the project or business on the day before the first bad act occurred or the likely EV on the date of the third bad act assuming that none of the three bad acts would have occurred. The damages could even be the EV on the date of the trial, assuming that none of the three bad acts would have occurred. Underlying all these options, we would construct a but-for scenario that assumes the absence of all three of the bad acts. The quantum’s resulting magnitude would nevertheless differ depending on the choice of valuation date: before the first bad act, upon the last bad act or at the trial.
An alternative construction might view the three bad acts as unrelated and seek to isolate the individual harm associated with each of them. In this alternative view, we might seek to identify the decline in EV arising due to the first bad act at the date it occurred. We would then repeat the process to estimate the decline in EV a year later due to the entry of the second bad act and then repeat a third time to estimate the further decline in EV due to the third bad act. Total damages would equal the sum of the three individual EV impacts. We could measure the individual impact of each act on the date each act occurred or on a common date, such as the present date or that of the trial. Again, the choices depend in part on the legal framework and the claims being advanced, and the resulting magnitude of the quantum will differ depending on the choice.
Even if the bad acts were unrelated, their financial impacts might be interrelated. For example, the first bad act might involve a reduction in sales quantities, the second a reduction in prices and the third an early termination of a contract or joint venture. The individual financial impact of the first bad act – a reduction in sales quantities – necessarily depends on assumptions about sales prices and contract duration, and thus on assumptions about the second and third bad acts. Similarly, the individual financial impact of the second bad act – a reduction in sales prices – depends on assumptions about sales quantities and contract duration and thus on assumptions about the first and third bad acts. Reliable damages assessment in such circumstances must take account of the interrelationships and avoid double-counting. It must also transparently explain the relationship of the financial impacts of each of the separate bad acts.
Choosing the analytical framework requires close collaboration between legal and expert teams, usually during the initial stages of a proceeding. The relevant choices depend on the law, facts and legal claims being advanced, and economic and practical considerations, such as the ability to observe and measure the discrete financial impact of different bad acts. Designing the framework also involves a choice of the valuation date. This, in turn, determines the information available to the experts for their assessments as a valuation usually does not consider information that became available after the valuation date.
Damages estimation requires the construction of a coherent counterfactual or but-for scenario, which compares to the actual scenario. But-for construction asks: what would have happened in the absence of the bad act(s)?
Due to greater sales quantities and/or higher prices, revenues might have been higher. In turn, greater sales quantities may have prompted (1) increased variable or semi-variable costs of sales and (2) increased selling expenses. Increased sales quantities may have likewise prompted a need for more capital spending, which would, in turn, impact annual depreciation charges. More sales revenues and cash flows might have enabled a company to repay debt and avoid financial charges (interests or penalties). More sales and income may have triggered additional taxes.
Whatever the precise effects, the damages analysis must coherently construct a scenario of financial performance and identify a consistent theory of harm. For example, a bad act could have delayed a project or business’s ability to generate cash. The end result of the delay in cash generation will depend on specific facts. One possibility is that a business ends with more debt. Delayed cash flow generation might result in a failure to pay scheduled debt interest. If so, the relevant but-for scenario would imagine cash generation on schedule and the payment of debt interest. The resulting damages would represent the increase in outstanding debt due to the inability of the business to pay debt interest.
Another fact pattern might end with the opposite result – a reduction in debt. A delay in cash generation might trigger an event of default under a loan and a lender’s demand for early repayment. To meet the repayment demand, a business may have required an infusion of new equity from a third party, diluting the claimant. If so, the relevant but-for scenario would imagine cash generation on schedule, no early debt repayment or dilution. The resulting damages would represent the impact on the claimant of the dilution but, at the same time, acknowledge that the business would have had more debt.
In both cases, reliable but-for construction must engage with the specific facts and work through their impacts on all aspects of a project or business’s financial performance. A failure to do so will contaminate the resulting damages and fail to isolate the financial impact of the conduct at issue.
But-for construction often draws on available information such as management projections, extrapolation of trends, the performance of peers and even contract terms themselves. Contemporaneous documents may include management projections, which reflect one party’s expectations prior to a bad act(s) and, as such, provide useful information about potential but-for outcomes. However, management projections could be flawed, simplistic or overly optimistic, so interpretative care is required. Third-party review and confirmation of management projections, such as by lenders or outside investors, can provide comfort about the reasonableness of management expectations.
The conduct at issue may have broken or diverted a clear trend in performance. Trends can sometimes be unstable or difficult to discern. Their identification requires proper statistical tools. Peer performance may be a useful but-for guide if the peers are unaffected by the conduct at issue. However, the relevance of peer performance depends on the extent of comparability. Peers may engage in slightly different activities, be larger or smaller and/or enjoy different competitive advantages and challenges. But-for construction must consider these differences, and the available peer performance may need to be adjusted accordingly. A contract may contain minimum purchase quantities or some sort of volume and pricing expectations, which could form a clear basis for but-for construction.
In certain cases, but-for construction will require the use of economic models to capture demand and substitution effects and the extent of cost pass-through to customers. Standard economic models exist and will likely form the basis for expert assessment and debate.
But-for construction should rely on available market evidence where possible to minimise or avoid subjectivity. For example, traded spot and futures prices of commodities are often available, along with long-term price forecasts. Industry datasets from firms like Euromonitor or Nielsen often provide detailed market information about pricing and market shares and are useful for but-for construction. Even equity analyst reports can contain contemporaneous and independent forecasts of market developments, which can provide a basis for but-for construction.
A key part of a damages assessment is to compile, analyse and then use the best available information as the basis for a coherent and well-grounded construction of the but-for scenario. Completion of this task demands a combination of analytical care and creative engagement.
Most legal systems require damages to reflect the potential for mitigation. A claimant cannot obtain damages if they could have taken reasonable steps to mitigate a loss. Suppose, for example, two parties established a joint venture (JV) to invest in a particular type of real estate during a recession. One party had relevant contacts but no money; the other had money but no contacts. The JV agreement defined investment obligations and prospective rent sharing.
A dispute then emerges because the party with money failed to answer a capital call when required to do so under the JV agreement. What are the resulting damages? If the claimant could secure a replacement investment from a third party, there was no total loss of the investment opportunity. In that event, damages should reflect only the economic loss due to the delay in obtaining a replacement investment and the deterioration, if any, in the envisaged rent sharing.
Any assessment of mitigation focuses on the actual world and may prompt analysis of the choices made by a claimant in response to the conduct at issue. It requires consideration of the nature of the financial harm at issue, whether it is likely to linger over the remaining life of the business or whether there is scope for a claimant to catch up over time to where it would likely have been in the but-for scenario. The essential mitigation question is whether a claimant responded rationally post-breach and will continue to do so in the future.
Damages quantification requires identification of an analytical framework, construction of a coherent but-for scenario and, in many cases, an assessment of potential mitigation. The task entails compilation and analysis of available information and close collaboration between the client, legal and expert teams. The but-for scenario is necessarily hypothetical, but not just pure speculation. On the contrary and at best, but-for analysis consists of an imaginative and systematic engagement with the facts and legal claims at issue.
The ‘science’: accurate implementation
The art is to construct what would have happened absent a bad act(s), choose the appropriate framework for analysis and determine the questions requiring an answer. The science entails the accurate implementation of the framework. Established valuation methods exist, each with strengths and weaknesses. The choice of method depends on the nature of the valuation exercise and sometimes on data limitations.
For example, direct transaction evidence – a stock price or an offer to purchase the asset in question – can represent the best benchmark to assess value at a given point in time. The reason is that traded prices reveal market participants’ perception of value. Willing, unforced and knowledgeable buyers and sellers have natural and conflicting financial incentives to assess value accurately. Traded prices reveal their independent and arm’s length meeting of minds. For example, if a breach caused the collapse of a company’s stock price, then we could measure damages by comparing the stock price before and after the ‘event’. Such ‘event studies’ are routinely used in financial research to measure economic impact, and financial econometrics textbooks outline the relevant statistical analysis required to produce robust results.
Other methods include the analysis of comparable transactions or companies, which involve identifying a set of similar assets and inference of the value of the subject asset with reference to appropriate metrics of value, or ‘multiples’, of comparable assets. Of course, no comparator is ever fully comparable, so the validity of any assessment of comparables depends on the ability to establish similarity and explain the variability in observed multiples.
Discounted cash flow (DCF) analysis has become the workhorse method for damages estimation. DCF analyses estimate the present value of a series of future cash flows, which are appropriately discounted to account for the time value of money and risk. Market participants routinely use DCF analysis to value a wide range of different assets. Investors use it to evaluate potential investments, banks use it to determine creditworthiness and regulators use it to set subsidy levels. The DCF method is well suited for but-for analysis because it permits (and indeed, requires) analysts to model the cash flow impact of the relevant breaches explicitly. This is often done by changing input parameters to reflect, for example, delays, equipment failures and loss of supply.
Figure 1 illustrates the generic steps for a DCF valuation involving both historical and future periods. Historical cash flows are rolled forward to the valuation date using a pre-award interest rate. Future cash flows are discounted back to the valuation date using an appropriate risk-adjusted discount rate.
Figure 1: Stylised Framework for Calculating Lost Cash Flows
DCF analyses can come in different flavours. The most common approach is the WACC valuation method, which forecasts free cash flows to the firm and discounts them at the weighted average cost of capital (WACC). The adjusted present value (APV) approach also focuses on the free cash flows to the firm but discounts them at the cost of capital, assuming the absence of debt financing. In a second step, the APV approach assesses the value created through financing choices. Both the WACC valuation method and the APV first calculate the overall enterprise value of a business, from which we can subtract outstanding debt obligations to derive the value of equity. A third approach is the free cash flows to equity (FCFE) method, which focuses directly on the expected stream of free cash flows to equity, but this method can be difficult to implement correctly. Each of the methods has advantages in particular circumstances; for example, textbooks recommend the APV approach in cases of project financing. If implemented consistently, all of the various DCF flavours should generate the same essential result.
Respondents in arbitration proceedings can attempt to characterise DCF analysis as speculative or unreliable. Whether a DCF analysis is reliable depends in large part on the choice of underlying inputs. It is a scientific exercise to compile a reliable set of inputs and consider the interdependency between the choice of inputs and risk adjustments.
DCF analyses are more reliable where inputs are objective and predictable. Contractual quantities, prices and costs may be available and a clear and objective source of inputs. Market prices may also provide a reliable basis for input assumptions, reducing the scope for debate. For example, rather than forecasting commodity or energy prices, an analysis could use the market prices for liquid traded forward products that often extend several years into the future. Such forward prices can be used in a DCF valuation even if a business does not hedge using them. Nevertheless, the use of forward prices to construct cash flows ensures that the analysis incorporates current market expectations, and has implications for any risk discounting.
Market evidence extends to inputs such as inflation. A DCF model could use information from traded instruments such as inflation-linked bonds or swaps. Long-term forecasts for many economic variables are also routinely published and can provide an independent basis for the construction of forecast cash flows.
The construction of forecast cash flows sometimes requires an analyst to consider possible management responses explicitly. For example, management could choose to shut down an activity if prices and margins decline at some point in the future or expand activities if prices and margins improve. The ability of management to respond to future changes in market circumstances can sometimes contribute a significant fraction of value. Various techniques, often drawn from the world of financial options, can be used to assess the value of such ‘real options’.
Consider a business whose cash flows are set by contractual quantities for supply and procurement and that is able to fully hedge input and sales prices using forward contracts. The business would have minimised risk and locked in its sales margins. As a result, the required discount rate may be low and even close to the risk-free rate. An analyst might be concerned about counterparty risk – to account for the possibility that, for example, suppliers could fail to meet contractual obligations – and make an explicit adjustment for the risk of a counterparty default. At the other end of the risk spectrum, consider a wholly new venture or ‘greenfield’ project that requires development activity and which has not yet concluded any significant contracts. Such a venture or project may face a considerable risk of failure and attract more severe risk discounting.
Financial theory categorises risks into two generic types: systematic risk (also known as market risk) and unsystematic risk (also known as unique asset-specific risk). The term asset here encompasses individual projects as well as entire business areas. Systematic or market risk relates to risk that cannot be eliminated through diversification (by expanding the portfolio to different types of businesses). This risk resolves as time passes. In hindsight, we know how inflation turned out, how the S&P 500 fared or whether oil prices increased or declined. Future cash flows require discounting to the extent that they are exposed to systematic or market risks. Standard discount rate techniques measure the extent of exposure to systematic risk.
Unsystematic or asset-specific risks are not included in standard discount rates and may or may not resolve as time passes. For example, we may observe the prices at which a business sold its production, which could provide information for the estimation of fees for the incremental but-for sales. Similarly, we might know how inflation turned out so we can update prices and costs. However, other risks may not have been resolved by the time of the arbitration. For example, we might never know if a wind farm would have been built or how much electricity it would have generated, if a drug would have passed all of the relevant clinical trials and testing and made it into production or if a cancelled product could have obtained market share. Unsystematic risk can require specific adjustments outside of standard discount rate assessments and relate to both past and future cash flows.
Practitioners commonly account for such unsystematic risks, either through a premium on a standard discount rate or via a separate cash flow or valuation haircut. Leading finance textbooks recommend adjusting cash flows directly via haircuts, although various approaches among practitioners remain. Finance theory requires a DCF to focus on the ‘best estimate’ of forecast cash flows, meaning the probability-weighted average of all potential cash flow outcomes. Cash flow or valuation haircuts represent an attempt to probability weight forecast cash flows for potential downside outcomes related to unsystematic risks.
To illustrate, imagine a dispute involving the failure to fund an oil field exploration, triggering delay and ultimately the loss of an exploration permit. Based on a preliminary assessment of contingent reserves, the claimant advances a DCF-based valuation suggesting a value of US$1 billion. The respondent highlights the lack of a development plan and the presence of significant development uncertainties that could undermine value entirely.
Such a fact pattern would raise legal questions around causation, upon which economists cannot offer an opinion. With respect to valuation, the claimant’s simple DCF valuation is likely to overstate the project’s value since it fails to adequately factor in the significant developmental risks highlighted by the respondent. Yet, contrary to the respondent’s position, neither does the mere presence of such development uncertainty imply that there was no economic harm at all. Neither claimant nor respondent knows if exploration would have been successful, but it might have been, and the presence of some chance of success would have created investor willingness to pay for the opportunity. Depending on the legal framework, this fact pattern may call for an assessment of the chance of success and the attendant cash flow and valuation haircuts.
In such cases, close engagement with the facts and documentary record can provide a way forward – or, indeed, reveal a ‘valuation smoking gun’. Transactions in the subject asset and contract terms often reveal party expectations.
Continuing our example, now suppose that the respondent acquired 50 per cent of the relevant shares for US$25 million shortly before the dispute arose. We would have a direct market signal suggesting a market value of US$50 million (US$25 million/50 per cent) for the opportunity. If a simplified DCF valuation suggests US$1 billion, then the necessary development risk adjustment would involve a 95 per cent haircut on the DCF value (1 – US$50 million/US$1 billion). Such a risk haircut would account for a host of factors, including the success probability of achieving commercial production levels and any risks related to the facility’s construction and marketing of the production.
Damages quantification requires the implementation of well-established economic and financial techniques. All the relevant techniques involve making assumptions, and each one is only applicable in certain circumstances, so they must be implemented with care. DCF remains the workhorse technique for damages estimation in arbitration, in part because it allows for explicit modelling of disputed conduct. DCF comes in different forms, benefits from the use of objective inputs and requires a robust and principled risk assessment. In this context, analysis of the factual background can produce illuminating and even determinative valuation evidence.
A final step often performed in damages analyses involves ‘sense-checking’ the reasonableness and plausibility of the valuation results. However, our experience is that insufficient attention is often given to sense-checks. The relevant checks are more than a purely mechanical exercise and require careful thought to inform the issues in debate.
For example, experts routinely identify sets of peers and examine valuation metrics, such as earnings multiples. Experts assert that the exercise confirms the reliability of their damages conclusions so long as the average of the peer group valuation multiples is broadly comparable to their damages assessment. Analysing peer group valuation multiples is generally useful, and we routinely do it ourselves in expert work. However, it does not always confirm the reasonableness of a damages assessment.
It is possible that a relevant peer group indicates a spread of valuation multiples so wide as to accommodate all of the damages estimates in discussion. Another possibility arises due to the fact that one commonly used multiple involves determining the ratio of value to earnings (eg, enterprise value to earnings before interest, taxes, depreciation and amortisation (EBITDA)). As such, two vastly different valuations can sometimes display similar multiples. In such cases, the relevant debate concerns not the valuation method or the earnings multiple itself but the underlying earnings forecast. One expert might forecast ‘high’ earnings, a ‘high’ value and a standard multiple; the other forecast ‘low’ earnings and a ‘low’ value, also resulting in a standard multiple. In such circumstances, a routine peer group multiple survey will be uninformative. The plausibility check should focus on the earnings levels themselves.
Plausibility checks should focus on the fundamental economic realities of a business or investment. For example, a regulator may cap prices to permit an efficient company or investment to recover costs and earn a reasonable return consistent with the time value of money and risk. Given such regulation, if an investor must spend US$100 to construct a project, we would expect to forecast a stream of cash flows allowing the investor to earn a present value roughly equivalent to US$100 throughout the life of the project. Otherwise, we would have to believe that the regulator incorrectly set prices too high or too low, or that the project or business in question was particularly efficient or inefficient. ‘Incorrect’ prices and/or particular efficiencies are certainly possible, but both raise the potential for inquiry of the available evidence and therefore the availability of a plausibility test of any damages claim for more or less than US$100.
Two cautionary tales
To close, we discuss two concrete case examples that illustrate the importance of combining art and science in damages assessment. The first case involves the implementation of a well-established statistical technique but a failure to perform a coherent but-for analysis and to recognise the limitations of the chosen method. The second case involves the DCF technique and the use of contemporaneous information to construct cash flow forecasts, but a failure to consider the economic plausibility of the results. In both cases, reliable damages assessment required art as well as science.
Rompetrol v Romania
The Rompetrol Group (TRG), an international oil company, sued Romania in 2005 for harm due to an investigation by Romania into fraudulent activities by its owner and certain managers. TRG claimed that the investigation was unlawful since Romania made conclusory statements and public comments that harmed the reputations of the individuals concerned and TRG itself, raising the cost of doing business. TRG claimed damages of close to US$150 million based on an ‘event study’, which analysed the stock price response of one of TRG’s subsidiaries to news about the allegations and investigation. The event study followed well-established techniques.
An ICSID tribunal found Romania partially liable but ultimately awarded zero damages. The tribunal recognised that TRG’s event study technique was well established and often used to estimate damages in other contexts. However, it concluded that the event study analysis failed to prove causation in this particular matter. The event study measured the impact of news and events related to the investigation, and implied a but-for scenario without any investigation at all. The tribunal instead considered that the relevant but-for scenario should have incorporated the possibility of a legal investigation by Romania, which would have triggered some stock price movement.
Moreover, the tribunal noted that the event study technique faced a variety of other problems in the particular case of TRG. For example: (1) news and speculation about the investigation into TRG occurred over an extended period and did not, therefore, match the type of surprise and sharp announcements well suited to measuring price responses in an event study; (2) the event study failed to identify all of the possible news days relevant to the investigation, and so missed potential confounding events; and (3) the event study focused on the traded minority shares of a TRG subsidiary as opposed to TRG itself, and the prices of minority shares could react differently to the investigation than those of the majority.
In TRG, the science and statistics were undermined by the lack of art of but-for construction.
SCFC v Visa
The second case illustrating the importance of combining art and science in damages assessment is SCFC ILC, Inc. v. Visa USA, which became known as the ‘MountainWest’ case. In the 1990s, MountainWest, a US savings bank owned by Sears, attempted to issue a new Visa payment card offering customers low charges. The proposed pricing structure was innovative and expected to attract customer interest. Visa vetoed this attempt due to the connection between MountainWest and Sears. Visa had previously blocked Sears from becoming a Visa network member due to Sears’s introduction of the Discover payment card, a competitor to Visa cards.
Sears’s subsidiary, Sears Consumer Financial Corporation (SCFC), filed a lawsuit against Visa, claiming roughly US$1 billion in damages, representing the lost profits from MountainWest issuing Visa cards with an innovative pricing structure. The damages analysis relied on a DCF model, which involved the construction of a but-for scenario using objective inputs and assumptions drawn from MountainWest’s contemporaneous business plan. An important assumption was that the proposed pricing structure would attract millions of customers.
The core problem of the DCF was not the method itself, the choice of inputs or even the discount rate, but a failure to consider the economic plausibility of the management forecasts. If the proposed pricing structure was attractive, then it would doubtless attract customers for several years, but would soon be copied by rival Visa card issuers. MountainWest could, at best, expect to obtain a competitive advantage for a limited number of years, but not over an extended period. Over the long run, a reasonable expectation was that competition between card issuers would drive MountainWest’s profits back to a competitive or reasonable level. Implementation of an economically plausible but-for construction acknowledged the presence of some damages, due to the loss of several years of profits, but only a fraction of the US$1 billion claimed.
Damages assessment must follow rigorous economic and financial methodologies and accurate mathematics. Damages assessment must also imaginatively engage with the facts and legal claims of each case. Even assessment based on well-established economic and financial techniques can become unreliable without careful construction of a theory of harm and a coherent but-for framework.
 In all cases, plus interest during the delay between the measurement of the harm and the date of trial.
 In all cases, plus interest during the delay between the measurement of the harm and the date of trial.
 For example, see chapter 4 of Campbell, John Y., Andrew W. Lo and A. Craig MacKinlay, The Econometrics of Financial Markets, Princeton University Press (1997).
 Some valuations also require an adjustment for liquidity.
 For example, if financial leverage changes over time, the discount rate under WACC and FCFE approaches has to be recalculated. For this reason, finance textbooks highlight the difficulty of applying the WACC and the FCFE methodologies to assets with fixed debt repayment schedules and changing financial leverage over time. Recommended reads include Principles of Corporate Finance by Brealey, Myers and Allen and Corporate Finance by Berk and DeMarzo.
 Forward prices derive from contracts for physical delivery or settlement in cash and therefore reflect expectations of market participants.
 Forward contracts involve a commitment to pay a given price in advance. The resulting forward prices therefore already involve an adjustment for price risk. It would be a clear analytical mistake to discount forward prices in the same way as a simple price forecast. See Pindyck, ‘The Dynamics of Commodity Spot and Futures Markets: A Primer’, The Energy Journal, Vol. 22, No. 3 (2001).
 See, for example, Haubrich, Penacchi, and Ritchken, ‘Inflation Expectations, Real Rates, and Risk Premia: Evidence from Inflation Swaps’, Working Paper 11-07 (2011).
 The standard framework to measure exposure to systematic risk is the capital asset pricing model (CAPM), which models an asset’s risk premium in proportion to its ‘beta’. The beta coefficient measures the volatility of the return on a specific asset relative to the average volatility of returns on the market as a whole. The beta should be 1 if the relevant asset has exactly the same risk as the average investment in the stock market. It exceeds 1 for assets that are riskier than the market, and is less than 1 for assets that have less risk than the stock market as a whole. If an asset had no systematic risk at all, then its beta would be zero and the CAPM framework would support a discount rate equal to the risk-free rate.
 See, for example, Principles of Corporate Finance by Brealey, Myers and Allen.
 Plausibility and robustness checks also form part of any economist’s curriculum, in particular in the context of regression analysis, a statistical method that estimates the relationship between different variables of interest. Regression analysis allows the analyst to isolate the effect of one factor as it measures the correlation between two variables conditional on (that is, controlling for) other factors. Statistical assessments are routine in economic analysis and well established. They are a common tool in antitrust analysis, in particular when estimating cartel overcharges. While regression analysis is well established, it does not prove causation. It always requires a theory (of harm), a structural model explaining results or a compelling narrative as support.
 Overall the investor is left with zero net present value (NPV) in expectation, as the present value of the benefits (+US$100) equal the necessary investment costs (-US$100). Such a test is known as the ‘NPV Test’, a phrase first popularised by Brattle in an early 2000s report for the European Commission considering tariff setting for electricity and gas transmission assets.
 For example, a damages claim for more than US$100 could prompt a plausibility check if the subject project was more efficient (cost less or produced more) than considered by a regulator when setting prices.
 Rompetrol Group N.V. v. Romania, ICSID Case No. ARB/06/3, Award (May 6, 2013), ¶286.
 Rompetrol Group N.V. v. Romania, ICSID Case No. ARB/06/3, Award (May 6, 2013), ¶284-5, 287.
 The case is also discussed in Paying with Plastic: The Digital Revolution in Buying and Borrowing by Evans and Schmalensee.