# Determining the Weighted Average Cost of Capital

## Introduction

The financial impact of a damaging action normally stretches some years into the future; indeed, it may continue without limit, as when a firm loses a line of business that might otherwise have lasted indefinitely. If a damages calculation were based on a simple arithmetic summation of the estimated damage for each future year, the claimant could be greatly overcompensated – for permanently damaged businesses, infinite awards would result.[2]

To correctly assess financial damages, it is necessary to apply a conversion factor that discounts a forecast loss in a future year for the purpose of compensating it reasonably today. The measure used to effect this discount is known as the weighted average cost of capital, or WACC.

This chapter sets out the principles underlying the WACC as applied in damage assessments, and presents current best practice in its estimation.

## Basic principles

A damages award often compensates a claimant in advance: the claimant receives payment, now, to replace income that, without the damaging act, would have been earned in the future. Money has time value, and it is self-evident that an award must incorporate an adjustment – a downwards adjustment, or discount – to reflect any advance component of compensation.

A first step to effect this adjustment would be to discount future years’ assessed losses by a prevailing interest rate (more specifically by what it known as the risk-free interest rate.[3] Applying a discount based on an interest rate would ensure that the financial award has been adjusted to reflect what we might term the pure time factor – the passage of time between the award and any future losses that the award is intended to compensate.[4]

However, while discounting on the basis of an interest rate would adjust an award for the fact that future losses to the business are paid in advance, it would not adjust the award for fact that the future losses are subject to uncertainty. It is not reasonable or fair to recompense, dollar for dollar, uncertain future losses with a certain payment today. A fair compensation in respect of future years’ lost earnings must incorporate an adjustment to reflect the uncertain character of those future earnings.

The discipline of financial economics has established a procedure to convert forecast future cash flows of a business to an equivalent present-day value, to reflect both the passage of time and the uncertainty of those future cash flows. The procedure is to calculate, by analysis of financial market data, the cost of capital of the business and, more specifically, the WACC. The WACC is a blend of the firm’s cost of debt (interest) and cost of equity, the average being weighted by the proportions (or weights) of debt and equity financing available to the firm.

The WACC is built up from a number of inputs, or components. One of the components is the prevailing (risk-free) interest rate; the inclusion of this component will account in the completed financial damages calculation for the time value of money in the economy. Other components of the WACC are concerned with the volatility and riskiness of business investment; the inclusion of these components will ensure that the completed financial damages assessment accounts for the uncertainty associated with a business’s future earnings. The components of the WACC are discussed in detail later in this chapter.

Effectively the WACC teases out the consensus of the broad business community – investors, executives, analysts – as to the fair discount to apply when replacing a future uncertain gain by a current and certain one. Just as information on prevailing interest rates in an economy reveals the time value of money to participants in that economy, so securities market data (information, for example, on share prices) can reveal the reasonable adjustment to apply to forecast company earnings to account for the uncertainty and volatility associated with those earnings.

Like an interest rate, the WACC is expressed as a percentage per year; for illustration, a WACC of 7 per cent per annum signifies that money received this year is worth 7 per cent more to the business than money that it forecasts to receive next year. Also, like an interest rate, its effect compounds through time. It is noteworthy that WACCs are inevitably much higher than prevailing interest rates, meaning that – unsurprisingly – the fair adjustment in respect of uncertainty of earnings is significantly larger in practice than the adjustment in respect of the passage of time.

The WACC is now universally accepted in commercial arbitration practice as the correct figure to apply as the discount rate in the financial discounted cash flow (DCF) model used to assist in damages assessment. The line of business for which the WACC is calculated is the damaged business of the claimant, and the resulting WACC figure is entered as the discount rate in the financial damages calculation.

In summary, when the WACC is applied to a financial damages model, the calculation of damages adjusts properly – or as well as modern finance theory allows – for both the pure time effect (that money available now is more valuable than money received later) and in respect of risk and uncertainty (a damages award should compensate fairly, with a definite payment now, a loss of profit that the claimant’s business may incur in the future).

## Estimating the WACC

The WACC has not been developed specifically for damage assessment; it is a very widely used analytic tool. For example:

• a firm’s management applies the WACC to help it decide whether to proceed with an investment proposal, such as a new capital project or corporate acquisition;
• auditors use a firm’s WACC for the purposes of financial reporting;
• brokers and investment bankers use WACCs in connection with the purchase, sale or issuance of shares and in connection with acquisitions, mergers or spin-offs; and
• government bodies use WACCs to assess fair and allowable prices and profits in regulated industries.

In a damages assessment, the figure arrived at for the WACC is likely to have a very important effect on the level of financial claim – particularly if, as in most major claims, long-term losses are alleged.[5] By way of example, with all other inputs to the financial analysis of damages kept constant, a movement of the WACC estimate by just one percentage point (say from 7 per cent per annum to 6 per cent per annum), could increase the final claim by 15 per cent.[6] In a proceeding involving long-term damage, there will almost certainly be no other single figure entering the financial model to which the final claim is as sensitive.

For this reason, the correct assessment of the WACC is of great importance in commercial arbitrations. The professional expertise required differs from that required to create the financial (DCF) model into which the WACC figure is inserted. The creation of a DCF model of a firm requires very detailed knowledge of the industry in which the firm operates, to ensure that the model contains high-quality line-by-line data on revenues and costs. By contrast, as will become clear in this chapter, WACC estimation requires very detailed knowledge of financial markets – of stock market volatilities, bond market yields and the quantitative analysis thereof.[7]

The WACC is estimated on the basis of six components or inputs, each of which is discussed below.

### Risk-free rate

A starting point for assessing the WACC is the risk-free rate, which is the prevailing rate of interest paid on debt to a lender considered completely creditworthy. In broad terms, the remaining inputs to a firm’s WACC act to increase the cost of capital above the risk-free rate.[8]

The risk-free rate does not have an objective existence – there is no such thing as a loan without risk of default. As with other parameters entering the WACC formula, the risk-free rate is a construct of finance theory, and must be estimated by means of proxies or approximations.

The accepted approximation to the risk-free rate is the yield on government bonds issued in the relevant currency. In the case of a claim based on US dollars, this is the return to US Treasury bonds. While holding these bonds is not completely risk-free, the chance of repayment is considered extremely high – or, in any event, ‘as good as it gets’. When the currency of the financial model is other than US dollars, the risk-free rate is estimated on the basis of the return on bonds issued in that currency – usually the bonds issued by the relevant national treasury.[9]

The actual estimation process for the risk-free rate typically involves calculating an average yield for primary offering tenders taking place close to the damages reference date, for bond maturities of (say) five, 10 and 20 years.[10]

### Debt risk premium

The debt risk premium is the additional return, above the risk-free rate, which a firm must pay to its debt holders to compensate for the risk that the terms of the loan will not be honoured.

The debt risk premium is relatively easy to assess if the claimant firm issues bonds: the return on those bonds is compared against the return on bonds with similar maturity issued by government. If the firm itself does not issue bonds – or as further input to the estimation procedure even if it does – the premium can be estimated by analysing the return to the bonds of firms with similar perceived risk profiles, such as competitor businesses of similar size.

The debt risk premium is widely studied by investment banks, stockbrokers and other institutions. Experts assigned to a proceeding can supplement a direct analysis of this WACC input with a review of the estimates published by reputable third parties.

### Equity risk premium

The equity risk premium is the amount by which, over a long term, stock markets generate higher returns for investors than do holdings in (near risk-free) government bonds. As its name implies, it is the premium paid to equity investors to compensate them for the risk – volatility, uncertainty – of stock market investing. It is a figure that applies to stock markets generally, rather than to a firm specifically.

Experts in arbitrations do not attempt to calculate this parameter from primary data sources – which would be a major computational task. The figure is stable over quite long periods, and general practice allows the expert to review financial and academic literature and apply a consensus estimate. Currently, the equity risk premium stands at about 5 per cent per annum for major stock markets.

### Beta

Although the equity risk premium (discussed immediately above) reflects the return investors expect to make by investing in shares generally, it does not reflect the return investors expect to make by investing in a particular firm’s shares. Finance theory holds that the firm-specific return is obtained by multiplying the equity risk premium by a ‘risk multiplier’ known as ‘beta’ (after its Greek symbol). The beta is a measure of the volatility of the firm’s share value relative to volatility in the stock market as a whole.[11]

The estimation of a firm’s beta is one of the most difficult parts of a WACC estimation.[12] Although competent finance professionals can undertake the necessary computations themselves, in an arbitration setting experts typically rely on third-party estimates published on commercial database services, such as Bloomberg. A value of beta obtained by careful selection and averaging of reputable third-party estimates may be more reliable, and easier to defend, than a fresh set of calculations produced by the expert.[13]

Although the estimation of beta is complex, its interpretation is relatively straight­forward. A firm’s beta reflects the degree to which the firm’s business is affected strongly or weakly by general economic turbulence. In broad terms, a firm whose business has a high degree of resilience in the face of economic cycles will have a beta (or risk multiplier) of less than 1; examples are firms supplying staple or essential goods. A firm whose business is heavily affected by economic cycles will have a beta of greater than 1: examples are firms supplying discretionary goods. Fortunately, the expert in an arbitration does not have to speculate as to whether the firm’s output has greater or lesser risk – the assessment of beta is a mathematical process that relies only on analysis of share price volatility data.

### Debt-equity ratio

The debt-equity ratio generates the ‘weights’ in the weighted average cost of capital. As with the beta, its estimation presents significant challenges to the expert in an arbitration setting: there are a number of alternative approaches to its assessment, which produce different results; there is little by way of directly applicable published assessments; and the final WACC computation is quite sensitive to the figure selected.

The expert must seek to identify the ratio of debt to equity that optimises the value of the firm to its owners. The degree to which a firm sources its capital from debt as opposed to equity markets is (within limits) a matter of its choice – it can issue more debt or more equity; consequently one approach to estimation is simply to take the ratio of debt to equity present in the firm at the time of the assessment. However, in practice, direct measurements of the actual debt and equity levels of the firm in question may not produce a good estimate of the optimal debt-to-equity ratio as required for a WACC estimation.[14] Practice has shown that a better estimate is achieved by taking an average (such as the median) of the debt-to-equity ratios of a group of companies deemed by the expert to be comparable for the WACC estimation purpose – typically companies in the same industry.

Other measurement problems arise because there are conflicting definitions as to what constitutes debt; good practice requires the expert to follow quite detailed guidance as to which debt categories should be included when calculating the debt-to-equity ratio for the purpose of assessing a WACC.[15]

Nevertheless, this ratio can, with diligence and by following good practice, be assessed to a good standard of accuracy.

### Tax rate

The presence of the tax rate as an input to the WACC calculation arises because payment of interest on debt can be offsest against a company’s taxable profits. This tax deductibility, known as a tax shield, reduces the effective cost of debt capital compared to the cost of equity capital; there is no analogous offsetting of dividend payments (i.e., payments to equity shareholders) against corporation tax.

Generally, the determination of the tax rate for a WACC estimation is straightforward: the expert applies the marginal rate of tax on corporate profits, as specified in the tax statutes applicable to the jurisdiction in which the relevant profits are taxed.

There are, nevertheless, some precautions to be observed: the tax rate entering the WACC calculation may be different from the tax rate used to estimate post-tax cash flows in the DCF model;[16] and the tax rate must be adjusted downwards for WACC estimation purposes if the profits of the firm are, over a relevant period, insufficient to cover all interest payments; in that event, the tax shield will not be fully effective.

With the six above-mentioned inputs correctly estimated, the calculation of the WACC itself and its insertion into the DCF model of damages are straightforward. The six inputs are entered into a standard formula that generates the WACC figure.[17] This is then entered as the discount rate input into the financial model. The mechanics of the model ensure that any future cash flows are discounted back by the discount rate to the present day (strictly, to the reference date), compounded annually.

## Concluding reflections

The development of a technique to determine the fair present-day value of future (and uncertain) cash flows by analysis of objectively measurable data, such as share price volatility, was a landmark in financial economics.[18] For damages proceedings, the development has meant that the discount rate – the WACC – entering a financial model can be calculated on the basis of evidential data, lending objectivity to the seemingly intractable task of accounting for forecasting uncertainty.

What the theory and practice of WACC estimation has done for dispute resolution is to introduce objectivity (and some degree of precision) into what would otherwise be a highly speculative aspect of claim evaluation. When an arbitration proceeding is presented with a model of how the business would have performed in an undamaged situation, it is clear that predicted profits must in general be discounted to arrive at a fair compensation – a forecasted gain (or loss) is not equal in value to a certain gain (or loss). The WACC methodology requires that the experts estimate this discount by analysing the best available current data (on such metrics as stock price volatility). The experts can still disagree on the discount, but the disagreement can be resolved by reference to evidence.

It is essential, however, that those involved in commercial arbitrations have crystal clarity as to which forecasting uncertainties are, and which are not, taken into account by the inclusion in the financial model of a WACC-based discount.

The WACC takes into account the discount that is generally applied by market practitioners – investors, executives and analysts – to the value of forecast future cash flows, to reflect the level of risk and uncertainty normal in a firm and a line of business comparable to the one under review.

The WACC cannot, and does not, take into account the possibility that the forecast (typically of undamaged cash flows) may simply be biased. In lay terms, the forecast must, at the time of its creation, be equally likely to be too low as too high.[19] The WACC adjusts the claim for the effects of business risk and randomness, not for the possibility that the forecast was set too high, perhaps by one of the parties. The judgement as to whether an expert forecast is deliberately biased, rather than merely uncertain, remains one for the arbitral process, on which the WACC is silent.

Finally, and obviously, the WACC adjustment does not adjust a claim for errors or bias in the estimation of the extent to which the undamaged and damaged cash flows differ.

The above limitations having been noted, the WACC remains a powerful and now standard tool in DCF calculation of damages, bringing a high level of objectivity to accounting for the time value of money and for the uncertainties of business outcomes.

## Annex: Worked example

This annex contains a worked example of the derivation of the weighted average cost of capital (WACC) of ABC Inc (ABC), a hypothetical major food products company listed on the New York Stock Exchange. The currency of the valuation is the United States dollar, and the valuation date is 1 January 2020 (the Reference Date). As noted in the main text of this chapter, the assessment of a WACC in the context of a dispute resolution proceeding requires quite detailed analysis of financial (debt and equity) securities. By contrast, this worked example is simplified, presenting each step in outline only.

We first obtain values for each of the six input parameters of the WACC equation:

### Risk-free rate

For the risk-free rate (Rf ) applicable to this worked example, we use the mean of the yields of US Treasury 5-year, 10-year and 20-year bonds as at (or very near) the Reference Date. The respective yields were 1.67 per cent, 1.88 per cent and 2.19 per cent. The mean of these values is 1.91 per cent; hence Rf, expressed as a fraction, is 0.0191.

### Debt risk premium

ABC’s debt risk premium (DRP) is assessed in this example as the margin by which yields of its corporate bonds exceed the yields of similar-tenor US Treasury bonds, at or around the Reference Date. We estimate this margin at 2.00 per cent; hence DRP expressed as a fraction is 0.02. For illustration and comparison, 10-year corporate bonds issued by major US food products companies in the period shortly after the Reference Date had yields with the following premiums over 10-year US Treasury bonds: Campbell Soup Co, 1.75 per cent; General Mills Inc, 2.18 per cent; Kraft Heinz Co, 2.00 per cent and 2.11 per cent (two issues); McCormimck and Co, 1.74 per cent.

### Equity risk premium

As noted in the main text of this chapter, experts engaged in WACC assessments for damages select a value for the equity risk premium (ERP) that, in their view, reflects the current consensus of financial practitioners and academic researchers. As at mid 2020, the consensus of this research in regard to US stock markets is that the ERP is between 5.3 per cent and 5.7 per cent. We apply to this assessment a value of 5.5 per cent, or 0.055.

### Beta

The value of beta (β) is obtained by computational analysis of the volatility of a firm’s stock price. As in the case of the ERP, it is normal for experts in damages proceedings to rely on published third-party calculations of β rather than to undertake the computations themselves. For illustration, the major food companies General Mills Inc, Kellogg Co and Kraft Heinz Co have published beta figures of 0.57, 0.61 and 1.01 respectively. We assume for the hypothetical company ABC a consensus published β of 0.7.

### Debt-equity ratio

The book value debt equity ratios (DERs) of major US companies are widely published, and in the case of the food products industry, the average ratio is somewhat above unity. However, substantial adjustments must be made to these ratios before they can correctly be applied as the DER for WACC assessment. Most importantly, market rather than book value (of both debt and equity) should be used, which results normally in a much lower ratio. For the purpose of this worked example, we assume that the DER of ABC, after the necessary adjustments, is 0.6.

### Tax rate

The statutory tax rate (T) in the United States is currently 21 per cent. For the present purpose, we assume that the effective marginal tax rate of ABC is equal to the statutory rate (a common assumption). Hence, we carry forward to the WACC formula a T of 0.21.

We then enter these six parameter values (Rf = 0.0191, DRP = 0.02, ERP = 0.055, β = 0.7, DER = 0.6 and T = 0.21) into the standard formula:

WACC = [Rf + (β × ERP)] × (1 – g) + [(Rf + DRP) × (1 – T)] × g,
where g = DER/(1 + DER)
.

The following result is obtained:

WACC = 0.0476

Expressed as a percentage, the WACC is 4.76 per cent. We therefore assess the WACC of ABC at 4.76 per cent per annum, with a Reference Date of 1 January 2020.

It is instructive to disassemble this WACC result into components, as follows:

• the cost of equity [Rf + (β × ERP)] is equal to 0.0567, or 5.677 per cent;
• the after-tax cost of debt [(Rf + DRP) × (1 – T)] is equal to 0.0309, or 3.097 per cent;
• the value g, which equates to the proportion of debt (gearing) in the capital structure, is equal to 0.375;
• the value (1 – g), which equates to the proportion of equity in the capital structure, is equal to 0.625; and
• the WACC is then the weighted average of the cost of equity (5.67 per cent) and the after-tax cost of debt (3.097 per cent), with respective weightings (1–g) and g.

## Notes

[1] Charles Jonscher is president of the CET Group of Companies.

[2] If a discounted cash flow [DCF] model shows damage to a business in all future years, and no time discount is applied, the loss calculation will consist of an infinite sum of (undiscounted) future losses; mathematically this is likely to yield an infinite compensation figure.

[3] The risk-free interest rate is discussed later in this chapter.

[4] The successful claimant could place on deposit that part of the award that relates to any given future year’s losses; by the time that year arrives the deposit would have grown, by accumulation of interest, to be equal to the amount that the claimant is estimated to lose in that year through the damaging action.

[5] If the damage can be completely remedied in the short term – if, for example, equipment is damaged and is replaced – then the level of WACC will have only a modest effect on the final level of the financial claim. If, however, the claim is for the loss of a business position or business opportunity, the claim will be for damage that is permanent, or at least very long term, and the level of the WACC will have a large effect on the level of the claim.

[6] If a broadly constant long-term loss of earnings is alleged, the final calculation of damages will respond, very roughly speaking, in inverse relation to a change in the assessed annual percentage WACC. However, this is an approximate heuristic guide only; many factors will affect the detailed mathematical relationship between the WACC estimate and the final claim level; a greater weight on near-term losses will tend to reduce the sensitivity of the final claim to the level of the WACC, while the inclusion of a perpetual growth factor in the DCF model will tend to increase the sensitivity.

[7] WACC estimation has therefore become a distinct sector of expertise in damages proceedings (and, indeed, merits a specialist chapter in this book).

[8] The exception is the tax rate, which acts to reduce the firm’s cost of capital due to the tax deductibility of debt repayments.

[9] Complications arise if the bonds of the national treasury in question are considered a poor risk. Fortunately for estimation purposes, national treasuries typically issue bonds both in their own currency and in a global reserve currency, such as US dollars or euros. The premium that the government in question pays on (say) its US dollar bonds over US government rates serves as a measure of the perceived risk of that government defaulting, and can therefore be used to adjust the rate on its local currency bonds to arrive at a good estimate of the local currency risk-free rate.

[10] The selection of bond maturities is important, as bonds of different maturities typically have significantly different yields, and an incorrect selection of maturities can introduce significant errors into the WACC. Broadly speaking, the basket of bond maturities should be selected that best reflects, in the judgement of a qualified expert, the future time pattern of damages in the financial model.

[11] Mathematically, the beta of a firm’s shares is the covariance of the return on the firm’s equity and the return to the stock market, divided by the variance of the return to the stock market.

[12] The estimation of beta is sensitive to the selection of data analysed. To increase the sample size, it is recommended that the estimation is supplemented by inclusion of companies considered comparable in their riskiness to the firm in question – to the extent possible, of companies in the same line of business and of similar scale. The application of beta values from a comparable company group is not straightforward (even if the betas are taken from third-party sources); good practice requires that the comparisons are made not directly on the basis of firms’ betas but on the basis of a related parameter known as the asset beta. A discussion of the conversion of betas to asset betas and vice versa is beyond the scope of this chapter.

[13] Care must be taken when interpreting other parties’ beta estimates (and, indeed, in working generally with the beta parameter) to differentiate between what are known as the unlevered beta and the levered beta. Again, a discussion of these variants of the beta parameter is beyond the scope of this chapter.

[14] Firms do not as a practical matter continually fine-tune their ratio of debt to equity to maintain an optimal level implied by finance theory; among other difficulties, they would have to issue or retire debt every time their share price moved.

[15] Debt should normally include all borrowings, capital leases, licence fee liabilities and liabilities embedded in financial instruments, and should be reduced by the level of cash holdings, marketable securities, investments available for sale and receivables from financial instruments.

[16] The tax rate entering the WACC calculation must be the marginal rate of tax on each extra unit of profit generated. The tax rate used to calculate post-tax cash flows in the same DCF model will be average rates of tax on the total profit (for a given period).

[17] The formula is: WACC = [Rf + (ꞵ × ERP)] × (1 – g) + [(Rf + DRP) × (1 – T)] × g, where g = DER/(1 + DER) and the remaining symbols have the following meanings: Rf is the Risk-Free Rate; ꞵ is the Beta; ERP is the Equity Risk Premium; DRP is the Debt Risk Premium; DER is the Debt-Equity Ratio; and T is the Tax Rate.

[18] The theory, developed in the 1960s, earned its authors the Nobel Prize in Economics.

[19] In mathematical terms, the forecast must be set at the centre of the probability distribution of future outcomes.

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