An investment is a choice to foregore present consumption in favour of future consumption, in exchange for which the investor is given a return which can simply be referred to as “interest”. The interest promised to the investor is either contractually defined, and capped, as with bonds, or, is uncertain and uncapped, as with equities, or some blend of both. By deferring present consumption and investing, investors stake a claim to a financial asset’s defined and capped or undefined and uncapped future cash flows, the net present value of which are estimated by discounting them at the prospective “interest rate”, or cost of capital. The weighted average cost of capital (WACC), first proposed by Franco Modigliani and Merton H. Miller in their paper, “The Cost of Capital, Corporation Finance and the Theory of Investment”, blends the interest rates promised to a firm’s differing sources of capital into a single number. Or, more properly, WACC blends a real cost, the cost of debt, and an expected return, that of equity, into a single number. Properly calculated, free cash flows (FCF) discounted by WACC will return the same value as equity cash flows discounted by the required return on equity. WACC allows one to properly value a firm’s future cash flows based on the differing interest rates its sources of capital require, whether they are certain claimants, its debt investors, or residual claimants, its equity investors, or some hybrid of the two. It is against this number that firms weigh, or should weigh their returns on invested capital (ROIC) to determine if they are creating value.
WACC is estimated by assessing the opportunity cost that investors bear when they invest. Given two equally risky propositions, an investor will “lend” their savings to that risky proposition that offers the highest rate of return. When one invests with a firm, that firm uses that capital to earn a greater rate of return, ROIC, than the rate of return the investor could get in a similarly risky investment. A firm with a ROIC of 15% at a time when investors could earn 8% in similarly risky propositions, creates value for its investors, because that means that their claim to future cash flows are either more certain, or larger.
WACC is composed of three elements: the cost of equity, the after-tax cost of debt, and the firm’s target capital structure. The formula I generally use to estimate WACC is given below, a formula that grows more complex the more complex the firm’s capital structure and simpler the simpler the firm’s capital structure:
WACC = (D/V)kd(1-Tm) + (E/V)ke + (P/V)kp
where
- D/V = target level of debt to value using market-based values
- E/V = target level of equity to value using market-based values
- kd = cost of debt
- ke = cost of equity
- Kp = cost of preferred capital
- Tm = company’s marginal tax rate on income
I estimate the cost of equity using the capital asset pricing model (CAPM), with an important adjustment to reflect my views on risk. Eugene Fama and Kenneth French’s three-factor and five-factor models and other factor models are more accurate than standard CAPM, but one buys accuracy along with almost unmanageable complexity. Beta is the critical factor in CAPM, and measures a stock’s sensitivity to changes in a benchmark index, which serves as a proxy for the market. in the United States, I use the S&P 500 as the market proxy. Under CAPM, the expected return on a security is calculated as below:
Expected return = Risk-free rate + β(Market return – Risk-free rate)
where “β”, is, of course, beta, which measures firm-specific risk and can, because it is “unsystematic”, be reduced through portfolio diversification, and “Market return – Risk free rate” is the equity risk premium (ERP), the difference between the market’s expected return for the market and the risk-free rate and captures “systematic risk,” or that risk that cannot be diversified away. I use the yield on 30-year Treasuries as a proxy for the risk-free rate.
Of expected return, I cannot resists recalling an anecdote by Merton Miller,
I still remember the teasing we financial economists, Harry Markowitz, William Sharpe, and I, had to put up with from the physicists and chemists in Stockholm when we conceded that the basic unit of our research, the expected rate of return, was not actually observable. I tried to tease back by reminding them of their neutrino –a particle with no mass whose presence was inferred only as a missing residual from the interactions of other particles. But that was eight years ago. In the meantime, the neutrino has been detected.
Not only is the expected return not observable, the literature tends to conflate historical, expected, required and implied ERPs. The historical ERP (HEP) is the most objective, but it tells us little about the size of the premium in future, although even here there are differences in calculations and benchmarks that lead to different HEPs. I calculate the HEP by subtracting the average geometric return for the S&P 500 from the average geometric return for 30-year Treasuries (DGS30), for the 1977 to 2023 period, and then adjusting the figure downwards for survivorship bias, by the 0.8% excess returns by which Dimson, Marsh and Staunton found the U.S. markets had exceeded a 17-country composite return.
Is this the same as what I expect the premium to be? No, as I have discussed, I anticipate that this decade will see average S&P 500 returns of just over 1%, meaning my expected risk premium (EEP) is negative, but this is not the market's EEP. Moreover, I do not think there is a single and unique implied equity risk premium (IEP) or required risk premium (REP): these are subject values. In effect, I treat the HEP as my REP.
In his pathbreaking paper, "Portfolio Selection", Harry Markowitz equated risk with “volatility of returns” and this broad view of risk forms part of modern portfolio theory. Markowtiz proposed that investors maximise a utility function that matched expected returns, the arithmetic average of available returns, with their associated volatility. Under this model, investors seek to reduce their volatility for a given return or increase their returns for a given level of volatility. The trouble with his model was and has always been clear to Markowitz: this broad view of risk runs counter to one's intuition and ideas of risk, as I have explained before:
Since Harry Markowitz’s seminal 1952 paper, “Portfolio Selection”, it is generally accepted that risk is best measured in terms of a “volatility of returns”, in other words, the upward and downward swings in prices. Under this measure, if one expects a return of 10% from an investment, both the chance that the return will be lower, or higher than that expected return, are classed as risk! Few investors and managers, if any, would accept this view. Just eighteen years after Markowitz’ paper, one survey found that, across eight industries, most managers said they believed that semivariance, a measure of “downside risk”, was a more plausible measure of risk than variance. Decades later, that unease with theory remains. This notion of risk clearly goes against our intuition. One does not say, “There is a risk I will make a return greater than expected on this investment”. This notion of risk is also self-contradictory: it would seem perverse to imagine as rational behaviour a situation in which a person sought to limit all their risk, that is, both downside and “upside” risk. Defenders of the position would claim that when they refer to risk, they are of course referring to downside risk, which begs the question why the scope of this definition of “risk” allows for “upside risk” to be defined as such. It is not a merely academic argument: investors and managers make decisions based on risk measures that imply this very logic. It seems evident that whereas a person would want to limit their downside risk, they would be happy to have their profits run far in excess of what they expected.
Markowitz himself observed in his similarly titled tome, that his earlier use of variance as opposed to semi-variance, a measure of downside risk, was due to a lack of computing power and the greater familiarity that practitioners had with variance as opposed to semi-variance. Not only is "upside risk" not a risk, but, Markowitz observed that the use of variance assumes that returns are normally distributed. The great man was aware of the inherent absurdity of so catholic a notion of risk, saying that semi-variance was a “more plausible measure of risk” and that, “the semideviation produces efficient portfolios somewhat preferable to those of the standard deviation” . About the same time, A.D. Roy, in his paper, "Safety First and the Holding of Assets", noted that an investor is not interested in what happens on average, but will happen in a particular instance, and that the maximisation of expected value is incompatible with diversification. Roy criticised economic theory as being “set against a background of ease and safety”, rather than “poorly chartered waters” or hostile jungles, assumes “economic survival”, and thus being incapable of understanding why investors act as if they see disaster everywhere. Consequently, he modelled downside risk, or mean semivariance, because he felt that investors are driven by a “safety first” logic. Nevertheless, it was only in the 1980s, when post-modern portfolio theory was delivered by Frank Sortino and others, that a more myopic view of risk became the foundation of an alternative way of forming portfolios.
To conform with my myopic view of risk, I calculate downside beta as the sensitivity of a stock's excess logarithmic returns to the market's downside excess returns, where "excess return" is the difference between the stock or market return and the returns on the risk-free security. This is known as the D-CAPM approach. I use industry and sector averages based on five years of weekly prices, in order to minimise the impact of beta on my cost of equity measure. An example of this can be seen in this spreadsheet.
To estimate the cost of debt for firms, I use 30-year Treasuries as the risk-free rate, in conformity with prior remarks, and where that is unavailable, the 20-year rate. To that, I add the debt spread associated with its debt rating, per Moody's or S&P, on its long-term debt. This pre-tax cost of debt is then multiplied by (1-Tm) to get the after-tax cost of debt.
The cost of preferred stock is simply the preferred dividends divided by the value of preferred capital.
Regarding the target capital structure, I tend to use historical values rather than try and presume to know what managers will do. This is because firms tend to be very conservative about changing capital structures.
Diamond Hill's' WACC, for the period 2019 to the last twelve months (LTM) ending 2Q 2024, as I estimate it, is given below: