Cost of Capital: CAPM and WACC

CAPM, and what it is actually claiming

The capital asset pricing model says the return investors require from a share equals the risk-free rate plus beta times the equity risk premium. The risk-free rate represents the time value of money — you can get it by buying a government bond rather than a share. The equity risk premium is the extra return the market has historically demanded for owning equities at all. Beta scales it: a beta of 1.0 means the share moves with the market, 1.5 means it amplifies market moves by half again, and 0.6 means it is quieter than the market. What the model claims is narrow and worth stating precisely: the only risk that earns a premium is the part that cannot be diversified away, which is why beta measures co-movement with the market rather than total volatility. This is a beautiful argument and an imperfect description of reality — the empirical record shows low-beta stocks earning more than the model predicts and high-beta stocks earning less, which is why practitioners adjust betas and add size and value terms. Use the model as a structured estimate, not as a law. The three inputs are unequal in quality. The risk-free rate is observable, at least for the currency and the maturity you pick. Beta can be estimated from history but is unstable — it changes with the period chosen and with the business. The equity risk premium is the softest of the three: credible estimates for the same market and the same year have ranged from about 3% to 6%, and that spread applied to a beta of 1.25 is a full point of cost of equity. If you are asked which input you trust least, the answer is the premium, and if you are asked which single input moves a valuation most, it is sometimes the premium and sometimes the rate — which is why the argument should be about the range, not the point estimate. Three inputs, one rate — Risk-free rate: 4.10% — observable, if you choose a currency and a maturity · Beta of 1.25 against a 5.00% premium: 6.25 percentage points of required premium · Cost of equity: 10.35% ← · Where the disagreement lives: The premium: 3% to 6% moves the answer a full point Do not use a company’s own historical beta uncritically when its business has changed. A beta is backward-looking; if the company has been transformed by an acquisition or a divestiture, the estimate describes a business that no longer exists.

The blend, and where each piece comes from

The weighted average cost of capital weights the cost of equity and the after-tax cost of debt by their market values. Market values, not book values: if the shares have doubled and the debt has not, the company is now mostly equity-financed and the WACC has risen without anything about the business changing. That is not an accounting subtlety — it is the reason a company whose share price has fallen sharply becomes a cheaper borrower of equity than one whose share price has risen. The weights explain most of the surprising results. A company with 84% of its capital in equity has a WACC close to its cost of equity, so WACC discussions are usually cost-of-equity discussions. A company with equal debt and equity has a WACC much closer to the middle, which is why leverage lowers the discount rate — and why it is tempting to lower the discount rate by borrowing. What stops that from being free is that beta rises with leverage, because debt service comes before equity, so the cost of equity goes up as the debt weight goes up. Modigliani and Miller’s insight in one sentence: adding cheap debt makes the remaining equity more expensive by exactly the amount that would make the WACC constant, before tax and before the costs of financial distress. Two practical refinements matter in real work. Use the marginal cost of capital rather than the average — the question a new investment asks is what the next dollar costs, not what the existing stock cost. And remember that the WACC is a rate for a business, not for a company: a conglomerate with a utility and a software division has two different costs of capital, and applying one number to both systematically overvalues the risky division and undervalues the safe one. For a private company, beta comes from comparable listed businesses, un-levered and re-levered to the target’s capital structure. For a project, the right beta is the beta of businesses in that line of work — which is why a discount rate should be argued about one layer below the company.

Beta is an estimate, and it is not stable

Beta is the one input in the cost of capital that is presented as a measurement. It is a regression of a stock’s returns on the market’s over a chosen window, which means it depends on the window, the frequency and the peer group you selected — three choices, each of which changes the answer. A five-year monthly beta and a two-year weekly beta for the same large company can differ by 0.4. The standard repair is to stop treating a single regression as the truth and to use a **bottom-up** beta instead: take the average unlevered beta of the industry the company actually competes in, then relever it for this company’s capital structure. That has two advantages — industry betas are far more stable than single-stock betas, and the relevering step makes the effect of adding debt explicit rather than implicit. The other input worth interrogating is the **equity risk premium**, which is not observable at all. Survey estimates and long-run historical averages differ, and the choice moves the cost of equity by a full percentage point or more. The honest response is not to find the right number but to be consistent within a valuation and to know what the whole valuation is worth if the premium is a point lower. For a company with most of its value in the terminal period, that one point is usually several tens of percent of the answer. • Window, frequency and peer group each move the regression beta • Industry (bottom-up) betas are far more stable than single-stock betas • Unlever, average across peers, relever — and the debt effect becomes visible • The equity risk premium is an assumption, not a measurement • Stress the two together: they enter the terminal value in the same direction Because the discount rate sits in the denominator of every projected year and dominates the terminal value, small changes here move the valuation more than a full percentage point of growth. That is why a valuation is an argument about inputs rather than a result.

The WACC is a hurdle, not a discovery

The number you compute is the *marginal* cost of the next dollar of capital, which is the right number for valuing a new project and the wrong number for describing the capital a firm already has. The two diverge when leverage changes: the weighted average that describes the debt and equity a company *has* is not the blend it would *raise* today, and using the historical one for a valuation quietly assumes the capital structure never moves. Most valuations assume a target structure for exactly this reason, and then state it. A second error is treating one WACC as the discount rate for a whole company. Capital costs differ by business: a stable regulated division can justify a lower rate than a cyclical one, and a company that rewards shareholders with a single blended rate will systematically over-invest in its riskiest division and starve its safest. Large firms build division-level hurdle rates for this reason. If a company reports one segment with the earnings of a utility and another with the volatility of a startup, a single WACC is a modelling shortcut with a directional bias. Finally, the WACC belongs to the *enterprise*, so it must be paired with enterprise cash flows. Matching a firm-wide WACC to equity cash flows, or a cost of equity to free cash flow to the firm, is a category error that misprices leverage — and it is one of the most common mistakes in a first DCF. Precision is not the goal. A WACC carried to two decimals from inputs estimated to the nearest percent is false precision; what matters is the method and the sensitivity.

The two inputs nobody can look up

Most of the cost of capital is assembled from things that can be looked up — a debt yield, a tax rate, a capital structure. Two of its inputs cannot be observed at all, and they happen to be the two that move the answer most: the risk-free rate you match to the cash flows, and the equity risk premium. Both are choices, and the range of defensible values is wider than the implied precision of a single discounted number suggests. The first is **duration matching**. The risk-free rate should reflect the horizon of the cash flows being discounted, so a valuation projecting a decade of cash flows wants a long-dated government yield rather than a three-month bill. In a steep curve the mismatch is not cosmetic: discounting distant cash flows at a short rate understates the discount rate, and the error lands hardest on the terminal value, which is where most of the value usually sits. Where the government’s own credit is in question, analysts add a spread, and that spread is the first of the country adjustments. The second is the **equity risk premium**, and there are two families of estimate. The historical family averages the excess return of equities over the risk-free rate across a long sample; it is simple and backwards-looking, and it is sensitive to choices that sound trivial and are not — the start date, the geography, and whether the average is arithmetic or geometric can shift the number by more than a percentage point. The forward-looking family inverts the exercise: it asks what premium makes today’s index price equal the present value of expected future cash flows. That estimate is the market’s own expectation, it moves when prices move, and it therefore reacts to exactly the conditions a valuation is attempting to describe. Neither family is right, which is the point. A single-point cost of capital conceals a range, and the honest way to present it is to run the valuation across a band of plausible inputs and report the output as a range. The sensitivity is worth stating plainly: a one-point change in the equity premium changes the cost of equity by a point, and through the terminal value that can move the valuation by a fifth in either direction. A conclusion that flips inside that band is a conclusion the model cannot support. The discipline that follows is short. Choose one method for the premium, apply it consistently across the companies you compare, show the output across a range of premiums rather than at one, and resist the temptation to tune the premium until the valuation matches the price. The premium is an estimate of a market-wide quantity. Tuning it per company converts an input into a conclusion. • Match the risk-free rate to the horizon of the cash flows, not to convenience. • Historical and implied premia are different estimates and disagree by design. • A point on the premium is worth roughly a fifth of a terminal-value-heavy valuation. • Report a range, and never tune the premium until it produces the price. Where a company earns cash in more than one currency, each set of cash flows is discounted at its own currency’s risk-free rate before translation. Discounting foreign cash at a domestic rate is a common error that hides as a growth assumption.

Sources

• The capital asset pricing model and its empirical problemsSharpe (1964); Lintner (1965); Fama & French (2004), "The Capital Asset Pricing Model: Theory and Evidence"
• The weighted average cost of capital and the tax shield of debtModigliani & Miller (1958, 1963); standard corporate-finance texts
• The equity risk premium: measurement, disagreement and its effect on valuationsDamodaran, "Equity Risk Premiums"; Ibbotson/SBBI yearbooks
• Country risk and the adjustments required outside developed marketsDamodaran, "Country Risk"; standard valuation practice