Cost of capital: WACC and CAPM

Key takeaways

• WACC weights the cost of equity and the after-tax cost of debt by their shares of total capital at market value.
• CAPM sets the cost of equity at the risk-free rate plus beta times the equity risk premium; each input is an estimate that must match the currency and horizon of the cash flows.
• Peer betas reflect each peer's leverage, so unlever them with the Hamada formula, take a central value, and relever it at the target's capital structure.
• The cost of debt is the yield a lender would require today, from traded debt or a rating-based spread, not the coupon on old borrowings; it enters WACC after tax.
• Size and country risk premiums are practitioner adjustments outside CAPM itself; if used, state the source and the reason, and do not also adjust the cash flows for the same risk.

What WACC measures

A company's operating cash flows are shared by its lenders and its shareholders. Lenders require a return that compensates for default risk and the time value of money; shareholders, who are paid only after lenders, require more. WACC is the average of the two required returns, weighted by how much of the company's capital each group provides. It is the return the operating business must earn to satisfy everyone.

The cost of debt enters after tax because interest is deductible in most tax systems: each dollar of interest reduces taxable income, so the net cost to the company is lower than the rate the lender receives. Putting the tax shield in the discount rate is why unlevered free cash flow is taxed as if the company had no debt.

WACC must match the cash flows it discounts: the same currency, the same inflation assumption (nominal cash flows with a nominal rate), and a capital structure the company is expected to maintain over the life of the forecast. If leverage will change sharply, as in a buyout, a single WACC is a poor tool and the analysis moves to an explicit debt schedule.

Cost of equity: the CAPM

The capital asset pricing model holds that investors who hold diversified portfolios are paid only for risk they cannot diversify away: the sensitivity of a stock to the market as a whole. That sensitivity is beta. A stock with a beta of 1.0 tends to move with the market; a beta of 1.5 means it has tended to move one and a half times as much.

The risk-free rate is the yield on a government bond with no meaningful default risk in the currency of the cash flows. Practitioners commonly use a long-dated yield, such as a 10-year or 20-year government bond, to match the long duration of equity cash flows, and they use the same maturity consistently.

The equity risk premium (ERP) is the extra return investors expect from the equity market as a whole over the risk-free rate. It cannot be observed. It is estimated from long histories of realized returns, from implied premiums backed out of current index prices and expected cash flows, or from surveys, and the approaches give different answers. Whatever figure is used, state it and its basis, and keep it consistent with the risk-free rate chosen. The 5.5 percent used below is an illustrative assumption, not a recommendation.

Beta is usually estimated by regressing a stock's returns on a broad index over a period such as two years of weekly returns or five years of monthly returns. Raw regression betas are noisy. Some data providers publish an adjusted beta that pulls the raw figure toward 1.0 (a common form is two thirds of raw beta plus one third), on the view that extreme betas tend to drift toward the average over time.

Unlevering and relevering beta

A levered equity beta mixes two kinds of risk: the business risk of the operations and the financial risk of the company's debt. Two firms in the same business, one with heavy debt and one with none, will show different equity betas because debt makes the equity more volatile. The target's own beta may also be unavailable (it is private) or unreliable (thinly traded).

The solution is to strip financial risk out of peer betas, take a central value of the resulting asset betas (also called unlevered betas), and add back the financial risk of the target's own capital structure. The most widely used formula is the Hamada equation. It assumes debt carries no market risk (a debt beta of zero) and that the company maintains a fixed amount of debt, so the tax shield is as risky as the debt itself.

Other formulas exist. The Harris-Pringle version drops the tax term (assuming debt is rebalanced to a constant ratio of value), and some practitioners include a positive debt beta for highly levered companies. The choice changes the result. Use one formula consistently for unlevering and relevering.

Cost of debt: yield or rating

The cost of debt in WACC is the rate the company would pay to borrow today on its expected capital structure, not the coupon on debt it issued years ago. If rates or the company's credit quality have changed, the historical coupon is irrelevant.

When the company has traded bonds, the yield to maturity on its long-dated bonds is the most direct estimate. For loans, the current margin over the reference rate for similar new facilities serves the same purpose. When there is no traded debt, estimate a rating, either an actual agency rating or a synthetic one inferred from credit metrics such as interest coverage and leverage, and add the spread currently observed on debt with that rating to the risk-free rate.

One caution applies to lower-rated debt. A yield to maturity is a promised return that assumes every payment is made. For investment grade debt the gap between promised and expected return is small; for high yield and distressed debt the expected return is meaningfully below the promised yield because some borrowers default. Using the full promised yield overstates the cost of debt for those companies.

Market value weights, not book value

The weights in WACC should reflect what investors have at stake today, which is the market value of each claim. For a listed company, equity value is share price times diluted shares; debt is usually taken at book value unless it trades far from par. For a private company, the weights come from a target capital structure, often the median of peers at market values, or the structure the owner intends to keep.

Book equity is an accounting residual built from historical costs and retained earnings. For a profitable company it is usually far below market value, so book weights overweight debt, the cheaper source, and understate WACC. The error compounds if the beta is relevered at market leverage but the weights use book leverage, because the two halves of the formula then describe different companies.

Using a target structure also avoids a circularity. For a company being valued, market equity value is the output of the DCF, so it cannot be an input. Iterating until the assumed and implied weights agree is possible, but a stated target structure is simpler and more transparent.

Size and country risk premiums

CAPM says only market risk is priced. Practitioners valuing small companies or businesses in emerging markets often add premiums anyway, because they believe CAPM with a standard beta understates the return investors actually require. These additions are practitioner conventions, not part of the model, and they are contested.

A size premium adds a percentage to the cost of equity of smaller companies, commonly taken from published studies of historical returns by size decile. The evidence for a persistent size effect has been debated extensively, and it varies with the period and method studied. Some of what a size premium captures (thin trading, customer concentration, key person risk) can alternatively be addressed in the cash flows, by haircutting the forecast.

A country risk premium (CRP) adds compensation for political, currency convertibility and macroeconomic risks in a country whose government bonds are not free of default risk. One widely taught approach starts from the country's sovereign default spread, the extra yield on its US dollar government bonds over US Treasuries, and scales it by the ratio of that country's equity market volatility to its bond market volatility. Another adds the spread directly. Both are estimates, and a company's exposure depends on where it earns revenue, not where it is headquartered.

A complete WACC for Fenwick Labels

Assembling the pieces in order makes each choice visible. The table that follows is the form an investment committee memo or valuation report would show, with every input on its own line so a reviewer can change one and see the result.