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Corporate Finance Unit 7: CAPM and the Cost of Capital (WACC)

The CAPM turns systematic risk (beta) into a required return, and the WACC blends the costs of debt, preferred and equity into a single discount rate for the firm. This unit shows how to estimate both and when to adjust them for project risk.

Covers: Beta and systematic risk, The CAPM and the security market line, Cost of equity: CAPM and dividend growth, Cost of debt and preferred stock, WACC with market-value weights, Divisional and project-specific discount rates, Flotation costs and leverage-adjusted betas

Study guide

Since only systematic risk is rewarded, we need a measure of it. Beta measures how strongly an asset's returns move with the market: β = Cov(Ri, Rm) ÷ σm². The market has a beta of 1; a beta of 1.5 means the stock tends to rise or fall 1.5% when the market moves 1%. A portfolio's beta is the weighted average of its assets' betas. The Capital Asset Pricing Model (CAPM) states that E(Ri) = rf + βi[E(Rm) − rf], where E(Rm) − rf is the market risk premium. Plotting required return against beta gives the security market line (SML).

In equilibrium, every asset lies on the SML, so all assets offer the same reward-to-risk ratio, (E(R) − rf) ÷ β. A stock whose expected return is above the SML is undervalued: investors buy it, its price rises and its expected return falls back to the line. A stock below the line is overvalued. A zero-beta asset earns only the risk-free rate, however volatile it is, because its risk is all diversifiable. The CAPM gives the cost of equity directly; the dividend growth model, RE = D₁ ÷ P₀ + g, is a second estimate, and analysts often compare or average them.

The cost of debt is the yield to maturity on the firm's existing bonds, not the coupon rate, because the cost of capital is a current market rate. Interest is tax-deductible, so the after-tax cost of debt is RD(1 − t). The cost of perpetual preferred stock is its dividend divided by its price, with no tax adjustment because preferred dividends are paid from after-tax income. The weighted average cost of capital combines them: WACC = (E/V)RE + (P/V)RP + (D/V)RD(1 − t). Weights should use market values (or target weights), not book values.

The WACC is the right discount rate only for projects with the same risk as the firm's existing assets. Using one company-wide WACC for every project leads the firm to accept too many risky projects and reject too many safe ones. For a division or project in a different line of business, find a pure-play firm whose only business is similar, and use its beta. Because leverage raises equity beta, adjust for differences in debt using the Hamada relation: βL = βU[1 + (1 − t)(D/E)]. Unlever the comparable's beta, then relever at your own capital structure.

Raising new capital costs money. Flotation costs, such as underwriting fees, mean a firm must raise more than the investment it needs. A common approach computes a weighted average flotation cost, fA = (E/V)fE + (D/V)fD, and grosses up the amount needed: amount raised = need ÷ (1 − fA). The flotation cost is then treated as part of the project's initial cost. Finally, the discount rate depends on the use of funds, not the source: a project financed with cheap debt today still uses the firm's WACC, because borrowing now uses up debt capacity that future projects would otherwise use.

Key ideas

• Beta measures systematic risk; the market's beta is 1.
• CAPM: required return = risk-free rate + beta × market risk premium.
• All correctly priced assets plot on the SML with the same reward-to-risk ratio.
• The cost of debt is the current YTM, adjusted for taxes; the cost of preferred is D ÷ P.
• WACC uses market-value weights and after-tax component costs.
• Discount each project at a rate that matches its own risk, using pure-play betas if needed.
• The cost of capital depends on how money is used, not where it comes from.

Formulas and rules

Common mistakes

• Multiplying beta by the market return instead of the market risk premium.
• Using the coupon rate instead of the current YTM as the cost of debt.
• Applying the tax adjustment to preferred stock or equity.
• Using book-value weights instead of market-value weights in the WACC.
• Using the firm's WACC for a project whose risk differs from the firm's.

Before the test, make sure you can

• Calculate required returns with the CAPM and identify over- or undervalued stocks.
• Calculate beta from covariance and variance, and portfolio beta from weights.
• Estimate the cost of equity with both the CAPM and the dividend growth model.
• Calculate the after-tax cost of debt from a bond's price and the cost of preferred.
• Calculate WACC with market-value weights for debt, preferred and equity.
• Unlever and relever betas to find a project's cost of equity.
• Adjust a project's cost for flotation costs.
• Explain why a single company-wide WACC can lead to wrong project decisions.

Words to know

Beta

A measure of an asset's systematic risk relative to the market; Cov(Ri, Rm) ÷ σm².

Market risk premium

The expected market return minus the risk-free rate.

CAPM

E(Ri) = rf + βi[E(Rm) − rf]; links systematic risk to required return.

Security market line

The line showing the CAPM required return for each beta.

Reward-to-risk ratio

(E(R) − rf) ÷ β; equal for all assets in equilibrium.

Cost of equity

The return shareholders require, estimated with the CAPM or dividend growth model.

Cost of debt

The current yield on the firm's debt; after tax it is RD(1 − t).

Cost of preferred stock

The preferred dividend divided by the preferred price.

WACC

Weighted average cost of capital: the overall required return on the firm's assets.

Market-value weights

Capital structure weights based on current market values of debt and equity.

Pure-play approach

Using the beta or cost of capital of a firm focused only on a similar business.

Divisional cost of capital

A discount rate tailored to the risk of one division.

Levered beta

The equity beta of a firm that uses debt; higher than its unlevered beta.

Unlevered beta

The beta the firm's equity would have with no debt; reflects business risk only.

Hamada equation

βL = βU[1 + (1 − t)(D/E)].

Flotation costs

Fees and costs of issuing new securities, such as underwriting spreads.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.