CAPM, Beta and Cost of Capital Explained

Understand Capital Asset Pricing Model and Cost of Capital

Key rules to remember

CAPM

E(Ri) = Rf + βi × (E(Rm) − Rf)

Rf is the risk-free rate. E(Rm) − Rf is the market risk premium. Result is the required return on asset i.

Beta

βi = Cov(Ri, Rm) ÷ Var(Rm) = ρim × σi ÷ σm

ρim is the correlation between the asset and the market. σ is standard deviation.

Cost of equity from dividend growth model

Ke = D1 ÷ P0 + g

Assumes dividends grow at a constant rate g forever. D1 is next year's dividend. P0 is the current ex-dividend price.

After-tax cost of debt (irredeemable)

Kd = i × (1 − T)

i is the interest rate on the debt at its market value. T is the corporate tax rate. Assumes interest is fully tax-deductible.

Cost of redeemable debt

Kd (pre-tax) is the IRR of: market price now, interest flows, redemption value

Find the rate that makes the present value of the flows equal the market price. Then multiply by (1 − T) for the after-tax cost.

WACC

WACC = [E × Ke + D × Kd(1 − T)] ÷ (E + D)

Use market values of equity E and debt D. Add terms for preference shares if present.

Portfolio beta

βp = Σ wi × βi

wi are the proportions of the portfolio's value in each asset. Weights sum to 1.

How to solve Capital Asset Pricing Model and Cost of Capital questions

1. 1Read what is asked: a required return, a beta, a cost of one source, or the WACC. Note whether the question gives a tax rate.
2. 2List the data with labels: Rf, market return or premium, beta, share price, dividend, growth, debt price, coupon, redemption terms.
3. 3Check whether the market return or the market risk premium is given. The premium is E(Rm) − Rf. Do not subtract Rf twice.
4. 4Calculate the cost of equity using CAPM or the dividend growth model, as the data allow. State the formula first.
5. 5Calculate the pre-tax cost of debt, using the IRR if it is redeemable. Then apply (1 − T) to get the after-tax cost.
6. 6Work out the market values of equity and debt. Use number of shares times price for equity, and market price for debt, not nominal value.
7. 7Find the weights as each value divided by the total, then compute WACC. Keep at least two decimal places in percentages until the final answer.
8. 8State the answer with a unit and one line of interpretation. Mention the assumptions, such as constant growth or same risk as the company.

Quickest way: Three-line WACC check

Common mistakes in Capital Asset Pricing Model and Cost of Capital

• Using the market return in place of the market risk premium in CAPM.

  The question gives Rm, and students multiply beta by it directly.

  Fix: Always compute Rm − Rf first. Then multiply by beta and add Rf.

• Forgetting the tax adjustment on debt, or applying it to equity.

  Students memorise WACC without understanding that interest is tax-deductible but dividends are not.

  Fix: Apply (1 − T) only to the interest cost of debt. Dividends and equity returns are not adjusted.

• Using book values or nominal values as weights.

  Balance sheet figures are easier to find than market prices.

  Fix: Use market values unless the question says otherwise. Debt at ₹100 nominal trading at ₹92 has a market value of ₹92 per ₹100.

• Using the coupon rate as the cost of redeemable debt.

  The coupon is stated clearly, while the IRR needs more work.

  Fix: The cost of debt is the yield that equates the market price with the future payments. Use the coupon only when the debt trades at its redemption value.

• Saying a high-beta share is always 'bad' or that beta measures total risk.

  Beta is confused with standard deviation.

  Fix: Beta measures only systematic risk relative to the market. A high beta means a higher required return, not necessarily a poor investment.

• Using WACC for every project regardless of its risk.

  WACC is taught as the standard discount rate.

  Fix: State that WACC is suitable only when the project has the same business and financial risk as the company. Otherwise adjust the rate.

Worked examples