A cash-flow valuation needs a discount rate as well as a cash-flow estimate. This lesson builds a hypothetical CAPM cost of equity, uses it for a single equity payoff, and explains why a correct calculation can still be a poor model of reality.
You need percentages, beta, diversification and present value. A percentage point is the difference between two percentage rates: 8% minus 3% is 5 percentage points, not a 5% relative increase. Beta measures sensitivity to market returns. Diversification spreads company-specific exposures; it does not remove market-wide risk. Present value converts a future cash amount into an amount today using a discount rate.
Required return is the compensation for bearing risk used as a valuation hurdle or discount rate. Expected return is an uncertain average of possible future outcomes. Realised return is the outcome observed afterwards. In the CAPM equilibrium model, required and expected return coincide. Outside that model, a CAPM estimate does not establish the true expected return.
The capital asset pricing model links expected return to systematic risk, meaning exposure to market-wide movements. A diversified shareholder can reduce company-specific risk by spreading holdings, so the model does not reward that risk with an extra expected-return premium. It still matters for anyone exposed to a single company.
The formula is cost of equity = Rf + beta × [E(Rm) − Rf]. Rf is the risk-free rate. E(Rm) is the expected total market return. The bracketed term is the expected equity market risk premium. Beta scales exposure to that premium; it is unitless and is not the stock’s total risk.
Assume all rates are annual, nominal US-dollar rates for the same one-year horizon. Nominal means before adjusting for inflation. Let Rf = 3%, beta = 1.2 and the expected market premium = 5 percentage points. These inputs are hypothetical assumptions, not observations or recommendations.
First recover the assumed total market return: 3% + 5% = 8%. Then calculate the equity risk premium for this exposure: 1.2 × 5% = 6 percentage points. Add the risk-free rate: 3% + 6% = 9% per year. In decimals, 0.03 + 1.2 × 0.05 = 0.09.
The 8% belongs to the assumed market return; the 9% is the model-implied cost of equity for beta 1.2. Do not treat the 5% premium as a total market return and subtract Rf again. Do not read the resulting 9% as a promise that an investment will gain that amount.
Consider a hypothetical equity investment with exactly one expected total payoff of $109 to its shareholder one year from now, after obligations to lenders have been met, and no later payoff. This is the entire equity payoff, not a dividend plus an uncounted continuing share value. The amount is uncertain.
Using the assumed 9% annual cost of equity, present value = $109 ÷ (1 + 0.09) = $100. This is the value of that hypothetical expected payoff under these assumptions. It is not a real share-price target, a known future payment or an instruction to transact.
Cash flow and discount rate must match. An equity payoff uses a cost of equity. Cash flows available to both lenders and shareholders require a firm-level cost of capital, commonly the weighted average cost of capital (WACC), which combines financing costs using appropriate weights. Substituting this CAPM rate directly into a whole-firm cash-flow model mixes two different claims.
Also match currency, time horizon and inflation treatment. Nominal cash flows use nominal rates; inflation-adjusted cash flows use real rates. A one-year example does not justify using one fixed rate for every maturity in a multi-year valuation. Damodaran’s valuation-input notes explain why mismatching cash flows and rates produces valuation errors.
The standard model starts with investors choosing one-period portfolios using expected return and variance, a measure of return dispersion. It assumes shared expectations, borrowing and lending at a common risk-free rate, and frictionless trading. Those conditions simplify the theory; they do not describe every investor or market.
A historical beta depends on the index, sampling frequency and estimation window, and can change as a business changes. The future market premium is not directly observable. Historical average premiums are estimates, not known forward returns. Changing either input changes the discount rate even if the arithmetic is flawless.
The theoretical market portfolio includes risky wealth more broadly than a stock index. An index used to estimate beta is a proxy, meaning a practical substitute. Fama and French’s 2004 review documents serious empirical contradictions of CAPM and explains the difficulty of testing an unobserved market portfolio. Their critique is stronger than a warning about short-term noise: beta alone has not reliably explained the observed differences in average returns.
Keep the hypothetical Rf of 3% and expected market premium of 5 percentage points, but change beta to 0.8. What are the assumed total market return and the new CAPM cost of equity? Does the result guarantee an investment’s return? Could that rate directly discount cash flows to both lenders and shareholders?
Answer: the assumed total market return remains 8%, because its inputs did not change. The new cost of equity is 3% + 0.8 × 5% = 7%. Only the asset’s exposure changed. The 7% is model-implied, not guaranteed. It is an equity rate; firm cash flows need a matching firm-level cost-of-capital framework.
Explain in your own words why the worked example divides $109 by 1.09 rather than subtracting 9% of $109. Answer: the discount rate is a return on today’s value. The denominator reverses one period of compounding: $100 × 1.09 = $109. Subtracting a percentage of the future amount uses a different base.
General education, not investment advice. Every number in the worked example and assessment is hypothetical, not a current market estimate or a company valuation. CAPM has restrictive assumptions and serious empirical failures; neither the discount rate nor the payoff is guaranteed.
The hypothetical market premium is 5 percentage points above a 3% risk-free rate, so the total market return is 8%. Beta 1.2 scales that premium to 6 percentage points, producing a 9% cost of equity.
No. CAPM equates required and expected return within its equilibrium assumptions. A model output does not establish the true future expected return, and realised returns are the outcomes observed later.
CAPM gives a cost of equity. A DCF of cash flows to all capital providers requires a matching cost of capital, commonly WACC. Currency, horizon and nominal versus real treatment must also match.
Investor education only — not investment advice, and never a promise of profit. Every investment can lose value.