Cost of equity and CAPM: the return owners require

Debt has a price that anyone can see: the interest rate in the loan agreement. Equity seems to have none. Owners are promised no payment, and a company that skips its dividend breaks no contract. It is easy to conclude that equity is free money. It is not. Owners could have put their money elsewhere, and they will supply it only if they expect a return that compensates for the risk. That expected return is the cost of equity. The company does not pay it as a bill, but it pays it in the form of a share price that rises, a dividend, or both, and if it fails to earn it, owners sell and the share price falls.

The cost of equity is higher than the cost of debt, because owners are paid last and carry more risk. Putting a number on it is harder, because it cannot be read off a contract. This lesson covers the standard method, the capital asset pricing model, and a cross-check from the dividend growth formula that the annuities lesson introduced.

Return and risk go together, but not all risk is rewarded. A share's price moves for two kinds of reason. Some are specific to the company: a product fails, a factory burns down, a competitor wins. An investor who holds many different shares suffers little from these, because the good surprises and the bad ones offset each other. That is diversifiable risk, and markets pay nothing for carrying it. The other kind affects nearly everything at once: interest rates, recessions, and swings in confidence. This is market risk, and it cannot be diversified away, so investors need extra expected return to bear it.

Beta measures how much market risk a share carries. It compares how far the share's returns tend to move when the market's returns move. A beta of 1 means the share moves with the market on average. A beta of 1.5 means it moves one and a half times as much, so it is riskier than the market. A beta of 0.5 means it moves half as much. Beta is estimated by comparing the share's past returns with the market's. It is not a number in a company's accounts.

The capital asset pricing model (CAPM) turns that idea into a formula. The expected return on a share equals the return on a risk-free investment plus a reward for market risk, which is the share's beta times the extra return the market as a whole is expected to give over the risk-free rate.

• The risk-free rate is the yield on a government bond of long maturity, in the same currency as the cash flows being valued.
• The equity risk premium is the extra return expected from the stock market as a whole above the risk-free rate. It cannot be observed. It is estimated from history or from market prices, and estimates differ.
• Beta scales the premium to the share's own market risk.

Set the risk-free rate, the beta and the equity risk premium. The left page shows the premium the share must offer and the cost of equity, and what it would be if beta were half a point lower or higher. The right page ties the result to value with the growing perpetuity formula from the annuities lesson: a share paying a dividend of $5 next year, growing at the rate you set, is worth the dividend divided by the cost of equity less the growth rate. The settings are illustrative.

CAPM looks at the market. A second route looks at the share itself. If a share's price is the present value of dividends that grow at a steady rate, then price equals next year's dividend divided by the cost of equity less growth. Solving for the cost of equity gives:

For a share priced at $83.33 paying $5 and growing 3%, the cost of equity is 5 ÷ 83.33 + 3% = 9%, which is the CAPM answer in the calculator. The method needs a stable dividend and a view of its growth, so it suits mature companies with a long record, and it is hard to apply where dividends are small or irregular. That is the situation at Apple, and the next section uses it to show what a market price implies.

Apple's reports give the cash it paid owners in fiscal 2025: $15,421 million in dividends and $90,711 million to buy back its own shares. They also give the market value of the shares held outside the company, $3,253,431 million at 28 March 2025. Dividends of $15,421 million spread over the roughly 15.0 billion diluted shares is about $1.03 a share. The market value is an approximation of the whole, because it leaves out shares held by insiders.

The dividend yield, dividends divided by market value, is 0.47%. The total payout yield, counting buybacks, is 3.26%. Now run the dividend growth approach backwards. If the cost of equity were 9%, the growth that makes the payout worth the market value is far from zero. The table solves for that growth at five illustrative costs of equity, once for dividends alone and once for dividends plus buybacks. It uses the exact form: price = this year's payout × (1 + g) ÷ (cost − g), so g = (cost × price − payout) ÷ (price + payout).

The capital asset pricing model builds the required return on equity from three inputs: a risk-free rate, the stock's beta and the market risk premium. The risk-free rate is the only input that depends directly on currency. A dollar investment is compared with the dollar government bond rate, and a yen investment with the yen rate. The example is hypothetical: the dollar risk-free rate is 4%, the yen risk-free rate is 1%, beta is 1.1 and the market risk premium is 5%.

• In dollars: 4% plus 1.1 times 5% gives a required return of 9.50%.
• In yen, by converting the dollar figure: restating the same required return so that it is consistent with the lower yen interest rate gives 6.34%.
• In yen, with CAPM directly: 1% plus 1.1 times 5% gives 6.50%.

The two yen answers are close, and the difference arises only because the premium does not scale exactly. The required return on the same equity is 3.16% lower in yen, about the same as the 3-point gap between the two interest rates. The point is not that yen shareholders are satisfied with less. The yen has lower inflation and interest, and a return expressed in yen reflects that.

Two more choices have an international side. The first is the market against which beta is measured. A company listed in Tokyo can be compared with the local index or with a global one, and the answer can differ. A multinational that earns revenue in many countries has risks that are not tied to its home market, which favours a global comparison. The second is country risk. An investment in a country with a higher risk of political or economic disruption demands extra return, and practitioners add a country risk premium to the cost of equity in the currency of the investment. These are judgements, and two analysts can reasonably differ.

What cannot differ is consistency. If cash flows are in one currency, use a risk-free rate in that currency, a premium suited to the markets where the money is at risk, and forecasts in the same currency. A dollar cost of equity applied to yen forecasts, or the reverse, is the same mistake as mixing currencies when discounting.