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# Cost of equity and its calculation approaches

The cost of common equity (simply referred to as the cost of equity) is the rate of return required by common shareholders. Equity capital is utilized either through reinvestment of earnings or the issue of new stock.

Commonly used approaches for estimating the cost of equity include the capital asset pricing model, the dividend discount model, and the bond yield plus risk premium method.

## Capital asset pricing model

In the capital asset pricing model, the cost of equity (re) is determined as follows.

$r_e=r_f+β×(r_m-r_f)$

rf is the risk-free rate, the return on a default-free asset, such as government debt instrument having the same maturity as the maturity of the cash flows to which the cost of equity will be applied. β is the beta coefficient, a measure of the sensitivity of a stock’s return to change in market risk, and rm is the market return, the return on the broad market such as S&P 500.

An alternative to CAPM is to use a multi-factor model that bases a stock’s premium on a number of priced risks such as inflation, business cycles, exchange rate, etc. while separately identifying its sensitivity to each risk premium.

The excess market return over the risk-free rate is the compensation that equity-investors demand by investing in the market instead of the risk-free rate. The equity risk premium is determined using either the historical risk premium approach, the dividend discount model or the survey method.

In the historical equity risk premium approach, equity risk premium is derived from the historical comparison of market return with the risk-free rate. The arithmetic average is better for single period comparison while the geometric average should be used for multi-period analysis. However, it ignores the fact that the riskiness of a market may change, risk aversion of investors may change and that the historical return calculation depends on the period selected and the calculation method.

#### Implied risk premium using the dividend discount model

The dividend discount model (or implied risk premium) approach calculates equity risk premium by calculating the required rate of return on an equity index such as S&P500 and subtracting the risk-free rate. The required return equals expected dividends on index companies next year (D1) divided by the current value of the index (P0) plus the constant growth rate in dividends (g). The following equation shows this ERP calculation approach:

$ERP=\frac{D_1}{P_0+g}-r_f$

#### Survey method

In the survey method, experts are surveyed to obtain their estimates of ERP.

## Dividend discount model approach

Under the dividend discount model, the intrinsic value of a stock equals the present value of its dividend payments. In the Gordon growth model, dividends are assumed to grow at a constant growth rate g and the value of the stock (P0) is determined as the present value of a perpetuity:

$P_0=\frac{D_1}{r_e-g}$

By rearranging the above equation, we can obtain an expression for the cost of equity:

$r_e=\frac{D_1}{P_0}+g$

The D1/P0 is the forward dividend yield which can be determined easily if a company has a consistent dividend policy. g is the growth rate which is either based on forecasted growth rate obtained from an external vendor, or on the sustainable growth rate, which represents the growth rate achievable changing capital structure, and which is calculated as the product of the retention rate (which equals 1 minus dividend payout ratio) and return on equity.

$g=(1-\frac{D}{EPS})×ROE$

## Bond yield plus risk premium approach

Under the bond yield plus risk premium approach, the cost of equity is calculated by adding a risk premium to the cost of debt. It is because cash flows to equity shareholders are riskier than cash flows to debtholders.

$r_e=r_d+Risk\ Premium$

Even though this risk premium ought to be forward-looking, it is often based on historical spreads between bond yields and stock yields.