## Cost of equity

##### Published: Feb 2007

A company’s cost of equity can be seen as the equity investor’s required return on equity. There are two commonly used methods for calculating the cost of equity: the dividend capitalisation model and the capital asset pricing model.

### Dividend capitalisation model

The expected return from a share can be broken down into dividend yield and capital appreciation. Proponents of dividend growth models argue that only future cash dividends can give a reliable estimate of a share’s value and effectively replace an estimate of capital appreciation with the predicted growth rate of dividend payments.

As these individual payments are difficult to predict in the long term, the constant growth model assumes that dividends grow at a constant rate in perpetuity. The dividend capitalisation model estimates the cost of equity by adding together dividend yield and the expected growth in dividends using the following formula:

$$\mathrm{Cost\: of\: Equity}= \frac{Dividends\: per\: shade \:following \:year}{Current\: market\: value\: of\: stock}\: +\:{Growth \:rate\: of\: dividends}$$

However, the dividend model cannot be employed for companies that do not pay a dividend, nor is it able to handle variable dividend growth rates.

### Capital asset pricing model

The CAPM is nowadays more widely used than the dividend model. It is based on the theory of a relationship between the risk of an asset, in this case the company’s equity, and the expected rate of return that is required by investors on the asset.

According to the formula the opportunity cost of equity capital is equal to the return on a risk-free asset plus a combination of market risk and a company’s individual risk (beta):

$$\mathrm{K_e}={\mathrm{r_f\:+\:ß \: r_m\:–\:r_f}}$$

Where:

• $$\mathrm{K_e}= {\mathrm{cost\:of \:equity, rf}= \mathrm{rate\: of\: interest\: on\:the\: risk-free \:asset}}$$
• $$\mathrm{ß}={\mathrm{ Beta\: representing\: the \:risk\: of \:the \:company \:versus\: the \:market\: risk}}$$
• $$\mathrm{r_m}= {\mathrm{(expected)\: equity\: market\: return,\:r_m\:-\:r_f}=\mathrm{equity\: risk\: premium}}$$

The CAPM assumes that investors expect two types of return. Firstly, any investment must yield a return that is at least equal to what could be earned by investing into a risk-free asset. This return represents the time value of money that is generated by investing into any type of investment without considering the risks taken. Generally, a long-term government bond can be used as a reference for the risk-free rate.

In addition, the investor expects a premium as compensation for any risks that are taken compared to the riskfree asset. In the CAPM these additional risks are composed of the risk of investing into the stock market instead of any other market (market risk) and the risk that is associated with an individual company’s share.

The market risk premium can be derived from historical data referencing the difference between stock market returns and risk-free rates $$r_m \: – \: r_f$$ . This difference tends to be relatively stable in the long term.

The individual risk of a company’s share is expressed as beta. Beta measures the volatility of the share in comparison to the general stock market movement. A beta of 1, for example, means that the share is expected to move in line with movements in the stock market as a whole. A beta higher than 1 signals a share that is relatively more volatile than the index and therefore slightly riskier than the market in general. For example, a beta of 1.5 indicates that a 1% change of the index rate would result in a 1.5% change in the share value.

It is important to recognise that CAPM has significant problems. Some studies have found that the beta factor alone cannot be used reliably to forecast the return of a share. Nevertheless, due to the lack of a practical substitute and because of its ease of use, the CAPM remains widely employed to determine the cost of equity.