Cost of equity

In finance, the cost of equity is the expected rate of return that any equity investor can expect to earn on an investment given the asset's level of risk. As noticed by Lundholm and Sloan (2007), we can use an "equivalent risk" investment to evaluate the correct Cost of Equity of an asset.

Risk

As one can noticed from the definition above, the estimation of risk is fundamental to a correct value of the cost of equity. The higher the risk, the higher the cost of equity would be (as it compensates for any additional risk beared by the investor).

The most common measure of the riskiness of an asset in finance is the standard deviation of returns. It expressed the dispersion of the expected returns around the mean. The higher it is, the more uncertain the returns are.

Evaluation of the Cost of Equity

Dividend Growth Model

According to the Dividend Growth Model proposed by Myron Gordon that the price of a stock should be equal to :

$P={\frac {D_{1}}{k-g}}$,

where $D_{1}$ is the expected dividend one year from now, $g$ is the expected constant growth rate in dividend, and $k$ is the cost of equity.

Rearranging, we have the defintion of the cost of equity:

$k={\frac {D_{1}}{P}}+g$.

Thus, from the dividend growth model, we can deduct that the cost of equity is equal to the sum of the forward dividend yield and the constant growth rate in dividends.

Asset Pricing Model

Practionners usually use some asset pricing models to estimate the cost of capital of an investment. It appears from a survey by Bruner et al. (1998) that the Capital Asset Pricing Model (CAPM) proposed by Sharpe (1964) and Lintner (1965).

It proposed that the expected stock return (or equivalently the cost of equity capital) is equal to:

$E(R_{i})=R_{f}+\beta _{im}(E(R_{m})-R_{f}).\,$

Where:

• $E(R_{i})~~$ is the expected return on the capital asset
• $R_{f}~$ is the risk-free rate of interest
• $\beta _{im}~~$ (the beta coefficient) the sensitivity of the asset returns to market returns, or also $\beta _{im}={\frac {\mathrm {Cov} (R_{i},R_{m})}{\mathrm {Var} (R_{m})}}$,
• $E(R_{m})~$ is the expected return of the market
• $E(R_{m})-R_{f}~$ is sometimes known as the market premium or risk premium (the difference between the expected market rate of return and the risk-free rate of return).

Using the CAPM gives an expected return that is composed of the risk-free rate, $R_{F}$, and a compensation for the risk (proportional to the market risk premium).

References

• Bruner, R. F., K. Eades, R. Harris and R. Higgins (1998), “Best Practices in Estimating the Cost of Capital: Survey and Synthesis”, Financial Practice and Education, Vol. 8(1), 13-28.
• Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47 (1), 13-37
• Lundholm and Sloan (2007), "Equity Valuation and Analysis with eVal", 2nd Edition, McGraw-Hill
• Sharpe, William F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk, Journal of Finance, 19 (3), 425-442