# Cost of equity

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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.

The cost of equity is one of the input of the Weighted Cost of Capital (or WACC) that gives the real cost of capital source of the firm, taking in account debt and equity fundings.

## 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 borne by the investor).

The most common measure of the riskiness of an asset in finance is the standard deviation of returns. It expresses 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 :

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

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

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

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

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

Practitioners usually use some asset pricing models to estimate the cost of capital of an investment. It is showed, see below, that their use mainly the Capital Asset Pricing Model (CAPM). Basically, the CAPM proposed that the expected stock return (or equivalently the cost of equity capital) is equal to:

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

Where:

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

### Cost of Equity in Practice

It appears from a survey by Bruner et al. (1998) that the Capital Asset Pricing Model (CAPM) proposed by Sharpe (1964) and Lintner (1965)is the dominant model for estimating cost of equity capital. They showed that practice is largely consistent with finance theory, despite many shortcomings related to the theory.

Graham and Harvey (2002) also showed that the CAPM is the most popular methoed used by firm to determined the cost of equity. They based their study on a survey responded by some 400 corporate Chief Financial Officiers.

## 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.
• Graham, John R. and Harvey, Campbell (2002), "The Theory and Practice of Corporate Finance: Evidence from the Field", Survey sponsored by the Financial Executives International and Duke's Fuqua School of Business.
• 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