Calculating Cost of Equity Capital

A company can increase its common equity either by reinvesting its earnings or issuing new stock. The cost of equity will, therefore, be the rate of return that its shareholders require.

Three methods are used to estimate the cost of equity. These are the capital asset pricing model and the bond yield plus risk premium method.

Capital Asset Pricing Model

The application of the Capital Asset Pricing Model (CAPM) in the computation of the cost of equity is based on the following relationship:

$$ E\left( { R }_{ i } \right) ={ R }_{ F }+{ \beta }_{ i }\left[ E\left( { R }_{ M } \right) -{ R }_{ F } \right] $$

Where:

E(R_i) = The cost of equity or the expected return on a stock.

R_f = The risk-free rate of interest.

B_i = The equity beta or return sensitivity of stock i to changes in the market return.

E(R_m) = The expected market return.

Note that the expression E(R_m) – R_f is known as the expected market risk premium or equity risk premium.

The risk-free interest rate may be estimated by the yield on a default-free government debt instrument.

Example: Using CAPM to Derive the Cost of Equity

A company’s equity beta is estimated to be 1.2. If the market is expected to return 8% and the risk-free rate of return is 4%, what is the company’s cost of equity?

Solution

The company’s cost of equity = 4% + 1.2(8% – 4%) = 4% + 4.8% = 8.8%

The expected market risk premium, or E(R_m) – R_f, is the premium investors demand for investing in a market portfolio relative to the risk-free rate.

There is an alternative to the CAPM that accommodates risks that may not be captured by the market portfolio alone. It is a multifactor model that incorporates macroeconomic factors and company-specific factors.

$$
\left.\left.E\left(R_{F}\right)=R_{F}+\beta_{i 1}(\text { Factor risk premium })_{1}+\beta_{i 2} \text { (Factor risk premium }\right)_{2}+\cdots+\beta_{i j} \text { (Factor risk premium }\right)_{j}
$$

Where

\(\beta_{ij}\)= stock i’s sensitivity to changes in the j^th factor

\((\text{Factor Risk Premium})_j\) = expected risk premium for the j^th factor

The basic idea behind these multifactor models is that the CAPM beta may not capture all the risks, especially in a global context, including inflation, business cycle, interest rate, exchange rate, and default risks.

There are two ways to estimate the equity risk premium, the historical equity risk premium approach and the survey approach.

The historical equity risk premium approach assumes that the realized equity risk premium observed over a long period is a good indicator of the expected equity risk premium. This approach requires the compilation of historical data to find the average rate of return of a country’s market portfolio and the average rate of return for the risk-free rate in that country.

Example: Estimating Risk Premium Using Historical Rates of Return

Assume that the arithmetic T-bond rate observed historically is 5.00%. In addition, assume that the arithmetic average return on the market is 8.5%. The equity risk premium can be calculated as follows:

Solution

$$
E R P=R_{M}-R_{F}=8.5 \%-5.0 \%=3.5 \%
$$

The survey approach involves asking a panel of finance experts for their estimates and taking the mean response.

Bond Yield Plus Risk Premium Approach

According to the bond yield plus risk premium approach, the cost of equity may be estimated by the following relationship:

r_e = r_d + Risk Premium.

Where:

r_e = The cost of equity.

r_d = Bond yield.

Risk premium = Compensation that shareholders require for the additional equity risk compared with debt.

Example: Using the Bond Yield Plus Risk Premium Approach to Derive the Cost of Equity

If a company’s before-tax cost of debt is 4.5% and the extra compensation required by shareholders for investing in the company’s stock is 3.2%, then the cost of equity is simply 4.5% + 3.2% = 7.7%.

Question

A company’s equity beta is estimated to be 1.4, and the market is expected to return 8.5%. The risk-free rate of return is 3.5%. Using the Capital Asset Pricing Model Approach, what is the company’s cost of equity?

1. 9.5%.
2. 10.5%.
3. 15.4%.

Solution

The correct answer is B.

Using the equation:

$$\begin{align} E(R i)&=R F+\beta_{i}[E(R M)-R F]\\ &=3.5 \%+1.4(8.5 \%-3.5 \%)\\ &=10.5\% \end{align}  $$