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 is required by its shareholders.

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

Capital Asset Pricing Model

The application of the Capital Asset Pricing Model (CAPM) to compute 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 rate of interest 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%

Dividend Discount Model

According to the dividend discount model, the intrinsic value of a share of stock is the present value of the share’s expected future dividends. Based on Gordon’s constant growth model, dividends are expected to grow at a constant rate, g. Therefore, assuming that the share price reflects the intrinsic value, the value of a stock is:

$$ { P }_{ 0 }=\frac { { D }_{ 1 } }{ { r }_{ e }-g } $$

Where:

P₀ = the current share price

D₁ = the dividend to be paid in the next period

r_e = the cost of equity

Rearranging the equation,

$$ { r }_{ e }=\frac { { D }_{ 1 } }{ { P }_{ 0 } } +g $$

Where:

$$ \frac { { D }_{ 1 } }{ { P }_{ 0 } } $$

is known as the forward annual dividend yield.

g may also be referred to as the sustainable growth rate and can be estimated by the following relationship:

$$ g=\left( 1-\frac { D }{ EPS } \right) \left( ROE \right) $$

Where ROE is the return on equity, and

$$ \frac { D }{ EPS } $$

is the assumed stable dividend ratio, which makes

$$ \left( 1-\frac { D }{ EPS } \right) $$

the earnings retention ratio.

Example: Using Gordon’s Constant Growth Model to Derive the Cost of Equity

If a company’s sustainable growth rate is 8.24% and its forward annual dividend yield is 4.16%, what is the estimate of its cost of equity?

Solution

The company’s cost of equity = 4.16% + 8.24% = 12.40%

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 which shareholders require for the additional risk of equity 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 current share price is $11.24, and it intends to pay a dividend of $1.38 next year. Using the dividend discount model and assuming a constant growth rate of 5%, what is the company’s cost of equity?

1. 17.28%
2. 16.38%
3. 9.58%

Solution

The correct answer is A.

Using the equation:

$$ \begin{align}
{ r }_{ e } & =\frac { { D }_{ 1 } }{ { P }_{ 0 } } +g \\
& =\frac { $1.38 }{ $11.24 } + 0.05 \\
&= 0.12278 + 0.05 = 17.28\% \\
\end{align}$$