# 3. Cost of Common Equity

## h. calculate and interpret the cost of equity capital using the capital asset pricing model approach, the dividend discount model approach, and the bond-yield-plus risk-premium approach;

What is the Cost of Common Equity? What is the decision the firm must make associated with this cost?

The cost of common equity (re) is the rate of return stockholders require on common equity capital the firm obtains. If the firm cannot invest newly obtained equity or retained earnings and earn at least re, it should pay these funds to its stockholders and let them invest directly in other assets that do provide this return. Firms should earn on retained earnings at least the rate of return shareholders expect to earn on alternative investments with equivalent risk.

What is the formula for the CAPM approach to estimating the cost of common equity?

$$r_e = R_F + [E(R_M) - R_F] \beta_i$$

- `R_F`

= =the risk-free rate

- `E(R_M)`

= the expected rate of return on the market

- `β_i`

= the stock's beta coefficient

Inside of the CAPM formula for estimating the cost of common equity, what is the equity risk premium (ERP) portion of the formula?

$$ERP = [E(R_M) - R_F]$$

What is the historical equity risk premium approach of estimating equity risk premium?

The historical equity risk premium approach examines the historical data of realized returns from a country's market portfolio and uses the average rate for both the market portfolio and risk-free assets.

When estimating an equity risk premium, what is the dividend discount model approach? What is the formula?

- The dividend discount model approach (or implied risk premium approach) analyzes how the market prices an index using the Gordon growth model:

- $$r_e = \frac{D_1}{P_0} + g$$

What is the bond yield plus risk premium approach of estimating the cost of common equity?

- Because the cost of capital of riskier cash flows is higher than that of less risky cash flows:

- $$r_e = r_d + risk\ premium$$

##### Source:

- CFA