The cost of common equity (r_e) is the rate of return stockholders require on common equity capital the firm obtains. It has no direct costs but is related to the opportunity cost of capital: if the firm cannot invest newly obtained equity or retained earnings and earn at least r_e, 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.

Estimating the cost of common equity is challenging due to the uncertain nature of the amount and timing of future cash flows.

The CAPM Approach

where R_F is the risk-free rate, E(R_M) is the expected rate of return on the market, and β_i is the stock's beta coefficient. [E(R_M) - R_F] is called the equity risk premium (ERP). Both E(R_M) and β_i need to be estimated.

For example, firm A has a β_i of 0.6 for its stock. The risk-free rate, R_F, is 5%. The expected rate of return on the market, E(R_M), is 10%. The firm's cost of common equity is therefore calculated as 5% + (10% - 5%) x 0.6 = 8%.

There are several ways to estimate the 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. One study, cited in the textbook, found that the annualized U.S. equity risk premium relative to U.S. Treasury bills was 5.6% (geometric mean). However, there are some limitations to this approach. For example, the level of risk of the stock index and risk aversion of investors may change over time.

• The survey approach is a direct one: ask a panel of financial experts for their estimates and take the mean response.

• The dividend discount model approach (not covered in the textbook), or implied risk premium approach, analyzes how the market prices an index using the Gordon growth model:
  
  where r_e is the required rate of return on the market, D₁ is the dividends expected next period on the index, P₀ is the current market value of the equity market index, and g is the expected growth rate of the dividends.

Bond Yield Plus Risk Premium Approach

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

This is a subjective, ad hoc procedure: bond yield is the interest rate on the firm's long-term debt, and the risk premium is a judgmental estimate (usually 3-5%). For example, suppose that ABC, Inc.'s interest rate on long-term debt is 10%. Assume the risk premium is 5%. ABC's cost of retained earnings is 10% + 5% = 15%.

Practice Question 1

As an investor, how would you determine the total market value of a publicly traded corporation such as General Motors?

I. The values of debt and equity as they appear on the most recent financial statements.
II. The value of debt as it appears on the most recent financial statements plus the current market value of GM's common stock.
III. The current market value of GM's stock plus the market value of GM's debt.

Correct Answer: III only

Practice Question 2

Assume the risk-free interest rate is 7% and the market return is 12%. If the beta of a stock is 1.4, according to CAPM, what is the required rate of return on the stock?

A. 7%
B. 9.5%
C. 14%

Correct Answer: C

According to CAPM, the required return is 7 + (12 - 7) x 1.4 = 14%.

Practice Question 3

A company wants to determine the cost of equity to use in calculating its weighted average cost of capital. The controller has gathered the following information:

Rate of return on 3-month Treasury bills: 3.0%
Rate of return on 10-year Treasury bonds: 3.5%
Market equity risk premium: 6.0%
The company's estimated beta: 1.6
The company's after-tax cost of debt: 8.0%
Risk premium of equity over debt: 4.0%
Corporate tax rate: 35%

Using the capital asset pricing model (CAPM) approach, the cost of equity (%) for the company is closest to ______.

A. 8.5
B. 11.6
C. 13.1

Correct Answer: C

The cost of equity using the CAPM = risk-free rate + Beta x market equity risk premium = 3.5 + 1.6 x (6.0) = 13.1%.

Practice Question 4

The historical premium approach has some limitations, including:

I. the level of risk of stock index may change over time.
II. the risk aversion of investors may change over time.
III. the risk free rate changes over time.
IV. the estimates are sensitive to the method of estimation and the historical period covered.
V. the company's beta (return sensitivity of its stock to changes in the market returns) may change over time.

Correct Answer: I, II and IV.

Practice Question 5

In the Bond Yield plus Risk Premium Approach, the "risk premium" refers to:

A. the company's equity risk premium
B. the market risk premium
C. the difference between the cost of equity and the cost of debt of the company.

Correct Answer: C

This risk premium is not the equity/market risk premium.

Practice Question 6

In the Bond Yield plus Risk Premium Approach, the ______ cost of debt should be used if the firm is profitable.

A. before-tax
B. after-tax

Correct Answer: A

Practice Question 7

A company has a constant return on equity of 12% and a payout ratio equal to 35%. If the company expects to pay a dividend of $2 and has a stock price equal to $24, what is the expected rate of return?

A. 7.8%
B. 12%
C. 16.13%

Correct Answer: C

The growth rate can be computed from the payout and ROE rate: g = (1 - 0.35) x 12 = 7.8. Then the required return can be computed using the dividend-yield-plus-growth rate model: k_s = D₁/P₀ + g.

Note: this is not in the required reading.

Practice Question 8

WC Ltd. is a constant growth company that expects to grow at 5% and plans to raise some equity. The current stock price for the company is $45 and the company is expected to pay a dividend of $4 next period. What is the cost of the new equity if flotation costs are 10% of the issue?

A. 5%
B. 9.88%
C. 14.88%

Correct Answer: C

4/[45(1-0.10)] + 0.05 = 14.88

Note: this is not in the required reading.

Practice Question 9

An analyst gathers the following information about a company and the market:

Current market price per share of common stock: $32.00
Most recent dividend per share paid on common stock: $2.40
Expected dividend payout rate: 40%
Expected return on equity (ROE): 15%
Beta for the common stock: 1.5
Expected return on the market portfolio: 12%
Risk-free rate of return: 4%

Using the dividend discount model approach, the cost of common equity for the company is closest to ______.

A. 16.4%
B. 17.2%
C. 18.1%

Correct Answer: B

According to the dividend discount model approach, the cost of common equity is equal to the dividend yield plus the growth rate. In this case, the growth rate is the earnings retention rate times the expected ROE or (1 - dividend payout rate) x expected ROE = 1 - 0.4) x 15% = 9%. The expected dividend = 2.40 x (1 + 0.09) = 2.616. The expected dividend yield = 2.616 / 32 = 8.175%. The cost of common equity = 8.175% + 9.0%.

Note: this is not in the required reading.

Practice Question 10

A company wants to determine the cost of equity to use in the calculation of its weighted average cost of capital. The CFO has gathered the following information:

Rate of return on 3-month Treasury bills: 3.0%
Rate of return on 10-year Treasury bonds: 3.5%
Market equity risk premium: 6.0%
The company's estimated beta: 1.6
The company's after-tax cost of debt: 8.0%
Risk premium of equity over debt: 4.0%
Corporate tax rate: 35%

Using the bond-yield-plus-risk-premium approach, the cost of equity (%) for the company is closest to ______.

A. 12.3
B. 16.3
C. 18.3

Correct Answer: B

The cost of equity using the bond-yield-plus-risk-premium approach is determined by the before-tax cost of debt plus the risk premium of equity over debt. The before-tax cost of debt is the after-tax cost of debt divided by (1- tax rate). 8.0/(1 - 0.35) = 12.3%

Adding the risk premium results in a cost of equity of 12.3% + 4% = 16.3%.