Q: A company has a target capital structure of 40% debt and 60% equity. The company is a constant growth firm that just paid a dividend of $2.00, sells for $27.00 per share, and has a growth rate of 8%.
The company’s bonds pay 10% coupon (semi-annual payout), mature in 20 years, and sell for $849.54.
The company’s stock beta is 1.2.
The company’s marginal tax rate is 40%.
The risk-free rate is 10%.
The market risk premium is 5%.
The cost of equity using the capital asset pricing model (CAPM) is?
Shouldn’t the answer be 4%? 10 + 1.2(5-10) = 4
A: But the answer is supposedly 16%. Is this an error? Thanks in advance.
You’ve done the [risk-free rate + beta (market risk premium - risk-free rate)]. The underlined part is where you are wrong. There is a difference between the expected return on the market, and the expected market risk premium.
The expected return on the market is the risk-free rate + the market-risk premium (ie 10% + 5%). The market risk premium is the market return - the risk-free rate (15% - 10%). Think of the premium as compensation for additional risk you are taking on.
So, the correct answer would be 10 + 1.2(15-10) = 10 + 6 = 16.