Question

6.2 A project's cost of capital The DW Media Group has an equity beta of 1.2 and 50% debt (debt over firm value) in its capital structure. The company has risk-free debt that costs 4% before taxes, and the expected rate of return of the stock market is 12%. DW is considering the acquisition of a new project in publishing business that is expected to yield 20% on after-tax operating cash flow. Penguin Publishing House, which has the same business model (and risk class) as the project being considered, has an equity beta of 1.5 and has no debt in its capital structure. Assume that the marginal tax rate for both companies is 40%. 1. What is the cost of capital of Penguin Publishing House? 2. If DW finances the new publishing project with 50% debt, what is the cost of capital of this project? 3. Under the estimated cost of capital, should DW take the project or not?

Answer 1

(1) Penguin Publishing House:

All equity-financed firm, hence the equity beta of the firm equals its asset beta. Equity Beta = 1.5, Risk-Free Rate = Rf = 4 % and Market Return = Rm = 12 %

Cost of Capital = Rf + Equity Beta x (Rm - Rf) = 4 + 1.5 x (12 - 4) = 16%

(2) DW: As DW is getting into publishing, a suitable asset beta for the business would be the one for Penguin Publishing House. Hence, Asset Beta = 1.5 and Debt to Equity Ratio = DE = 0.5/0.5 = 1

Tax Rate = 40 %

Therefore, Equity Beta for Publishing Business = Asset Beta x [1+(1-Tax Rate) x DE Ratio] = 1.5 x [1+(1-0.4) x 1] = 1.5 x 1.6 = 2.4

Cost of Capital of the Project = Rf + Publishing Equity Beta x (Rm - Rf) = 4 + 2.4 x (12-4) = 23.2 %

(3) The expected yield (return) of the business is 20% whereas its cost of capital is 23,2%. As the expected return to be earned is lower than the required cost of capital DW should not take up the publishing project.