Question

You are tasked with estimating the cost of capital for a firm. The risk-free rate is 3%, the expected rate of return on the market is 10.7%. Now, another similar company (similar unlevered cost of capital) has a debt-to-equity ratio of 1 to 4. It has a debt beta near zero and an equity market-beta of 1.7. Your own firm has more debt, for a debt-to-equity ratio of 1 to 1, with a debt beta of 0.3. What is a good estimate for your equity cost of capital?

Answer 1

First we have to find the beta from the given debt beta and equity market beta

The Asset beta of similar firm = Ve /(Ve+Vd) * equity beta + Vd/(Ve+Vd) * debt beta = 4/(1+4) * 1.7 + 0 = 1.36

We use the asset beta of 1.36, we calculate the equity beta of the firm

The Asset beta of similar firm = Ve /(Ve+Vd) * equity beta + Vd/(Ve+Vd) * debt beta

1.36 = 1/2*equity beta = 1/2*0.3

1.21 = 1/2 * equity beta

equity beta = 2.42

Equity beta of your own firm = 2.42

Estimate of equity cost of capital as per CAPM = Rf + beta *(Rf - Rm) where Rf = 3%, Rm =10.7% and beta = 2.42

Estimate of equity cost of capital = 3 + 2.42*(10.7-3) = 21.63%