Question

The risk-free rate is 6%, the market risk premium (=E(RM) - RF) is 8%. Assume CAPM holds. A firm has a debt-to-equity ratio of 0.4. The firm's before-tax cost of debt is 10%. The firm's tax rate is 30%. If it had no debt, its cost of equity would be 16%.

a) What is the beta of the firm's debt?

b) What is the beta of the firm's equity if the firm had no debt?

c) What is the beta of the firm's equity when the debt-to-equity ratio is 0.4?

d) What is the cost of the firm's equity when the debt-to-equity ratio is 0.4?

Answer 1

a. Cost of debt = before tax cost(1-tax rate) = 0.1(1-0.3) = 0.07 or 7%

The beta of debt, using CAPM, Rd = RF + Beta(RM-RF)

7 = 6 + 8Beta

Beta = 0.125

The beta of debt is generally assumed to be zero, but practically it is not zero as there is some risk of company not able to paying the interest. But the beta is always very low as there is minimum risk.

b. When firm has no equity the Ke(cost of equity) is 16%. So calculating beta is easy. The beta calculated without debt in capital structure is the asset beta or unlevered beta.

Beta calculation:

Ke = RF + Beta(RM-RF)

16 = 6 + 8Beta

Beta = 1.25

c. Beta of the firm's equity with debt as a part of the capital structure is called the levered beta. When the debt-to-equity ratio is 0.4, the equity beta is calculated as given below:

Asset beta = equity beta/[1+(1-tax

rate)(debt/equity)]

equity beta = asset beta*[1+(1-tax rate)(debt/equity)]

asset beta is calculated above which is 1.25

equity beta = 1.25*[1+(1-0.3)(0.4)]

equity beta = 1.25*1.28

therefore, equity beta = 1.6

d. Cost of equity when debt to equity ratio is 0.4. When debt to equity ratio is 0.4 the beta is 1.6, therefore cost is calculated as:

Ke = RF + Beta(RM-RF)

Ke = 6 + 1.6*8

Ke = 18.8%