Aaron Athletics is trying to determine its optimal capital structure. The company's capital structure consists of debt and common stock. In order to estimate the cost of debt, the company has produced the following table:
|
Percent financed with debt (wd)
|
Percent financed with equity (wc)
|
Debt-to-equity ratio (D/S)
|
Bond
rating
|
Before-tax cost of debt
|
|
0.10
|
0.90
|
0.10/0.90 = 0.11
|
AAA
|
7.0%
|
|
0.20
|
0.80
|
0.20/0.80 = 0.25
|
AA
|
7.2
|
|
0.30
|
0.70
|
0.30/0.70 = 0.43
|
A
|
8.0
|
|
0.40
|
0.60
|
0.40/0.60 = 0.67
|
BBB
|
8.8
|
|
0.50
|
0.50
|
0.50/0.50 = 1.00
|
BB
|
9.6
|
The company uses the CAPM to estimate its cost of common equity, rs. The risk-free rate is 5% and the market risk premium is 6%. Aaron estimates that if it had no debt its beta would be 1.0. (Its "assets beta," bA, equals 1.0) The company's tax rate, T, is 40%.
On the basis of this information, what is the company's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure assuming that the beta of debt is zero in all cases?