Black Keys Manufacturing is considering making a change to its capital structure
ID: 2710198 • Letter: B
Question
Black Keys Manufacturing is considering making a change to its capital structure in hopes of increasing its value. 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:
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%. Black Keys estimates that if it had no debt its beta would be 1.1. (Its "unlevered beta," bU, equals 1.1.) The company's tax rate, T, is 40%.
On the basis of this information, what is Black Keys' optimal capital structure, and what is the firm's cost of capital at this optimal capital structure?
we = 0.9; wd = 0.1; WACC = 11.01%
we = 0.8; wd = 0.2; WACC = 10.96%
we = 0.7; wd = 0.3; WACC = 10.75%
we = 0.6; wd = 0.4; WACC = 10.15%
we = 0.5; wd = 0.5; WACC = 10.18%
Percent financed Percent financed Bond Before-tax Levered Cost of equity with debt (wd) with equity (we) Rating cost of debt Beta re WACC 0.1 0.9 AAA 7.00% 0.2 0.8 AA 7.20% 0.3 0.7 A 8% 0.4 0.6 BBB 9.60% 0.5 0.5 BB 10.75%Explanation / Answer
Correct answer is where the WACC is minimized which is wd = 0.3, we = 0.7 WACC = 10.75%
Risk-free rate = 5%
Market risk Premium = 6%
Tax rate = 40%
Beta = 1.1
Cost of Equity re = rf + Beta * market risk premium
= 5% + 1.1 * 6%
= 5% + 6.6%
= 11.6%
The table with all data points filled is as follows
% Financed
With debt (wd)
% Financed
With equity
(we)
Bond
Rating
Before Tax
Cost of Debt
Levered
Beta
Cost of
Equity
WACC
0.1
0.9
AAA
7%
1.184
12.10%
10.86%
0.2
0.8
AA
7.20%
1.265
12.59%
10.94%
0.3
0.7
A
8%
1.383
13.298%
10.75%
0.4
0.6
BBB
9.60%
1.54
14.24%
10.85%
0.5
0.5
BB
10.75%
1.76
15.56%
11.01%
Calculation of WACC and Levered Beta
Levered Beta = Unlevered Beta * (1+(1-tax rate) * (Debt/Equity)
WACC = wd * cost of debt * (1-tax rate) + we * cost of equity
wd = 0.1, we = 0.9, cost of equity = 11.6%, pre-tax cost of debt = 7%
Levered Beta = 1.1 * (1+(1-0.40) * (0.1/0.9) = 1.1 * (1+0.6 * 0.1111) = 1.11 * (1+0.066667)
= 1.184
Cost of Equity = 5% + 1.184 * 6% = 12.104 or 12.10%
WACC = 0.1 * 7% * 0.6 + 0.9 * 12.10% = 0.42 + 10.89 = 11.31%
wd = 0.2, we = 0.8, cost of equity = 11.6%, pre-tax cost of debt = 7.20%
Levered Beta = 1.1 * (1+(1-0.4) * (0.2/0.8)) = 1.1 * (1+0.6 * 0.25) = 1.1 * 1.15
= 1.265
re = 5% + 1.265 * 6% = 12.59%
wacc = 0.2 * 7.2 * 0.6 + 0.8 * 12.59 = 0.864 + 10.072 = 10.936 or 10.94%
wd = 0.3, we = 0.7, cost of equity = 11.6%, pre-tax cost of debt = 8%
Levered Beta = 1.1 * (1+(1-0.4) * (0.3/0.7)) = 1.1*(1+ 0.6 *0.428571) = 1.1 * 1.2571428
= 1.382571 or 1.383 (rounded off)
re = 5% + 1.383 * 6% = 13.298%
WACC = 0.3 * 8 * 0.6 + 0.7 * 13.298% = 1.44 + 9.3086 = 10.7486 or 10.75%
wd = 0.4, we = 0.6, cost of equity = 11.6%, pre-tax cost of debt = 9.6%
Levered Beta = 1.1 * (1+(1-0.4) * (0.4/0.6) = 1.1 * (1+0.6 *0.66667) = 1.1 * 1.4 = 1.54
re = 5% + 1.54 * 6% = 14.24%
wacc = 0.4 * 9.6% * 0.6 + 0.6 * 14.24% = 2.304% + 8.544% = 10.848% or 10.85%
wd = 0.5, we = 0.5, cost of equity = 11.6%, pre-tax cost of debt = 10.75%
Levered Beta = 1.1 * (1+(1-0.4) * (0.5/0.5)) = 1.1 * (1+ 0.6 * 1) = 1.1 * 1.6 = 1.76
re = 5% + 1.76 * 6% = 15.56%
wacc = 0.5 * 10.75% * 0.6 + 0.5 * 15.56% = 3.225% + 7.78% = 11.005% or 11.01%
Correct answer is where the WACC is minimized which is wd = 0.3, we = 0.7 WACC = 10.75%
% Financed
With debt (wd)
% Financed
With equity
(we)
Bond
Rating
Before Tax
Cost of Debt
Levered
Beta
Cost of
Equity
WACC
0.1
0.9
AAA
7%
1.184
12.10%
10.86%
0.2
0.8
AA
7.20%
1.265
12.59%
10.94%
0.3
0.7
A
8%
1.383
13.298%
10.75%
0.4
0.6
BBB
9.60%
1.54
14.24%
10.85%
0.5
0.5
BB
10.75%
1.76
15.56%
11.01%
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