LeCompte Learning Solutions is considering making a change to its capital struct
ID: 2761240 • Letter: L
Question
LeCompte Learning Solutions 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:
Percent financed Percent financed Debt-to-equity Bond Before-tax
with debt (wd) with equity (ws) ratio (D/S) Rating 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%. LeCompte estimates that if it had no debt its beta would be 1.0. (Its "unlevered beta," bU, equals 1.0.) The company's tax rate, T, is 40%. On the basis of this information, what is LeCompte's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure? (the lowest WACC)
Explanation / Answer
Answer
Calculation of Beta of equity at different Debt equity ratio
Particulars
Levered equity beta=Beta Unlevered *{1+[D(1-t)/E]}
0.1
1*{1+(0.11*0.60)}
1.066
0.2
1*{1+(0.25*0.60)}
1.15
0.3
1*{1+(0.43*0.60)}
1.258
0.4
1*{1+(0.67*0.60)}
1.402
0.5
1*{1+(0.1*0.60)}
1.6
Calculation of WACC
Particulars
Ke=Rf+Beta(Rm-Rf)
Kd= I(1-t)
WACC=(Ke*We)+(Kd*Wg)
0.1
5+(1.066*6)
11.396
7*(0.60)
4.2
(11.396*0.9)+(4.2*0.1)
10.6764
0.2
5+(1.15*6)
11.9
7.2*(0.60)
4.32
(11.9*0.8)+(4.32*0.2)
10.384
0.3
5+(1.258*6)
12.548
8*(0.60)
4.8
(12.548*0.7)+(4.8*0.3)
10.2236
0.4
5+(1.402*6)
13.412
8.8*(0.60)
5.28
(13.412*0.6)+(5.28*0.4)
10.1592
0.5
5+(1.6*6)
14.6
9.6*(0.60)
5.76
(9.6*0.5)+(5.76*0.5)
10.18
Answer:
The optimal structure of Lecompte is debt 40% and equity 60%.
The company’s cost of capital will be 10.16%.
Calculation of Beta of equity at different Debt equity ratio
Particulars
Levered equity beta=Beta Unlevered *{1+[D(1-t)/E]}
0.1
1*{1+(0.11*0.60)}
1.066
0.2
1*{1+(0.25*0.60)}
1.15
0.3
1*{1+(0.43*0.60)}
1.258
0.4
1*{1+(0.67*0.60)}
1.402
0.5
1*{1+(0.1*0.60)}
1.6
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