Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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