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 (wc)	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, r_s. 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," b_U, 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?

a. wc = 0.8; wd = 0.2; WACC = 10.96%

b. wc = 0.6; wd = 0.4; WACC = 10.15%

c. wc = 0.5; wd = 0.5; WACC = 10.18%

d. wc = 0.9; wd = 0.1; WACC = 14.96%

e. wc = 0.7; wd = 0.3; WACC = 7.83%

Answer 1

Beta levered =Beta unlevered*(1+(1-Tax Rate)*Debt/equity)
AT equity 0.80 and debt 0.20
Beta levered =1*(1+(1-40%)*0.20/0.80)=1.15
Cost of equity =Risk Free Rate+Beta levered*(Market return -risk free rate) =5%+1.15*6% =11.90%
WACC =Weight of Equity *Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)
=0.8*11.90%+0.2*7.2%*(1-40%) =10.38%

AT equity 0.60 and debt 0.40
Beta levered =1*(1+(1-40%)*0.40/0.60)=1.40
Cost of equity =Risk Free Rate+Beta levered*(Market return -risk free rate) =5%+1.40*6% =13.40%
WACC =Weight of Equity *Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)
=0.6*13.40%+0.4*8.8%*(1-40%) =10.15%

AT equity 0.50 and debt 0.50
Beta levered =1*(1+(1-40%)*0.50/0.50)=1.60
Cost of equity =Risk Free Rate+Beta levered*(Market return -risk free rate) =5%+1.60*6% =14.60%
WACC =Weight of Equity *Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)
=0.5*14.60%+0.5*9.6%*(1-40%) =10.18%

AT equity 0.90 and debt 0.10
Beta levered =1*(1+(1-40%)*0.10/0.90)=1.0667
Cost of equity =Risk Free Rate+Beta levered*(Market return -risk free rate) =5%+1.0667*6% =11.40%
WACC =Weight of Equity *Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)
=0.9*11.40%+0.1*7%*(1-40%) =10.68%

AT equity 0.70 and debt 0.30
Beta levered =1*(1+(1-40%)*0.30/0.70)=1.25714
Cost of equity =Risk Free Rate+Beta levered*(Market return -risk free rate) =5%+1.25714*6% =12.5428%
WACC =Weight of Equity *Cost of Equity+Weight of Debt*Cost of Debt*(1-Tax Rate)
=0.70*12.5428%+0.30*8%*(1-40%) =10.22%

Based on above calculation it is clear that option b is correct.
option b w_c = 0.6; w_d = 0.4; WACC = 10.15%