Question

1. Smith’s HVAC 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%. Smith’s 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 Smith's optimal capital structure, and what is the firm's cost of capital at this optimal capital structure?

Answer 1

Percent financed	Percent financed	Debt-to-equity	Bond	Before-tax	Post tax	Levered beta	Ke	WACC
with debt (wd)	with equity (wc)	ratio (D/S)	Rating	cost of debt	Cost of debt
0.1	0.9	0.10/0.90 = 0.11	AAA	7.00%	7%*(1-40%) = 4.20%	1*(1+(1-40%)*0.11) = 1.07	5%+(1.07*6%) = 11.42 %	(0.1*4.2%)+(0.9*11.42%) = 10.70%
0.2	0.8	0.20/0.80 = 0.25	AA	7.20%	7.2%*(1-40%) = 4.32%	1*(1+(1-40%)*0.25) = 1.15	5%+(1.15*6%) = 11.90%	(0.2*4.32%)+(0.8*11.9%) = 10.38%
0.3	0.7	0.30/0.70 = 0.43	A	8.00%	8%*(1-40%) = 4.80%	1*(1+(1-40%)*0.43) = 1.26	5%+(1.26*6%) = 12.56%	(0.3*4.8%)+(0.7*12.56%) = 10.23%
0.4	0.6	0.40/0.60 = 0.67	BBB	8.80%	8.8%*(1-40%) = 5.28%	1*(1+(1-40%)*0.67) = 1.40	5%+(1.4*6%) = 13.40%	(0.4*5.28%)+(0.6*13.4%) = 10.15%
0.5	0.5	0.50/0.50 = 1.00	BB	9.60%	9.6%*(1-40%) = 5.76%	1*(1+(1-40%)*1) = 1.60	5%+(1.6*6%) = 14.60%	(0.5*5.76%)+(0.5*14.6%) = 10.18%
Levered Beta = Unlevered Beta * [1 + (1 – Tax Rate) * (Debt / Equity)]
Answer : 40% debt & 60% equity is optimal capital structure with WACC 10.15%