Question

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

F. Pierce uses the CAPM to estimate its cost of common equity, rs and at the time of the analysis the risk-free rate is 5%, the market risk premium is 6%, and the company's tax rate is 40%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 0.8. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure?

 

 

Answer 1

Tax rate = 40% rRF = 5.0%

bU = 0.8 rM - rRF = 6.0%

 

From data given in the problem and table we can develop the following table:

 

wd	wce	D/S	rd	rd(1 - T)	Levered betaa	rsb	WACCc
0	100%	0.00	6.0%	3.60%	0.80	9.80%	9.80%
0.2	80%	0.25	7.0%	4.20%	0.92	10.52%	9.26%
0.4	60%	0.67	8.0%	4.80%	1.12	11.72%	8.95%
0.6	40%	1.50	9.0%	5.40%	1.52	14.12%	8.89%
0.8	20%	4.00	10.0%	6.00%	2.72	21.32%	9.06%

 

Notes:

a These beta estimates were calculated using the Hamada equation,

b = bU[1 + (1 - T)(D/S)].

b These rs estimates were calculated using the CAPM, rs = rRF + (rM - rRF)b.

c These WACC estimates were calculated with the following equation:

WACC = wd(rd)(1 - T) + (wce)(rs).

 

 

The firm's optimal capital structure is that capital structure which minimizes the firm's WACC. The WACC is minimized at a capital structure consisting of 60% debt and 40% equity. At that capital structure, the firm's WACC is 8.89%.