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:

Market Debt- to-Value Ratio (wd)	Market Equity-to-Value Ratio (ws)	Market Debt- to-Equity Ratio (D/S)	Before-Tax Cost of Debt (rd)
0.0	1.0	0.00	6.0%
0.2	0.8	0.25	7.0
0.4	0.6	0.67*	8.0
0.6	0.4	1.50	9.0
0.8	0.2	4.00	10.0

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 7%, the market risk premium is 8%, 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 1. 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? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

Answer 1

Given,

Risk free rate= Rf=7%

risk premium = Rm=8%

Tax rate =T= 40%

beta =1

lets assume,

Re= cost of equity

Rd=cost of debt

rd= interest rate

formula to calculate cost of equity is as follows,

Re= Rf+beta*Rm

Re=7%+(1*8%)=15%

formula to calculate weighted average cost of capital (Wacc)as follows,

wacc = weight of debt * Rd + weight of equity * Re

wacc = D*Rd + E*Re

where Rd= cost of debt = interest rate * (1-tax rate) = rd*(1-T)

Let’s calculate Weighted average cost of capital for each possibilities.

1) D/E=0

D= 0 , E =1

as there no debt hence cost of equity becomes cost of capi

wacc= 15%

2)D=0.2,E=0.8

D/E=0.25

Rd=7%*(1-0.4)=7%*0.6=4.2%

wacc= 0.2*4.2% + 0.8*15%

wacc=12.84%

3)D=0.4, E=0.6

D/E=0.67

Rd=8%*(1-0.4)=4.8%

wacc=0.4*4.8% + 0.6*15%

wacc=10.92%

4) D=0.6, E=0.4

D/E=1.5

Rd=9%*(1-0.4)=5.4%

wacc= 0.6*5.4% + 0.4*15%

wacc= 9.24%

5) D=0.8,E=0.2

D/E=4

Rd=10%*(1-0.4) = 6%

wacc = 6%*0.8 + 15%*0.2

wacc= 7.80%

From the above options one can observe that minimum wacc is 7.80% with D/E = 4

hence optimal capital structure would be D= 0.8,  E=0.2 and wacc = 7.80%