Question

WACC and Optimal Capital Structure

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 35%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1.2. 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

F. Pierce uses the CAPM to estimate its cost of common equity (rs).

• The company estimates that at the time of analysis, the risk-free rate = r = 7%
• The Market risk premium = Rp = 8%
• And beta, β = 1.2

Cost of common equity is calculated using following formula

rs = r + β x Rp

= 0.07 + 1.2 x 0.08

= 0.07 + 0.096 = 0.166

As we use more debt source of fund, β will increase, due to increased risk. Thus,

Beta ( Levered ) = Beta (Unlevered) x [1 + ( 1 - Tax) x Debt equity ratio]

To calculate, WACC following formula will be used

WACC = We * Ke + Wd * Kd

where,

• We is the weight of equity in capital structure = Equity as a % of capital
• Wd is the weight of debt in capital structure = Debt as a % of capital
• Ke is the cost of equity
• Kd is the cost of debt ( after tax)
• The company's tax rate = T = 35%

Market Debt- to-Value Ratio (wd)	Market Equity-to-Value Ratio (ws)	DER	Before-Tax Cost of Debt (rd)	After Tax Cost of Debt (rd)*(1-T)	Beta (Levered)	Cost of equity (ke)	Weighted Average cost of capital
A	B	C	D	E = [D*(1-T)] * 100	F = β*[1+(1-35%) DER]	G = r+F*Rp	H = (A * E) + (B * G)* 100
0.0	1.0	0.0	6.00%	3.90%	1.2	16.60%	16.60%
0.2	0.8	0.25	7.00%	4.55%	1.395	18.16%	15.40%
0.4	0.6	0.67	8.00%	5.20%	1.723	20.78%	14.50%
0.6	0.4	1.5	9.00%	5.85%	2.37	25.96%	13.80%
0.8	0.2	4.0	10.00%	6.50%	4.32	41.56%	13.51%

Optimal debt-equity combination for the firm is minimum when debt as a % of capital is 80% and WACC = 13.51%. Thus, debt as a % of capital = 80%, WACC = 13.51% is the optimum debt equity combination for the firm.