Problem 16-11 WACC and Optimal Capital Structure F. Pierce Products Inc. is cons
ID: 2784259 • Letter: P
Question
Problem 16-11 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 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- Market Equity Market Debt- Before- to-Equity Tax Cost Ratio (wd) Ratio (ws) Ratio (D/S) of Debt to-Value to-Value (rd) 0.0 0.2 0.4 0.6 1.0 0.8 0.6 0.4 0.2 0.00 0.25 0.67 1.50 4.00 8.0 10.0 12.0 15.0 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 8%, and the company's tax rate is 35%. F Pierce estimates that its beta now (which is "unlevered" since it currently has no debt) is 1.35. Based on this information, what is the firm's optimal capital structure, and what would the weighted average cost of capital be at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places. DEBT EQUITY WACCExplanation / Answer
Beta unlevered=beta levered/(1+(1-t)*D/E)
So, beta levered=beta unlevered * (1+(1-t)*D/E)
Hence,
for D/E=0, beta=1.35
for D/E=0.25, beta=1.569375
for D/E=0.67, beta=1.935
for D/E=1.5, beta=2.66625
for D/E=4, beta=4.86
cost of equity=risk free+beta*market risk premium
Hence,
for D/E=0, cost of equity=5+1.35*8=15.80%
for D/E=0.25, cost of equity=5+1.569375*8=17.56%
for D/E=0.67, cost of equity=5+1.935*8=20.48%
for D/E=1.5, cost of equity=5+2.66625*8=26.33%
for D/E=4, cost of equity=5+4.86*8=43.88%
after tax-cost of debt=pre-tax cost of debt*(1-tax rate)
Hence,
for D/E=0, pre-tax cost of debt=7%..after tax cost of debt=7*(1-35%)=4.55%
for D/E=0.25, pre-tax cost of debt=8%....after tax cost of debt=8*(1-35%)=5.20%
for D/E=0.67, pre-tax cost of debt=10%..after tax cost of debt=10*(1-35%)=6.50%
for D/E=1.5, pre-tax cost of debt=12%..after tax cost of debt=12*(1-35%)=7.80%
for D/E=4, pre-tax cost of debt=15%..after tax cost of debt=15*(1-35%)=9.75%
proprtion of debt=(D/E)/(D/E+1)
proportion of equity=1-proportion of debt
Hence,
for D/E=0, proprtion of debt=0, proportion of equity=1
for D/E=0.25, proprtion of debt=0.2, proportion of equity=0.8
for D/E=0.67, proprtion of debt=0.4, proportion of equity=0.6
for D/E=1.5, proprtion of debt=0.6, proportion of equity=0.4
for D/E=4, proprtion of debt=0.8, proportion of equity=0.2
WACC=proportion of debt*after tax cost of debt+proportion of equity*cost of equity
Hence,
for D/E=0, WACC=0*4.55+1*15.8=15.8%
for D/E=0.25, WACC=0.2*5.2+0.8*17.56=15.088%
for D/E=0.67, WACC=0.4*6.5+0.6*20.48=14.888%
for D/E=1.5, WACC=0.6*7.8+0.4*26.33=15.212%
for D/E=4, WACC=0.8*9.75+0.2*43.88=16.576%
Hence, we see the optimal capital strucutre is D/E=0.67 because WACC is lowest at 0.67 D/E.
Proportion of debt=0.4=40%
Proportion of equity=0.6=60%
WACC=14.888%