Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1.05. The company has a target debt–equity ratio of .4. The expected return on the market portfolio is 12 percent, and Treasury bills currently yield 4.4 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 7.8 percent. The bond currently sells for $1,120. The corporate tax rate is 40 percent. What is the company’s cost of debt? What is the company’s cost of equity? What is the company’s weighted average cost of capital?

Answer 1

Levered beta = unlevered beta * (1 + (1 - tax rate) * (debt / equity))

Levered beta = 1.05 * (1 + (1 - 40%) * (0.4))

Levered beta = 1.302

cost of equity = risk free rate + (beta * (expected market return - risk free rate))

cost of equity = 4.4% + (1.302 * (12% - 4.4%))

cost of equity = 14.2952%

cost of debt = YTM of bond * (1 - tax rate)

YTM is calculated using RATE function in Excel with these inputs :

nper = 20 (20 years to maturity with 1 annual coupon payment each year)

pmt = 1000 * 7.8% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1120 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 6.6941%. This is the YTM.

cost of debt = YTM * (1 - tax rate)

cost of debt = 6.6941% * (1 - 40%) ==> 4.0164%

Weight of debt = debt / (debt + equity) = 0.4 / (0.4 + 1) = (0.4 / 1.4)

Weight of equity = equity / (debt + equity) = 1 / (0.4 + 1) = (1 / 1.4)

WACC = (weight of debt * cost of debt) + (weight of equity * cost of equity)

WACC = ((0.4 / 1.4) * 4.0164%) + ((1 / 1.4) * 14.2952%)

WACC = 11.36%