Question

Problem 18-4 WACC If Wild Widgets, Inc., were an all-equity company, it would have a beta of .95. The company has a target debt-equity ratio of .50. The expected return on the market portfolio is 12 percent and Treasury bills currently yield 3.1 percent. The company has one bond issue outstanding that matures in 25 years, a par value of $1,000, and a coupon rate of 6 percent. The bond currently sells for $1,050. The corporate tax rate is 23 percent. a. What is the company's cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) b. What is the company's cost of equity? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. What is the company's weighted average cost of capital? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) a. Cost of debt b. Cost of equity c. WACC

Answer 1

Solution:
a.	Cost of debt	5.63	%
b.	Cost of equity	14.81	%
c.	WACC	11.32	%
Working Notes:
	Given beta is for all equity firm means unlevered firm , and we need to calculate WACC means in which there will both debt and equity i.e. levered firm so we should also get levered beta value to compute cost of equity and WACC.
	We calculate Levered beta using Hamada Equation
	B levered = ( 1 + ( 1- tax rate) (debt/equity)) x B unlevered
	B levered = ( 1 + ( 1- 0.23) (0.50)) x 0.95
	B levered = ( 1 + (0.77 x 0.50)) x 0.95
	B levered = ( 1 + 0.385) x 0.95
	B levered = 1.31575
	Hence Levered Beta of the is 1.31575
a.	Cost of debt
	Since details of the bond paying coupon semi annual or annual , we go with general assumption of semi annual coupon paying bond.
	As the bond is paying coupon semi annually , its Ytm can be calculated by Excel or financial calculator
	First we get the semi annual YTM
	No. of period = years to maturity x no. of coupon in a year = 25 x 2 =nper = N = 50
	Face value of bond = FV= $1,000
	Price of the bond = PV = -$1050
	Semi-annual Coupon amount = PMT = coupon rate x face value/2 = 6% x $1,000 /2= $30
	For calculation YTM by excel
	type above data in below format
	=RATE(N,pmt,PV,FV)
	=RATE(50,30,-1050,1000)
	2.8125328%
	=2.8125328%
	The YTM calculated is semi annual
	YTM annual = Semi annual YTM x 2
	YTM annual = 2.8125328% x 2
	YTM annual = 5.6250655154%
	Current YTM of the bond is 5.6250655154%
Hence	Company's cost of debt                  5.63%
b.	Cost of Equity                                        14.81%
	For computation of cost of Equity given details suggest to go for CAPM Method
	Levered Beta (B) = 1.31575 computed above
	Cost of Equity Ke= ??
	rf= risk free rate = 3.1%
	Market rate of return   rm = 12%
	As per CAPM
	Cost of equity Ke = rf +(rm -rf) x B
	Cost of equity Ke = 3.1% + (12% -3.1%) x 1.31575
	Cost of equity Ke = 3.1% + 8.9% x 1.31575
	Cost of equity Ke = 3.1% + 11.710175%
	Cost of equity Ke = 14.810175%
C.	WACC
	Debt equity ratio = 0.50
	Weight of Debt     D/V= 0.50 / (1 +0.50) =0.3333333
	Weight of Equity    E/V= 1 / (1 + 0.50) =1/1.5 = 0.66667
	WACC = (E/V)Ke + (D/V) (1 –Tax rate) Kd
	Cost of equity (Ke) =14.810175%
	Cost of debt (Kd) = 5.6250655154%
	tax rate = 23%
	WACC = (E/V)Ke + (D/V) (1 –Tax rate) Kd
	WACC = (1 / (1 + 0.50)) x 14.810175% + (0.50 / (1 +0.50) ) (1 -0.23) x 5.6250655154%
	WACC = 9.87345% + 1.44377%
	WACC =11.31722%
	WACC =11.32%
Please feel free to ask if anything about above solution in comment section of the question.