Question

If Wild Widgets, Inc., were an all-equity company, it would have a beta of 1. The company has a target debt–equity ratio of .2. The expected return on the market portfolio is 10 percent, and Treasury bills currently yield 4.3 percent. The company has one bond issue outstanding that matures in 20 years and has a coupon rate of 7.6 percent. The bond currently sells for $1,110. The corporate tax rate is 34 percent.

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.)

  

Cost of debt

  

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.)

  

Cost of equity

  

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.)

  

WACC

Answer 1

Solution 1 - Company's cost of debt

Assume Face value of Bond = $1000 Sell price of bond = C*(PVIF, rn) + F*(PVIFA, rn) C = coupon payment = 7.6% = $76 Sell Price of Bond = $1110 F = Face value = $1000 n = Year = 20 r = 'x' (cost of debt) Equation = $1110 = $76*(PVIF, r, 20) + $1000*(PVIFA,r,20) Solving the equation, we get r = 6.6% (Cost of debt)

Solution 2 - Cost of Equity

Step 1 = Calculation of return on equity on unlevered beta

Ro = Rf + Bunlevered*(Rm - Rf) Ro = Let 'x' Rf = 4.3% (Treasury bill rate i.e. risk free rate) Rm = 10% (Market rate of portfolio) Bunlevered = 1 Equation - x = 4.3% + 1*(10% - 4.3%) x = 4.3% + 5.7% x = 10%

Step 2 - cost of Levered equity

Rs = Ro + D/E*(Ro - Rd)(1 - tax) Rs = Let 'x' cost of levered equity Ro = Cost of unlevered equity = 10% or 0.1 D/E = debt equity ratio = 0.2 Rd = cost ot debt = 6.6% or 0.066 Tax rate = 34% or 0.34 Equation = x = 0.1 + 0.2*(0.1 - 0.066)(1-0.34) x = 10.45%

Step 3 - Calculation of weighted average cost of capital

cost of debt for wacc calculation = cost of debt(1-tax rate)

= 6.6% (1-0.34)

= 4.356%

Debt equity Ratio = 0.2

let equity = x

debt + equity = 1.0

0.2x + x = 1.0

x = 1.0/1.2

Particulars	Cost	Weightage	Weighted average cost of capital
Equity	10.45%	1/1.2	8.71
Debt	4.356%	0.2/1.2	0.73
Total		1.00	9.44%