Question

Adjusted WACC. Thorpe and Company is currently an​ all-equity firm. It has three million shares selling for $40 per share. Its beta is 1.4​, and the current​ risk-free rate is 3.5​%. The expected return on the market for the coming year is 13.4​%. Thorpe will sell corporate bonds for $40,000,000 and retire common stock with the proceeds. The bonds are​ twenty-year semiannual bonds with a 8.6​% coupon rate and ​$1,000 par value. The bonds are currently selling for ​$1,135.64 per bond. When the bonds are​ sold, the beta of the company will increase to 1.9.

1. What was the WACC of Thorpe and Company before the bond​ sale?

2. What is the adjusted WACC of Thorpe and Company after the bond sale if the corporate tax rate is 20%​? Hint​: The weight of equity before selling the bond is​ 100%.

Answer 1

1

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 3.5 + 1.4 * (13.4 - 3.5)

Expected return% = 17.36 =WACC for all equity firm

2

As per CAPM

expected return = risk-free rate + beta * (expected return on the market - risk-free rate)

Expected return% = 3.5 + 1.9 * (13.4 - 3.5)

Expected return% = 22.31 = cost of equity

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

1135.64 =∑ [(8.6*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^20x2

k=1

YTM% = 7.3 = cost of debt

All equity amount of equity = price*shares= 3000000*40=120000000

Equity after repurchase using debt =120000000-40000000=8000000

D/E = 4000000/8000000 = 0.5

D/A = D/(E+D)

D/A = 0.5/(1+0.5)

=0.3333

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

After tax cost of debt = 7.3*(1-0.2)

= 5.84

Weight of equity = 1-D/A

Weight of equity = 1-0.3333

W(E)=0.6667

Weight of debt = D/A

Weight of debt = 0.3333

W(D)=0.3333

WACC=after tax cost of debt*W(D)+cost of equity*W(E)

WACC=5.84*0.3333+22.31*0.6667

WACC% = 16.82