Question

Thorpe and Company is currently an​ all-equity firm. It has three million shares selling for ​$32 per share. Its beta is 0.8​, and the current​ risk-free rate is 2.1​%. The expected return on the market for the coming year is 9.1​%. Thorpe will sell corporate bonds for ​$32,000,000 and retire common stock with the proceeds. The bonds are​ twenty-year semiannual bonds with a 9.4​%coupon rate and ​$1,000 par value. The bonds are currently selling for ​$893.61 per bond. When the bonds are​ sold, the beta of the company will increase to 1.3 What was the WACC of Thorpe and Company before the bond​ sale? What is the adjusted WACC of Thorpe and Company after the bond sale if the corporate tax rate is 15%​? Hint​: The weight of equity before selling the bond is​ 100%.

Answer 1

Before the Bond Sale;

Before the sale of bonds the WACC is the cost of equity:

Re = Rf + [Beta * (Expected Market Return - Rf)]

= 2.1% + [0.8 * (9.1% - 2.1%)] = 2.1% + [0.8 * 7%] = 2.1% + 5.6% = 7.7%

This is the adjusted WACC before the bond sale.

After the Bond Sale;

New Re = Rf + [Beta * (Expected Market Return - Rf)]

= 2.1% + [1.3 * (9.1% - 2.1%)] = 2.1% + [1.3 * 7%] = 2.1% + 9.1% = 11.2%

No. of shares sold = Amount of Debt / Current Stock Price = $32,000,000 / $32 = 1,000,000

Market Value of Equity = Current Stock Price * No. of shares outstanding

= $32 * 2,000,000 = $64,000,000

Market Value of Debt = $32,000,000

Total Market Value = Market Value of Debt + Market Value of Equity

= $32,000,000 + $64,000,000 = $96,000,000

To find the cost of debt, we need to put the following values in the financial calculator:

N = 20*2 = 40;

PV = -893.61;

PMT = (9.4%/2)*1000 = 47;

FV = 1000;

Press CPT, then I/Y, which gives us 5.35

Periodic Rate = 5.35%

So, YTM = Periodic Rate * No. of compounding periods in a year

= 5.35% * 2 = 10.70%

Adjusted WACC = [wD * kD * (1 - t)] + [wE * kE]

= [(32/96) * 10.70% * (1 - 0.15)] + [(64/96) * 11.2%]

= 3.03% + 7.47% = 10.50%