A firm has 1 million shares trading at $36 and 10,000 bonds with $1000 par. The
ID: 2649670 • Letter: A
Question
A firm has 1 million shares trading at $36 and 10,000 bonds with $1000 par. The bonds have a
YTM of 10%, an 8% annual coupon rate paid semiannually, and 10 years until maturity. The firm has
EBIT of $9.8 million and pays all of its residual cashflow as dividends. Assume the earnings and
interest continue in perpetuity. The firm has a 40% tax rate. All-equity firms that are otherwise
similar have a cost of capital of 14%.
(a) What is the WACC?
(b) Suppose the firm refinances to have a D/E ratio of 0.5. What is the new cost of equity?
Explanation / Answer
(a) What is the WACC?
Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the semi annual period) = 10*2 = 20
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*8%*1/2 = 40
FV (indicates the face value) = 1000
Rate (indicates YTM) = 10%*1/2 = 5%
Bond Value = pv( 5%,20,40,1000)
Bond Value = $ 875.38
Market Value of Common Stock = 1Milion * 36 = $ 36 Million
Market Value of Bond = 10000*875.38 = $ 8.7538 Million
Weight of Common Stock = 36/44.7538
Weight of Debt = 8.7538/44.7538
Interest Expenses = 10000*8%*1000= 800000 = 0.8 Million
Cost of Equity = (EBIT - Interest Expenses)*(1-tax rate)/Market Value of Common Stock
Cost of Equity = (9.8 - 0.8)*(1-40%)/36
Cost of Equity = 15%
After tax cost of debt = 10*(1-40%) = 6%
WACC = Weight of Common Stock* Cost of Common Stock + Weight of Debt* After Tax cost of Debt
WACC = 36/44.7538*15 + 8.7538/44.7538*6
WACC = 13.24%
(b) Suppose the firm refinances to have a D/E ratio of 0.5. What is the new cost of equity?
Total Market value = 44.7538
After firm refinances
Debt Market Value = 44.7538 * 0.5/(1+0.5)
Debt Market Value = $ 14.9179 Million
Bond Face Value = 14.9179/875.38 *1000 = $ 17.04 Million
Interest Expenses = 17.04*8% = 1.3632 Million
Market Value of Common Stock = 44.7538 * 1/(1+0.5)
Market Value of Common Stock = 29.8358
New cost of equity= (EBIT - Interest Expenses)*(1-tax rate)/Market Value of Common Stock
New cost of equity = (9.8 - 1.3632)*(1-40%)/29.8358
New cost of equity = 16.97%
New cost of equity = 17% approx
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