Question

Voltaire Steel is a highlevered company with 20 million shares, trading at $10/share and $800 million in debt (in market and book value terms) outstanding. The pre-tax cost of debt for the company is 10%, the marginal tax rate is 40% and the levered beta for the company is 3.06. The risk free rate is 3% and the equity risk premium is 5%.

a. Estimate the cost of capital for the company. (1 point)

b. A bondholder in the firm is willing to accept 20 million newly issued shares in the company in exchange for $200 million in debt (which will be retired). This transaction will raise the company’s bond rating to BBB and lower their pre-tax cost of debt to 7.5%. Estimate the new cost of capital, if you go through with the swap. (2 points)

c. Assuming that you go through with the swap of equity for debt (from part b), estimate the value per share after the transaction. (You can assume that the firm is in perpetual growth, growing 2% a year forever) ( 3 points)

Answer 1

market value of equity (Ve) = $10*20m = $200 million

market value of debt (Vd) = $800m

a. Weighted average cost of capital formula = (Vd/(Vd+Ve)*pertax cost of debt*(1-tax rate)) + (Ve/(Vd+Ve)*cost of equity*(1-tax rate))

cost of equity = risk free rate + beta*(equity risk premium) = 3% + 3.06*5% = 18.3%

Putting the values in the above formula

Cost of capital = 8.5%

b. New Market value of equity after issuance of 20m new shares = $10*20m + $200m= $400m

New Market Value of Debt = $800m-$200m = $600m

Hence Vd = $600m/($600m+$400m) = 60%

Similarly Ve = 40%

So new cost of capital = 10.0%

c. Market Value of Equity = $400m (calculated in b)

WACC = 10.0%

g = 2%

Debt =$600m

Market Value of the firm = $600m + $400m =$1000m

Hence, Market Value of firm assuming Perpetual Growth of 2% = 1000*(1+2%)/(10%-2%) = $12750m

Market Value of Equity = $12750m - $600m = $12150m

Per Share Value = $12150m/40m = $303.75