Question

7) Steinway has expected earnings before interest and taxes of $1,360,000, an unlevered cost of capital of 9.8 percent, and a tax rate of 25 percent. The company has $1,200,000 of debt that carries a 6.4 percent coupon. The debt is selling at par value. Assume the firm maintains this debt amount forever. What is the interest tax shield of the firm in a given year? What is the value of the firm?

A)$18,900 and $10,475,216

B)$18,600 and $10,475,216

C)$18,600 and $11,328,410

D)$19,200 and $11,328,410

E)$19,200 and $10,708,163

8)Yankee Company is currently an all equity firm. Its current cost of equity is 10.4 percent and the tax rate is 25 percent. The firm has 1,700,000 shares of stock outstanding with a market price of $46 a share. The firm is considering capital restructuring that allows $12 million of debt with a coupon rate of 6.4 percent. The debt will be sold at par value and the proceeds will be used to repurchase shares. What is the value per share after the recapitalization? (Hint: You need to determine the total value of equity after recapitalization that accounts for the PV of interest tax shield and the number of shares outstanding after repurchased)

A)$49.27

B)$48.08

C)$47.15

D)$46.50

E)$50.33

Answer 1

7) As the debt sells at par. So Face value of debt = Total debt or market value of debt = $1200000

We know that if debt is selling at par then coupon rate will equal to yield to maturity or cost of debt

Interest tax shield = Total debt x cost of debt x tax rate = 1200000 x 6.4% x 25% = 19200

So interest tax shield = $19200.

Perpetual Unlevered cash flow = Expected or next year EBIT(1-tax rate) = 1360000(1-25%) = 1360000 x 75% = 1020000

We know the Value of a firm = Value of unlevered firm + Present value of interest tax shield

Unlevered cash flow form a perpetuity, Present value of perpetuity = cash flow / discount

Value of unlevered firm = Present value of unlevered cash flow discounted at unlevered cost of capital =Perpetual unlevered cash flow / Unlevered cost of capital = 1020000 / 9.8% = 10408163.2653

As debt is constant, so so interest tax shield is perpetual

Present value of interest tax shield = Interest tax shield / Cost of debt = 19200 / 6.4% = 300000

Value of firm = 10408163.2653 + 300000 = 10708163.2653 = 10708163 (rounded to nearest dollar)

Value of firm = $10708163

Answer: E) $19200,$10708163

8) Since before recapitalization firm in unlevered

So Value of firm = Value of unlevered firm = No of shares x price per share = 1700000 x 46 =$78200000

After recapitalization

As the debt sells at par. So Face value of debt = Total debt or market value of debt = $12000000

We know that if debt is selling at par then coupon rate will equal to yield to maturity or cost of debt

Interest tax shield = Total debt x cost of debt x tax rate = 1200000 x 6.4% x 25% = 192000

So interest tax shield = $192000

As debt is constant, so so interest tax shield is perpetual

Present value of interest tax shield = Interest tax shield / Cost of debt = 192000 / 6.4% = 3000000

Value of firm = Value of unlevered firm + Present value of interest tax shield = 78200000 + 3000000 = 81200000

Value of equity = Value of firm - Total debt = 81200000 - 12000000 = $69200000

Equity repurchased = Total debt = 12000000

No of shares repurchased = Equity repurchased / Price per share = 12000000 / 46 = 260869.56 = 260870 (rounded to next number as shares cannot be in decimal)

No of shares outstanding after repurchase = No of shares outstanding before repurchase - No of shares repurchased =1700000 - 260870 = 1439130

Price per share after recapitalization = Value of equity / No of shares after repurchase = 69200000 / 1439130 = 48.0846 = 48.08

Answer: B) $48.08