Miller's Dry Goods is an all equity firm with 45,000 shares of stock outstanding at a market price of $50 a share. The company's earnings before interest and taxes are $128,000. Miller's has decided to add leverage to its financial operations by issuing $250,000 of debt at 8 percent interest. The debt will be used to repurchase shares of stock. You own 400 shares of Miller's stock. You also loan out funds at 8 percent interest. How many shares of Miller's stock must you sell to offset the leverage that Miller's is assuming? Assume you loan out all of the funds you receive from the sale of stock. Ignore taxes.

Question

Quizplus · Accepted Answer

Miller's interest = $250,000 F1F1F1S1F1F1F10 0.08 = $20,000Miller's shares repurchased = $250,000/$50 = 5,000Miller's shares outstanding with debt = 45,000 - 5,000 = 40,000Miller's EPS, no debt = $128,000/45,000 = $2.844444Miller's EPS, with debt = ($128,000 - $20,000)/40,000 = $2.70Miller's value of stock = 40,000 F1F1F1S1F1F1F10 $50 = $2,000,000Miller's value of debt = $250,000Miller's total value = $2,000,000 + $250,000 = $2,250,000Miller's weight stock = $2,000,000/$2,250,000 = 0.888889Miller's weight debt = $250,000/$2,250,000 = 0.111111Your initial investment = 400 F1F1F1S1F1F1F10 $50 = $20,000Your new stock position = 0.888889 F1F1F1S1F1F1F10 $20,000 = $17,777.78Your new number of shares = $17,777.78/$50 = 355.5556Number of shares sold = 400 - 355.5556 = 44.4 sharesCheck:Your new loans = 0.111111 F1F1F1S1F1F1F10 $20,000 = $2,222.22Your total unlevered income = 400 F1F1F1S1F1F1F10 $2.844444 = $1,137.78Your total levered income = (355.5556 F1F1F1S1F1F1F10 $2.70) + ($2,222.22 F1F1F1S1F1F1F10 0.08) = $1,137.78

Miller's Dry Goods Is an All Equity Firm with 45,000