Naylor\'s is an all equity firm with 60,000 shares of stock outstanding at a mar

Question

Naylor's is an all equity firm with 60,000 shares of stock outstanding at a market price of $50 a share. The company has earnings before interest and taxes of $87,000. Naylor's has decided to issue $750,000 of debt at 7.5 percent. The debt will be used to repurchase shares of the outstanding stock. Currently, you own 500 shares of Naylor's stock. How many shares of Naylor's stock will you continue to own if you unlever this position? Assume you can loan out funds at 7.5 percent interest. Ignore taxes.

300 shares

350 shares

375 shares

425 shares

500 shares

Explanation / Answer

Ans=375 shares

Interest = $750,000 X0.075 = $56,250
Shares repurchased = $750,000/50 = 15,000
Shares outstanding with debt = 60,000 - 15,000 = 45,000
EPS, without debt = $87,000/60,000 = $1.45
EPS, with debt = ($87,000 - $56,250)/45,000 = $0.683333
The value of stock = 45,000 X50 = $2,250,000
The value of debt = $750k
The total value = $2,250,000 + $750,000 = $3,000,000
Naylor's weight stock = $2,250,000/$3,000,000 = 0.75
Naylor's weight debt = $750,000/$3,000,000 = 0.25
The initial investment = 500 X$50 = $25,000
The new stock position = 0.75X $25,000 = $18,750
New number of shares = $18,750/$50 = 375 shares

New loans = 0.25X $25,000 = $6,250
Unlevered income = 500X $1.45 = $725
Levered income = (375X $0.683333) + ($6,250X 0.075) = $725

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