Joe and Co., an online options broker, is an all equity firm with 60,000 shares

Question

Joe and Co., an online options broker, 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. Joe and Co. 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 their stock. How many shares of stock will you continue to own if you unlever this position? Assume you can loan out funds at 7.5 percent interest. Ignore taxes.

Explanation / Answer

Naylor's interest = $750,000 0.075 = $56,250
Naylor's shares repurchased = $750,000/$50 = 15,000
Naylor's shares outstanding with debt = 60,000 - 15,000 = 45,000
Naylor's EPS, no debt = $87,000/60,000 = $1.45
Naylor's EPS, with debt = ($87,000 - $56,250)/45,000 = $0.683333
Naylor's value of stock = 45,000 $50 = $2,250,000
Naylor's value of debt = $750k
Naylor's 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
Your initial investment = 500 $50 = $25,000
Your new stock position = 0.75 $25,000 = $18,750
Your new number of shares = $18,750/$50 = 375 shares
Check:
Your new loans = 0.25 $25,000 = $6,250
Your unlevered income = 500 $1.45 = $725
Your levered income = (375 $0.683333) + ($6,250 0.075) = $725Naylor's interest = $750,000 0.075 = $56,250
Naylor's shares repurchased = $750,000/$50 = 15,000
Naylor's shares outstanding with debt = 60,000 - 15,000 = 45,000
Naylor's EPS, no debt = $87,000/60,000 = $1.45
Naylor's EPS, with debt = ($87,000 - $56,250)/45,000 = $0.683333
Naylor's value of stock = 45,000 $50 = $2,250,000
Naylor's value of debt = $750k
Naylor's 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
Your initial investment = 500 $50 = $25,000
Your new stock position = 0.75 $25,000 = $18,750
Your new number of shares = $18,750/$50 = 375 shares

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