Naylor's is an all-equity firm with 48,000 shares of stock outstanding at a market price of $25 a share. The company has earnings before interest and taxes of $87,000. Naylor's has decided to issue $400,000 of debt at 7.3 percent and use the proceeds to repurchase shares. Currently, Angela owns 600 shares of Naylor's stock. How many shares of this stock will she continue to own if she unlevers this position? Assume she can loan out funds at 7.3 percent interest. Ignore taxes.

The number shares of this stock Angela will continue to own if she unlevers this position is 400 shares.

Explanation:

This can be calculated as follows:

Naylor's value of debt = $400,000

Naylor's interest on debt = Naylor's value of debt * Interest rate = $400,000 * 7.3% = $29,200

Naylor's shares repurchased = Debt / Price per share = $400,000 / $25 = 16,000

Naylor's shares outstanding with debt = Shares outstanding without debt -  Naylor's shares repurchased = 48,000 - 16,000 = 32,000

Naylor's EPS without debt = Earnings before interest and taxes / Shares outstanding without debt = $87,000/48,000 = $1.8125

Naylor's EPS with debt = (Earnings before interest and taxes - Naylor's interest on debt) / Naylor's shares outstanding with debt = ($87,000 - $29,200)/32,000 = $1.80625

Naylor's value of stock after issuing debt = Naylor's shares outstanding with debt * Price per share = 32,000 * $25 = $800,000

Naylor's total value with debt = Naylor's value of stock after issuing debt + Naylor's value of debt = $800,000 + $400,000 = $1,200,000

Naylor's weight of stock = Naylor's value of stock after issuing debt / Naylor's total value with debt =  $800,000/$1,200,000 = 0.666666666666667

Naylor's weight debt = Naylor's value of debt / Naylor's total value with debt = $400,000/$1,200,000 = 0.333333333333333

Angela’s initial investment = Angela's initial number of shares * Price per share = = 600 * $25 = $15,000

Angela’s new stock position = Naylor's weight of stock * Angela’s initial investment = 0.666666666666667 * $15,000 = $10,000

Angela’s new number of shares = Angela’s new stock position / Price per share = $10,000 / $25 = 400

Therefore, the number shares of this stock Angela will continue to own if she unlevers this position is 400 shares.

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