You currently own 250 shares of Pluto, Inc. Pluto is an all equity ﬁrm that has 36,000 shares of stock outstanding at a market price of $25 a share. The company's earnings before interest and taxes are
$48,000. Pluto, Inc. has decided to issue $200,000 of debt at a 9% rate of interest. This debt will be
Used to repurchase shares of stock. How many shares of Pluto, Inc. stock must you sell to unlever
Your position if you can lend out funds at a 9% rate of interest?
A) 43 shares
B) 51 shares
C) 56 shares
D) 64 shares
E) 72 shares

Question

Quizplus · Accepted Answer

First, we need to calculate the current market value of Pluto, Inc.

Market Value of Pluto, Inc. = 36,000 x $25 = $900,000

Next, we need to calculate the new capital structure of the company after the debt issue:

Value of Debt = $200,000 
Value of Equity = $900,000 - $200,000 = $700,000

After the debt issue, the company will have 36,000 shares outstanding and $700,000 in equity. Therefore, the price per share will be:

Price per Share = $700,000 / 36,000 = $19.44

Now, we need to figure out how many shares we need to sell to achieve an unlevered position. We know that we can lend out funds at a 9% rate of interest, which is the same as the interest rate on the debt. Therefore, we want to sell enough shares such that the proceeds from the sale (at $19.44 per share) are equal to $200,000.

Shares to Sell = $200,000 / $19.44 = 10,280 shares

Therefore, we must sell:

Total Shares to Sell = 10,280 + 250 = 10,530 shares

To find out how many shares we must sell from our original position of 250 shares, we subtract the number of shares we need to hold in the unlevered position from our original position:

Shares to Sell from Original Position = 250 - 10,530 = -10,280

Since we cannot sell a negative number of shares, we must round up to the nearest whole number, which gives us:

Shares to Sell from Original Position = 11,530

Finally, to find the number of shares we must sell, we subtract our original position from the number of shares we need to hold in the unlevered position:

Shares to Sell = 11,530 - 250 = 11,280

Therefore, the answer is (C) 56 shares.

You Currently Own 250 Shares of Pluto, Inc