Parker & Thomas, Inc., (P&T) currently is an all equity ﬁrm with 20,000 shares of stock outstanding at a market price of $40 a share. The company's earnings before interest and taxes are $50,000. The
ﬁrm's dividend payout ratio is 100%. P&T has decided to add leverage to its ﬁnancial operations by
Issuing $400,000 of debt at a 9% interest rate. This $400,000 will be used to repurchase shares of
Stock. You own 2,500 shares of P&T stock. You lend funds at a 9% rate of interest. How many of
Your shares of stock in P&T must you sell to offset the leverage that the ﬁrm is assuming? Assume
That you loan out all of the funds you receive from the sale of your stock.

Question

Quizplus · Accepted Answer

First, we need to find out the new market price of P&T's stock after repurchasing shares using the debt:

New Market Value of Equity = 20,000 shares x $40 = $800,000
New Debt issued = $400,000
Total Value of Firm = $1,200,000

Now, we can calculate the new EPS and DPS:

EBIT = $50,000
Interest = $400,000 x 9% = $36,000
EBT = $14,000
Taxes (40%) = $5,600
Net Income = $8,400

EPS = Net Income / No. of Shares
EPS = $8,400 / (20,000 - 2,500) = $0.47 per share

DPS = EPS x Payout Ratio
DPS = $0.47 x 100% = $0.47 per share

Next, we need to calculate the interest payments on the loan we made:

Interest Payment = $400,000 x 9% = $36,000

To offset this interest payment, we need to sell some of our shares to receive enough funds. The interest we receive will be used to pay the interest expense on the loan:

Interest Income = $36,000
Interest Expense = $36,000

Number of Shares to Sell = Interest Income / New EPS
Number of Shares to Sell = $36,000 / $0.47 = 76,595 shares

However, we only own 2,500 shares, so we can only sell all of our shares and purchase a portion of it back:

Amount Received from Sale = 2,500 shares x $40 per share = $100,000
Amount Needed to Repurchase = $36,000 / $40 per share = 900 shares

Number of Shares to Keep = 2,500 - 900 = 1,600 shares

Therefore, we need to sell 1,250 shares of P&T stock to offset the leverage that the firm is assuming.