Question

R&F Enterprises is an all equity firm with 70,000 shares of stock outstanding at a market price of $8 a share. The company has earnings before interest and taxes of $42,000. R&F decides to issue $200,000 of debt at a 7 percent rate of interest. The $200,000 will be used to repurchase shares of the outstanding stock. Currently, you own 1,500 shares of R&F stock A) How many shares of this stock must you sell to unlevered your position if you can loan out funds at a 7 percent rate of interest? B) Show that your total unlevered income will be the same as your levered income
how to solve this ?

Answer 1

Value of unlevered firm = number of shares*price per share = 70,000*8 = 560,000

Earnings per share = EBIT/number of shares = 42,000/70,000 = 0.60

Cash flow for the shareholder = 1,500*0.60 = 900

Now, 200,000 of debt is issued which is used to buy back shares.

Number of shares bought back = 200,000/8 = 25,000

Number of shares left = 70,000 - 25,000 = 45,000

Now, Earnings for the firm will be: 42,000 - interest expense = 42,000 - (7%*200,000) = 42,000 - 14,000 = 28,000

New EPS (with levered capital structure) = 28,000/45,000 = 0.62

Cash flow for the shareholder = 1,500*0.62 = 933.33

Now, to replicate the levered capital structure, the shareholder must also hold debt and equity in the same ratio as the firm:

Debt ratio = 200,000/value of the firm = 200,000/560,000 = 35.71%

So, the shareholder must sell 35.71% of the shares held which is 35.71%*1,500 = 535.71

The amount gained = 535.71* share price = 535.71*8 = 4,285.71

This amount should be lent at an interest rate of 7%, so interest income will be 7%*4,285.71 = 300

On the remaining shares, the shareholder will still get dividends so total dividend income will be

0.62*(1,500-535.71) = 600

Total cash flow = 300 + 600 = 900

This is the same cash flow which the shareholder was getting when the firm was unlevered.