Martin and Sons (M and S) currently is an all equity firm with 48,000 shares of

Question

Martin and Sons (M and S) currently is an all equity firm with 48,000 shares of stock outstanding at a market price of $30 a share. The company's earnings before interest and taxes are $82,000. M and S has decided to add leverage to their financial operations by issuing $570,000 of debt with a 8% percent interest rate. This $570,000 will be used to repurchase shares of stock. You own 1,200 shares of M and S stock. You also loan out funds at a 8% percent rate of interest. How many of your shares of stock in M and S 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.

513 shares

505 shares

437 shares

475 shares

483 shares

Martin and Sons (M and S) currently is an all equity firm with 48,000 shares of stock outstanding at a market price of $30 a share. The company's earnings before interest and taxes are $82,000. M and S has decided to add leverage to their financial operations by issuing $570,000 of debt with a 8% percent interest rate. This $570,000 will be used to repurchase shares of stock. You own 1,200 shares of M and S stock. You also loan out funds at a 8% percent rate of interest. How many of your shares of stock in M and S 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.

Explanation / Answer

Let x be the final number of shares with him and thus 1000-x be the shares sold which would be loaned out at 7%

As no taxes, EPS before leverage=82000/48000=1.7083333
Earnings after leverage=82000-570000*8%=36400
Number of shares after leverage=48000-570000/30=29000
EPS after leverage=36400/29000=1.255172

So,
To offset leverage, Earnings to him before leverage must equal to earnings after leverage
Hence,

1.7083333*1200=x*1.255172+(1200-x)*30*8%
=>2050=x*1.255172+2880-2.4x
=>x*1.14483=2880-2050
=>x=830/1.14483
=>x=725
So,
you will sell 1000-725=475 shares to offset the leverage

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