Question

Suppose you buy 100 shares of stock XYZ at $10 a share with a margin of 50%. You also buy 200 shares of stock ABC at $50 a share with an 60% margin. You are very sure that, in six month, the price of the first stock would be $15 because you got insider information, but you are not so sure about the price of the second stock. Suppose you want to achieve a 20% return from your portfolio, then the price of the second stock needs to be at least how much to achieve that goal. (Assuming the broker charges you an 6% margin loan interest and the stocks pay no dividend)

Answer 1

Solution:-

Let the price of the stock have to be $X in order to generate a 20% return. Now, let's first calculate the investment made and the dollar return required.

Investment made in shares purchased= (100 shares*$10)*50% + (200 shares*$50)*60% = $6,500

$ return required= $6,500*20% = $1,300

Now, the required return of $1,300 is after the interest expense on borrowed money.

Interest payable= [(100 shares*$10)*(100%-50%) + (200 shares*$50)*(100%-60%)]*6% = $270

Thus, the gross return required for a net return of $1,300 is $1,570 (i.e. 1,300+270).

Expected dollar return from XYZ= ($15-$10)*100= $500

Required return from ABC= Total required return - Expected return from XYZ= $1,570-$500 = $1,070

In order to have a profit of $1,070 on ABC, the required price $X is calculated as follows:

($X-$50)*200 shares= $1,070

$X= $55.35

Thus, the required price is $55.35