Question

# Suppose you buy 100 shares of stock XYZ at \$10 a share with a margin of...

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)

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

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