Question

You purchased 900 shares of TTB at $98.03 per shares on your margin, which as an initial margin of 55% (or 0.55 ). Your objective is to make a Holding Period Return of 20% (or 0.20 ). At what price per share will you get to your goal and sell your shares? (neglect any interest paid on your loan.)

Answer 1

To achieve a 20% Holding Period Return on an initial margin investment of 55% for 900 shares purchased at $98.03 each, you need to sell the shares at $64.70 per share.

Step-by-step explanation:

To reach a Holding Period Return of 20%, you must calculate the future price per share that will give you this return on your investment. Since you've invested with a 55% margin, you effectively paid 55% of the total investment, and the rest was borrowed. The purchase price of TTB shares was $98.03 per share.

Your total investment in buying 900 shares is 900 shares × $98.03 per share = $88,227. To find out the price at which you should sell your shares to achieve a 20% return on your initial margin, you need to calculate the amount that represents a 20% increase over your initial investment, which is 55% of $88,227.

The initial margin is 55% × $88,227 = $48,524.85. A 20% increase on $48,524.85 is $48,524.85 × 20% = $9,704.97. Therefore, the total amount you should aim to receive from the sale is $48,524.85 + $9,704.97 = $58,229.82.

To find the selling price per share, divide the total amount by the number of shares: $58,229.82 ÷ 900 shares = $64.70 per share. Therefore, to achieve a 20% Holding Period Return on your investment, you need to sell your shares at $64.70 per share.

Answer 2

To achieve a 20% Holding Period Return on 900 shares purchased at $98.03 per share with a 55% initial margin, the student would need to sell the shares at approximately $64.70 per share.

Step-by-step explanation:

To calculate the price per share required to achieve a Holding Period Return (HPR) of 20%, we must first determine the total amount invested initially and then calculate the total future value (FV) which will reflect a 20% increase in the investment's value.

The initial investment is calculated as:

Number of shares × Purchase price per share

900 × $98.03 = $88,227

The total investment made using the investor's own money, given a 55% initial margin, is:

Initial Investment × Initial Margin

$88,227 × 0.55 = $48,524.85

The desired future value, reflecting a 20% HPR, is:

Initial Investment × (1 + HPR)

$48,524.85 × (1 + 0.20) = $58,229.82

To find the needed selling price per share, we divide the future value by the number of shares:

FV / Number of shares

$58,229.82 / 900 = approximately $64.70

Therefore, the student will need to sell the shares at approximately $64.70 per share to achieve a 20% holding period return, assuming no interest is paid on the margin loan.