Question

Part A: You make a cash purchase of 100 shares of a stock at $55 per share. You hold the stock for one year, during which dividends of $5 a share are distributed. Commissions are 2 percent of the value of a purchase or sale.

Assume all of the same conditions of the transaction as in part a (i.e. stock purchase price, dividends, commission) but now you make the purchase using margin. If the Margin Requirement is 60% and the interest rate on borrowed funds is 10%, what is your percentage earned at the following prices:

1. $60

2. $70

Answer 1

Initial margin = 5500 * 0.60 = 3300

commission on purchase = 5500 * 0.02 = 110

initial investment = 3300 + 110 = 3410

interest paid on borrowed funds (2200) = 2200 * 0.10 = 220

Dividend received = 5 * 100 = 500

1. Price of the stock is $60

Capital gain at the end of the year = (60 - 55) * 100 = 500

return at the end of the year = (Capital gain + Dividend received - interest paid for borrowed funds) / Initial investment

= (500 + 500 - 220) / 3410

= (780) / 3410

= 22.87%

2. Price of the stock is $70

Capital gain at the end of the year = (70 - 55) * 100 = 1500

return at the end of the year = (Capital gain + Dividend received - interest paid for borrowed funds) / Initial investment

= (1500 + 500 - 220) / 3410

= (1780) / 3410

= 52.2%

* In the first case when there was no margin used the return percentage would have been 17.83% [Gain = 1000 / initial investment = 5610 (5500 + 110 Commission)].