Question

7

A) Suppose you buy stock at a price of $82 per share. Three months later, you sell it for $88. You also received a dividend of $0.50 per share. What is your annualized return on this investment? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

B) You just sold short 950 shares of Wetscope, Inc., a fledgling software firm, at $72 per share. You cover your short when the price hits $66.00 per share one year later. If the company paid $0.46 per share in dividends over this period, what is your rate of return on the investment? Assume an initial margin of 55 percent. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Rate of return:

Answer 1

A) Purchase value per share = $82

Period of holding = 3 months

Sale Proceeds per share = $88

Dividend per share = $0.50

Return on investment per 3 months = (Sale Proceeds + Dividend - Purchase Cost) / Purchase Cost

= ($88 +$0.5 - $82 / $82) = 7.927% per 3 months/quarter

Annualized Return = (1+r)n -1 where r is the rate of return per period and  n is the number of periods in a year(i.e 4 quarters) = (1+7.927%)4 - 1 = 35.68%

B) This is the case of Short-selling where we borrow shares and sell them with the expectation that the share price will fall at a later period. So, to avoid the risk of share price increasing abnormally and the investor not being able to repay the higher amount later, companies require the investors who short-sell to maintain an initial margin.

So, in a short sale the investor benefits by difference in share price between two periods by investing the initial margin on the initial sale value from his investment account.

Sale value per share = $72

No of shares shorted = 950

Total Sale Proceeds per share = $72 * 950 = $68,400

Initial Margin to be held @ 55% i.e $ 68,400 * 55% = $37,620

Total amount to be held in investment = $68,400 + $37,620 = $106,020

Cost of covering short position (i.e amount to be paid later on the future price) = $66 * 950 = $62,700

Net amount in Account equity = $106,020 - $62,700 = $43,320

Cost of covering dividends = $0.46 * 950 = $437

Profit on Investment = Total Sale Proceeds - Cost of covering short position and dividends

= $68,400 - $62,700 - $437 = $5,263

Rate of Return on Investment = Profit on Investment / Investment made

= $5,263 / $37,620 = 13.99%