1. A stock sells for $10 per share. You purchase 100 ...
FCS5510 Sample Homework Problems and Answer Key Unit01
CHAPTER 2. SECURITIES MARKETS
1. A stock sells for $10 per share. You purchase 100 shares for $10 a share (i.e., for $1,000), and after a year the price rises to $17.50. What will be the percentage return on your investment if you bought the stock on margin and the margin requirement was 50%? (Ignore commissions, dividends, and interest expense.)
Gain on the stock: $1,750 - $1,000 = $750
Margin Requirement 50%
Margin $500
Return on Investor's Funds
$750/$500 = 150%
2. A stock sells for $10 per share. You purchase 100 shares for $10 a share (i.e., for $1,000), and after a year the price falls to $7.50. What will be the percentage return on your investment if you bought the stock on margin and the margin requirement was 25 percent? (Ignore commissions, dividends, and interest expense.)
Loss on the stock: $750 - $1,000 = ($250)
Margin Requirement 25%
Margin $250
Return on Investor's Funds
-$250/$250 = -100%
The generalization implied by problems 1 and 2 is that if the margin requirement is small (e.g., 25 percent), then the potential return or loss on the investor's funds (i.e., the margin) is magnified for a given change in the stock's price.
3. You purchase 100 shares of stock at $100 ($10,000); the margin requirement is 40 percent. What are the dollar return if you sell the stock for $112 and buy the stock with cash?
Cost of 100 shares: $10,000
a. profit on the stock: $11,200 - $10,000 = $1,200 percentage return (100% cash) $1,200/$10,000 = 12%
4. Investor A buys 100 shares of SLM Inc. at $35 a share and holds the stock for a year. Investor B buys 100 shares on margin. The margin requirement is 60 percent, and the interest rate on borrowed funds is 8 percent. If they both sell the stock for $40 after a year, what percentage reurn does each investor earn?
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This problem adds the interest that must be paid on the borrowed funds.
The capital gain for both investors is $4,000 - $3,500 = $500
The percentage return for investor A is $500/$3,500 = 14.3%
The percentage return for investor B is ($500 ? 112)/($3,500 ? 1,400) = $388/$2,100 = 18.5%
6. Ms. Tejal Grandhi has decided that the stock of Small Cap Inc is overvalued at $4 a share and wants to sell it short. Since the price is relatively low, short sales cannot be executed on margin so Ms. Grandhi must put up the entire value of the stock when it is sold short. What is the percentage loss if the price of the stock rises to $8?
Short sellers must put up collateral, so the percentage returns depend on the amount of cash the short seller must commit. In this problem, the collateral is 100 percent of the value of the stock sold short ($4 per share).
If the stock's price doubles to $8, the loss on the position is $4 and percentage loss is ($4)/$4 = (100%). The short seller loses the entire collateral.
7. An investor sells a stock short for $36 a share. A year later, the investor covers the position at $30 a share. If the margin requirement is 60 percent, what is the percentage return earned on the investment?
If an investor sells a stock short at $36 and the margin requirement is 60 percent, the investor must deposit $21.60 (.6 x $36) with the broker. If the stock subsequently falls to $30, the investor earns a profit of $6 ($36 - 30). The percent earned on the investor's funds is $6/$21.60 = 27.8%
Notice that this problem does not consider brokerage fees and dividend payments (for which the short seller is responsible). In addition, the percentage earned or lost is not the rate of return except in the case that the holding period is one year.
8. A speculator sells a stock short for $50 a share. The company pays a $2 annual cash dividend. After a year has passed, the seller covers the short position at $42. What is
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the percentage return on the position (excluding the impact of any interest expense and commissions)? In this problem the investor sells the stock short at $50 and covers the short at $42, so there is an $8 gain on the transaction. The short seller, however, is responsible for the $2 dividend, so the net gain on the transaction is $6. The percentage return is $6/$50 = 12%.
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