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FIN 540 chapter 3 problems
Problems
Margin purchase
1. Assume you buy 100 shares of stock at $40 per share on margin (50 percent). If the price rises to $55 per share, what is your percentage gain on the initial equity?
Margin purchase
2. In problem 1, what would the percentage loss on the initial equity be if the price had decreased to $28?
Minimum margin
3. Assume you have a 25 percent minimum margin standard in problems 1 and 2. With a price decline to $28, will you be called upon to put up more margin to meet the 25 percent rule? Disregard the $
2,000
minimum margin balance requirement.
Minimum margin
4. Recompute the answer to problem 3 based on a stock decline to $23.75.
Selling short
5.You sell 100 shares of Norton
Corporation
short. The price of the stock is $60 per share. The margin requirement is 50 percent.
a.How much is your initial margin?
b.If stock goes down to $42, what is your percentage gain or loss on the initial margin (equity)?
c.If stock goes up to $67.50, what is your percentage gain or loss on the initial margin (equity)?
d.In partc, if the minimum margin standard is 30 percent, will you be required to put up more margin? (Do the additional necessary calculations to answer this question.)
Margin purchase and Selling short
6.You are very optimistic about the personal computer industry, so you buy 200 shares of Microtech Inc. at $45 per share. You are very pessimistic about the machine tool industry, so you sell short 300 shares of King Tools Corporation at $55. Each transaction requires a 50 percent margin balance.
a.What is the initial equity in your account?
b.Assume the price of each stock is as follows for the next three months (month-end).
Commission percentage
7.Lisa Loeb is considering buying 100 shares of CMA Record
Company
. The price of the shares is $52. She has checked around with different types of brokers and has been given the following commission quotes for the trade: online broker, $7; discount broker, $45; full-service broker, $98.
a.Compute the percentage commission for all three categories.
b.How many times larger is the percentage commission of the full-service broker compared with the online broker? Round two places to the right of the decimal point for this answer.
Computing tax obligations
8. Compute the tax obligation for the following using Table 3–1 on page 52.
a.An individual with taxable income of $59,000.
b.A married couple with taxable income of $130,000.
c.What is the average tax rate in partb?
Capital gains tax
9.Gill Thomas is in the 35 percent tax bracket. Her long-term capital gains tax rate is 15 percent. She makes $16,200 on a stock trade. Compute her tax obligation based on the following holding periods:
a.6 months.
b.14 months.
3-9.
Selling short and capital gains
10.Al Rodriguez sells 500 shares of Gold Mine Corp. short at $80 per share. The margin requirement is 50 percent. The stock falls to $62 over a three-month time period, and he closes out his position.
a.How much is his initial margin?
b.What is his percentage gain or loss on his initial margin?
c.If he is in a 35 percent tax bracket for short-term capital gains and a 15 percent bracket for long-term capital gains, what is his tax obligation?
d.If the stock went up to $94 instead of down to $62, what would be his dollar loss?
e.Assuming this is his only transaction for the year (2007), how large a tax deduction could he take against other income?
Price-weighted average
11. There are three stocks in a price-weighted index:
A $100
B 20
C 60
a.What is the average value for the index?
b.Assume stock A goes down by 25 percent and stock B goes up by 25 percent, and stock C remains the same. What is the new average value for the index?
c.Explain why in partbthe average changed with two stocks moving up and down by the same percentage amount.
Computing an index
12. Assume the following five companies are used in computing an index:
|
Shares Outstanding |
Base Period January 1, 1984 |
Market Price |
Current Period December 31, 2007 Market Price |
|
|
6,000 |
$ 6 |
$12 |
||
|
10,000 |
||||
|
1,000 |
||||
|
4,000 |
a.If the index is price weighted, what will be the value of the index on December 31, 2007? (Take the average price on December 31, 2007, and divide by the average price on January 1, 1984, and multiply by 100.)
b.If the index is value weighted, what will be the value of the index on December 31, 2007? (Take the total market value on December 31, 2007, and divide by the total market value on January 1, 1984, and multiply by 100.)
c.Explain why the answer in partbis different from the answer in parta.
Changing index values in a value-weighted index
13. Assume the following stocks make up avalue-weightedindex:
|
Reese |
$35 |
|
Robinson |
16,000 |
|
Snider |
|
|
Hodges |
40,000 |
a.Compute the total market value and the weights assigned to each stock. Round to two places to the right of the decimal point. (The weights may add up to slightly more than 100 percent due to rounding.)
b.Assume the price of the shares of the Snider Corporation go up by 50 percent, while those of the Hodges Corporation go down by a mere 10 percent. The other two stocks remain constant. What will be the newly established value for the index?
c.Explain why the index followed the pattern it did in partb.
Changing index values in a value-weighted index
14.In problem 13, if the initial price of the shares of the Snider Corporation double while those of the Hodges Corporation go down by 7.5 percent, would the value of the index change? The other two stocks remain constant. Do the necessary computations.
