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 (monthend).
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; fullservice broker, $98.
a.Compute the percentage
commission for all three categories.
b.How many times larger
is the percentage commission of the fullservice 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 longterm 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.
39.
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 threemonth 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 shortterm capital gains and a 15 percent bracket for
longterm 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?
Priceweighted
average
11.
There are three stocks in a priceweighted 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:
Company

Shares Outstanding

Base Period January 1, 1984 Market
Price

Current Period December 31, 2007 Market
Price

A

6,000

$ 6

$12

B

2,000

5

18

C

10,000

8

40

D

1,000

20

10

E

4,000

15

32

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 valueweighted index
13.
Assume the following stocks make up avalueweightedindex:
Corporation

Shares Outstanding

Market Price

Reese

4,000

$35

Robinson

16,000

4

Snider

6,000

10

Hodges

40,000

20

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 valueweighted 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.