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Student Problem Manual Sample (Chapter 4)
1. If you deposit $10,000 today in a bank account paying
10.38%, how much will you have in one year? If you need $12,000 in one year,
how much do you have to deposit today?
2. An art collector has the opportunity to invest in
paintings; the investment requires an initial outlay of $2 million today. The
collector is certain that he will be able to sell the paintings for $2.18 million
one year from now. He also has the opportunity to invest in bank certificates
of deposit which pay 10% per year. What is the future value of the $2 million
if the collector elects to purchase a bank certificate of deposit? Is the investment
in the paintings a good investment?
3. In Problem 2, what is the rate of return for the
investment in paintings?
4. For the paintings described in Problem 2, what is
the PV of the future cash flow the collector would receive if he sold the paintings
one year from now? What is the value of the paintings to the collector?
5. Calculate the present value for each of the following
cash flows to be received one year hence:
|
Future cash flow
|
Interest
rate
|
Present
value
|
|
$ 10,000
|
10%
|
|
|
153,200
|
13%
|
|
|
153,200
|
10%
|
|
|
2,567,450
|
5%
|
|
|
120,600
|
9%
|
|
6. As a newly-minted MBA embarking on a career in investment
banking, you naturally must own a BMW immediately. The car costs $28,320. You
also have to spend $3,248 on blue pin-stripe suits. Your salary this year is
$42,000, and next year it will be $46,000. Your routine living expenses this
year will be $34,000. You plan to make up the difference between current income
and current consumption by borrowing; the interest rate for the loan is 14%
and you intend to repay the loan, plus interest, in one year. How much will
you have left to spend next year?
7. An individual has the opportunity to invest $1000
today to acquire an asset which will generate $300 in income one year from today
and which can be sold for $900 at that time. Determine the minimum level of
the market interest rate for which this investment would be attractive.
8. An investment requires an initial outlay of $195.
The cash inflow from this investment will be $114 one year from today (year
1) and $144 two years from today (year 2). The market rate of interest is 20%.
Find the present value for this investment. Is the investment acceptable?
9. An entrepreneur has purchased an asset for $200,000
which will produce a cash inflow of $300,000 one year from now. He plans to
issue 100 shares of common stock to himself and sell 900 shares of stock to
the general public. His business, which consists entirely of this one asset,
will cease to exist after one year. The market rate of interest is 20%, and
the future cash inflow to the firm is guaranteed. At what price per share should
the entrepreneur sell the common stock? What gain will the entrepreneur realize?
10. What is the present value of $145 to be received
in 5 years if the market interest rate is 8%?
11. What is the future value of $235 invested at 12%
for 4 years?
12. For each of the following, compute the present value:
|
Future value
|
Years
|
Interest
rate
|
Present
value
|
|
$ 498
|
7
|
13%
|
|
|
1,033
|
13
|
6
|
|
|
14,784
|
23
|
4
|
|
|
898,156
|
4
|
31
|
|
13. For each of the following, compute the future value:
|
Present value
|
Years
|
Interest
rate
|
Future
value
|
|
$ 123
|
13
|
13%
|
|
|
4,555
|
8
|
8
|
|
|
74,484
|
5
|
10
|
|
|
167,332
|
9
|
1
|
|
14. Solve for the unknown time period in each of the
following:
|
Present
value
|
Future value
|
Interest
rate
|
Time
(years)
|
|
$ 100
|
$ 348
|
12%
|
|
|
123
|
351
|
10
|
|
|
4,100
|
8,523
|
5
|
|
|
10,543
|
26,783
|
6
|
|
15. Solve for the unknown interest rate in each of the
following:
|
Present value
|
Future
value
|
Interest
rate
|
Time
(years)
|
|
$ 100
|
$ 466
|
|
20
|
|
123
|
218
|
|
6
|
|
4,100
|
9,064
|
|
7
|
|
10,543
|
21,215
|
|
12
|
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