CHAPTER 11: Asset Markets
TRUE/FALSE
1. If the interest rate is 10%, then an asset that returns $1 a year forever is worth $1/1.1.
2. The interest rate is 10% and there is no inflation. A bond is available that can be redeemed either after
one year or after two years. If it is redeemed after one year, the investor gets $110. If it is redeemed
after two years, the investor gets $117.70. The investor gets no other payments than what she receives
when she redeems the bond. In equilibrium, investors will be willing to pay more than $100 for this
bond.
3. The interest rate is 9% and there is no inflation. A bond is available that can be redeemed either after
one year or after two years. If it is redeemed after one year, the investor gets $109. If it is redeemed
after two years, the investor gets $115.54. The investor gets no other payments than what she receives
when she redeems the bond. In equilibrium, investors will be willing to pay more than $100 for this
bond.
4. In a perfect asset market, it is known with certainty that an asset will sell for $24 in one year. If the
annual interest rate is 10%, then the asset will sell for $26.40 right now.
5. A consumer who can borrow and lend at the same interest rate should prefer an endowment with a
higher present value to an endowment with a lower present value, no matter how he plans to allocate
consumption over the course of his life.
6. If everybody has the same information, then a well-functioning market for assets would, in
equilibrium, leave no opportunities for arbitrage.
7. Suppose that the cost of cutting down a tree is zero and the tree grows on land that is useless for
anything else, that the interest rate is constant, and that the price of lumber does not change. The
optimal time to cut the tree is when the difference between its growth rate and the interest rate is
maximized.
8. According to the theory of asset markets, if the interest rate is constant, then the competitive market
price of a bottle of wine will rise at a constant rate per year until it is consumed, even if the amount
that wine drinkers are willing to pay for it does not rise at a constant rate.
MULTIPLE CHOICE
1. Vincent Smudge’s paintings are unappreciated now. Nobody is willing to pay anything to have them
on the walls. In 5 years Smudge’s work will gain enduring popularity. People will suddenly be willing
to pay $1,000 a year to have an original Smudge on their walls and will continue to be willing to do so
ever after. If investors realize that this is the case and if the interest rate is and always will be r, a
painting by Smudge will currently be worth about
a.
$(1,000/r)[1/(1 + r)4].
b.
$1,000/r − 5,000/r.
c.
$1,000(1 + r)5.
d.
$1,000(1/r)5.
e.
$200/r.
2. If the interest rate is r and will remain r forever, then a bond that will pay 95 dollars a year forever,
starting one year from now, is worth how much today?
a.
95/(1 + r) dollars.
b.
95(1 + r) dollars.
c.
95/r dollars.
d.
95/(1 + r + r2 +...+ rn +...) dollars.
e.
None of the above.
3. If the interest rate is r and will remain r forever, then a bond that will pay 75 dollars a year forever,
starting one year from now, is worth how much today?
a.
75/(1 + r) dollars.
b.
75(1 + r) dollars.
c.
75/(1 + r + r2 +...+ r n +...) dollars.
d.
75/r dollars.
e.
None of the above.
4. If the nominal interest rate is 80% and the rate of inflation is 50%, then the exact real rate of interest is
a.
10%.
b.
20%.
c.
30%.
d.
40%.
e.
None of the above.
5. The interest rate is 10%. A certain piece of land can be used for a parking lot, in which case there are
no construction costs and it will yield a net return of $5,000 per year forever starting one year from
now. Or it can have a house built on it. Building a house would cost $50,000 now. If a house is built
on the lot, it will yield a stream of net income equal to $12,000 per year starting one year from now.
No other uses are contemplated. The theory of asset markets predicts that the lot will sell for
a.
$120,000 and a house will be built on it.
b.
$50,000 and it will be used as a parking lot.
c.
$70,000 and a house will be built on it.
d.
$13,200 and a house will be built on it.
e.
$80,000 and it will be used as a parking lot.
6. Today is January 1. The interest rate is 8% and investors are convinced that it will stay at 8% for the
next 10 years. A corporate bond comes on the market that for the next 7 years will pay $160 on
December 31 to whoever owns the bond on that date. On January 1, 7 years from today, the issuer of
the bond will redeem the bond by buying it back from the bondholder for $2,000. What should this
bond sell for?
a.
$3,120
b.
$2,160
c.
$1,600
d.
$2,000
e.
$2,780
7. The interest rate will be 10% for one more year, but a year from now, it will fall to 5% and stay at 5%
forever. What is the market value of an investment that is sure to pay $220 a year forever, starting two
years from today?
a.
$4,000
b.
$4,400
c.
$2,000
d.
$2,200
e.
$5,000
8. The interest rate will be 10% for one more year, but a year from now, it will fall to 5% and stay at 5%
forever. What is the market value of an investment that is sure to pay $440 a year forever, starting two
years from today?
a.
$4,000
b.
$8,800
c.
$4,400
d.
$8,000
e.
$9,000
9. A certain wine costs $3 a bottle to produce. It improves in taste if stored properly for a period of time.
When it is newly bottled, people are willing to pay only $2 a bottle to drink it. But the amount that
people are willing to pay to drink a bottle of this wine will rise by $3 a year for the next 50 years.
Storage costs, not including interest, are $.50 per year. If the interest rate is 5% and the wine is kept by
rational investors, how old will it be when it is drunk and what will be its price at that time?
a.
50 years old and $152
b.
16 years old and $50
c.
50 years old and $153
d.
20 years old and $63
e.
4 years old and $14
10. The amount people are willing to pay to drink a bottle of a certain vintage of wine when it is t years
old is $2 + 3t. It costs $.50 a bottle per year to store this wine. The interest rate is 5%. If the annual
cost of storing the wine rises to $1, what will be the effect on the price of this wine when it is
consumed and on the length of time for which it is stored before it is consumed?
a.
Both will rise.
b.
Both will fall.
c.
The price will rise and the time for which it is stored will fall.
d.
The price will not change but the time for which it is stored will fall.
e.
The price will rise and the time for which it is stored will stay constant.
11. You buy a painting for $1,280. Its market value will rise by $80 per year for the next 30 years. It is
worth $80 a year to you to have it hanging on the wall. The interest rate is 10%. In how many years
will you sell it?
a.
30
b.
Immediately
c.
8
d.
4
e.
5
12. Art Dreck’s paintings are terribly unpopular now. In fact nobody would pay a dime to have one of his
paintings on the wall now. But experts believe that 10 years from now, there will be a craze for Dreck
paintings. The craze will last for 2 years and then nobody will ever want to see a Dreck again. During
this 2-year period, people will be willing to pay $1,100 a year to have an original Dreck on the wall.
The interest rate is r. If the experts’ belief is widely held among investors, today’s market value of
Dreck should be about
a.
2,200/r.
b.
2,200/(1+ r).
c.
1,100(1 + r)10 + 1,100(1 + r)11.
d.
1,100/(1 + r)10 + 1,100/(1 +r)11.
e.
1,100r + 1,100r2.
13. A large (subterranean) pool of oil lies in a remote region of Ohio. Oil companies have explored this
region and know how much oil there is. They have purchased the rights to drill and extract oil when
they wish to do so. Because of the extremely forbidding geography and the savagery of the natives, the
companies have decided to postpone extraction until the price of oil is higher. The theory of
intertemporal arbitrage predicts that
a.
the companies are behaving irrationally.
b.
the price of rights to this oil must rise at the interest rate.
c.
the oil companies will not drill unless production costs fall.
d.
the price of rights to this oil will stay constant until it pays to extract.
e.
None of the above.
14. The interest rate is 10% and will remain so forever. You do not drink wine but are interested in buying
some for investment purposes. Assume that there are no transactions costs or storage costs and that a
certain bottle of wine will be worth $44 one year from now, $51 two years from now, and $55 three
years from now. After that it turns to worthless vinegar. How much should you be willing to pay for a
bottle? (Pick the closest answer.)
a.
$40
b.
$42.15
c.
$47.15
d.
$41.32
e.
$49.30
15. The interest rate is 10% and will remain so forever. You do not drink wine but are interested in buying
some for investment purposes. Assume that there are no transactions costs or storage costs and that a
certain bottle of wine will be worth $55 one year from now, $58 two years from now, and $64 three
years from now. After that it turns to worthless vinegar. How much should you be willing to pay for a
bottle? (Pick the closest answer.)
a.
$47.93
b.
$53.12
c.
$48.08
d.
$50
e.
$57.08
16. Suppose that a dispute in the Persian Gulf halts the sale of oil from the Persian Gulf for one year. At
the same time an important new oil field is found in a place where nobody expected there to be oil.
What does economic theory predict will be the effect on the future price of oil to be delivered two
years from now?
a.
It will fall if the new pool is larger than the stock of oil in the Persian Gulf and rise
otherwise.
b.
It will fall.
c.
It will rise unless the new pool can be brought into production before the Persian Gulf
supply is resumed.
d.
It will rise.
e.
It will rise if the cost of extraction for the new oil is greater than the cost of extraction in
the Gulf and fall otherwise.
17. Bank 1 offers a deal on deposits of $1,000 or more. You must leave your money in the bank for three
years, but bank 1 will pay you 4% interest for the first year, 4% interest for the second year, and 7%
interest for the third year. In response, bank 2 offers a deal that it claims is even better. It also requires
you to deposit at least $1,000 and to leave it in the bank for three years, but it will pay 7% interest in
the first year and then 4% in the second and third years. After three years, you can take your money
out of either bank and do what you want with it. Both banks compound interest annually.
a.
Bank 2 offers a better deal than bank 1.
b.
Bank 1 offers a better deal than bank 2.
c.
The two offers are equally valuable.
d.
The offer of bank 2 becomes relatively more attractive as the size of your initial deposit is
larger.
e.
None of the above.
18. Bank 1 offers a deal on deposits of $1,000 or more. You must leave your money in the bank for three
years, but bank 1 will pay you 8% interest for the first year, 8% interest for the second year, and 7%
interest for the third year. In response, bank 2 offers a deal that it claims is even better. It also requires
you to deposit at least $1,000 and to leave it in the bank for three years, but it will pay 12% interest in
the first year and then 8% in the second and third year. After three years, you can take your money out
of either bank and do what you want with it. Both banks compound interest annually.
a.
The offer of bank 2 becomes relatively more attractive as the size of your initial deposit is
larger.
b.
Bank 2 offers a better deal than bank 1.
c.
Bank 1 offers a better deal than bank 2.
d.
The two offers are equally valuable.
e.
None of the above.
19. If the rate of inflation is greater than the interest rate,
a.
you should consume all of your wealth in the first period.
b.
you are better off keeping your money in a mattress at home (assuming no risk of it being
stolen) than at a bank.
c.
you will necessarily consume less this period than you would if the rate of inflation were
less than the interest rate.
d.
you will necessarily consume more this period than you would if the rate of inflation were
less than the interest rate.
e.
None of the above.
20. A zero coupon bond is a bond that pays no return until it comes due and then pays the holder of the
bond its face value. Suppose that a $2,000 zero coupon bond will come due on January 1, 2020. If the
interest rate is 5% and will remain 5% forever, what will this bond be worth on January 1, 2005?
a.
$2,000/0.5
b.
$2,000/0.0515
c.
$2,000 + 2,000/15
d.
$2,000/1.0515
e.
None of the above.
21. A zero coupon bond is a bond that pays no return until it comes due and then pays the holder of the
bond its face value. Suppose that a $4,000 zero coupon bond will come due on January 1, 2020. If the
interest rate is 5% and will remain 5% forever, what will this bond be worth on January 1, 2005?
a.
$4,000/0.05
b.
$4,000/0.0515
c.
$4,000 + 4,000/15
d.
$4,000 + 1.0515
e.
None of the above.
22. The sum of the terms of the infinite geometric series 1, 0.86, 0.862, 0.863, . . . , is closest to which of
the following numbers?
a.
B0
b.
1.86
c.
7.14
d.
0.54
e.
116.28
23. The sum of the terms of the infinite geometric series 1, 0.85, 0.852, 0.853, . . . , is closest to which of
the following numbers?
a.
0.54
b.
1.85
c.
B0
d.
6.67
e.
117.65
24. Ashley, from your workbook, has discovered another wine, wine D. Wine drinkers are willing to pay
40 dollars to drink it right now. The amount that wine drinkers are willing to pay will rise by 20 dollars
each year that the wine ages. The interest rate is 10%. How much would Ashley be willing to pay for
the wine if he buys it as an investment? (Pick the closest answer.)
a.
93 dollars
b.
40 dollars
c.
200 dollars
d.
440 dollars
e.
71 dollars
25. Ashley, from your workbook, has discovered another wine, wine D. Wine drinkers are willing to pay
45 dollars to drink it right now. The amount that wine drinkers are willing to pay will rise by 15 dollars
each year that the wine ages. The interest rate is 10%. How much would Ashley be willing to pay for
the wine if he buys it as an investment? (Pick the closest answer.)
a.
76 dollars
b.
45 dollars
c.
150 dollars
d.
495 dollars
e.
71 dollars
26. Shivers’s annual fuel bill for home heating is 800 dollars per year. He considers three alternative plans
for insulating his house. Plan A would reduce his annual fuel bill by 15%, plan B would reduce it by
20%, and plan C would eliminate his need for heating fuel altogether. The plan A insulation job would
cost Shivers 800 dollars, plan B would cost him 1,100, dollars, and plan C would cost him 8,800
dollars. If the interest rate is 10% and his house and the insulation job last forever, which plan is the
best for Shivers?
a.
Plan A.
b.
Plan B.
c.
Plan C.
d.
Plans A and B are equally good.
e.
He is best off using none of the plans.
27. Shiver’s annual fuel bill for home heating is 900 dollars per year. He considers three alternative plans
for insulating his house. Plan A would reduce his annual fuel bill by 15%, plan B would reduce it by
20%, and plan C would eliminate his need for heating fuel altogether. The plan A insulation job would
cost Shivers 900 dollars, plan B would cost him 1,600 dollars, and plan C would cost him 9,900
dollars. If the interest rate is 10% and his house and the insulation job last forever, which plan is the
best for Shivers?
a.
Plans A and B are equally good.
b.
Plan B.
c.
Plan C.
d.
Plan A.
e.
He is best off using none of the plans.
28. The price of an antique is expected to rise by 4% during the next year. The interest rate is 6%. You are
thinking of buying an antique and selling it a year from now. You would be willing to pay a total of
400 dollars for the pleasure of owning the antique for a year. How much would you be willing to pay
to buy this antique?
a.
6,666.67 dollars
b.
8,400 dollars
c.
400 dollars
d.
20,000 dollars
e.
4,000 dollars
29. The price of an antique is expected to rise by 8% during the next year. The interest rate is 12%. You
are thinking of buying an antique and selling it a year from now. You would be willing to pay a total
of 800 dollars for the pleasure of owning the antique for a year. How much would you be willing to
pay to buy this antique?
a.
6,666.67 dollars
b.
20,000 dollars
c.
800 dollars
d.
16,800 dollars
e.
8,000 dollars
30. A bond has a face value of 7,000 dollars. It will pay 700 dollars in interest at the end of every year for
the next 50 years. At the time of the last interest payment, 50 years from now, the company that issued
the bond will redeem the bond at face value. That is, the company will buy back the bond from its
owner at a price equal to the face value of the bond. If the interest rate is 10% and is expected to
remain at 10%, how much would a rational investor pay for this bond right now?
a.
7,000 dollars
b.
42,000 dollars
c.
35,000 dollars
d.
More than any of the above amounts
e.
Less than any of the above amounts
31. A bond has a face value of 5,000 dollars. It will pay 500 dollars in interest at the end of every year for
the next 45 years. At the time of the last interest payment, 45 years from now, the company that issued
the bond will redeem the bond at face value. That is, the company will buy back the bond from its
owner at a price equal to the face value of the bond. If the interest rate is 10% and is expected to
remain at 10%, how much would a rational investor pay for this bond right now?
a.
5,000 dollars
b.
27,500 dollars
c.
22,500 dollars
d.
More than any of the above amounts
e.
Less than any of the above amounts
32. If the interest rate is 17%, and will remain 17% forever, how much would a rational investor be willing
to pay for an asset that will pay him 7,020 dollars 1 year from now, 1,368 dollars 2 years from now,
and nothing at any other time?
a.
7,000 dollars
b.
6,000 dollars
c.
41,176.47 dollars
d.
126,000 dollars
e.
8,000 dollars
33. If the interest rate is 18%, and will remain 18% forever, how much would a rational investor be willing
to pay for an asset that will pay him 9,440 dollars 1 year from now, 1,392 dollars 2 years from now,
and nothing at any other time?
a.
9,000 dollars
b.
171,000 dollars
c.
8,000 dollars
d.
50,000 dollars
e.
10,000 dollars
34. The interest rate is 10% and is expected to stay constant at that level forever. The present discounted
value of $50,000 a year forever starting today is
a.
$500,000.
b.
$550,000.
c.
$ infinity.
d.
$1 million.
e.
$45,454.45.
PROBLEM
1. The interest rate is 10% and will remain 10% forever. Suppose that you do not drink wine but are
interested in buying it for investment purposes. How much would you be willing to pay for each of the
following?
a. A bottle of wine that will be worth $22 a year from now and will then go bad and be worthless.
b. A bottle of wine that will be worth $22 a year from now and will rise in value by $1 a year forever?
Explain your answer.
2. A certain wine costs $3 a bottle to produce. The amount that people are willing to pay to drink it t
years after it has been bottled is $2 + 3t. Storage costs, not including interest, are $.50 per year. If the
interest rate is 5%, how much would a rational investor be willing to pay for it at the time it is bottled?
Explain how you got your answer. Feel free to write formulas for present value calculations without
working out the numerical answer if it involves long calculations. (Hint: How long would the wine be
kept before it is drunk? At what price would it sell?)
3. Suppose that the cost of personal computers falls by 20% per year. To make this problem relatively
easy, we will assume that their quality does not change and that computers never wear out. You plan to
get one sometime. What is the rational way to decide when to buy one?
4. According to a recent story in the New York Times, the South African gold strike has been costing
South African mining companies about $7.5 million per day. Assuming that this number is the value of
the gold that was not mined because of the strike, minus the labor costs (and other operating costs) that
are saved by shutting down the mines, what is wrong with this calculation?