154 ASSET MARKETS (Ch. 11)
(e) What is the most that Ashley would be willing to pay today for a case
of Wine C? (Hint: What is the present value of his investment if he sells
it to a drinker at the optimal time?) Express your answer in exponential
11.7 (0) Fisher Brown is taxed at 40% on his income from ordinary
bonds. Ordinary bonds pay 10% interest. Interest on municipal bonds is
not taxed at all.
(a) If the interest rate on municipal bonds is 7%, should he buy municipal
(b) Hunter Black makes less money than Fisher Brown and is taxed at
only 25% on his income from ordinary bonds. Which kind of bonds should
(c) If Fisher has $1,000,000 in bonds and Hunter has $10,000 in bonds,
how much tax does Fisher pay on his interest from bonds? 0.
(d) The government is considering a new tax plan under which no interest
income will be taxed. If the interest rates on the two types of bonds do
not change, and Fisher and Hunter are allowed to adjust their portfolios,
(e) What would the change in the tax law do to the demand for municipal
(f) What interest rate will new issues of municipal bonds have to pay
NAME 155
(g) What do you think will happen to the market price of the old mu-
11.8 (0) In the text we discussed the market for oil assuming zero
production costs, but now suppose that it is costly to get the oil out of
the ground. Suppose that it costs $5 dollars per barrel to extract oil from
the ground. Let the price in period tbe denoted by ptand let rbe the
interest rate.
(a) If a firm extracts a barrel of oil in period t,howmuchprofitdoesit
(b) If a firm extracts a barrel of oil in period t+1, how much profit does
(c) What is the present value of the profits from extracting a barrel of oil
in period t+1? (pt+1−5)/(1+r)t+1.What is the present value of
(d) If the firm is willing to supply oil in each of the two periods, what
must be true about the relation between the present value of profits
pt+1−5
(1+r)t+1 =pt−5
(1+r)t.
(e) Solve the equation in the above part for pt+1 as a function of ptand
r.pt+1 =(1+r)pt−5r.
(f) Is the percentage rate of price increase between periods larger or
11.9 (0) Dr. No owns a bond, serial number 007, issued by the James
Company. The bond pays $200 for each of the next three years, at which
time the bond is retired and pays its face value of $2,000.
156 ASSET MARKETS (Ch. 11)
(a) How much is the James bond 007 worth to Dr. No at an interest rate
(b) How valuable is James bond 007 at an interest rate of 5%?
(c) Ms. Yes offers Dr. No $2,200 for the James bond 007. Should Dr. No
(d) In order to destroy the world, Dr. No hires Professor Know to develop
a nasty zap beam. In order to lure Professor Know from his university
position, Dr. No will have to pay the professor $200 a year. The nasty
zap beam will take three years to develop, at the end of which it can be
built for $2,000. If the interest rate is 5%, how much money will Dr. No
were 10%, would the world be in more or less danger from Dr. No?
11.10 (0) Chillingsworth owns a large, poorly insulated home. His
annual fuel bill for home heating averages $300 per year. An insulation
contractor suggests to him the following options.
Plan A. Insulate just the attic. If he does this, he will permanently
reduce his fuel consumption by 15%. Total cost of insulating the attic is
$300.
Plan B. Insulate the attic and the walls. If he does this, he will perma-
nently reduce his fuel consumption by 20%. Total cost of insulating the
attic and the walls is $500.
Plan C. Insulate the attic and the walls, and install a solar heating unit.
If he does this, he will permanently reduce his fuel costs to zero. Total cost
of this option is $7,000 for the solar heater and $500 for the insulating.
NAME 157
(a) Assume for simplicity of calculations that the house and the insulation
will last forever. Calculate the present value of the dollars saved on fuel
from each of the three options if the interest rate is 10%. The present
(b) Each plan requires an expenditure of money to undertake. The differ-
ence between the present value and the present cost of each plan is: Plan
(c) If the price of fuel is expected to remain constant, which option should
he choose if he can borrow and lend at an annual interest rate of 10%?
A.
(d) Which option should he choose if he can borrow and lend at an annual
(e) Suppose that the government offers to pay half of the cost of any
insulation or solar heating device. Which option would he now choose at
(f) Suppose that there is no government subsidy but that fuel prices are
expected to rise by 5% per year. What is the present value of fuel savings
from each of the three proposals if interest rates are 10%? (Hint: If
a stream of income is growing at x% and being discounted at y%, its
present value should be the same as that of a constant stream of income
11.11 (1) Have you ever wondered if a college education is financially
worthwhile? The U.S. Census Bureau collects data on income and educa-
tion that throws some light on this question. A recent census publication
(Current Population Reports, Series P-70, No. 11) reports the average an-
nual wage income in 1984 of persons aged 35–44 by the level of schooling
achieved. The average wage income of high school graduates was $13,000
per year. The average wage income of persons with bachelor’s degrees
was $24,000 per year. The average wage income of persons with master’s
degrees was $28,000 per year. The average wage income of persons with
Ph.D.’s was $40,000 per year. These income differences probably over-
state the return to education itself, because it is likely that those people
who get more education tend to be more able than those who get less.