Transcript Car ads in Switzerland

CHAPTER
15
Investment, Time,
and Capital Markets
CHAPTER OUTLINE
15.1 Stocks versus Flows
15.2 Present Discounted Value
15.3 The Value of a Bond
15.4 The Net Present Value Criterion for
Capital Investment Decisions
15.5 Adjustments for Risk
15.6 Investment Decisions by Consumers
15.7 Investment in Human Capital
15.8 Intertemporal Production
Decisions—Depletable Resources
15.9 How Are Interest Rates Determined?
Prepared by:
Fernando Quijano, Dickinson State University
with Shelly Tefft and Michael Brener
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Capital expenditures involve the purchases of factories and equipment
that are expected to last for years. This introduces the element of time.
When a firm decides whether to build a factory or purchase machines, it must
compare the outlays it would have to make now with the additional profit that the
new capital will generate in the future. To make this comparison, it must address
the following question: How much are future profits worth today? This problem
does not arise when hiring labor or purchasing raw materials.
In this chapter, we will learn how to calculate the current value of future flows of
money. This is the basis for our study of the firm’s investment decisions.
Individuals also make decisions involving costs and benefits occurring at
different points in time, and the same principles apply.
We will also discuss investments in human capital. Does it make economic
sense, for example, to go to college or graduate school rather than take a job
and start earning an income?
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15.1 Stocks versus Flows
Capital is measured as a stock. If a firm owns an electric motor factory worth
$10 million, we say that it has a capital stock worth $10 million.
To make and sell these motors, a firm needs capital—namely, the factory that it
built for $10 million. The firm’s $10 million capital stock allows it to earn a flow
of profit of $80,000 per month. Was the $10 million investment in this factory a
sound decision?
If the factory will last 20 years, then we must ask: What is the value today of
$80,000 per month for the next 20 years? If that value is greater than $10
million, the investment was a good one.
Is $80,000 five years—or 20 years—from now worth $80,000 today? Money
received over time is less than money received today because the money can
be invested to yield more money in the future.
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15.2 Present Discounted Value
● interest rate
Rate at which one can borrow or lend money.
● present discounted value (PDV)
cash flow.
Suppose the annual interest rate is
R. Then $1 today can be invested
to yield (1 + R) dollars a year from
now. Therefore, 1 + R dollars is the
future value of $1 today.
Now, what is the value today, i.e.,
the present discounted value
(PDV), of $1 paid one year from
now?
$1 a year from now is worth $1/(1
+ R) today. This is the amount of
money that will yield $1 after one
year if invested at the rate R.
$1 paid n years from now is worth
$1/(1 + R)n today
The current value of an expected future
We can summarize this as follows:
$1
PDV of $1 paid after 1 year =
1+𝑅
$1
PDV of $1 paid after 2 years =
1+𝑅
2
$1
1+𝑅
3
$1
PDV of $1 paid after n years =
1+𝑅
𝑛
PDV of $1 paid after 3 years =
⋮
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TABLE 15.1
PDV OF $1 PAID IN THE FUTURE
INTEREST
RATE
1 YEAR
2 YEARS
5 YEARS
10 YEARS
20 YEARS
30 YEARS
0.01
$0.990
$0.980
$0.951
$0.905
$0.820
$0.742
0.02
0.980
0.961
0.906
0.820
0.673
0.552
0.03
0.971
0.943
0.863
0.744
0.554
0.412
0.04
0.962
0.925
0.784
0.614
0.377
0.308
0.05
0.943
0.890
0.747
0.558
0.312
0.231
0.06
0.935
0.873
0.713
0.508
0.312
0.174
0.07
0.935
0.873
0.713
0.508
0.258
0.131
0.08
0.926
0.857
0.681
0.463
0.215
0.099
0.09
0.917
0.842
0.650
0.422
0.178
0.075
0.10
0.909
0.826
0.621
0.386
0.149
0.057
0.15
0.870
0.756
0.497
0.247
0.061
0.015
0.20
0.833
0.694
0.402
0.162
0.026
0.004
Table 15.1 shows, for different interest rates, the present value of $1 paid after 1, 2, 5,
10, 20, and 30 years. Note that for interest rates above 6 or 7 percent, $1 paid 20 or 30
years from now is worth very little today. But this is not the case for low interest rates. For
example, if R is 3 percent, the PDV of $1 paid 20 years from now is about 55 cents. In
other words, if 55 cents were invested now at the rate of 3 percent, it would yield about
$1 after 20 years.
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Valuing Payment Streams
TABLE 15.2
TWO PAYMENT STREAMS
TODAY
1 YEAR
2 YEARS
Payment Stream A:
$100
$100
$
Payment Stream B:
$ 20
$100
$100
0
Which payment stream in the table above would you prefer to receive? The
answer depends on the interest rate.
$100
PDV of Stream 𝐴 = $100 +
1+𝑅
PDV of Stream 𝐵 = $20 +
TABLE 15.3
$100
$100
+
1+𝑅
1+𝑅
2
PDV OF PAYMENT STREAMS
R = .05
R = .10
R = .15
R =.20
PDV of Stream A:
$195.24
$190.91
$186.96
$183.33
PDV of Stream B:
205.94
193.55
182.57
172.78
For interest rates of 10 percent or less, Stream B is worth more; for interest
rates of 15 percent or more, Stream A is worth more. Why? Because even
though less is paid out in Stream A, it is paid out sooner.
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EXAMPLE 15.1
THE VALUE OF LOST EARNINGS
In this example, Harold Jennings died in an automobile accident on January 1,
1996, at the age of 53. The PDV of his lost earnings, from 1996 until retirement
at the end of 2003 is calculated as follows:
𝑊0 1 + 𝑔 1 − 𝑚1
𝑊0 1 + 𝑔 2 1 − 𝑚2
𝑊0 1 + 𝑔 7 1 − 𝑚7
PDV = 𝑊0 +
+
+ ⋯+
2
1
+
𝑅
1+𝑅 7
1+𝑅
where W0 is his salary in 1996, g is the annual percentage rate at which his salary is likely to have grown
(so that W0(1 + g) would be his salary in 1997, W0(1 + g)2 his salary in 1998, etc.), and m1, m2, . . . , m7 are
mortality rates, i.e., the probabilities that he would have died from some other cause by 1997, 1998, . . . ,
2003.
TABLE 15.4
CALCULATING LOST WAGES
YEAR
W0(1 + g)t
(1 – mt)
1/(1 + R)t
W0(1 + g)t (1 – mt)/(1 + R)t
1996
$85,000
.991
1.000
$84,235
1997
91,800
.990
.917
83,339
1998
99,144
.989
.842
82,561
1999
107,076
.988
.772
81,671
2000
115,642
.987
.708
80,810
2001
124,893
.986
.650
80,044
2002
134,884
.985
.596
79,185
2003
145,675
.984
.547
78,409
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15.3 The Value of a Bond
● bond
Contract in which a borrower agrees to pay the bondholder
(the lender) a stream of money.
FIGURE 15.1
PRESENT VALUE OF THE
CASH FLOW FROM A BOND
Because most of the bond’s
payments occur in the
future, the present
discounted value declines
as the interest rate
increases.
For example, if the interest
rate is 5 percent, the PDV of
a 10-year bond paying $100
per year on a principal of
$1000 is $1386. At an
interest rate of 15 percent,
the PDV is $749.
PDV =
$100
$100
+
1+𝑅
1+𝑅
2 + ⋯+
$100
$1000
+
1 + 𝑅 10
1 + 𝑅 10
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(15.1)
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Perpetuities
● perpetuity Bond paying out a fixed amount of money each
year, forever.
The present value of the payment stream is given by the infinite summation:
$100
$100
$100
$100
PDV =
+
+
+
+⋯
1+𝑅
1+𝑅 2
1+𝑅 3
1+𝑅 4
The summation can be expressed in terms of a simple formula:
PDV = $100 𝑅
(15.2)
So if the interest rate is 5 percent, the perpetuity is worth $100/(.05) = $2000,
but if the interest rate is 20 percent, the perpetuity is worth only $500.
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The Effective Yield on a Bond
EFFECTIVE YIELD
● effective yield (or rate of return)
receives by investing in a bond.
Percentage return that one
Suppose the market price—and thus the value—of the perpetuity is P.
Then from equation (15.2), P = $100/R, and R = $100/P. Thus, if the price
of the perpetuity is $1000, we know that the interest rate is R =
$100/$1000 = 0.10, or 10 percent. This interest rate is called the effective
yield, or rate of return.
If the price of the bond is P, we write equation (15.1) as:
$100
$100
𝑃=
+
1+𝑅
1+𝑅
$100
2+ 1+𝑅
$100
$1000
3 + ⋯ + 1 + 𝑅 10 + 1 + 𝑅 10
The more risky an investment, the greater the return that an investor demands.
As a result, riskier bonds have higher yields.
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FIGURE 15.2
EFFECTIVE YIELD ON A BOND
The effective yield is the
interest rate that equates the
present value of the bond’s
payment stream with the bond’s
market price.
The figure shows the present
value of the payment stream as
a function of the interest rate.
The effective yield is found by
drawing a horizontal line at the
level of the bond’s price. For
example, if the price of this
bond were $1000, its effective
yield would be 10 percent.
If the price were $1300, the
effective yield would be about 6
percent.
If the price were $700, it would
be 16.2 percent.
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EXAMPLE 15.2
THE YIELDS ON CORPORATE BONDS
Microsoft
Rite Aid
Price ($):
106.60
93.00
Coupon ($):
5.300
9.500
Feb. 8, 2041
Jun. 15, 2017
Yield to Maturity (%):
4.877
11.099
Current Yield (%):
4.972
10.215
Rating:
AAA
CCC
Maturity Date:
The yield on the Microsoft bond is given by the following equation
5.3
5.3
5.3
5.3
5.3
106.60 =
+
+
+
⋯
+
+
1+𝑅
1+𝑅 2
1+𝑅 3
1 + 𝑅 29
1 + 𝑅 30
To find the effective yield, we must solve this equation for R. The solution is
approximately R* = 4.877 percent.
The yield on the Rite Aid bond is given by the following equation
93.00 =
9.5
9.5
+
1+𝑅
1+𝑅
2+
9.5
1+𝑅
3+
9.5
1+𝑅
4+
9.5
1+𝑅
5+
9.5
1+𝑅
6
R* = 11.099 percent. The yield on the Rite Aid bond was much higher because
the Rite Aid bond was much riskier.
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15.4 The Net Present Value Criterion for
Capital Investment Decisions
● net present value (NPV) criterion Rule holding that one should invest if
the present value of the expected future cash flow from an investment is larger
than the cost of the investment.
NPV criterion: Invest if the present value of the expected future cash flows from
an investment is larger than the cost of the investment.
Suppose a capital investment costs C and is expected to generate profits over
the next 10 years of amounts π1, π2, . . . , π10.
We then write the net present value as
𝜋1
𝜋2
NPV = −𝐶 +
+
1+𝑅
1+𝑅
2 + ⋯+
𝜋10
1+𝑅
10
(15.3)
where R is the discount rate that we use to discount the future stream of profits.
Equation (15.3) describes the net benefit to the firm from the investment. The
firm should make the investment only if that net benefit is positive—i.e., only if
NPV > 0.
● discount rate
the future.
Rate used to determine the value today of a dollar received in
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DETERMINING THE DISCOUNT RATE
● opportunity cost of capital Rate of return that one could earn by investing
in an alternate project with similar risk.
Had the firm not invested in this project, it could have earned a return by
investing in something else. The correct value for R is therefore the return that
the firm could earn on a “similar” investment.
By “similar” investment, we mean one with the same risk. We’ll see how to
evaluate the riskiness of an investment in the next section.
If we assume that this project has no risk (i.e., the firm is of its future profit
flows), then the opportunity cost of the investment is the risk-free return—e.g.,
the return one could earn on a government bond.
If the project is expected to last for 10 years, the firm could use the annual
interest rate on a 10-year government bond to compute the NPV of the project.
If the benefit from the investment was equal the opportunity cost, the firm would
be indifferent between investing and not investing. If the NPV is greater than
zero, the benefit exceeds the opportunity cost, so the investment should be
made.
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The Electric Motor Factory
With an initial investment of $10 million, 8000 electric motors per month
are produced and sold for $52.50 over the next 20 years.
The production cost is $42.50 per unit, for a profit of $80,000 per month.
The factory could be sold for scrap (with certainty) for $1 million after it
becomes obsolete. Annual profit equals $960,000.
NPV = −10 +
.96
1+𝑅
.96
+⋯+
1+𝑅
+
.96
1+𝑅
2+
1
20 + 1 + 𝑅
.96
1+𝑅
3
(15.4)
20
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FIGURE 15.3
NET PRESENT VALUE OF A
FACTORY
The NPV of a factory is the
present discounted value of all
the cash flows involved in
building and operating it.
Here it is the PDV of the flow
of future profits less the
current cost of construction.
The NPV declines as the
discount rate increases.
At discount rate R*, the NPV is
zero.
For discount rates below 7.5 percent, the NPV is positive, so the firm should
invest in the factory. For discount rates above 7.5 percent, the NPV is negative,
and the firm should not invest. R* is sometimes called the internal rate of
return on the investment.
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Real versus Nominal Discount Rates
The real interest rate is the nominal rate minus the expected rate of
inflation. If we expect inflation to be 5 percent per year on average, the
real interest rate would be 9 − 5 = 4 percent. This is the discount rate that should
be used to calculate the NPV of the investment in the electric motor factory. Note
from Figure 15.3 that at this rate the NPV is positive.
Negative Future Cash Flows
Negative future cash flows create no problem for the NPV rule; they are simply
discounted, just like positive cash flows.
Suppose that our electric motor factory will take a year to build: $5 million is
spent right away, and another $5 million is spent next year. Also, suppose the
factory is expected to lose $1 million in its first year of operation and $0.5
million in its second year. Afterward, it will earn $0.96 million a year until year
20, when it will be scrapped for $1 million, as before. (All these cash flows are
in real terms.) Now the net present value is
NPV = −5 −
5
1+𝑅
−
+⋯+
1
1+𝑅
2−
.96
1+𝑅
.5
1+𝑅
20 +
3+
1
1+𝑅
.96
1+𝑅
4+
.96
1+𝑅
5
(15.5)
20
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EXAMPLE 15.3
THE VALUE OF A NEW YORK CITY TAXI MEDALLION
The value of a taxi medallion is $880,000. Let’s calculate the flow of income a taxi
company can expect from leasing a medallion.
The taxi company charges the driver a flat fee for use of the medallion, but that
fee is capped by the city. In 2011, the fee was $110 per 12-hour shift, or $220 per
day. Assuming the cab is driven 7 days per week and 50 weeks per year, the taxi
company would earn (7)(50)($220) = $77,000 per year from the medallion.
Little risk is involved (there is a shortage of taxis, so it is easy to find drivers
willing to lease the medallion), and the capped fee has increased with inflation.
Therefore a 5-percent discount rate would probably be appropriate for discounting
future income flows.
Assuming a time horizon of 20 years, the present value of this flow of income is
therefore:
70,000 70,000 70,000
70,000
PV =
+
+
+⋯ +
= $872,355
1.05
1.052
1.053
1.0520
Thus a medallion price in the range of $880,000 is consistent with the flow of
income that the medallion will bring to the taxi company.
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15.5 Adjustments for Risk
● risk premium Amount of money that a risk-averse individual will
pay to avoid taking a risk.
Diversifiable versus Nondiversifiable Risk
DIVERSIFIABLE RISK
● diversifiable risk Risk that can be eliminated either by investing in many
projects or by holding the stocks of many companies.
Because investors can eliminate diversifiable risk, assets that have only
diversifiable risk tend on average to earn a return close to the risk-free rate. if the
project’s only risk is diversifiable, the opportunity cost is the risk-free rate. No risk
premium should be added to the discount rate.
NONDIVERSIFIABLE RISK
● nondiversifiable risk Risk that cannot be eliminated by investing in many
projects or by holding the stocks of many companies.
For capital investments, nondiversifiable risk arises because a firm’s profits tend
to depend on the overall economy. To the extent that a project has
nondiversifiable risk, the opportunity cost of investing in that project is higher than
the risk-free rate. Thus a risk premium must be included in the discount rate.
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The Capital Asset Pricing Model
● Capital Asset Pricing Model (CAPM)
Model in which the risk
premium for a capital investment depends on the correlation of the
investment’s return with the return on the entire stock market.
The expected return on the stock market is higher than the risk-free rate.
Denoting the expected return on the stock market by rm and the risk-free rate by
rf , the risk premium on the market is rm – rf. This is the additional expected
return you get for bearing the nondiversifiable risk associated with the stock
market.
The CAPM summarizes the relationship between expected returns and the risk
premium by the following equation:
•
𝑟𝑖 − 𝑟𝑓 = 𝛽 𝑟𝑚 − 𝑟𝑓
(15.6)
where ri is the expected return on an asset. The equation says that the risk
premium on the asset (its expected return less the risk-free rate) is proportional
to the risk premium on the market.
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● asset beta A constant that measures the sensitivity of an asset’s
return to market movements and, therefore, the asset’s nondiversifiable
risk.
If a 1-percent rise in the market tends to result in a 2-percent rise in the asset
price, the beta is 2.
THE RISK-ADJUSTED DISCOUNT RATE Given beta, we can determine the
correct discount rate to use in computing an asset’s net present value. That
discount rate is the expected return on the asset or on another asset with the
same risk. It is therefore the risk-free rate plus a risk premium to reflect
nondiversifiable risk:
•
Discount rate = 𝑟𝑓 + 𝛽 𝑟𝑚 − 𝑟𝑓
(15.7)
● company cost of capital
Weighted average of the expected return on a
company’s stock and the interest rate that it pays for debt.
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EXAMPLE 15.4 CAPITAL INVESTMENT IN THE
DISPOSABLE DIAPER INDUSTRY
In Example 13.6, we discussed the cost advantage that
deters entry into the disposable diaper industry. In this
example, we’ll examine the capital investment decision
of a potential entrant.
Suppose you are considering entering this industry. To take advantage of scale
economies in production, advertising, and distribution, you would need to build
three plants at a cost of $60 million each, with the cost spread over three years.
When operating at capacity, the plants would produce a total of 2.5 billion diapers
per year. These would be sold at wholesale for about 16 cents per diaper, yielding
revenues of about $400 million per year. You can expect your variable production
costs to be about $290 million per year, for a net revenue of $110 million per year.
You will, however, have other expenses. Using the experience of P&G and
Kimberly-Clark as a guide, you can expect to spend about $60 million in R&D
before start-up to design an efficient manufacturing process, and another $20
million in R&D during each year of production to maintain and improve that
process. Finally, once you are operating at full capacity, you can expect to spend
another $50 million per year for a sales force, advertising, and marketing. Your
net operating profit will be $40 million per year. The plants will last for 15 years
and will then be obsolete.
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EXAMPLE 15.4 CAPITAL INVESTMENT IN THE
DISPOSABLE DIAPER INDUSTRY
Is the investment a good idea? To find out, let’s calculate its net present value.
We assume that production begins at 33 percent of capacity when the plant is
completed in 2015, takes two years to reach full capacity, and continues through
the year 2030.
Given the net cash flows, the NPV is calculated as
93.4
56.6
NPV = −120 −
−
1+𝑅
1+𝑅
40
2+ 1+𝑅
40
3+ 1+𝑅
40
4 + ⋯+ 1 + 𝑅
15
Table 15.5 shows the NPV for discount rates of 5, 10, and 15 percent.
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EXAMPLE 15.4 CAPITAL INVESTMENT IN THE
DISPOSABLE DIAPER INDUSTRY
TABLE 15.5
DATA FOR NPV CALCUALTION ($ MILLIONS)
PRE-2005
Sales
2015
2016
2017
133.3
266.7
400.0
…
2030
400.0
LESS
Variable cost
96.7
290.0
…
290.0
Ongoing R&D
20.0
20.0
…
20.0
Sales force, ads,
and marketing
50.0
50.0
…
50.0
Operating profit
–33.4
40.0
…
40.0
LESS
Construction cost
60.0
Initial R&D
60.0
NET CASH FLOW
–120.0
Discount
Rate:
NPV:
60.0
60.0
–93.4
–56.6
0.05
80.5
0.10
–16.9
40.0
40.0
0.15
–75.1
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EXAMPLE 15.4 CAPITAL INVESTMENT IN THE
DISPOSABLE DIAPER INDUSTRY
Note that the NPV is positive for a discount rate of 5
percent, but it is negative for discount rates of 10 or 15
percent. What is the correct discount rate? First, we
have ignored inflation, so the discount rate should be
in real terms. Second, the cash flows are risky—we don’t know how efficient our
plants will be, how effective our advertising and promotion will be, or even what
the future demand for disposable diapers will be. Some of this risk is
nondiversifiable. To calculate the risk premium, we will use a beta of 1, which is
typical for a producer of consumer products of this sort. Using 4 percent for the
real risk-free interest rate and 8 percent for the risk premium on the stock market,
our discount rate should be
𝑅 = 0.04 + 1 0.08 = 0.12
At this discount rate, the NPV is clearly negative, so the investment does
not make sense. You will not enter the industry, and P&G and Kimberly-Clark
can breathe a sigh of relief. Don’t be surprised, however, that these firms
can make money in this market while you cannot. Their experience, years of
earlier R&D, and brand name recognition give them a competitive advantage that
a new entrant will find hard to overcome.
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15.6 Investment Decisions by Consumers
The decision to buy a durable good involves comparing a flow of
future benefits with the current purchase cost
Let’s assume a car buyer values the service at S dollars per year. Let’s also
assume that the total operating expense (insurance, maintenance, and
gasoline) is E dollars per year, that the car costs $20,000, and that after six
years, its resale value will be $4000.
The decision to buy the car can then be framed in terms of net present value:
NVP = −20,000 + 𝑆 − 𝐸 +
𝑆−𝐸
1+𝑅
+
𝑆−𝐸
𝑆−𝐸
4000
+
⋯
+
+
1+𝑅 2
1+𝑅 6
1+𝑅 6
(15.8)
What discount rate R should the consumer use? The consumer should apply
the same principle that a firm does: The discount rate is the opportunity cost of
money.
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EXAMPLE 15.5
CHOOSING AN AIR CONDITIONER AND A NEW CAR
Assuming an eight-year lifetime and no resale, the
PDV of the cost of buying and operating air
conditioner i is
PDV = 𝐶𝑖 + 𝑂𝐶𝑖 +
𝑂𝐶𝑖
1+𝑅
+
𝑂𝐶𝑖
1+𝑅
+⋯+
2
𝑂𝐶𝑖
1+𝑅
8
where Ci is the purchase price of air conditioner i and
OCi is its average annual operating cost.
The preferred air conditioner depends on your discount rate. A high discount
rate would make the present value of the future operating costs smaller. In this
case, you would probably choose a less expensive but relatively inefficient unit.
As with air conditioners, a consumer can compare two or more cars by
calculating and comparing the PDV of the purchase price and expected
average annual operating cost for each.
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15.7 Investments in Human Capital
● human capital Knowledge, skills, and experience that make an
individual more productive and thereby able to earn a higher income
over a lifetime.
THE NPV OF A COLLEGE EDUCATION Let’s assume that the total economic
cost of attending college to be $40,000 per year for each of four years. For
simplicity, however, we will assume that this $20,000 salary differential persists
for 20 years.
In that case, the NPV (in $1000’s) of investing in a college education is
NPV = −40 −
40
40
−
1+𝑅
1+𝑅
2−
40
1+𝑅
3+
20
1+𝑅
4 + ⋯+
20
1+𝑅
23
A reasonable real discount rate would be about 5 percent. This rate would
reflect the opportunity cost of money for many households. The NPV is then
about $66,000.
A college education is an investment with close to free entry. In markets with
free entry, we should expect to see zero economic profits, which implies that
investments will earn a competitive return.
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EXAMPLE 15.6
SHOULD YOU GO TO BUSINESS SCHOOL?
The typical MBA program in the United States takes
two years and involves tuition and expenses of
$45,000 per year. It is important to include the
opportunity cost of the foregone pre-MBA salary, i.e.,
another $45,000 per year. Thus, the total economic
cost of getting an MBA is $90,000 per year for each
of two years.
The NPV of this investment is therefore
NPV = −90 −
90
90
+
1+𝑅
1+𝑅
2 + ⋯+
30
1+𝑅
21
Using a real discount rate of 5 percent, the NPV comes to about $180,000.
Because many more people apply to MBA programs than there are spaces, the
return on the degree remains high.
As the table in this example shows, increases in salaries after earning an MBA are
dramatic. Keep in mind that the table includes many of the top MBA programs, and
that the salaries are self-reported, and probably overstate the average MBA
salaries for all graduates.
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EXAMPLE 15.6
TABLE 15.6
SHOULD YOU GO TO BUSINESS SCHOOL?
SALARIES BEFORE AND AFTER BUSINESS SCHOOL
PRE-MBA SALARY
AVERAGE SALARY 3
YEARS AFTER MBA
Stanford University
$84,998
$182,746
University of Pennsylvania
$78,544
$175,153
Harvard Business School
$79,082
$170,817
Columbia Business School
$77,127
$167,366
MIT Sloan School of Management
$71,653
$158.353
Dartmouth College: Tuck
$73,114
$155.732
University of Chicago
$72,904
$152.370
Yale School of Management
$65,000
$151,451
Northwestern University: Kellogg
$71,889
$143,777
Cornell University: Johnson
$67,852
$140,454
New York University: Stern
$63,195
$138,398
UCLA: Anderson
$66,459
$136,906
Duke University: Fuqua
$65,820
$136,248
University of Michigan
$65,788
$130,082
University of Virginia
$64,397
$130,082
Carnegie Mellon
$63,509
$127,018
UNIVERSITY
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EXAMPLE 15.6
TABLE 15.6
SHOULD YOU GO TO BUSINESS SCHOOL?
SALARIES BEFORE AND AFTER BUSINESS SCHOOL
PRE-MBA SALARY
AVERAGE SALARY 3
YEARS AFTER MBA
Georgetown University
$60,817
$126,500
University of Texas at Austin
$61,359
$118,422
University of Southern California
$62,701
$116,624
Vanderbilt University: Owen
$55,886
$114,567
Indiana University: Kelly
$60,497
$112,524
University of Rochester: Simon
$52,965
$111,226
Pennsylvania State University
$58,556
$110,085
Purdue University: Krannert
$51,676
$100,252
UNIVERSITY
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EXAMPLE 15.6
TABLE 15.6
SHOULD YOU GO TO BUSINESS SCHOOL?
SALARIES BEFORE AND AFTER BUSINESS SCHOOL
PRE-MBA SALARY
AVERAGE SALARY 3
YEARS AFTER MBA
Indian Institute of Management,
Ahmedabad (India)
$69,222
$174,440
Insead (France/Singapore)
$71,141
$147,974
London Business School
$63,074
$146,332
International Institute for Management
Development (IMD) (Switzerland)
$77,005
$145,539
University of Cambridge: Judge (UK)
$67,400
$135,475
Hong Kong UST Business School (China)
$55,097
$133,475
HEC Paris (France)
$59,848
$123,287
Incae Business School (Costa Rica)
$43,307
$89,212
UNIVERSITY
INTERNATIONAL BUSINESS SCHOOLS
Should you go to business school? As we have just seen, the financial part of
this decision is easy: Though costly, the return on this investment is very high.
Of course, there are other factors that might influence your decision.
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15.8 Intertemporal Production
Decisions—Depletable Resources
Production decisions often have intertemporal aspects—production today
affects sales or costs in the future. Intertemporal production decisions involve
comparisons between costs and benefits today with costs and benefits in the
future.
The Production Decision of an Individual Resource Producer
How fast must the price rise for you to keep the oil in the ground?
Your production decision rule is: Keep all your oil if you expect its price less its
extraction cost to rise faster than the rate of interest. Extract and sell all of it if
you expect price less cost to rise at less than the rate of interest.
Letting Pt be the price of oil this year, Pt+1 the price next year, and c the cost of
extraction, we can write this production rule as follows:
If 𝑃𝑡+1 − 𝑐 > 1 + 𝑅 𝑃𝑡 − 𝑐 , keep the oil in the ground.
If 𝑃𝑡+1 − 𝑐 < 1 + 𝑅 𝑃𝑡 − 𝑐 , sell the oil now.
If 𝑃𝑡+1 − 𝑐 = 1 + 𝑅 𝑃𝑡 − 𝑐 , makes no difference.
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FIGURE 15.4
PRICE OF AN EXHAUSTIBLE RESOURCE
In (a), the price is shown rising over time. Units of a resource in the ground must
earn a return commensurate with that on other assets. Therefore, in a competitive
market, price less marginal production cost will rise at the rate of interest.
Part (b) shows the movement up the demand curve as price rises.
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The Behavior of Market Price
Suppose there were no OPEC cartel and the oil market consisted of many
competitive producers with oil wells like our own.
We could then determine how quickly oil prices are likely to rise by considering
the production decisions of other producers.
Price less marginal cost must rise at exactly the rate of interest. To see why,
suppose price less cost were to rise faster than the rate of interest. In that case,
no one would sell any oil. Inevitably, this would drive up the current price.
If, on the other hand, price less cost were to rise at a rate less than the rate of
interest, everyone would try to sell all of their oil immediately, which would drive
the current price down.
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User Cost
● user cost of production Opportunity cost of producing and selling
a unit today and so making it unavailable for production and sale in the
future.
We saw in Chapter 8 that a competitive firm always produces up to the point at
which price is equal to marginal cost. However, in a competitive market for an
exhaustible resource, price exceeds marginal cost (and the difference between
price and marginal cost rises over time).
The reason is that the total marginal cost of producing an exhaustible resource
is greater than the marginal cost of extracting it from the ground. There is an
additional opportunity cost because producing and selling a unit today makes it
unavailable for production and sale in the future.
In Figure 15.4, user cost is the difference between price and marginal
production cost. It rises over time because as the resource remaining in the
ground becomes scarcer, the opportunity cost of depleting another unit
becomes higher.
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Resource Production by a Monopolist
Since the monopolist controls total output, it will produce so that marginal
revenue less marginal cost—i.e., the value of an incremental unit of resource—
rises at exactly the rate of interest:
MR 𝑡+1 − 𝑐 = 1 + 𝑅 MR 𝑡 − 𝑐
If marginal revenue less marginal cost rises at the rate of interest, price less
marginal cost will rise at less than the rate of interest.
We thus have the interesting result that a monopolist is more conservationist
than a competitive industry.
In exercising monopoly power, the monopolist starts out charging a higher price
and depletes the resource more slowly.
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EXAMPLE 15.7
HOW DEPLETABLE ARE DEPLETABLE RESOURCES
Depletable resources, such as oil, natural gas, and
helium, have known and potentially discoverable inground reserves equal to only 50 to 100 years of
current consumption. For these resources, the user
cost of production can be a significant component of
the market price. Other resources, such as coal and
iron, have very large reserves. For these resources,
the user cost is very small.
TABLE 15.7
If the market is competitive, user cost can
be determined from the economic rent
earned by the owners of resource-bearing
lands.
Resource depletion has not been very
important as a determinant of resource
prices over the past few decades. Much
more important have been market structure
and changes in market demand. But over
the long term, depletion will be the ultimate
determinant of resource prices.
RESOURCE
USER COST AS A FRACTION
OF COMPETITIVE PRICE
USER COST/
COMPETITIVE PRICE
Crude oil
.4 to .5
Natural gas
.4 to .5
Uranium
.1 to .2
Copper
.2 to .3
Bauxite
.005 to .2
Nickel
.1 to .3
Iron ore
.1 to .2
Gold
.05 to .1
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15.9 How Are Interest Rates Determined?
An interest rate is the price that borrowers pay lenders to use their
funds.
FIGURE 15.5
SUPPLY AND DEMAND FOR
LOANABLE FUNDS
Market interest rates are
determined by the demand and
supply of loanable funds.
Households supply funds in
order to consume more in the
future; the higher the interest
rate, the more they supply.
Households and firms both
demand funds, but the higher
the interest rate, the less they
demand.
Shifts in demand or supply
cause changes in interest
rates.
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A Variety of Interest Rates
● Treasury Bill Rate A Treasury bill is a short-term (one year or less) bond
issued by the U.S. government. It is a pure discount bond—i.e., it makes no
coupon payments but instead is sold at a price less than its redemption
value at maturity.
● Treasury Bond Rate A Treasury bond is a longer-term bond issued by the
U.S. government for more than one year and typically for 10 to 30 years.
Rates vary, depending on the maturity of the bond.
● Discount Rate Commercial banks sometimes borrow for short periods from
the Federal Reserve. These loans are called discounts, and the rate that the
Federal Reserve charges on them is the discount rate.
● Federal Funds Rate This is the interest rate that banks charge one another
for overnight loans of federal funds. Federal funds consist of currency in
circulation plus deposits held at Federal Reserve banks.
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● Commercial Paper Rate Commercial paper refers to short-term (six
months or less) discount bonds issued by high-quality corporate borrowers.
Because commercial paper is only slightly riskier than Treasury bills, the
commercial paper rate is usually less than 1 percent higher than the
Treasury bill rate.
● Prime Rate This is the rate (sometimes called the reference rate) that large
banks post as a reference point for short-term loans to their biggest
corporate borrowers.
● Corporate Bond Rate Newspapers and government publications report the
average annual yields on long-term (typically 20-year) corporate bonds in
different risk categories (e.g., high-grade, medium-grade, etc.). These
average yields indicate how much corporations are paying for long-term
debt. However, as we saw in Example 15.2, the yields on corporate bonds
can vary considerably, depending on the financial strength of the
corporation and the time to maturity for the bond.
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