Transcript Chapter 14 - Capital Markets

Chapter 14
Capital
Markets
© 2004 Thomson Learning/South-Western
Time Periods and the Flow of
Economic Transactions
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Ways transactions can occur across periods.
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Individual Savings--The Supply of Loans.
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Durable goods that last more than one period.
An individual can borrow or lend.
Savings frees up resources that can be used to
produce investment goods.
Savings provide funds for firms to finance
investment goods.
Two-Period Model of Saving
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Suppose there are only two time periods.
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C0 is consumption this year.
C1 is consumption in the following year.
Only consumption yields utility which can be
purchased with current income, Y.
Income saved earns interest (at a real interest rate
of r) before it is used to buy C1.
The consumers goal is to maximize utility.
A Graphical Analysis
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The indifference curves in Figure 14.1 show
the utility obtainable from various combinations
of C0 and C1.
When C0 = Y, no income is saved for the
second period.
When C0 = 0, C1 = (1 + r)Y.
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The person can consume all income in the second
period plus what is earned in interest.
FIGURE 14.1: The Savings Decision
C
1
(1+r) Y
U3
U2
U1
5
Y
C0
A Graphical Analysis
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Between these two endpoints, the budget
constraint is the black straight line.
Utility is maximized at C*0, C*1 where the MRS
equals (1 + r).
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Utility is maximized where the rate the individual is
willing to trade C0 for
C1 equals the rate he or she is able to trade these in
the market through savings.
FIGURE 14.1: The Savings Decision
C
1
(1+r) Y
C*
1
U3
U2
U1
7
C*
0
Y
C0
Substitution and Income Effects of
a Change in r
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A change in r changes the “price” of future
versus current consumption.
The substitution effects of an increase in r are
shown in Figure 14.2.
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The move along U2 to S.
The higher opportunity cost of C0 rises and the
person substitutes C1 for C0.
The person saves more do to the increase in r.
FIGURE 14.2: Effect of an Increase in r
on Savings Is Ambiguous
C1
(1+r’) Y
(1+r) Y
S
C*
1
U2
9
C*0
Y
C0
Substitution and Income Effects of
a Change in r
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The income effect is S to C0**, C1**.
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The net effect of increased r on C0 (and on
savings) is ambiguous.
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If consumption in both periods is a normal good,
both should increase.
Savings increase if the substitution effect
dominates (as shown in Figure 14.2), but
decrease if the income effect dominates.
Savings probably increase with higher r.
FIGURE 14.2: Effect of an Increase in r
on Savings Is Ambiguous
C1
(1+r’) Y
(1+r) Y
C**
1
S
U3
C*
1
U2
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C** C*
0 0
Y
C0
Firms’ Demand for Capital and
Loans
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The profit maximizing firm will rent additional
capital equipment up to the point at which the
marginal revenue product of the equipment is
equal to the rental rate on the equipment.
Assume all firms rent all of the capital they use
from other firms.
Rental Rates and Interest Rates
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The per-period rate that firms have to pay to
rent the equipment will be determined by the
average costs that the rental firms incur.
Two important costs of the equipment are:
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Depreciation costs reflect the wear and tear.
Borrowing costs are the explicit or implicit
opportunity (interest) costs for the funds tied up in
the equipment.
Rental Rates and Interest Rates
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If depreciation (d) and borrowing (r = interest) costs are
proportional to the market price of the equipment being
rented (P) we have the following expression for the
per-period rental rate, v.
Rentalrate  v  Depreciation  Borrowing Costs
 dP  rP  (d  r ) P.
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Rental Rates and Interest Rates
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This equation shows why there is an inverse
relationship between the demand for
equipment and the interest rate.
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When the interest rate is high, rental rates will be
high and firms will try to substitute toward cheaper
inputs while low interest rates induce firms to rent
more equipment.
This will change the demand for loans, with low
rates encouraging greater borrowing.
Ownership of Capital Equipment
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Firms that own equipment are really in two
businesses.
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They produce goods.
They lease capital equipment to themselves.
The implicit rates they pay for leasing capital
equipment are the same as for a firm that rents
such equipment.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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Total U.S. personal savings amounted to less
than one percent of disposable income in
1998.
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This is a steep decline from earlier savings levels in
the U.S.
This is much lower than typical 10 percent rates
found in other countries.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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Concerns are whether individuals will have
adequate savings for their own retirement or to
provide sufficient capital accumulation for
future generations.
Recent attempts to stimulate savings.
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All allow tax deductions for contributions, and do not
tax assets in the plan until paid at retirement.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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Individual Retirement Accounts (IRAs).
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401(k) Plans
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Set up by individuals acting on their own.
Only low-income individuals receive tax deductions,
but everyone can avoid taxation of returns from
assets in the plan.
Set up by employers who sometimes match
employees contributions.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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Keogh Plans
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Both contributions and assets returns are taxexempt until retirement.
Similar to the other plans except that they are
intended for self-employed individuals.
These generally have higher contribution limits.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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The effect of these plans on savings is
ambiguous.
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The after-tax interest rate for savers is higher, but
the substitution and income effects work in opposite
directions.
Also, since only the contributions to specific plans
are apply, they provide incentives for individuals to
shift to these plans without changing their total
amount of savings.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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Most studies use date on individual savings
behavior.
Studies suggest that people have very different
attitudes toward savings.
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Some are serious savers who will accumulate
assets in many forms.
Others never save.
Plan participants are the serious saver types.
APPLICATION 14.1: Do We Need Tax
Breaks for Savers?
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But it is not possible to determine if these plans
themselves have increased savings.
A more correct interpretation is that plan
participation acts only to identify savers who
are predisposed to save more.
The true impact of these savings plans remains
unknown.
Determination of the Real Interest
Rate
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Figure 14.3 shows the supply of loans
assumed to be an upward sloping function of
the interest rate, r.
The demand for loans is negatively related to
the interest rate.
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Higher rates increase the equipment rental rate.
Q*, r* is the equilibrium, with the rate that links
economic time periods together.
FIGURE 14.3: The Real Interest Rate Is
Determined in the Market for Loans
Real interest
rate
S
r*
D
25
Q*
Quantity of loans
per period
Changes in the Real Interest Rate
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Factors that increases firms’ demand for
capital equipment will increase the demand
for loans. These include:
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Technical progress that makes equipment more
productive.
Declines in the equipment market prices.
Optimistic views of the demand for products.
The increased demand causes an increase in
the real interest rate.
Changes in the Real Interest Rate
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Factors that affect savings by individuals will
shift the supply curve of loans. These include
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Government-provided pension plans that reduce
individuals’ current savings which increases the real
interest rate.
Reductions in taxes on savings increase the supply
of loans and decrease the real interest rate.
APPLICATION 14.3: Inflation-Indexed
Bonds
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Most government bonds do not explicitly take
account of economy-wide inflation.
Recently, however, several nations have
issued “inflation-indexed” bonds that adjust
payments for changes in inflation.
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In theory, these bonds pay a real interest rate.
Israel, Australia, Turkey, and Brazil are significant
issuers of such bonds.
APPLICATION 14.3: Real and Nominal
Interest Rates
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Assume the nominal interest rate of i for a one-period
loan of $1 with a e percent expected increase in the
price level by next year.
The real value of your repayment will be:
(1  i )
Real Value of Repayment 
e
(1   ).
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APPLICATION 14.3: Real and Nominal
Interest Rates
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As previously shown, this real payment is also given by
(1 + r), where r is the real interest rate.
So,
(1  i )
.
e
(1   )
For reasonbly small rates this can be approximat ed by :
1 r 
r  i   e.
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APPLICATION 14.3: Real and Nominal
Interest Rates
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Nominal and real interest rates differ by the
expected rate of inflation, e.
This equation also provides a way to estimate
expected inflation.
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For example, on August 11, 1999 a 30-year U.S.
Treasury bond yield was 6.13 percent with a 4.00
percent rate on an indexed bond
The expected inflation rate was over 2 percent.
APPLICATION 14.3: The Design of
Inflation-Indexed Bonds
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The previous calculation assumed that
inflation-indexed bonds paid the real interest
rate.
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In the U.S., changes in the Consumer Price Index
(CPI) is used to adjust such bonds.
But, the IRS has decided that both the higher
interest payments caused by inflation and the
annual increase in redemption value are taxable.
APPLICATION 14.3: The Design of
Inflation-Indexed Bonds
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In addition, these bonds are subject to differing
risk factors.
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Thus, the actual, after-tax real interest rate
promised by inflation-indexed bonds may be much
lower than reported.
For nominal bonds, the risk is in higher inflation
rates.
For these bonds, the risk is in possible changes in
government policy toward them.
Present Discounted Value
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Transactions that take place at different times
cannot be compared directly because of the
interest that is received or paid.
A promise to pay a dollar today is not the same
as a promise to pay a dollar in one year.
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A dollar today is more valuable because it can be
invested at interest for the year.
Single-Period Discounting
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In a two period model, a dollar invested today
will grow by a factor of (1 + r) next year.
The present value of a dollar that will not be
received until next year is 1/(1 + r) dollars.
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The present value of $1 a year from now, with r =
0.05 is $0.95 [$0.95 = $1/(1.05)].
Present Value
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The present value is discounting the value of
future transactions back to the present day to
take account of the effect of potential interest
payments.
Table 14.1 demonstrates the discount factor for
various interest rates.
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The first row demonstrates that the higher the
interest rate, the smaller the discount factor.
Table 14.1: Present Discounted Value of $1 for
Various Time Periods and Interest Rates
Interest Rate
Years until Payment
Is Received
1
2
3
5
10
25
50
100
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1 Percent
$.99010
.98030
.97059
.95147
.90531
.78003
.60790
.36969
3 Percent
$.97087
.94260
.91516
.86281
.74405
.47755
.22810
.05203
5 Percent
$.95238
.90703
.86386
.78351
.61391
.29531
.08720
.00760
10 Percent
$.90909
.82645
.75131
.62093
.38555
.09230
.00852
.00007
Multiperiod Discounting
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The present value of $1 that is not to be paid
until n years in the future is given by:
$1
Present Value of $1 in n years 
.
n
(1  r )
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Table 14.1 shows various interest rates and
different values of n.
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For example, with r = 0.10 and n = 10, the present
value of $1 is $0.39.
Present Value and Economic
Motives
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The goal of the firm making decisions over time
is changed to “maximize the present value of
all future profits.”
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This yields nearly the same results as we have
shown for one period profit maximization.
This is sometimes stated as the firm makes
decisions to “maximize the present value of the
firm.”
Present Value and Economic
Motives
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For individuals, present value enters the utility
maximization decision through the budget
constraint.
In some cases, individuals may “discount” the
future in that they would prefer to consume in
the present relative to the future.
APPLICATION 14.4: Discounting Cash
Flows and Derivative Securities
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Mortgages typically are long-lived and there is an
active secondary market that permits the initial
lender to sell the mortgage.
Often many mortgages are sold in a bundle to gain
economies of scale in buying and selling.
Collateralized mortgage operations (CMOs) carry
this one step further by selling only a portion of the
cash flow such as the interest payments from a
given pool of mortgages.
APPLICATION 14.4: Discounting Cash
Flows and Derivative Securities
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Each expected cash flow from the CMO must
be appropriately discounted to the present.
Variability in payment complicates this
calculation:
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For example, an unexpected increase in
repayments increases the value of a “repayment
CMO” because the funds are available sooner.
APPLICATION 14.4: Discounting Cash
Flows and Derivative Securities
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A security, such as a CMO, is called a
“derivative” because its value is derived from
some underlying, more basic security such as
a mortgage.
Other examples include futures contracts on
commodities, metals, and foreign currencies
and options on common stocks or indexes of
common stocks.
APPLICATION 14.4: Discounting Cash
Flows and Derivative Securities
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Some firms aggregate their derivative portfolios
into a single stream of discounted cash flows.
They use historical data to study how changes
in the general economic environment might be
expected to affect those cash flows.
APPLICATION 14.4: Discounting Cash
Flows and Derivative Securities
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The Long-Term Capital Management hedge
fund, run by two recent Nobel prize winners in
economics, was such a fund.
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In the summer of 1998, cash flows did not follow
previous historical relationships and this fund ran
into serious problems.
The fund was bailed out by the U.S. Federal
Reserve.
Pricing of Exhaustible Resources
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Scarcity costs are the opportunity costs of
future production foregone because current
production depletes exhaustible resources.
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These are in addition to the usual production costs.
In Figure 14.4, the usual production marginal
costs are reflected in the supply curve, S.
FIGURE 14.4: Scarcity Costs Associated
with Exhaustible Resources
Price
S
P*
D
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0
Q*
Quantity
per week
Pricing of Exhaustible Resources
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Scarcity costs shift the marginal cost curve up
to S’.
Because of scarcity costs, current output falls
from Q* to Q’, and the market price increases
from P* to P’.
The charges effectively encourage
“conservation” of the exhaustible resource.
FIGURE 14.4: Scarcity Costs Associated
with Exhaustible Resources
S’
Price
P’
S
P*
D
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0
Q’
Q*
Quantity
per week
The Size of Scarcity Costs
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The actual value depends upon the future
resource price.
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For example, suppose the firm believes that
copper will sell for $1 per pound in 10 years.
Selling one pound today will mean $1 foregone in
the future since copper supply is fixed.
If r = 5 percent, the present value equals $0.61.
If production marginal costs = $0.35 per pound,
scarcity costs = $0.26 per pound ($0.61-$0.35).
Time Pattern of Resource Prices
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In the absence of change in real production
costs or firms’ expectations about future prices,
the relative price of resources should be
expected to rise over time at the real rate of
interest.
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In the previous example, with r = 5 percent, copper
prices would increase by 5 percent per year to equal
$1 in 10 years.
Time Pattern of Resource Prices
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If resource prices rose more slowly that the
real rate of interest, firms would invest
elsewhere decreasing supply and increasing
the resource price.
If resource prices rose faster than the real
rate of interest, firms would increase supply
and decrease its price.
Equilibrium could only occur if the price
increase equaled the real rate of interest.
APPLICATION 14.5: Are Any
Resources Scarce?
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Resource Price Trends
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As shown in Table 1, there has been a general trend
of a decrease in resource prices.
However, declining relative costs of extraction and
development may be masking rising scarcity costs.
Nevertheless, rising real resource prices driven by
scarcity is not yet a foregone conclusion.
Table 1: Real Prices for Natural
Resources (1990 = 100)
Resource
Petroleum
Coal
Copper
Iron Ore
Aluminum
Farmland
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1870
700
550
1,000
1,000
200
1910
250
350
500
750
800
375
1950
150
200
250
200
180
80
1970
80
110
160
120
110
105
1990
100
100
100
100
100
100
APPLICATION 14.5: Implications of
Scarcity
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The effect of rising natural resource prices on
GDP would depend upon such factors as:
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The ability of firms to substitute other inputs.
Types of resource-saving technical innovations.
Willingness of consumers to reduce consumption.
A fairly careful estimate suggests a reduction of
real economic growth of 0.3 percent by the
year 2050.