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Capital, Interest, and
Corporate Finance
CHAPTER
13
© 2003 South-Western/Thomson Learning
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Production, Saving, and Time
Since production takes time, it cannot
occur without prior saving
For example, while Jones is waiting for
his current crop to grow, he must rely
on food saved from prior production
Jones could take some of his time to
make a plow which would increase his
productivity
However, making the plow is time
consuming
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Production, Saving, and Time
In making the plow, Jones engages in
roundabout production
That is, when Jones produces capital he
hopes to increase his future productivity
An increased amount of roundabout
production in an economy means that
more capital accumulates  more
goods can be produced in the future
Advanced industrial economies are
characterized by much roundabout
production  capital accumulation
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Production, Saving, and Time
Production requires saving because
both direct and roundabout production
requires time
Time during which goods and services
are not available from current
production
In modern economies, producers need
not rely exclusively on their own prior
saving by relying on financial
intermediaries for funds
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Consumption, Saving, and Time
Most consumers value present
consumption more than future
consumption  they have a positive
rate of time preference
Another explanation for this positive
rate of time preference is uncertainty
Because present consumption is valued
more than future consumption,
households must be rewarded to
postpone consumption  they must be
rewarded
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Consumption, Saving, and Time
By saving a portion of their income in
financial institutions, households forgo
present consumption for a greater
ability to consumer in the future
Interest is the reward offered
households for forgoing present
consumption
The interest rate is the annual interest
as a percentage of the amount saved
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Consumption, Saving, and Time
The higher the interest rate, other
things constant, the more consumers
are rewarded for saving  the more
willing they are to save
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Optimal Investment
In a market economy characterized by
specialization and exchange, firms need
not produce their own capital, nor must
they rely upon their own saving
They can purchase capital using
borrowed funds
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Optimal Investment
Suppose that the equipment is so
durable that it lasts indefinitely, and
that the price is expected to remain the
same in the future
Thus, the farm equipment will increase
revenue not only in the first year but
every year into the future
The optimal investment requires that
Jones take time into consideration
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Optimal Investment
Jones can’t simply equate the marginal
resource cost with marginal revenue
product
The marginal cost is an outlay this year,
whereas the marginal product is an
annual amount this year and each year
into the future
Markets bridge this time discrepancy
with the interest rate
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Optimal Investment
Jones must decide how much to invest
The first task is to compute the
marginal rate of return he would earn
each year by investing in farm
machinery
The marginal rate of return on
investment is capital’s marginal revenue
product as a percentage of its marginal
resource cost
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Optimal Investment
For example, the Tractor-Tiller yields a
marginal revenue product of $4,000 per
year and has a marginal resource cost of
$10,000
The rate of return Jones could earn on
this investment is $4,000 / $10,000 is
40%
The rates of return for all the pieces of
farm equipment are shown in column
(6)
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Optimal Investment
Given the marginal rates of return on
each piece of equipment, how much
should Jones invest in order to
maximize profits?
Suppose he borrows the money, paying
the market interest rate  Jones will
buy more capital as long as its marginal
rate of return exceeds the market
interest rate  he will stop before
capital’s marginal rate of return falls
below the market rate of interest
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Optimal Investment
If the market rate of interest is 20%,
Jones would invest in the first three
pieces of equipment  $30,000
Conversely, if the market rate of
interest falls to 10%, he will invest in
the Harrow as well and at 6% he will
invest in the Crop Sprayer
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Optimal Investment
The results would not change if Jones
used his own funds so long as he could
save at the market interest rate
That is, whether Jones borrows the
money or uses savings on hand, the
market interest rate represents his
opportunity cost of investing
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Summary of Steps
First, compute the marginal revenue
product of capital
Next divide the marginal revenue
product by the marginal resource cost
to determine the marginal rate of return
 the firm’s demand curve for
investment
The market interest rate is the
opportunity cost of investing
Firm should invest more as long as the
marginal rate of return on capital
exceeds the market interest rate
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Market for Loanable Funds
The major demanders of loans are firms
that borrow to invest in physical capital
At any time, each firm has a variety of
investment opportunities  they rank
their opportunities from highest to
lowest, based on their expected
marginal rates of return
Firms will increase their investment
until their expected marginal rate of
return just equals the market interest
rate
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Market for Loanable Funds
Firms are not the only demanders of
loans
Households are often willing to pay
extra to consume now rather than later
and one way to ensure that these goods
and services are available now is to
borrow for present consumption
Household demand curve for loans also
slopes reflecting consumers’ greater
willingness and ability to borrow at
lower interest rates, other things
constant
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Market for Loanable Funds
Banks play the role of financial
intermediaries in the market for
loanable funds
The loanable funds market brings
together savers, or suppliers of loanable
funds, and borrowers, or demanders of
loanable funds, to determine the market
rate of interest
The higher the interest rate, other things
constant, the greater the reward for saving
 the larger the quantity of loanable funds
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Demand for Loanable Funds
For the economy as a whole, if the
amount of other resources and the level
of technology are fixed, diminishing
marginal productivity causes the
marginal rate of return curve, which is
the demand curve for investment to
slope downward
The demand for loanable funds is based
on the expected marginal rate of return
these borrowed funds yield when
invested in capital
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Demand for Loanable Funds
Each firm has a downward-sloping
demand curve for loanable funds,
reflecting a declining marginal rate of
return on investment
With some qualifications, the demand
for loanable funds by each firm can be
summed horizontally to yield the
demand for loanable funds by all firms
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Why Interest Rates Differ
Thus far, we have been talking about
the market rate of interest, implying
that only one interest rate prevails in
the loanable funds market
At any particular time, however, a range
of interest rates coexist in the economy
Why do interest rates differ?
Risk  some borrowers are more likely than
others to default
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Why Interest Rates Differ
Duration of the loan
• Since the future is uncertain, and the further into
the future a loan is to be repaid, the more
uncertain that repayment becomes  lenders
require a higher interest rate
• Term structure of interest rates is the relationship
between the duration of the loan and the interest
rate charge
Cost of administration
• Costs of executing the loan agreement,
monitoring the loan, and collecting the payments
• These costs, as a proportion of the total amount
of the loan, decrease as the size of the loan
increases
Tax treatment
• Lower the tax rate, the lower the interest rate
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Present Value and Discounting
Because present consumption is valued
more than future consumption, present
and future consumption can’t be
directly compared
A way of standardizing the discussion is
to measure all consumption in terms of
its present value
Present value is the current value of a
payment or payments that will be
received in the future
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Present Value One Year Hence
Suppose the market interest rate is
10%, so you can either lend or borrow
at that rate
One way to determine how much you
would pay for the opportunity to receive
$100 one year from now is to ask how
much you would have to save now, at
the market interest rate, to end up with
$100 one year from now
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Present Value One Year Hence
That is, what amount of money, if saved
at a rate of interest of 10%, will
accumulate to $100 one year from now
We can calculate the answer with the
following formula
present value x 1.10 = $100, or
present value = ($100/1.10) = $90.91
That is, if the interest rate is 10%, $90.91 is
the present value of receiving $100 one year
from now
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Present Value One Year Hence
The procedure of dividing the future
payment by 1 plus the prevailing
interest rate in order to express it in
today’s dollars is called discounting
The interest rate used to discount future
payments is called the discount rate
Thus, the present value of $100 to be
received one year from now depends on
the interest or discount rate
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Present Value One Year Hence
The more that present consumption is
preferred to future consumption, the
higher the interest rate that must be
offered savers to defer consumption
That is, the higher the interest rate, or
discount rate, the more the future
payment is discounted and the lower its
present value
Alternatively, the higher the interest rate,
the less you need to save now to yield a
given amount in the future
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Present Value One Year Hence
Conversely, the less present
consumption is preferred to future
consumption, the less savers need to be
paid to defer consumption and the
lower the interest rate
The lower the interest rate, or discount rate,
the less the future income is discounted and
the greater its present value
A lower interest rate means that individuals
must save more now to yield a given
amount in the future
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Present Value One Year Hence
As a general rule, the present value of
receiving an amount one year from now is:
PV 
amount received one year from now
1  interest rate
Example: when the interest rate is 5%, the
present value of receiving $100 one year
from now is: $100/ 1.05 = $95.24
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Present Value in Later Years
Now consider the present value of
receiving $100 two years from now 
what amount of money, if deposited at
the market rate of interest of 5%,
would yield $100 two years from now?
At the end of the first year, the value
would be the present value x 1.05,
which would then earn the market
interest rate during the second year 
the following equation
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Present Value in Later Years
Present value x 1.05 x 1.05 =
present value x (1.05)2 = $100
$100
$
100
PV 

 $90.70
2
1.1025
(1.05)
M
PV 
t
(1  i )
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Present Value in Later Years
Because (1 + i) is greater than 1, the
more times it is multiplied by itself (as
determined by t), the smaller the
present value
Thus, the present value of a given
payment will be smaller the further into
the future that payment is to be
received
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Present Value of an Income Stream
The previous method is used to compute
the present value of a single sum to be
paid at some point in the future
More investments, however, yield a
stream of income over time
In cases where the income is received
over a period of years, the present value
of each receipt can be computed
individually and the results summed to
yield the present value of the entire
income stream
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Present Value of an Annuity
A given sum of money received each
year for a specified number of years is
called an annuity
Such an income stream is called a
perpetuity if it continues indefinitely
into the future
As a practical matter, the present value
of receiving a particular amount forever
is not much more than that of receiving
it for, say 20 years, because of
discounting
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Corporate Stock and Retained Earnings
Corporations acquire funds for
investment in three ways
Issuing stock
Retaining some of their profits
borrowing
An entrepreneur is a profit-seeking
decision-maker who organizes an
enterprise and assumes the risk of
operation
Pays resource owners for the opportunity to
use those resources in the firm
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Corporate Stock and Retained Earnings
The initial sale of stock to the public is
called an initial public offering, or an
IPO
A share of corporate stock
Represents a claim on the net income and
assets of a corporation, and
The right to vote on corporate directors and
on other important matters
One share of stock leads to one vote
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Corporate Stock and Retained Earnings
Corporations must pay corporate
income taxes on any profit
After-tax profit is either paid as
Dividends to shareholders
Reinvested profit is called retained earnings
and allows the firm to finance expansion
Corporations are not required to pay
dividends
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Corporate Bonds
A bond is the corporation’s promise to
pay back the holder a fixed sum of
money on the designated maturity date
plus make annual interest payments
until that date
The payment stream for bonds is more
predictable than that for stocks
Unless the corporation goes bankrupt, it
is obliged to pay bondholders the
promised amounts  less risky
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Securities Exchanges
Once stocks and bonds have been
issued and sold, owners of these
securities are free to resell them on
security exchanges
There are seven security exchanges in
the U.S. with the two largest being the
New York Stock Exchange and the
Nasdaq
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Securities Exchanges
Institutional investors, such as banks,
insurance companies and mutual funds
account for over half the trading volume
on major exchanges
By providing a secondary market for
securities, exchanges enhance the
liquidity of these securities
The secondary markets for stocks also
determine the current market value of
the corporation
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Securities Exchanges
The share price reflects the present
value of the discounted stream of
expected profit
Security prices give the firm’s
management some indication of the
wisdom of raising investment funds
through retained earnings, new stock
issues, or new bond issues
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Securities Exchanges
The greater a corporation’s expected
profit, other things constant, the higher
the value of shares on the stock market
and the lower the interest rate that
would have to be paid on new bond
issues
Thus, securities markets allocate funds
more readily to successful firms than to
firms in financial difficulty
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