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Chapter 15
Investment, Time and
Capital Markets
Topics to be Discussed
 Stocks Versus Flows
 Present Discounted Value
 The Value of a Bond
 The Net Present Value Criterion for
Capital Investment Decisions
 Adjustments for Risk
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Topics to be Discussed
 Investment Decisions by Consumers
 Investments in Human Capital
 Intertemporal Production Decisions –
Depletable Resources
 How Are Interest Rates Determined?
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Introduction
 Markets for factors and output give a
reasonably complete picture
 Capital markets are different
Capital is durable
It is an input that will contribute to output
over a long period of time
Must compare the future value to current
expenditures
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Stocks Versus Flows
 Stock
Capital is a stock measurement
 The
amount of plant and equipment a company
owns at a point in time
 Flow
Variable inputs and outputs are flow
measurements
 An
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amount needed or used per time period
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Stocks Versus Flows
 Profit is also a flow number
 Must know what the capital stock will
allow the firm to earn a flow of profit
Was the investment a sound decision?
 Must be able to value today the expected
profit flow over time
What is the flow of profit worth today?
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Present Discounted Value (PDV)
 Determining the value today of a future
flow of income
The value of a future payment must be
discounted for the time period and interest
rate that could be earned
rate – rate at which one can borrow or
lend money
 Interest
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Present Discounted Value (PDV)
 Future Value (FV)
One dollar invested today should yield
(1 + R) dollars a year from now
(1 + R) is the future value of the dollar today
What is the value today of getting $1 a year
from now?
What is the present discounted value of the
$1?
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Present Discounted Value (PDV)
Future Dollar Value of $1 invested today  (1  R) n
n  Number of years in future
PDV  Present dollar value of $1 received
1
in the future 
; (how much would you have to
n
(1  R)
invest today to have a dollar in the future?)
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Present Discounted Value (PDV)
 The interest rate impacts the PDV
 The lower the interest rate, the less you
money you needed invest to reach your
future goal
 We can see how different interest rates
will give different future values
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PDV of $1 Paid in the Future
R
1 YR
5 YR
1%
$0.990
$0.951
$0.905
$0.742
2%
$0.980
$0.906
$0.820
$0.552
5%
$0.952
$0.784
$0.614
$0.231
10%
$0.909
$0.621
$0.386
$0.057
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10 YR
30 YR
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Valuing Payment Streams
 Can determine a stream of payments
over time
 Choosing a payment stream depends
upon the interest rate
 Given two streams, we can compute and
add the present values of each year’s
payment
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Two Payment Streams
Today
Payment Stream A:
Payment Stream B:
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Chapter 15
$100
$20
1 Year
$100
$100
2 Years
0
$100
13
Two Payment Streams
100
PDV of Stream A  100 
(1  R)
100
100
PDV of Stream B  20 

2
(1  R) (1  R)
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PDV of Payment Streams
R = .05
R = .10
R = .15
R = .20
PDV of Stream A:
$195.24
$190.90
$186.96
$183.33
PDV of Stream B:
205.94
193.54
182.57
172.78
 Notice that which stream is worth more depends
on the interest rate
 At lower interest rates, B pays out more
 As interest rates increase, A ends up paying out
more
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The Value of Lost Earnings
 PDV can be used to determine the value
of lost income from a disability or death
 Scenario
Harold Jennings died in an auto accident
January 1, 1986 at 53 years of age
Salary: $85,000
Retirement Age: 60
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The Value of Lost Earnings
 What is the PDV of Jennings’ lost income
to his family?
Must adjust salary for predicted increase (g)
 Assume
an 8% average increase in salary for
the past 10 years
 Average rate of growth of airline pilot salary
over time
Must adjust for the true probability of death
(m) from other causes
 Derived
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from mortality tables
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The Value of Lost Earnings
 Must adjust for the true probability of
death (m) from other causes
Derived from mortality tables
 Assume R = 9%  The rate on
government bonds
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The Value of Lost Earnings
W0 (1  g )(1  m1 )
PDV  W0 
(1  R )
W0 (1  g ) (1  m2 )

 ...
2
(1  R )
2
W0 (1  g ) (1  m7 )

7
(1  R )
7
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Calculating Lost Wages
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The Value of Lost Earnings
 Finding PDV
The summation of column 4 will give the
PDV of lost wages – $650,252
Jennings’ family could recover this amount
as partial compensation for his death
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The Value of a Bond
 A bond is a contract in which a borrower
agrees to pay the bondholder (the lender)
a stream of money
 Example: A bond issued by a company
may make a “coupon” payment of $100
per year for the next 10 years and a final
payment of $1000
How much would you pay for this bond?
Present value of payment stream
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The Value of a Bond
 Determining the Price of a Bond
Coupon Payments = $100/yr. for 10 yrs.
Principal Payment = $1,000 in 10 yrs.
$100
$100
PDV 


2
(1  R) (1  R )
$100
$1000
... 

10
10
(1  R )
(1  R )
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Present Value of the Cash Flow
from a Bond
PDV of Cash Flow
($ thousands)
2.0
The higher the interest
rate, the lower the value of
the bond
1.5
1.0
0.5
0
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0.05
0.10
Interest Rate
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0.15
0.20
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The Value of a Bond
 Perpetuity is a bond that pays out a fixed
amount of money each year forever
 Present value of a perpetuity is an infinite
summation
 Can express the value of a perpetuity by
PDV = $100/R
 In general, PDV = payment/R
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The Effective Yield on a Bond
 Corporate and government bonds are
often traded on the bond market
 The price of the bond can be determined
by looking at the market price
The value placed on it by buyers and sellers
 To compare the bond with other
investment options, can determine the
interest rate consistent with that value
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Effective Yield on a Bond
 Calculating the Rate of Return from a
Bond
 P is value of perpetuity – market price
 Can use equations to find value of R
given P and the payment
Payment
Payment
P
then R 
R
P
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Effective Yield on a Bond
 From previous example
R = $100/$1000 = 0.10 = 10%
 The interest rate calculated here is the
effective yield
Rate of return one receives by investing in
the bond
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Effective Yield on a Bond
 Calculating the Rate of Return from a
Bond
$100
$100


2
(1  R) (1  R)
$100
$1000
... 

10
(1  R)
(1  R)10
Calculate R in terms of P
Coupon Bond : PDV 
 See graph showing how R depends on P
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PDV of Payments (Value of Bond)
($ thousands)
Effective Yield on a Bond
2.0
The effective yield is the interest
rate that equates the present
value of a bond’s payment
stream with the bond’s market price.
1.5
Notice the Bond Price
is inverse to the
effective yield
1.0
0.5
0
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0.05
0.10
Interest Rate
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0.15
0.20
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Effective Yield on a Bond
 Yields vary on different bonds
Ex: Corporate bonds yield more than
government bonds
The degree of risk a bond holds is reflected
in the yield
 Riskier
bonds have higher yields
 Government unlikely to default
 Some corporations are more stable than others
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The Yields on Corporate Bonds
 In order to calculate corporate bond
yields, the face value of the bond and the
amount of the coupon payment must be
known
 Assume:
IBM and Lucent both issue bonds with a face
value of $100 and make coupon payments
every six months
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Yields on Corporate Bonds
Closing prices for IBM on March 5, 2003
7 ½ 13
6.2
10
120.25
-.38
Closing prices for Lucent on March 5, 2003
5 ½ 08
7.5
129
73.50
-.38
Wall Street Journal, 3/6
•7.5: coupon payments for one year ($7.5)
•13: maturity date of bond (2013)
•6.2: annual coupon/closing price ($7.5/120.25)
•10: number of bonds traded that day (10)
•120.25: closing price ($120.25)
•-.38: change in price from previous day (down 0.38)
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The Yields on Corporate Bonds
 The IBM bond yield:
Assume annual payments and 10 years to
maturity
7.5
7.5
7.5
100
120 .25 

 ... 

2
10
(1  R) (1  R)
(1  R)
(1  R)10
R*  4.9%
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The Yields on Corporate Bonds
 The Lucent bond matures in 5 years and
has a yield of:
5.5
5.5
5.5
100
73.50 

 ... 

2
5
5
( 1  R) ( 1  R)
(1  R) ( 1  R)
R*  13.0%
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The Yields on Corporate Bonds
 In 2003, Lucent had significant decline in
revenue, laid off many workers and had
an uncertain future
 The more risky financial situation
required a higher yield on the bonds to
entice investors to buy
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The Net Present Value Criterion
for Capital Investment Decisions
 Firms have to decide when and how
much capital to invest in
 Comparing the present value (PV) of the
cash flows from the investment to the
cost of the investment can give firms
information needed to make worthwhile
decisions
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The Net Present Value Criterion
for Capital Investment Decisions
 NPV Criterion
Firms should invest if the present value of
the expected future cash flows from an
investment exceeds the cost of the
investment
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The Net Present Value Criterion
for Capital Investment Decisions
 C  capital cost
 n  profits for n years (n  10)
1
2
NPV  - C 

 ... 
 10
(1  R) (1  R)
(1  R)10
R  discount rate or opportunit y cost of capital
2
with a similar risk
Invest if NPV  0
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The Net Present Value Criterion
for Capital Investment Decisions
 Determining the Discount Rate
The firm must determine the opportunity cost
of its money
The correct value of the discount rate should
equal the rate that the firm could earn on a
similar investment
 One
with same risk
We assume no risk for now, so opportunity
cost is what the firm could earn on a
government bond
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The Net Present Value Criterion
for Capital Investment Decisions
 The Electric Motor Factory (choosing to
build a $10 million factory)
8,000 motors/ month for 20 yrs
 Cost
= $42.50 each
 Price = $52.50/motor
 Profit = $10/motor or $80,000/month
 Factory life is 20 years with a scrap value of $1
million
Should the company invest?
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The Net Present Value Criterion
for Capital Investment Decisions
 Assume all information is certain (no risk)
R = government bond rate
.96
.96


2
(1  R )
(1  R )
.96
1
... 

(1  R ) 20
(1  R ) 20
R*  7.5%
NPV  - 10 
Discount rates below 7.5, NPV is positive
Discount rates above 7.5, NPV is negative
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Net Present Value of a Factory
10
•Firm should not invest for
discount rates below 7.5
•Firm should not invest for
discount rates above 7.5
8
Net Present Value
($ millions)
6
4
2
0
-2
-4
-6
0
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0.05
0.10
Interest Rate, R
R* = 7.5
Chapter 15
0.15
0.20
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The Net Present Value Criterion
for Capital Investment Decisions
 When determining whether to invest or
not, must distinguish between real and
nominal rates
 Real versus Nominal Discount Rates
Adjusting for the impact of inflation
Assume price, cost, and profits are in real
terms
 Inflation
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= 5%
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Real Versus Nominal Discount
Rates
 Assume price, cost, and profits are in real
terms
Therefore,
P
= (1.05)(52.50) = 55.13, Year 2
P = (1.05)(55.13) = 57.88…
 C = (1.05)(42.50) = 44.63, Year 2, C =….
 Profit remains $960,000/year
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Real Versus Nominal Discount
Rates
 If the cash flows are in real terms, then
the discount rate must be in real terms as
well
Opportunity cost of the investment, so must
include inflation here if doing it elsewhere
Real R = nominal R - inflation = 9% - 5% =
4%
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Net Present Value of a Factory
10
If R = 4%, the NPV is
positive. The company
should invest in
the new factory.
8
Net Present Value
($ millions)
6
4
2
0
-2
-4
-6
0
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0.04**
0.10
Interest Rate, R
Chapter 15
0.15
0.20
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The Net Present Value Criterion
for Capital Investment Decisions
 Negative Future Cash Flows
Companies expect losses in certain
situations
 Take
time to build demand
 High up front costs that lower over time
Investment should be adjusted for
construction time and losses
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The Net Present Value Criterion
for Capital Investment Decisions
 Electric Motor Factory
Construction time is 1 year
 $5
million expenditure today
 $5 million expenditure next year
Expected loss is $1 million the first year and
$0.5 million the second year
Profit is $0.96 million/yr. until year 20
Scrap value is $1 million
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The Net Present Value Criterion
for Capital Investment Decisions
.5
1
5


NPV  - 5 3
2
(1  R) (1  R) (1  R)
.96
.96
 ...


5
4
(1  R) (1  R)
1
.96


20
(1  R) 20
(1  R)
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Adjustments for Risk
 Determining the discount rate for an
uncertain environment:
This can be done by increasing the discount
rate by adding a risk-premium to the riskfree rate
 Amount
of money that a risk-averse individual
will pay to avoid taking a risk
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Diversifiable vs.
Nondiversifiable Risk
 Diversifiable risk can be eliminated by
investing in many projects or by holding
the stocks of many companies
 Nondiversifiable risk cannot be
eliminated and should be entered into the
risk premium
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Diversifiable vs.
Nondiversifiable Risk
 Diversifying spreads risk over many
options
Invest in many types of investments –
diversify portfolio
Firms invest in many different projects
No reward for assets that have only
diversifiable risk – tend to earn return close
to risk free return on average
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Diversifiable vs.
Nondiversifiable Risk
 Some risk cannot be eliminated or
avoided
Company profits depend on the economy –
boom or recession
Future economic growth is uncertain so
cannot eliminate all risk
 Investors
should be rewarded for bearing this
risk
Opportunity cost of investing is higher – must
include risk premium
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Diversifiable vs.
Nondiversifiable Risk
 The 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
If you invest in a mutual fund, there is no
diversifiable risk but there is nondiversifiable
risk since stocks tend to move with economy
 Expected
return on stock is higher than risk free
investment
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Capital Asset Pricing Model
 Suppose you invest in the entire stock
market (mutual fund)
rm = expected return of the stock market
rf = risk free rate
rm - rf = risk premium for nondiversifiable risk
Additional expected return you get for
bearing the nondiversifiable risk of the stock
market
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Capital Asset Pricing Model
 Return on some assets is correlated with
stock market as a whole
CAPM summary of relationship between
expected return and risk premium
ri  r f   (rm  r f )
ri  expected return on an asset
  asset beta
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Adjustments for Risk
 The asset beta, , measures the
sensitivity of an asset’s return to market
movements and, therefore, the asset’s
nondiversifiable risk
1% rise in market resulting in a 2% rise in
asset price means the beta is 2
1% rise in market resulting in a 1% rise in
asset price means beta is 1
The larger the beta, the greater the expected
return on the asset
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Adjustments for Risk
 Given beta, we can determine the correct
discount rate to use in computing an
asset’s net present value:
Discount Rate  r f   ( rm  r f )
 Risk-free rate plus a risk premium to
reflect nondiversifiable risk
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Determining Beta
 For a stock, beta determined statistically
 For a factory, determining beta is more
difficult
 Firms often use the company cost of
capital as nominal discount rate
Weighted average of the expected return on
a company’s stock and the interest rate that
it pays for debt
Can depend on level of nondiversifiable risk
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Investment Decisions by
Consumers
 Consumers face similar investment
decisions when they purchase a durable
good
Compare flow of future benefits with the
current purchase cost
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Investment Decisions by
Consumers
 Benefits and Costs of Buying a Car
If you keep the car for 5 or 6 years, you have
benefits that occur in the future
Must compare the future flow of net benefits
from owning the car (having transportation
minus cost of insurance, maintenance and
gas) with the purchase price
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Benefits and Costs of Buying a
Car
S = dollar value of transportation services in
dollars to a consumer
E = total operating cost/yr
 Insurance,
Maintenance, and Gas
Price of car is $20,000
Resale value of car is $4,000 in 6 years
 Decision to buy the car can be framed in
net present value terms
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Investment Decisions by
Consumers
 Benefits and Cost
(S  E )
NPV   20,000  ( S  E ) 

(1  R)
(S  E )
(S  E )
4000
 ... 

2
6
6
(1  R)
(1  R) (1  R)
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Investment Decisions by
Consumers
 Whether you should buy the car or not
depends on the discount rate
If you have to borrow money, then use
interest loan rate
 When comparing to buy or lease, you
can use same calculation
High interest rate, often better to lease
Low interest rate, often better to buy
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Choosing an Air Conditioner
 When buying an air conditioner, must
typically face a tradeoff between
efficiency and cost
Efficiency – how much energy used to cool
Do you want to pay more now for lower long
run costs or do you want to pay less now for
higher long run costs?
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Choosing an Air Conditioner
 Buying a new air conditioner involves
making a trade-off
Air Conditioner B
 High
price and more efficient
Both have the same cooling power
Assume an 8 year life
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Choosing an Air Conditioner
OCi
PDV  Ci  OCi 

(1  R)
OCi
OCi
 ...
2
(1  R)
(1  R)8
Ci is the purchase price of i
OCi is the average operating cost of i
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Choosing an Air Conditioner
 Should you choose A or B?
Depends on the discount rate
 If
you borrow, the discount rate would be high
 Probably
choose a less expensive and inefficient
unit
 If
you have plentiful cash, the discount rate
would be low
 Probably
©2005 Pearson Education, Inc.
choose the more expensive unit
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Investments in Human Capital
 Individuals make choices on whether to
invest in human capital
Do I finish college?
Do I go to graduate school?
 Human capital is the knowledge, skills,
and experience that make an individual
more productive and thereby able to earn
a higher income over a lifetime
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Investments in Human Capital
 Typically the investment in human capital
pays off in the future in terms of higher
pay, better promotions, and/or more job
opportunities
 How does one decide to invest in human
capital?
Can use the net present value rule from
before
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Investments in Human Capital
 Suppose you are deciding to go to
college for 4 years or skip college and go
to work
Assume purely financial basis (ignore
pleasure or pain from college)
Calculate net present value of costs and
benefits of going to college
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Investments in Human Capital
 Major costs for college
Opportunity cost of lost wages –
approximately $20,000 per year
Costs for tuition, room and board, and
related expenses – assume $20,000 per year
Total economic costs of attending college are
$40,000 per year for 4 years
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Investments in Human Capital
 Benefits of college
Higher salary throughout working life
 On
average, college grad earns $20,000 higher
than high school grad
 Assume that persists for 20 years
 Can now calculate net present value of
investing in a college education
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Investments in Human Capital
40
40
40
NPV  40 

 ... 
2
(1  R) (1  R)
(1  R)3
20
20

 ... 
4
(1  R)
(1  R) 23
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Investments in Human Capital
 What discount rate should be used?
We are ignoring inflation, so you should use
a real discount rate
About 5% would reflect opportunity cost of
money for many households
 Return
of investing in other assets
This gives an NPV of about $66,000;
therefore, investing in college is a good idea
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Investments in Human Capital
 Although NPV is positive, it is not very
large
 Almost free entry system to attend
college
 Free entry markets tend to lead to zero
economic profits
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Should You Go to Business
School?
 Getting an MBA often means a large
increase in salary
 Can see the typical change in salary from
getting an MBA from top business
schools
 For US as a whole, average salary preMBA is about $45,000 and obtaining the
MBA increases salary by about $30,000
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Should You Go to Business
School?
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Should You Go to Business
School?
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Should You Go to Business
School?
 Assuming the $30,000 per year gain
persists for 20 years
 Typical MBA takes 2 years and has
expenses of about $45,000
 Opportunity cost of forgone pre-MBA
salary is also $45,000 per year
 Total economic cost of getting MBA is
$90,000
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Should You Go to Business
School?
 Net present value of the investment is
90
30
30
NPV  90 

 ... 
2
(1  R) (1  R)
(1  R) 21
 With real discount rate of 5%, NPV is
about $158,000
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Should You Go to Business
School?
 Why is payoff from MBA in Table 15.6 so
much greater than from 4-year undergrad
degree?
Entry into many MBA programs, especially
those listed in table, is highly selective and
difficult
Many more people apply than are accepted,
so return remains high
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Should You Go to Business
School?
 Financial decision is easy
Although costly, return is very high
But some find it more fun than others
Many do not have undergraduate grades and
test scores to go to business school
You may find a career you like better, such
as teaching or law
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Intertemporal Production Decisions
– Depletable Resources
 Firms’ production decisions often have
intertemporal aspects – production today
affects sales or costs in the future
Firms may gain experience, which lowers
future costs
Use of depletable resources – extracting the
resource today means less is available in the
future
 Must take these into account in decisions
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Intertemporal Production Decisions
– Depletable Resources
 Scenario
You are given an oil well containing 1000
barrels of oil
MC and AC = $10/barrel
Should you produce the oil or save it?
 If
you only look at extraction costs versus price,
you ignore an important piece – opportunity cost
 Decision depends on price today, but also on
how fast you expect the price to rise in future
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Intertemporal Production Decisions
– Depletable Resources
 If you expect price of oil to rise slowly,
might be better off extracting today
 If you expect price of oil to rise rapidly,
better off waiting and extracting later
 How fast must price rise to keep in
ground?
Value must rise at least as fast as the rate of
interest
Can show this mathematically
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Intertemporal Production Decisions
– Depletable Resources
 Scenario
Pt = price of oil this year
Pt+1 = price of oil next year
C = extraction costs
R = interest rate
If ( Pt 1  c)  (1  R)( Pt  c) : Keep the oil in the ground
If ( Pt 1  c)  (1  R)( Pt  c) : Sell all the oil now
If ( Pt 1  c)  (1  R)( Pt  c) : Indifferen t
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Intertemporal Production Decisions
– Depletable Resources
 Do not produce 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
 But how fast will the price of oil rise?
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The Behavior of Market Price
 If OPEC cartel didn’t exist, could estimate
oil prices by production decisions of
producers
 To maximize return, producers will follow
production rule stated previously
Price minus marginal cost must rise at
exactly the rate of interest
Why?
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The Behavior of Market Price
 If price – MC rose faster than R, no one
would produce oil
This would drive up market price of oil
 If price – MC rose slower than R,
everyone would try to sell all their oil
This would drive down the market price of oil
 Can show how market price must rise
given these situations
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Price of an Exhaustible
Resource
Price
Price
PT
Demand
P0
P-c
P0
c
c
Marginal Extraction
Cost
T
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Quantity
92
Price of an Exhaustible
Resource
 Notice P > MC
Is it a contradiction to the competitive rule
that P = MC?
 Total
marginal cost must include extraction
costs AND opportunity cost
User cost of production
 Opportunity
cost of producing and selling a unit
today, making it unavailable for production and
sale in the future
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Price of an Exhaustible
Resource
 P = MC
MC = extraction cost + user cost
User cost = P - marginal extraction cost
 User cost rises over time
As resource remaining in ground becomes
scarcer, opportunity cost of depleting another
unit becomes higher
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Resource Production by a
Monopolist
 How would a monopolist choose their
rate of production?
Value of unit is marginal revenue minus
marginal cost
They will produce so that marginal revenue
less marginal cost rises at exactly the rate of
interest, or
(MRt+1 – c) = (1 + R)(MRt – c)
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Resource Production by a
Monopolist
 For a monopolist with a downward
sloping demand, price is greater than MR
 (MR – MC) < (P – MC)
 The monopolist is more conservationist
than in a competitive industry
They start out charging a higher price and
deplete the resources more slowly
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How Depletable Are Depletable
Resources?
 For some resources such as oil, natural
gas and helium, in ground reserves are
only equal to about 50 – 100 years of
current consumption
User cost is a significant part of market price
 For resources like coal and iron, reserves
are close to thousands of years of current
consumption
User cost is very small
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How Depletable Are Depletable
Resources?
 Can estimate user cost from geological
information about existing and potential
reserves
 Also need to know demand curve and
likely factors shifting it over time
 In competitive market, determine user
cost from economic rent earned by
owners of resource-bearing lands
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User Cost as Fraction of
Competitive Price
Resource
User Cost/Competitive Price
Crude Oil
0.4 – 0.5
Natural Gas
0.4 – 0.5
Uranium
0.1 – 0.2
Copper
0.2 – 0.3
Bauxite
0.05 – 0.2
Nickel
0.1 – 0.3
Iron Ore
0.1 – 0.2
Gold
0.05 – 0.1
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How Depletable Are
Depletable Resources?
 Notice that only crude oil and natural gas
have a user cost as a substantial
component of price
 Of the sharp price fluctuations, user cost
has almost nothing to do with them
Oil prices change from OPEC and conflict in
Persian Gulf
 Resource depletion has not had much
effect on the prices of those resources
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How Are Interest Rates
Determined?
 The interest rate is the price that
borrowers pay lenders to use their funds
Determined by supply and demand for
loanable funds
Supply of loanable funds comes from
household savings
Demand for loanable funds comes from
 Household
consuming more than income
 Firms wanting to make capital investments
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How Are Interest Rates
Determined?
 For households, the higher the interest
rate, the greater the cost of consuming
Less willing to borrow
Demand is declining function of interest rate
 Firms invest in project when NPV > 0
Higher interest rate means lower NPV
Demand is downward sloping
 Total demand for loanable funds is sum
of household demand and firm demand
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How Are Interest Rates
Determined?
R
Interest
Rate
DH and DF, the quantity
demanded for loanable
funds by households (H)
and firms (F), respectively,
varies inversely
with the interest rate.
DF
DH
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Quantity of
Loanable Funds
103
Supply and Demand for
Loanable Funds
R
Interest
Rate
S
Equilibrium interest
rate is R*.
R*
DF
DH
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Quantity of
Loanable Funds
104
How Are Interest Rates
Determined?
 The supply and demand for loanable
funds determines the equilibrium interest
rate
If recession hits, the NPV of projects will fall,
firms will invest less, and demand for
loanable funds will fall
 DF
and DT will fall, causing interest rate to fall
If government has to borrow money, demand
will increase and R also increases
Fed shifts supply of loanable funds, as well
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Changes in the Equilibrium
R
Interest
Rate
S
During a recession, interest
rates fall due to a
decrease in the demand
for loanable funds.
R*
R1
DT
D’T
Q1
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Quantity of
Loanable Funds
106
Changes in the Equilibrium
R
Interest
Rate
S
When the federal
government runs large
budget deficits, the
demand for loanable
funds increases.
R2
R*
D’T
DT
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Quantity of
Loanable Funds
107
Changes in the Equilibrium
R
Interest
Rate
S
S’
When the Federal
Reserve increases
the money supply, the
supply of loanable
funds increases.
R*
R1
DT
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Quantity of
Loanable Funds
108
A Variety of Interest Rates
1. Treasury Bill Rate
 Short-term (1 yr or less) bond issued by US
government
 Pure discount bond – no coupon payments
 Short-term, risk-free rate
2. Treasury Bond Rate
 Longer-term bond, typically 10-30 yrs
 Rates depend on maturity of bond
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A Variety of Interest Rates
3. Discount Rate
 The rate the Federal Reserve charges
commercial banks for short period loans,
called discounts
4. Federal Funds Rate
 Interest rate banks charge one another for
overnight loans of federal funds
 Banks with excess reserves may loan them
to banks with reserve deficiencies
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A Variety of Interest Rates
5. Commercial Paper Rate
 Short-term (6 months or less) discount
bonds used by high-quality corporate
borrowers
 Slightly riskier than treasury bills, so rate is
less than 1% higher than Treasury bill rate
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A Variety of Interest Rates
6. Prime Rate
 Sometimes called the reference rate
 Rate large banks post as a reference point
for short-term loans to biggest corporate
borrowers
 Does not fluctuate from day to day
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A Variety of Interest Rates
7. Corporate Bond Rate
 Long-term (typically 20 yrs) corporate
bonds with different risks

High grade, medium grade, etc.
 Average yields indicate how much
corporations are paying for long term debt
 Vary considerably
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