Chapter 15
Investment,
Time,and
Capital Markets
Chapter 15 Slide 2
Topics to be Discussed
? Stocks Versus Flows
? Present Discounted Value
? The Value of a Bond
? The Net Present Value Criterion for
Capital Investment Decisions
Chapter 15 Slide 3
Topics to be Discussed
? Adjustments for Risk
? Investment Decisions by Consumers
? Intertemporal Production Decisions---
Depletable Resources
? How are Interest Rates Determined?
Chapter 15 Slide 4
Introduction
? Capital
? Choosing an input that will contribute to
output over a long period of time
? Comparing the future value to current
expenditures
Chapter 15 Slide 5
Stocks Versus Flows
? Stock
? Capital is a stock measurement,
?The amount of capital a company owns
Chapter 15 Slide 6
Stocks Versus Flows
? Flows
? Variable inputs and outputs are flow
measurements,
?An amount per time period
Chapter 15 Slide 7
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,
Chapter 15 Slide 8
Present Discounted Value (PDV)
? Future Value (FV)
f u t u r e ) t h e in d o l l a r a h a v e tot o d a y i n v e s t
to h a v e y o u w o u l dm u c h( h o w ;
(1
1
f u t u r e t h e in
r e c e i v e d $1 of v a l u e d o l l a r P r e s e n t P D V
(1 t o d a y i n v e s t e d $1 of V a l u eD o l l a r F u t u r e
n
)
)
n
R
R
?
?
?
??
Chapter 15 Slide 9
Present Discounted Value (PDV)
? Question
? What impact does R have on the PDV?
PDV of $1 Paid in the Future
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 0.822 0.676 0.456 0.308
0.05 0.952 0.907 0.784 0.614 0.377 0.231
0.06 0.943 0.890 0.747 0.558 0.312 0.174
Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
PDV of $1 Paid in the Future
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
Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
Chapter 15 Slide 12
Present Discounted Value (PDV)
? Valuing Payment Streams
? Choosing a payment stream depends upon
the interest rate,
Chapter 15 Slide 13
Two Payment Streams
Payment Stream A,$100 $100 0
Payment Stream B,$20 $100 $100
Today 1 Year 2 Years
Chapter 15 Slide 14
2
)(1
100
)(1
100
S t re a m of P D V
)(1
100
S t re a m of P D V
RR
B
R
A
?
?
?
?
?
?
Two Payment Streams
?
Chapter 15 Slide 15
PDV of Payment Streams
PDV of Stream A,$195.24 $190.90 $186.96 $183.33
PDV of Stream B,205.94 193.54 182.57 172.77
R =,05 R =,10 R =,15 R =,20
Why does the PDV of A
relative to B increase as
R increases and vice versa
for B?
Chapter 15 Slide 16
The Value of Lost Earnings
? PDV can be used to determine the
value of lost income from a disability or
death,
Chapter 15 Slide 17
The Value of Lost Earnings
? Scenario
? Harold Jennings died in an auto accident
January 1,1986 at 53 years of age,
? Salary,$85,000
? Retirement Age,60
Chapter 15 Slide 18
The Value of Lost Earnings
? Question
?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
Chapter 15 Slide 19
The Value of Lost Earnings
? Question
?What is the PDV of Jennings’ lost income
to his family?
?Must adjust for the true probability of
death (m) from other causes
?Derived from mortality tables
Chapter 15 Slide 20
The Value of Lost Earnings
? Question
?What is the PDV of Jennings’ lost income
to his family?
?Assume R = 9%
?Rate on government bonds in 1983
Chapter 15 Slide 21
7
7
7
0
2
2
2
0
10
0
)1(
)1()1(W
..,
)1(
)1()1(W
)1(
)1)(1(W
W P D V
R
mg
R
mg
R
mg
?
??
?
?
?
??
?
?
??
??
The Value of Lost Earnings
?
Calculating Lost Wages
1986 $ 85,000,991 1.000 $84,235
1987 91,800,990,917 83,339
1988 99,144,989,842 82,561
1989 107,076,988,772 81,671
1990 115,642,987,708 80,810
1991 124,893,986,650 80,043
1992 134,884,985,596 79,185
1993 145,675,984,547 78,408
Year W0(1 + g)t (1 - mt) 1/(1 + R)t W0(1 + g)t(1 - mt)/(1 + R)t
Chapter 15 Slide 23
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 compensation for his death,
Chapter 15 Slide 24
The Value of a Bond
? Determining the Price of a Bond
? Coupon Payments = $100/yr,for 10 yrs,
? Principal Payment = $1,000 in 10 yrs,
1010
2
)1(
1 0 0 0$
)1(
1 0 0$
.,,
)(1
$ 1 0 0
)(1
$ 1 0 0
P D V
RR
RR
?
?
?
?
?
?
?
?
?
Chapter 15 Slide 25
Present Value of
the Cash Flow from a Bond
Interest Rate
PD
V
of
Ca
sh
F
lo
w
($
th
ou
sa
nd
s)
0 0.05 0.10 0.15 0.20
0.5
1.0
1.5
2.0
Why does the value decline
as the rate increases?
Chapter 15 Slide 26
The Value of a Bond
? Perpetuities
? Perpetuities are bonds that pay out a fixed
amount of money each year,forever,
R
Pa y m e n t
PD V ?
Chapter 15 Slide 27
Effective Yield on a Bond
? Calculating the Rate of Return From a
Bond
%10
000,1$
100$
100$
?
??
??
?
R
P
P
R
RR
P
P
P a y m e n t
,P e r p e tu i ty
P D V
Chapter 15 Slide 28
Effective Yield on a Bond
? Calculating the Rate of Return From
a Bond
PR
RR
RR
of i n t er m s Ca l cu l at e
)1(
1 0 0 0$
)1(
1 0 0$
.,,
)(1
$ 1 0 0
)(1
$ 1 0 0
P D V,Bo n dCo u p o n
1010
2
?
?
?
?
?
?
?
?
?
Chapter 15 Slide 29
Effective Yield on a Bond
Interest Rate
0 0.05 0.10 0.15 0.20
0.5
1.0
1.5
2.0
PD
V
of
Pa
ym
en
ts
(V
alu
e o
f B
on
d)
($
th
ou
sa
nd
s)
Why do yields differ
among different bonds?
The effective yield is the interest
rate that equates the present
value of a bond’s payment
stream with the bond’s market price,
Chapter 15 Slide 30
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 Polaroid both issue bonds with a
face value of $100 and make coupon
payments every six months,
Chapter 15 Slide 31
The Yields on Corporate Bonds
? Closing prices for each July 23,1999,
IBM 53/8 09 5.8 30 92 -11/2
Polaroid 111/2 06 10.8 80 106 -5/8
a,coupon payments for one year ($5.375)
b,maturity date of bond (2009)
c,annual coupon/closing price ($5.375/92)
d,number traded that day (30)
e,closing price (92)
f,change in price from previous day (-11/2)
a b c d e f
Chapter 15 Slide 32
The Yields on Corporate Bonds
? The IBM bond yield,
? Assume annual payments
? 2009 - 1999 = 10 years
%5.6*
)1(
100
)1(
375.5
.,,
)(1
5, 3 7 5
)(1
5, 3 7 5
1010
2
?
?
?
?
?
?
?
?
?
?
R
RR
RR
92
Chapter 15 Slide 33
The Yields on Corporate Bonds
? The Polaroid bond yield,
%2.10*
)1(
50.11
)1(
5.11
..,
)(1
1 1, 5
)(1
1 1, 5
1 0 6
77
2
?
?
?
?
?
?
?
?
?
?
R
RR
RR
Why was Polaroid
R* greater?
Chapter 15 Slide 34
The Net Present Value Criterion
for Capital Investment Decisions
? In order to decide whether a particular
capital investment is worthwhile a firm
should compare the present value (PV)
of the cash flows from the investment to
the cost of the investment,
Chapter 15 Slide 35
? NPV Criterion
? Firms should invest if the PV exceeds the
cost of the investment,
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 36
?
0 N P V if I n v e s t
r i s k s i m i l a r a w i th
c a p i ta l of c o s ty o p p o r tu n i t or r a te d i s c o u n t
- N P V
10)(n y e a r s f o r p r o f i ts
c o s t c a p i ta l
n
?
?
?
?
?
?
?
??
??
?
R
RRR
C
n
C
10
10
2
21
)1()1()1(
???
?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 37
? 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
?Profit = $10/motor or $80,000/month
?Factory life is 20 years with a scrap
value of $1 million
? Should the company invest?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 38
? Assume all information is certain (no
risk)
? R = government bond rate
%5.7*
)1(
1
)1(
96.
.,,
)(1
,9 6
)(1
,9 6
10- NPV
2020
2
?
?
?
?
?
?
?
?
?
??
R
RR
RR
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 39
Net Present Value of a Factory
Interest Rate,R
0 0.05 0.10 0.15 0.20
-6
Ne
t Pr
es
en
t V
alu
e
($
mi
llio
ns
)
-4
-2
0
2
4
6
8
10
The NPV of a factory is the present
discounted value of all the cash
flows involved in building and
operating it,
R* = 7.5
Chapter 15 Slide 40
? Real versus Nominal Discount Rates
? Adjusting for the impact of inflation
? Assume price,cost,and profits are in real
terms
?Inflation = 5%
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 41
? 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 $960,000/year
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 42
? Real versus Nominal Discount Rates
? Real R = nominal R - inflation = 9 - 5 = 4
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 43
Net Present Value of a Factory
Interest Rate,R
0 0.05 0.10 0.15 0.20
-6
Ne
t Pr
es
en
t V
alu
e
($
mi
llio
ns
)
-4
-2
0
2
4
6
8
10
If R = 4%,the NPV is
positive,The company
should invest in
the new factory,
Chapter 15 Slide 44
? Negative Future Cash Flows
? Investment should be adjusted for
construction time and losses,
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 45
? Electric Motor Factory
? Construction time is 1 year
?$5 million expenditure today
?$5 million expenditure next year
? Expected to lose $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
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 46
?
2020
54
32
)1(
1
)1(
96.
.,,
)1(
96.
)1(
96.
)(1
.5
)(1
1
)(1
5
- 5- N P V
RR
RR
RRR
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 47
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 risk-free rate,
?Owners are risk averse,thus risky future
cash flows are worth less than those that
are certain,
Chapter 15 Slide 48
Adjustments for Risk
? Diversifiable Versus 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,
Chapter 15 Slide 49
Adjustments for Risk
? Measuring the Nondiversifiable Risk
Using the Capital Asset Pricing Model
(CAPM)
? 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
Chapter 15 Slide 50
Adjustments for Risk
? Measuring the Nondiversifiable Risk
Using the Capital Asset Pricing Model
(CAPM)
? Calculating Risk Premium for One Stock
m o v e m e n t s
m a r k e t r e tu r n to sa ss e t ' th eof
ys e n s i ti v i t th em e a su r e s b e t aa ss e t
r e tu r n e x p e c t e d
)(
1
1
??
?
???
?
?
r
rrrr
fmf
Chapter 15 Slide 51
Adjustments for Risk
? Question
? What is the relationship between the
nondiversifiable risk and the value of the
asset beta?
Chapter 15 Slide 52
Adjustments for Risk
? Given beta,we can determine the
correct discount rate to use in
computing an asset’s net present value,
)( R a t eD i s c o u n t fmf rrr ??? ?
Chapter 15 Slide 53
Adjustments for Risk
? Determining beta
? Stock
?Estimated statistically for each company
Chapter 15 Slide 54
Adjustments for Risk
? Determining beta
? Factory
?Weighted average of expected return on
the company’s stock and the interest on
the debt
? Expected return depends on beta
?Caution,The investment should be
typical for the company
Chapter 15 Slide 55
Investment Decisions by Consumers
? Consumers face similar investment
decisions when they purchase a durable
good,
? Compare future benefits with the current
purchase cost
Chapter 15 Slide 56
? Benefits and Cost of Buying a Car
? S = value of transportation services in
dollars
? E = total operating cost/yr
? Price of car is $20,000
? Resale value of car is $4,000 in 6 years
Investment Decisions by Consumers
Chapter 15 Slide 57
? Benefits and Cost
662
)1(
4000
)1(
)(
...
)1(
)(
)1(
)(
)(000,20
RR
ES
R
ES
R
ES
ES
?
?
?
?
??
?
?
?
?
?
?????
N P V
Investment Decisions by Consumers
Chapter 15 Slide 58
Choosing an Air Conditioner
? Buying a new air conditioner involves
making a trade-off,
? Air Conditioner A
?Low price and less efficient (high
operating cost)
Chapter 15 Slide 59
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
Chapter 15 Slide 60
Choosing an Air Conditioner
?
iOC
iC
R
OC
R
OC
R
OC
OCCP D V
i
i
ii
i
ii
of c o s t o p e r a t i n g a v e r g e t h e is
of p r i c e p u r c h a s e t h e is
82
)1(
.,,
)1(
)1(
?
?
?
?
?
???
Chapter 15 Slide 61
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 choose the more expensive unit
Chapter 15 Slide 62
Intertemporal Production
Decisions---Depletable Resources
? Firms’ production decisions often have
intertemporal aspects---production
today affects sales or costs in the
future,
Chapter 15 Slide 63
? 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?
Intertemporal Production
Decisions---Depletable Resources
Chapter 15 Slide 64
? Scenario
? Pt = price of oil this year
? Pt+1 = price of oil next year
? C = extraction costs
? R = interest rate
?
tI n d i f f e r e n If
now o i l t h e a l l S e l l If
g r o u n d t h e in o i l t h e K e e p If
:))(1()(
:))(1()(
:))(1()(
1
1
1
cPRcP
cPRcP
cPRcP
tt
tt
tt
????
????
????
?
?
?
Intertemporal Production
Decisions---Depletable Resources
Chapter 15 Slide 65
? 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,
? What will happen to the price of oil?
Intertemporal Production
Decisions---Depletable Resources
Price of an Exhaustible Resource
Time
Price
Quantity
Price
c c
Marginal Extraction
Cost
T
PT
P0 P - c P0
Demand
Chapter 15 Slide 67
? In a competitive market,Price - MC
must rise at exactly the rate of interest,
? Why?
? How would producers react if,
?P - C increases faster than R?
?P - C increases slower than R?
Price of an Exhaustible Resource
Chapter 15 Slide 68
? Notice
? P > MC
?Is this a contradiction to the competitive
rule that P = MC?
?Hint,What happens to the opportunity cost
of producing an exhaustible resource?
Price of an Exhaustible Resource
Chapter 15 Slide 69
? P = MC
? MC = extraction cost + user cost
? User cost = P - marginal extraction cost
Price of an Exhaustible Resource
Chapter 15 Slide 70
? How would a monopolist choose their
rate of production?
? They will produce so that marginal revenue
revenue less marginal cost rises at exactly
the rate of interest,or
? (MRt+1 - c) = (1 + R)(MRt - c)
Price of an Exhaustible Resource
Chapter 15 Slide 71
? The monopolist is more conservationist
than a competitive industry,
? They start out charging a higher price and
deplete the resources more slowly,
Price of an Exhaustible Resource
Resource Production by a Monopolist
Chapter 15 Slide 72
How Depletable Are
Depletable Resources?
Crude oil,4 to,5
Natural gas,4 to,5
Uranium,1 to,2
Copper,2 to,3
Bauxite,05 to,2
Nickel,1 to,2
Iron Ore,1 to,2
Gold,05 to,1
Resource User Cost/Competitive Price
Chapter 15 Slide 73
? The market structure and changes in
market demand have had a very
dramatic impact on resource prices over
the past few decades,
? Question
? Why would oil and natural gas have such a
high user cost ratio compared to the other
resources?
How Depletable Are
Depletable Resources?
Chapter 15 Slide 74
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,
Chapter 15 Slide 75
S
Households supply funds to
consume more in the future;
the higher the interest rate,the
more they supply,
Supply and Demand for Loanable Funds
Quantity of
Loanable Funds
R
Interest
Rate
DT
R*
Q*
DT = DH + DF and
equilibrium interest
rate is R*,
DH
DF
DH and DF,the quantity
demanded for loanable
funds by households (H)
and firms,respectively,
varies inversely
with the interest rate,
Chapter 15 Slide 76
Changes In The Equilibrium
S
DT
R*
Q*
During a recession interest
rates fall due to a
decrease in the demand
for loanable funds,
D’T
Q1
R1
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 77
Changes In The Equilibrium
S
DT
R*
Q*
When the federal
government runs large
budget deficits the
demand for loanable
funds increase,
Q2
R2
D’T
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 78
Changes In The Equilibrium
S
DT
R*
Q*
When the Federal
Reserve increases
the money supply,the
supply of loanable
funds increases,
S’
R1
Q1
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 79
? A Variety of Interest Rates
1) Treasury Bill Rate
2) Treasury Bond Rate
3) Discount Rate
How Are Interest Rates Determined?
Chapter 15 Slide 80
? A Variety of Interest Rates
4) Commercial Paper Rate
5) Prime Rate
6) Corporate Bond Rate
How Are Interest Rates Determined?
Chapter 15 Slide 81
Summary
? A firm’s holding of capital is measured
as a stock,but inputs of labor and raw
materials are flows,
? When a firm makes a capital
investment,it spends money now,so
that it can earn profits in the future,
Chapter 15 Slide 82
Summary
? The present discounted value (PDV) of
$1 paid n years from now is $1/(1 + R)n,
? A bond is a contract in which a lender
agrees to pay the bondholder a stream
of money,
Chapter 15 Slide 83
Summary
? Firms can decide whether to undertake
a capital investment by applying the
NPV criterion,
? The discount rate that a firm uses to
calculate the NPV for an investment
should be the opportunity cost of
capital,
Chapter 15 Slide 84
Summary
? An adjustment for risk can be made by
adding a risk premium to the discount
rate,
? Consumers are also faced with
investment decisions that require the
same kind of analysis as those of firms,
Chapter 15 Slide 85
Summary
? An exhaustible resource in the ground is
like money in the bank and must earn a
comparable return,
? Market interest rates are determined by
the demand and supply of loanable
funds,
End of Chapter 15
Investment,
Time,and
Capital Markets
Investment,
Time,and
Capital Markets
Chapter 15 Slide 2
Topics to be Discussed
? Stocks Versus Flows
? Present Discounted Value
? The Value of a Bond
? The Net Present Value Criterion for
Capital Investment Decisions
Chapter 15 Slide 3
Topics to be Discussed
? Adjustments for Risk
? Investment Decisions by Consumers
? Intertemporal Production Decisions---
Depletable Resources
? How are Interest Rates Determined?
Chapter 15 Slide 4
Introduction
? Capital
? Choosing an input that will contribute to
output over a long period of time
? Comparing the future value to current
expenditures
Chapter 15 Slide 5
Stocks Versus Flows
? Stock
? Capital is a stock measurement,
?The amount of capital a company owns
Chapter 15 Slide 6
Stocks Versus Flows
? Flows
? Variable inputs and outputs are flow
measurements,
?An amount per time period
Chapter 15 Slide 7
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,
Chapter 15 Slide 8
Present Discounted Value (PDV)
? Future Value (FV)
f u t u r e ) t h e in d o l l a r a h a v e tot o d a y i n v e s t
to h a v e y o u w o u l dm u c h( h o w ;
(1
1
f u t u r e t h e in
r e c e i v e d $1 of v a l u e d o l l a r P r e s e n t P D V
(1 t o d a y i n v e s t e d $1 of V a l u eD o l l a r F u t u r e
n
)
)
n
R
R
?
?
?
??
Chapter 15 Slide 9
Present Discounted Value (PDV)
? Question
? What impact does R have on the PDV?
PDV of $1 Paid in the Future
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 0.822 0.676 0.456 0.308
0.05 0.952 0.907 0.784 0.614 0.377 0.231
0.06 0.943 0.890 0.747 0.558 0.312 0.174
Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
PDV of $1 Paid in the Future
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
Interest
Rate 1 Year 2 Years 3 Years 4 Years 5 Years 6 Years
Chapter 15 Slide 12
Present Discounted Value (PDV)
? Valuing Payment Streams
? Choosing a payment stream depends upon
the interest rate,
Chapter 15 Slide 13
Two Payment Streams
Payment Stream A,$100 $100 0
Payment Stream B,$20 $100 $100
Today 1 Year 2 Years
Chapter 15 Slide 14
2
)(1
100
)(1
100
S t re a m of P D V
)(1
100
S t re a m of P D V
RR
B
R
A
?
?
?
?
?
?
Two Payment Streams
?
Chapter 15 Slide 15
PDV of Payment Streams
PDV of Stream A,$195.24 $190.90 $186.96 $183.33
PDV of Stream B,205.94 193.54 182.57 172.77
R =,05 R =,10 R =,15 R =,20
Why does the PDV of A
relative to B increase as
R increases and vice versa
for B?
Chapter 15 Slide 16
The Value of Lost Earnings
? PDV can be used to determine the
value of lost income from a disability or
death,
Chapter 15 Slide 17
The Value of Lost Earnings
? Scenario
? Harold Jennings died in an auto accident
January 1,1986 at 53 years of age,
? Salary,$85,000
? Retirement Age,60
Chapter 15 Slide 18
The Value of Lost Earnings
? Question
?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
Chapter 15 Slide 19
The Value of Lost Earnings
? Question
?What is the PDV of Jennings’ lost income
to his family?
?Must adjust for the true probability of
death (m) from other causes
?Derived from mortality tables
Chapter 15 Slide 20
The Value of Lost Earnings
? Question
?What is the PDV of Jennings’ lost income
to his family?
?Assume R = 9%
?Rate on government bonds in 1983
Chapter 15 Slide 21
7
7
7
0
2
2
2
0
10
0
)1(
)1()1(W
..,
)1(
)1()1(W
)1(
)1)(1(W
W P D V
R
mg
R
mg
R
mg
?
??
?
?
?
??
?
?
??
??
The Value of Lost Earnings
?
Calculating Lost Wages
1986 $ 85,000,991 1.000 $84,235
1987 91,800,990,917 83,339
1988 99,144,989,842 82,561
1989 107,076,988,772 81,671
1990 115,642,987,708 80,810
1991 124,893,986,650 80,043
1992 134,884,985,596 79,185
1993 145,675,984,547 78,408
Year W0(1 + g)t (1 - mt) 1/(1 + R)t W0(1 + g)t(1 - mt)/(1 + R)t
Chapter 15 Slide 23
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 compensation for his death,
Chapter 15 Slide 24
The Value of a Bond
? Determining the Price of a Bond
? Coupon Payments = $100/yr,for 10 yrs,
? Principal Payment = $1,000 in 10 yrs,
1010
2
)1(
1 0 0 0$
)1(
1 0 0$
.,,
)(1
$ 1 0 0
)(1
$ 1 0 0
P D V
RR
RR
?
?
?
?
?
?
?
?
?
Chapter 15 Slide 25
Present Value of
the Cash Flow from a Bond
Interest Rate
PD
V
of
Ca
sh
F
lo
w
($
th
ou
sa
nd
s)
0 0.05 0.10 0.15 0.20
0.5
1.0
1.5
2.0
Why does the value decline
as the rate increases?
Chapter 15 Slide 26
The Value of a Bond
? Perpetuities
? Perpetuities are bonds that pay out a fixed
amount of money each year,forever,
R
Pa y m e n t
PD V ?
Chapter 15 Slide 27
Effective Yield on a Bond
? Calculating the Rate of Return From a
Bond
%10
000,1$
100$
100$
?
??
??
?
R
P
P
R
RR
P
P
P a y m e n t
,P e r p e tu i ty
P D V
Chapter 15 Slide 28
Effective Yield on a Bond
? Calculating the Rate of Return From
a Bond
PR
RR
RR
of i n t er m s Ca l cu l at e
)1(
1 0 0 0$
)1(
1 0 0$
.,,
)(1
$ 1 0 0
)(1
$ 1 0 0
P D V,Bo n dCo u p o n
1010
2
?
?
?
?
?
?
?
?
?
Chapter 15 Slide 29
Effective Yield on a Bond
Interest Rate
0 0.05 0.10 0.15 0.20
0.5
1.0
1.5
2.0
PD
V
of
Pa
ym
en
ts
(V
alu
e o
f B
on
d)
($
th
ou
sa
nd
s)
Why do yields differ
among different bonds?
The effective yield is the interest
rate that equates the present
value of a bond’s payment
stream with the bond’s market price,
Chapter 15 Slide 30
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 Polaroid both issue bonds with a
face value of $100 and make coupon
payments every six months,
Chapter 15 Slide 31
The Yields on Corporate Bonds
? Closing prices for each July 23,1999,
IBM 53/8 09 5.8 30 92 -11/2
Polaroid 111/2 06 10.8 80 106 -5/8
a,coupon payments for one year ($5.375)
b,maturity date of bond (2009)
c,annual coupon/closing price ($5.375/92)
d,number traded that day (30)
e,closing price (92)
f,change in price from previous day (-11/2)
a b c d e f
Chapter 15 Slide 32
The Yields on Corporate Bonds
? The IBM bond yield,
? Assume annual payments
? 2009 - 1999 = 10 years
%5.6*
)1(
100
)1(
375.5
.,,
)(1
5, 3 7 5
)(1
5, 3 7 5
1010
2
?
?
?
?
?
?
?
?
?
?
R
RR
RR
92
Chapter 15 Slide 33
The Yields on Corporate Bonds
? The Polaroid bond yield,
%2.10*
)1(
50.11
)1(
5.11
..,
)(1
1 1, 5
)(1
1 1, 5
1 0 6
77
2
?
?
?
?
?
?
?
?
?
?
R
RR
RR
Why was Polaroid
R* greater?
Chapter 15 Slide 34
The Net Present Value Criterion
for Capital Investment Decisions
? In order to decide whether a particular
capital investment is worthwhile a firm
should compare the present value (PV)
of the cash flows from the investment to
the cost of the investment,
Chapter 15 Slide 35
? NPV Criterion
? Firms should invest if the PV exceeds the
cost of the investment,
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 36
?
0 N P V if I n v e s t
r i s k s i m i l a r a w i th
c a p i ta l of c o s ty o p p o r tu n i t or r a te d i s c o u n t
- N P V
10)(n y e a r s f o r p r o f i ts
c o s t c a p i ta l
n
?
?
?
?
?
?
?
??
??
?
R
RRR
C
n
C
10
10
2
21
)1()1()1(
???
?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 37
? 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
?Profit = $10/motor or $80,000/month
?Factory life is 20 years with a scrap
value of $1 million
? Should the company invest?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 38
? Assume all information is certain (no
risk)
? R = government bond rate
%5.7*
)1(
1
)1(
96.
.,,
)(1
,9 6
)(1
,9 6
10- NPV
2020
2
?
?
?
?
?
?
?
?
?
??
R
RR
RR
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 39
Net Present Value of a Factory
Interest Rate,R
0 0.05 0.10 0.15 0.20
-6
Ne
t Pr
es
en
t V
alu
e
($
mi
llio
ns
)
-4
-2
0
2
4
6
8
10
The NPV of a factory is the present
discounted value of all the cash
flows involved in building and
operating it,
R* = 7.5
Chapter 15 Slide 40
? Real versus Nominal Discount Rates
? Adjusting for the impact of inflation
? Assume price,cost,and profits are in real
terms
?Inflation = 5%
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 41
? 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 $960,000/year
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 42
? Real versus Nominal Discount Rates
? Real R = nominal R - inflation = 9 - 5 = 4
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 43
Net Present Value of a Factory
Interest Rate,R
0 0.05 0.10 0.15 0.20
-6
Ne
t Pr
es
en
t V
alu
e
($
mi
llio
ns
)
-4
-2
0
2
4
6
8
10
If R = 4%,the NPV is
positive,The company
should invest in
the new factory,
Chapter 15 Slide 44
? Negative Future Cash Flows
? Investment should be adjusted for
construction time and losses,
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 45
? Electric Motor Factory
? Construction time is 1 year
?$5 million expenditure today
?$5 million expenditure next year
? Expected to lose $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
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 46
?
2020
54
32
)1(
1
)1(
96.
.,,
)1(
96.
)1(
96.
)(1
.5
)(1
1
)(1
5
- 5- N P V
RR
RR
RRR
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
The Net Present Value Criterion
for Capital Investment Decisions
Chapter 15 Slide 47
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 risk-free rate,
?Owners are risk averse,thus risky future
cash flows are worth less than those that
are certain,
Chapter 15 Slide 48
Adjustments for Risk
? Diversifiable Versus 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,
Chapter 15 Slide 49
Adjustments for Risk
? Measuring the Nondiversifiable Risk
Using the Capital Asset Pricing Model
(CAPM)
? 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
Chapter 15 Slide 50
Adjustments for Risk
? Measuring the Nondiversifiable Risk
Using the Capital Asset Pricing Model
(CAPM)
? Calculating Risk Premium for One Stock
m o v e m e n t s
m a r k e t r e tu r n to sa ss e t ' th eof
ys e n s i ti v i t th em e a su r e s b e t aa ss e t
r e tu r n e x p e c t e d
)(
1
1
??
?
???
?
?
r
rrrr
fmf
Chapter 15 Slide 51
Adjustments for Risk
? Question
? What is the relationship between the
nondiversifiable risk and the value of the
asset beta?
Chapter 15 Slide 52
Adjustments for Risk
? Given beta,we can determine the
correct discount rate to use in
computing an asset’s net present value,
)( R a t eD i s c o u n t fmf rrr ??? ?
Chapter 15 Slide 53
Adjustments for Risk
? Determining beta
? Stock
?Estimated statistically for each company
Chapter 15 Slide 54
Adjustments for Risk
? Determining beta
? Factory
?Weighted average of expected return on
the company’s stock and the interest on
the debt
? Expected return depends on beta
?Caution,The investment should be
typical for the company
Chapter 15 Slide 55
Investment Decisions by Consumers
? Consumers face similar investment
decisions when they purchase a durable
good,
? Compare future benefits with the current
purchase cost
Chapter 15 Slide 56
? Benefits and Cost of Buying a Car
? S = value of transportation services in
dollars
? E = total operating cost/yr
? Price of car is $20,000
? Resale value of car is $4,000 in 6 years
Investment Decisions by Consumers
Chapter 15 Slide 57
? Benefits and Cost
662
)1(
4000
)1(
)(
...
)1(
)(
)1(
)(
)(000,20
RR
ES
R
ES
R
ES
ES
?
?
?
?
??
?
?
?
?
?
?????
N P V
Investment Decisions by Consumers
Chapter 15 Slide 58
Choosing an Air Conditioner
? Buying a new air conditioner involves
making a trade-off,
? Air Conditioner A
?Low price and less efficient (high
operating cost)
Chapter 15 Slide 59
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
Chapter 15 Slide 60
Choosing an Air Conditioner
?
iOC
iC
R
OC
R
OC
R
OC
OCCP D V
i
i
ii
i
ii
of c o s t o p e r a t i n g a v e r g e t h e is
of p r i c e p u r c h a s e t h e is
82
)1(
.,,
)1(
)1(
?
?
?
?
?
???
Chapter 15 Slide 61
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 choose the more expensive unit
Chapter 15 Slide 62
Intertemporal Production
Decisions---Depletable Resources
? Firms’ production decisions often have
intertemporal aspects---production
today affects sales or costs in the
future,
Chapter 15 Slide 63
? 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?
Intertemporal Production
Decisions---Depletable Resources
Chapter 15 Slide 64
? Scenario
? Pt = price of oil this year
? Pt+1 = price of oil next year
? C = extraction costs
? R = interest rate
?
tI n d i f f e r e n If
now o i l t h e a l l S e l l If
g r o u n d t h e in o i l t h e K e e p If
:))(1()(
:))(1()(
:))(1()(
1
1
1
cPRcP
cPRcP
cPRcP
tt
tt
tt
????
????
????
?
?
?
Intertemporal Production
Decisions---Depletable Resources
Chapter 15 Slide 65
? 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,
? What will happen to the price of oil?
Intertemporal Production
Decisions---Depletable Resources
Price of an Exhaustible Resource
Time
Price
Quantity
Price
c c
Marginal Extraction
Cost
T
PT
P0 P - c P0
Demand
Chapter 15 Slide 67
? In a competitive market,Price - MC
must rise at exactly the rate of interest,
? Why?
? How would producers react if,
?P - C increases faster than R?
?P - C increases slower than R?
Price of an Exhaustible Resource
Chapter 15 Slide 68
? Notice
? P > MC
?Is this a contradiction to the competitive
rule that P = MC?
?Hint,What happens to the opportunity cost
of producing an exhaustible resource?
Price of an Exhaustible Resource
Chapter 15 Slide 69
? P = MC
? MC = extraction cost + user cost
? User cost = P - marginal extraction cost
Price of an Exhaustible Resource
Chapter 15 Slide 70
? How would a monopolist choose their
rate of production?
? They will produce so that marginal revenue
revenue less marginal cost rises at exactly
the rate of interest,or
? (MRt+1 - c) = (1 + R)(MRt - c)
Price of an Exhaustible Resource
Chapter 15 Slide 71
? The monopolist is more conservationist
than a competitive industry,
? They start out charging a higher price and
deplete the resources more slowly,
Price of an Exhaustible Resource
Resource Production by a Monopolist
Chapter 15 Slide 72
How Depletable Are
Depletable Resources?
Crude oil,4 to,5
Natural gas,4 to,5
Uranium,1 to,2
Copper,2 to,3
Bauxite,05 to,2
Nickel,1 to,2
Iron Ore,1 to,2
Gold,05 to,1
Resource User Cost/Competitive Price
Chapter 15 Slide 73
? The market structure and changes in
market demand have had a very
dramatic impact on resource prices over
the past few decades,
? Question
? Why would oil and natural gas have such a
high user cost ratio compared to the other
resources?
How Depletable Are
Depletable Resources?
Chapter 15 Slide 74
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,
Chapter 15 Slide 75
S
Households supply funds to
consume more in the future;
the higher the interest rate,the
more they supply,
Supply and Demand for Loanable Funds
Quantity of
Loanable Funds
R
Interest
Rate
DT
R*
Q*
DT = DH + DF and
equilibrium interest
rate is R*,
DH
DF
DH and DF,the quantity
demanded for loanable
funds by households (H)
and firms,respectively,
varies inversely
with the interest rate,
Chapter 15 Slide 76
Changes In The Equilibrium
S
DT
R*
Q*
During a recession interest
rates fall due to a
decrease in the demand
for loanable funds,
D’T
Q1
R1
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 77
Changes In The Equilibrium
S
DT
R*
Q*
When the federal
government runs large
budget deficits the
demand for loanable
funds increase,
Q2
R2
D’T
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 78
Changes In The Equilibrium
S
DT
R*
Q*
When the Federal
Reserve increases
the money supply,the
supply of loanable
funds increases,
S’
R1
Q1
Quantity of
Loanable Funds
R
Interest
Rate
Chapter 15 Slide 79
? A Variety of Interest Rates
1) Treasury Bill Rate
2) Treasury Bond Rate
3) Discount Rate
How Are Interest Rates Determined?
Chapter 15 Slide 80
? A Variety of Interest Rates
4) Commercial Paper Rate
5) Prime Rate
6) Corporate Bond Rate
How Are Interest Rates Determined?
Chapter 15 Slide 81
Summary
? A firm’s holding of capital is measured
as a stock,but inputs of labor and raw
materials are flows,
? When a firm makes a capital
investment,it spends money now,so
that it can earn profits in the future,
Chapter 15 Slide 82
Summary
? The present discounted value (PDV) of
$1 paid n years from now is $1/(1 + R)n,
? A bond is a contract in which a lender
agrees to pay the bondholder a stream
of money,
Chapter 15 Slide 83
Summary
? Firms can decide whether to undertake
a capital investment by applying the
NPV criterion,
? The discount rate that a firm uses to
calculate the NPV for an investment
should be the opportunity cost of
capital,
Chapter 15 Slide 84
Summary
? An adjustment for risk can be made by
adding a risk premium to the discount
rate,
? Consumers are also faced with
investment decisions that require the
same kind of analysis as those of firms,
Chapter 15 Slide 85
Summary
? An exhaustible resource in the ground is
like money in the bank and must earn a
comparable return,
? Market interest rates are determined by
the demand and supply of loanable
funds,
End of Chapter 15
Investment,
Time,and
Capital Markets
