Chapter 15

Chapter 15

Investment, Time and Capital Markets

Chapter 15 2©2005 Pearson Education, Inc.

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


Topics to be Discussed

Investment Decisions by Consumers

Investments in Human Capital

Intertemporal Production Decisions – Depletable Resources

How are Interest Rates Determined?


Introduction

Markets for factors and output give a reasonably complete picture

Capital market 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


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 amount needed or used per time period


Stocks Versus Flows

Profit is also a flow numberMust know what the capital stock will

allow the firm to earn as 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?


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.

Interest rate – rate at which one can borrow or lend money



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?



future) the in dollar a have totoday invest

to have you wouldmuch(how ;(1

1 future the in

received $1 of value dollar Present PDV

future in yearof Number n

(1 today invested $1 of ValueDollar Future

n)

)n

R

R



The interest rate impacts the PDVThe lower the interest rate, the less you

have to invest to reach your goal in the future

We can see how different interest rates will give different future values


PDV of $1 Paid in the Future

R 1 YR 5 YR 10 YR 30 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


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


Two Payment Streams

Payment Stream A: $100 $100 0

Payment Stream B: $20 $100 $100

Today 1 Year 2 Years


2)(1

100

)(1

100 Stream of PDV

)(1

100 Stream of PDV

RR B

RA

Two Payment Streams


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

Notice which stream is worth more depends on interest rate

More is paid out in A even though it is paid out sooner


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



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 from mortality tables



Must adjust for the true probability of death (m) from other causes Derived from mortality tables

Assume R = 9% – The rate on government bonds


77

70

22

20

100

)1(

)1()1(W

...)1(

)1()1(W

)1(

)1)(1(W W PDV

R

mg

R

mg

R

mg



Calculating Lost Wages



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.


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


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(

1000$

)1(

100$...

)(1

$100

)(1

$100 PDV

RR

RR


Present Value of the Cash Flow from a Bond

Interest Rate0.05 0.10 0.15 0.20

PD

V o

f C

ash

Flo

w($

th

ou

san

ds)

00.5

1.0

1.5

2.0

The higher the interest rate, the lower the value of

the bond


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/RIn general, PDV = payment/R


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


Effective Yield on a Bond

Calculating the Rate of Return From a Bond

P is value of perpetuity – market priceCan use equations to find value of R

given P and the payment

P

PaymentRthen

R

PaymentP



From previous example

R = $100/$1000 = 0.10 = 10%The interest rate calculated here is the

effective yield Rate of return one received by investing in

the bond



Calculating the Rate of Return From a Bond

Can graph showing how R depends on P

PR

RR

RR

of in terms Calculate

)1(

1000$

)1(

100$...

)(1

$100

)(1

$100 PDV :BondCoupon

1010

2



Interest Rate0.05 0.10 0.15 0.200

0.5

1.0

1.5

2.0

PD

V o

f P

aym

ents

(V

alu

e o

f B

on

d)

($ t

ho

usa

nd

s)

The effective yield is the interestrate that equates the presentvalue of a bond’s payment

stream with the bond’s market price.

Notice the Bond Price is inverse to the effective yield



Yields vary on different bonds EX: Corporate bonds yield more than

government bonds The degree of risk a bond holds is reflected

in the yieldRiskier bonds have higher yieldsGovernment unlikely to defaultSome corporations more stable than others


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.


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 -.38Wall 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 bonds traded that day (10)•120.25: closing price ($120.25)•-.38: change in price from previous day (down 0.38)



The IBM bond yield: Assume annual payments and 10 years to

maturity

%9.4*

)1(

100

)1(

5.7...

)(1

7.5

)(1

7.5 25120

10102

R

RR.

RR



The Lucent bond matures is 5 years and has a yield of:

%.R*

R)(R...

R)(

.

R)(

013

1

100

)1(

5.5

1

55

1

5.550.73

552



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


The Net Present Value Criterionfor 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 firm information needed to make worthwhile 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.



0 NPV if Invest

risk similar a with

capital of costy opportunit or rate discount

- NPV

10)(n years for profits

cost capital

n

R

RRRC

n

C

1010

221

)1()1()1(



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



The Electric Motor Factory (choosing to build a $10 million factory) 8,000 motors/ month for 20 yrs

Cost = $42.50 eachPrice = $52.50/motorProfit = $10/motor or $80,000/monthFactory life is 20 years with a scrap value of $1

million Should the company invest?



Assume all information is certain (no risk) R = government bond rate

Discount rates below 7.5, NPV is positive Discount rates above 7.5, NPV is negative

%5.7*

)1(

1

)1(

96....

)(1

.96

)(1

.96 10- NPV

2020

2

R

RR

RR


Net Present Value of a Factory

Interest Rate, R0 0.05 0.10 0.15 0.20

-6

Net

Pre

sen

t V

alu

e($

mil

lio

ns)

-4

-2

0

2

4

6

8

10

•Firm should not invest for discount rates below 7.5

•Firm should not invest for discount rates above 7.5

R* = 7.5



When determining whether should 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

termsInflation = 5%


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


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%


Net Present Value of a Factory

Interest Rate, R0.10 0.15 0.200

-6

Net

Pre

sen

t V

alu

e($

mil

lio

ns)

-4

-2

0

2

4

6

8

10

0.04**

If R = 4%, the NPV ispositive. The company

should invest inthe new factory.



Negative Future Cash Flows Companies expect losses in certain

situationsTake time to build demandHigh up front costs that lower over time

Investment should be adjusted for construction time and losses.



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



2020

54

32

)1(

1

)1(

96.

...)1(

96.

)1(

96.

)(1

.5

)(1

1

)(1

5 - 5- NPV

RR

RR

RRR



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.

Amount of money that a risk-averse individual will pay to avoid taking a risk


Diversifiable v. Nondiversifiable Risk

Diversifiable risk that 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.



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



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 riskInvestors should be rewarded for bearing this

risk Opportunity cost of investing is higher – must

include risk premium



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 higher than risk free investment


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


Capital Asset Pricing Model

Return on some assets are correlated with stock market as a whole CAPM summary of relationship between

expected return and risk premium

beta asset

return expected

i

fmfi

r

rrrr )(



The asset beta, , measures the sensitivity of an asset’s return to market movements and, therefore, the asset’s nondiversifiable risk. 2% 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



Given beta, we can determine the correct discount rate to use in computing an asset’s net present value:

Risk-free rate plus a risk premium to reflect nondiversifiable risk

)( RateDiscount fmf rrr


Determining Beta

For a stock, beta determined statisticallyFor a factory, determining beta is more

difficultFirms often use the company cost of

capital as nominal discount rate Weighted average of he expected return on a

company’s stock and the interest rate that it pays for debt.

Can depend on level of nondiversifiable risk



Consumers face similar investment decisions when they purchase a durable good. Compare flow of future benefits with the

current purchase cost



Benefits and Costs of Buying a Car If keep the car for 5 or 6 years 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.


Benefits and Costs of Buying a Car

S = dollar value of transportation services in dollars to a consumer

E = total operating cost/yrInsurance, 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



Benefits and Cost

662 )1(

4000

)1(

)(...

)1(

)(

)1(

)()(000,20

RR

ES

R

ES

R

ESES

NPV



Whether you should buy the car or not depends on discount rate If have to borrow money, then use interest

loan rate

When comparing to buy or lease, can use same calculation High interest rate, often better to lease Low interest rate, often better to buy


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



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



iOC

iC

R

OC

R

OC

R

OCOCCPDV

i

i

ii

iii

of cost operating averge the is

of price purchase the is

82 )1(

...)1(

)1(



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



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



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



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



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



Benefits of college Higher salary throughout working life

On average college grad earns $20,000 higher than high school grad

Assume persists for 20 years

Can now calculate net present value of investing in a college education



234

32

)1(

20...

)1(

20

)1(

40...

)1(

40

)1(

4040

RR

RRRNPV



What discount rate should be used? We are ignoring inflation so should use a real

discount rate About 5% would reflect opportunity cost of

money for many householdsReturn of investing in other assets

This gives a NPV of about $66,000 therefore investing in college is a good idea



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


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 pre-MBA is about $45,000 and obtaining the MBA increase by about $30,000







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



Net present value of the investment is

With real discount rate of 5%, NPV is about $158,000

212 )1(

30...

)1(

30

)1(

9090

RRRNPV



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 excepted so return remains high



Financial decision is easy Although costly, return is very high But some find it more fun than others Many not have undergraduate grades and

test scores to go to business school May find career you like better such as

teaching or law



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 – extract the

resource today means less is available in the future

Must take these into account in decisions



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 only look at extraction costs versus price, ignore important piece – opportunity cost

Decision depends on price today, but on how fast you expect the price to rise in future



If expect price of oil to rise slowly, might be better off extracting today

If 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



Scenario Pt = price of oil this year

Pt+1 = price of oil next year C = extraction costs R = interest rate

tIndifferen If

now oil the all Sell If

ground the in oil the Keep If

:))(1()(

:))(1()(

:))(1()(

1

1

1

cPRcP

cPRcP

cPRcP

tt

tt

tt



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?


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?


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


Price of an Exhaustible Resource

Time

Price

Quantity

Price

c c

Marginal ExtractionCost

T

PT

P0P - c P0

Demand



Notice P > MC Is this 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



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


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

revenue less marginal cost rises at exactly the rate of interest, or

(MRt+1 – c) = (1 + R)(MRt – c)


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 a competitive industry. They start out charging a higher price and

deplete the resources more slowly.


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 significant part of market price

For resources like coal and iron, reserves are close to thousands of year of current consumption User cost is very small


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


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


How Depletable AreDepletable 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 GulfResource depletion has not had much

effect on prices of those resources


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 incomeFirms wanting to make capital investments



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



Quantity ofLoanable Funds

RInterest

Rate

DT

DH

DF

DH and DF, the quantity demanded for loanable

funds by households (H)and firms (F), respectively,

varies inverselywith the interest rate.


S

Supply and Demand for Loanable Funds


RInterest

Rate

R*

Q*

Equilibrium interestrate is R*.

DT

DH

DF



The supply and demand for loanable funds, determines the equilibrium interest rate If recession hits, 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


Changes In The Equilibrium

S

DT

R*

Q*

During a recession interestrates fall due to a

decrease in the demand for loanable funds.

D’T

Q1

R1


RInterest

Rate



S

DT

R*

Q*

When the federal government runs large

budget deficits the demand for loanable

funds increase.

Q2

R2

D’T


RInterest

Rate



S

DT

R*

Q*

When the FederalReserve increases

the money supply, thesupply of loanablefunds increases.

S’

R1

Q1


RInterest

Rate


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



3. Discount Rate Rate 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



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 less than 1% higher than Treasury bill rate



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 form day to day



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

Documents

Chapter 15