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Investment, Time, and Capital Markets

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Investment, Time, and Capital Markets

- Stocks Versus Flows
- Present Discounted Value
- The Value of a Bond
- The Net Present Value Criterion for Capital Investment Decisions

To Invest or not?

It is 1978 and a bright eyed inventor comes to you with a radical idea and wants you to invest in him and his company. He offers you great returns, he shows you projections and a picture of his “team”.

He says that to invest you need to put in $10,000 (all of your savings).

If you didn’t invest your savings would be worth today (assuming a 10% return on investment) 10,000*1.1^24 = $98497

If you had invested in the company your invest would be worth approximately $1.7 billion

And the company………….

Microsoft 1978

Bill Gates

- Adjustments for Risk
- Investment Decisions by Consumers
- Intertemporal Production Decisions--- Depletable Resources
- How are Interest Rates Determined?

- Capital
- Choosing an input that will contribute to output over a long period of time
- Comparing the future value to current expenditures

- Stock
- Capital is a stock measurement.
- The amount of capital a company owns

- Capital is a stock measurement.

- Flows
- Variable inputs and outputs are flow measurements.
- An amount per time period

- Variable inputs and outputs are flow measurements.

- 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.

- Future Value (FV)

- Question
- What impact does R have on the PDV?

- Valuing Payment Streams
- Choosing a payment stream depends upon the interest rate.

Payment Stream A: $100$1000

Payment Stream B:$20$100$100

Today1 Year2 Years

PDV of Stream A: $195.24$190.90$186.96$183.33

PDV of Stream B:205.94193.54182.57172.77

R = .05R = .10R = .15R = .20

Why does the PDV of A

relative to B increase as

R increases and vice versa

for B?

- 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

- 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

- Must adjust salary for predicted increase (g)

- What is the PDV of Jennings’ lost income to his family?

- 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

- Must adjust for the true probability of death (m) from other causes

- What is the PDV of Jennings’ lost income to his family?

- Question
- What is the PDV of Jennings’ lost income to his family?
- Assume R = 9%
- Rate on government bonds in 1983

- Assume R = 9%

- What is the PDV of Jennings’ lost income to his family?

YearW0(1 + g)t(1 - mt)1/(1 + R)tW0(1 + g)t(1 - mt)/(1 + R)t

1986$ 85,000.9911.000$84,235

198791,800.990.91783,339

198899,144.989.84282,561

1989107,076.988.77281,671

1990115,642.987.70880,810

1991124,893.986.65080,043

1992134,884.985.59679,185

1993145,675.984.54778,408

- 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.

- Determining the Price of a Bond
- Coupon Payments = $100/yr. for 10 yrs.
- Principal Payment = $1,000 in 10 yrs.

Why does the value decline

as the rate increases?

2.0

1.5

PDV of Cash Flow

($ thousands)

1.0

0.5

0

0.05

0.10

0.15

0.20

Interest Rate

- Perpetuities
- Perpetuities are bonds that pay out a fixed amount of money each year, forever.

- Calculating the Rate of Return From a Bond

- Calculating the Rate of Return From 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

PDV of Payments (Value of Bond)

($ thousands)

Why do yields differ

among different bonds?

1.0

0.5

0

0.05

0.10

0.15

0.20

Interest Rate

- 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.

- Closing prices for each July 23, 1999:

a b c d e f

IBM 53/8 09 5.830 92 -11/2

Polaroid 111/2 0610.8 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)

- The IBM bond yield:
- Assume annual payments
- 2009 - 1999 = 10 years

- The Polaroid bond yield:

Why was Polaroid

R* greater?

- 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.

- NPV Criterion
- Firms should invest if the PV exceeds the cost of the investment.

- 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?

- 8,000 motors/ month for 20 yrs

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

The NPV of a factory is the present

discounted value of all the cash

flows involved in building and

operating it.

R* = 7.5

10

8

6

4

Net Present Value

($ millions)

2

0

-2

-4

-6

0

0.05

0.10

0.15

0.20

Interest Rate, R

- Real versus Nominal Discount Rates
- Adjusting for the impact of inflation
- Assume price, cost, and profits are in real terms
- Inflation = 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

- Therefore,

- Assume price, cost, and profits are in real terms

- Real versus Nominal Discount Rates
- Real R = nominal R - inflation = 9 - 5 = 4

If R = 4%, the NPV is

positive. The company

should invest in

the new factory.

10

8

6

4

Net Present Value

($ millions)

2

0

-2

-4

-6

0

0.05

0.10

0.15

0.20

Interest Rate, R

- Negative Future Cash Flows
- 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

- Construction time is 1 year

- 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.

- This can be done by increasing the discount rate by adding a risk-premium to the risk-free rate.

- 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.

Diversification

The expected return on a portfolio is the weighted average of expected returns in the portfolio.

Portfolio risk depends on the weights, standard deviations of the securities in the portfolio, and on the correlation coefficients between securities.

The risk of a two-security portfolio is:

p = (WA2·A2 + WB2·B2 + 2·WA·WB·AB·A·B )

- If the correlation coefficient, AB, equals one, no risk reduction is achieved.
- When AB < 1, then p < wA·A + wB·B. Hence, portfolio risk is less than the weighted average of the standard deviations in the portfolio.

- Consumers face similar investment decisions when they purchase a durable good.
- Compare future benefits with the current purchase cost

- 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

- Benefits and Cost

- Firms’ production decisions often have intertemporal aspects---production today affects sales or costs in the future.

- 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?

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

- 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?

PT

Demand

P0

P - c

P0

c

c

Marginal Extraction

Cost

T

Price

Price

Quantity

Time

- 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?

- How would producers react if:

- 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?

- Is this a contradiction to the competitive rule that P = MC?

- P > MC

- P = MC
- MC = extraction cost + user cost
- User cost = P - marginal extraction cost

- 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)

Resource Production by a Monopolist

- The monopolist is more conservationist than a competitive industry.
- They start out charging a higher price and deplete the resources more slowly.

- The interest rate is the price that borrowers pay lenders to use their funds.
- Determined by supply and demand for loanable funds.

Households supply funds to

consume more in the future;

the higher the interest rate, the

more they supply.

S

DH and DF, the quantity

demanded for loanable

funds by households (H)

and firms, respectively,

varies inversely

with the interest rate.

R*

DT = DH + DF and

equilibrium interest

rate is R*.

DT

DF

DH

Q*

R

Interest

Rate

Quantity of

Loanable Funds

S

During a recession interest

rates fall due to a

decrease in the demand

for loanable funds.

R*

R1

DT

D’T

Q1

Q*

R

Interest

Rate

Quantity of

Loanable Funds

S

When the federal

government runs large

budget deficits the

demand for loanable

funds increase.

R2

R*

D’T

DT

Q*

Q2

R

Interest

Rate

Quantity of

Loanable Funds

S

S’

When the Federal

Reserve increases

the money supply, the

supply of loanable

funds increases.

R*

R1

DT

Q*

Q1

R

Interest

Rate

Quantity of

Loanable Funds

- 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.

- 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.

- 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.

- 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.

- 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.