Capital and Financial Market

Hall and Lieberman, 3rd edition, Thomson South-Western, Chapter 13

2

Consider…

1626, Peter Minuit bought Manhattan from the Man-a-hat-a Indians for goods valued at $24

The 12800 acres are now valued at $627 million/acre or $8 trillion unimproved

This was a heck a deal for the Dutch

Is this true?

3

The Value of Future Dollars Always preferable to receive a given sum of money

earlier rather than later Because present dollars can earn interest and Because borrowing dollars requires payment of interest

$1 one year from now is not equal to $1 today Mechanism (r = rate of interest) Opportunity cost of spending $1 today= $(1 + r)*1 = $(1 + r) at r = 0.1; opportunity cost is $1.10 next period

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Future Value

Future Value: the value in dollars at a future point in time of a sum of money today.

Compounding: successive application of interest payments to generate future values.

Period 0 Period 1 Period 2

$1 (1+r)*$1 $(1+r)*{(1+r)*$1}

= (1+r)2*$1

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Future Value

Generally, $1 today is worth $(1+r)t t years from nowAt r = 0.1

Period 0: $1

Period 1: $(1+ 0.1) = $1.10

Period 2: $(1 + 0.1)2 = $1.21

Period 3: $(1 + 0.1)3 = $1.33

……

Period 40: $(1 + 0.1)40 = $45.26

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Future Value: Man-a-hat-a Indians

How much is $24 in 1626 worth today if they just collected interest?

$1 in 1626 is worth $(1+r)T in 2006, T = 2006-1626 = 380

At r = 0.1; $24*(1+r)380 = $1,286,564 trillion

At r = 0.08; $24*(1+r)380 = $120.6 trillion

At r= 0.07; $24*(1+r)380 = $35.2 trillion

At r = 0.06; $24*(1+r)380 = $99.2 billion

At r = 0.05; $24*(1+r)380 = $2.7 billion

Breakeven r=7.23%

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Example: Investment for Retirement Suppose you want to be a millionaire when you

retire. How much should you start putting away

FV = $1 million

A = annual amount invested How much would you have after T years?

r

rrAFV

T )]1()1[(*

1

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Example: Investment for Retirement Suppose you want to be a millionaire when you retire.

How much should you start putting away FV = {[(1+r)T+1–(1+r)]/r}A Current age = 18; Millionaire by 40? 50? 60?

Annual amount to invest per year

r 40, T=22 50, T=32 60, T=420.1 $12,572 $4,499 $1,688

0.05 $24,137 $12,490 $6,993

Target Age

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Present Value Present value (PV) of a future payment is the value of that

future payment in today’s dollars Value of any asset is sum of present values of all future

benefits it generates Discounting

Converting a future value into its present-day equivalent Discount rate

Interest rate used in computing present valuesPeriod 0 Period 1$1 (1+r)*$1$1/(1+r) $1

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Present Value Suppose that the annual interest rate is r, PV of $Y to

be received T years in the future is equal to

Present value of a future payment is smaller if Size of the payment is smaller Interest rate is larger Payment is received later

Tr

Y

)1(

$

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Present Value

Generally Period 0 Period T

$1 (1+r)T*$1$1/(1+r)T $1

At r = 0.1; compute present value of $1 in Period X Period Present Value 1 $1/(1+ .1) = $0.91 2 $1/(1 + .1)2 = $0.83 3 $1/(1 + .1)3 = $0.75

40 $1/(1 + .1)40 = $0.02

12

Consider…

Furnace Advertisement Furnace costs $2,000 Energy Savings = $200/year Claim: The furnace will pay for itself in 10 years

Is this true?

13

Example : Furnace $200 T periods in the future will be worth $200/(1+r)T nowAt r = 0.1; Year Present Value 1 $200/(1+ .1) = $181.82 2 $200/(1 + .1)2 = $165.29 3 $200/(1 + .1)3 = $150.26…10 $200/(1 + .1)10 = $77.11

ADD UP THESE RETURNSADD UP THESE RETURNS

Present Value = $1,429Present Value = $1,429It would take 24 years to break even at r = 0.1It would take 24 years to break even at r = 0.1

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Conclusions Regarding Present & Future Value

General Formula PV : Present Value FV: Future Value

FVT = (1+r)T * PV0 (Compounding)

PV0 = FVT / (1+r)T (Discounting)

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Other Issues and Applications Present Value can be used in making capital/equipment

decisions. Consider the problem of purchasing a piece of

equipment with a MRP of $100/year and a lifespan of 10 years.

How would you compute the present value of this stream of returns?

Present value can be used to value returns that vary over time Modified to account for uncertainty

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Investment in Human Capital Suppose you are an account for an entertainment

company. You have to decide whether to take a specialized course in how to handle the books of entertainment companies.

Costs: $30,000 tuition + $25,000 foregone income Benefits: Increase your income by $10,000 a year for

the next eight years before you retire. If interest rate=10%, what’s your decision? What if interest rate=8%?

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Bonds One of the methods to finance the production is selli

ng bonds Bond is a promise to pay a specific sum of money at

some future date This amount of money is principal (face value)

Most common amount: $10,000 The date at which a bond’s principal will be paid

to bond’s owner is Maturity Date

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Bonds Principal: The value of the bond at maturity The face value on the bond Future Value Individuals buy bonds at the present value of

the principal

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The Bond Market Pure discount bond

Promises no payments except for principal it pays at maturity

Coupon payments Series of periodic payments that a bond promises

before maturity Yield

Rate of return a bond earns for its owner

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How Much is a Pure Discount Bond Worth? Value of a bond with a face value of $10,000 which

matures in exactly one year and has an interest rate of 10% is

Bond will sell for $9,091

091,9$10.1

000,10$

)1(

$

i

YPV

21

How Much Is A Coupon Payment Bond Worth? Bond with a principal of $10,000, a five-year

maturity and an annual coupon payment of $600 has a present value of

Total present value is what bond is worth Price at which it will trade

As long as buyers and sellers use the same discount rate of 10% in their calculations

483,8$)10.1(

000,10$

)10.1(

600$

)10.1(

600$

)10.1(

600$

)10.1(

600$

)10.1(

600$55432

PV

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How To Calculate Yield? Suppose bond matures in one period

PBOND = PV = FV/(1+r)Yield is implied by

(1+r) = FV/PV

If bond matures T periods from nowPBOND = PV = FV/(1+r)T

Annual yield is implied by (1+r) = ( FV/PV ) 1/T

The higher the price of any given bond the lower the yield on that bond

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Bond’s Yield: Example Suppose FV = $10,000;

PBOND = $9500;

Maturity in one period

Then, yield is

(1+r) = FV/PV = (10,000/9,500) = 1.053

Implying that annual interest rate r = 0.053

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Why Do Bond Prices (and Bond Yields) Differ? Each bond traded everyday has its own

unique yield Why doesn’t each bond sell at a price that

makes its yield identical to the yield on any other bond? A bond—like any asset—is worth the total

present value of its future payments

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Why Do Bond Prices (and Bond Yields) Differ? To put a value on riskier bonds, markets participants use

a higher discount rate than on safe bonds Leads to lower total present values and lower prices

for riskier bonds With lower prices, riskier bonds have higher yields

Higher risk, higher yield, lower price

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Why Do Bond Prices (and Bond Yields) Differ? Riskiness is only one reason that bond prices and bond

yields differ Other reasons include

Differences in maturity dates Differences in frequency of coupon payments Because one bond is more widely traded (and therefo

re easier to sell on short notice) than another

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Rating on Bonds According to the likelihood of default, bonds are rated

in the following (Moody’s Investor’s Services estimate):

U.S. Treasury bond - the least risky Aaa Corporate bond Aa Corporate bond A Corporate bond Baa Corporate bond Ba Corporate bond B Corporate bond - higher risk

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Can you outguess the market?

Suppose you expect that price of bond will fall tomorrow because the Federal Reserve Board of Governor’s is going to raise the reserve rate (the interest rate charged to banks by the Fed).

What will you do? If everyone has the same information, all act

similarly, what will happen?

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Fundamental value of stocks Stock: share of ownership in the firm Stockholder has a share of the future earnings

of the firm Stock price should be the present value of the

stream of future earnings per share

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Fundamental value of stocks Stock price should be the present value of the

stream of future earnings per share (E) PV = Price of stock = E + E/(1+r) + E/ (1+r)2 + E/ (1+r)3 + …= E/r Price Earnings (PE) ratio: Price of stock/E = (1/r) Very high PE ratios imply having to pay a lot

per $ of expected earnings

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Valuing a Share of Stock Important conclusions about factors that can affect a

stock’s value An increase in current profits increases value of a share of

stock An increase in anticipated growth rate of profits increases

value of a share of stock A rise in interest rates—or even an anticipated rise in inte

rest rates—decreases value of a share of stock An increase in perceived riskiness of future profits decrea

ses value of a share of stock

32

Gambling vs. Investing Expected return

Pi = probability that outcome i happens

Ri = Return when outcome i happensC = investment costsN outcomesProbabilities add up to 1

Expected Return = Σ Pi Ri - Ci=1

N

33

Gambling vs. investingFair bet: Expected return is zero

Coin flip: Pay C = $1 to play

Heads: Receive R1 = $2, P1 =.5

Tails: Receive R2 = $0, P2 = .5

Expected Return = P1R1 + P2 R2 - C= .5*2 + .5*0 - 1 = 0

34

Gambling Unfair bet:

Gambler: Expected return <0

Casino: Expected return >0 Example : slot machines pay 92¢ per $ bet

Expected return for customer = -8¢ Expected return for Casino = 8¢

Lottery Expected return for customer = -50¢/$ Expected return for Lottery = 50¢/$

35

Gambling Cards, Horses Gambler: Expected return depends on skill

Casino: Expected return >0 on average or else they rent the space (poker)

Casinos will not offer games that have negative expected return to the Casino

36

What proportion of ISU college students gamble?

Overall 56%Males 61%Females 49%

Gamblers spent64% < $20/month

18% $20-$60/month18% > $60/month

Average $33 per monthT. Hira and K. Monson. “A social learning perspective of gambling among college students”

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Why do ISU students gamble?Entertainment 65%

To win money 30%

Women more likely to say “for entertainment”

Men more likely to say “to win”

T. Hira and K. Monson. “A social learning perspective of gambling among college students”

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Risk From Uncertainty Future payment is not guaranteed sometimes

There is uncertainty in your investment The higher the risk, the higher the payoff Goal: maximize the expected future return by

choosing one or some among a bunch of financial assets, given the same risk Or reduce the risk to the least given the same expected

return

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The Higher the Risk, the Higher the payoff

Investment on A is less risky than investment on B, but has a lower expected return from investment tradeoff

Probability 0.2 0.8 Expected Return80

Payoff from A 0 100

Probability 0.8 0.2 Expected Return120Payoff from B 0 600

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Diversification - Portfolio

Holding several assets can lower risk without sacrificing return

The mixed portfolio yields higher utility—same expected return, lower variance

Probability 0.2 0.3 0.5Expected

ReturnSt Dev Return

A 30 0 20 16 11.14

B 0 20 20 16 8.00

0.5A+0.5B 15 10 20 16 4.36

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Diversification How can you low the risk?1. Mutual fund

Financial intermediary holds a portfolio of stock.2. Individual investors buy shares of the portfolio3. Holding assets over a long period can lower risk -

Higher average return wins out Warren Buffet: Asked when is the best time to

sell stock…………Never