Transcript Capital and Financial Market Hall and Lieberman, 3 edition, Thomson South-Western, Chapter 13

Capital and Financial Market
Hall and Lieberman, 3rd edition, Thomson
South-Western, Chapter 13
Consider…
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1626, Peter Minuit bought Manhattan from the Mana-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?
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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
$1
Period 1
(1+r)*$1
Period 2
$(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 now
At 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
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How much is $24 in 1626 worth today if they just
collected interest?
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$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
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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?
T 1
[(1  r )  (1  r )]
FV  A *
r
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Example: Investment for Retirement
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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
Target Age
r
40, T=22 50, T=32 60, T=42
0.1
$12,572
$4,499
$1,688
0.05
$24,137 $12,490
$6,993
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Present Value
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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 values
Period 0
$1
$1/(1+r)
Period 1
(1+r)*$1
$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
$Y
(1  r )T
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Present value of a future payment is smaller if
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Size of the payment is smaller
Interest rate is larger
Payment is received later
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Present Value
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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
1
2
3
Present Value
$1/(1+ .1) = $0.91
$1/(1 + .1)2 = $0.83
$1/(1 + .1)3 = $0.75
40
$1/(1 + .1)40 = $0.02
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Consider…
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Furnace Advertisement
Furnace costs $2,000
 Energy Savings = $200/year
 Claim: The furnace will pay for itself in 10 years
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Is this true?
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Example : Furnace
$200 T periods in the future will be worth $200/(1+r)T now
At 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
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ADD UP THESE RETURNS
Present Value = $1,429
It would take 24 years to break even at r = 0.1
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Conclusions Regarding Present & Future Value
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General Formula
PV : Present Value
 FV: Future Value
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FVT = (1+r)T * PV0 (Compounding)
PV0 = FVT / (1+r)T (Discounting)
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Other Issues and Applications
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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
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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
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One of the methods to finance the production is
selling bonds
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Bond is a promise to pay a specific sum of money at
some future date
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This amount of money is principal (face value)
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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
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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
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Pure discount bond
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Coupon payments
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Promises no payments except for principal it pays
at maturity
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?
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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
PV 

$Y
$10,000

 $9,091
(1  i )
1.10
Bond will sell for $9,091
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How Much Is A Coupon Payment
Bond Worth?
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Bond with a principal of $10,000, a five-year
maturity and an annual coupon payment of $600 has
a present value of
PV 
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$600
$600
$600
$600
$600 $10,000
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 $8,483
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3
4
5
5
(1.10) (1.10)
(1.10) (1.10)
(1.10)
(1.10)
Total present value is what bond is worth
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Price at which it will trade
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As long as buyers and sellers use the same discount rate of 10%
in their calculations
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How To Calculate Yield?
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Suppose bond matures in one period
PBOND = PV = FV/(1+r)
Yield is implied by
(1+r) = FV/PV
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If bond matures T periods from now
PBOND = PV = FV/(1+r)T
Annual yield is implied by
(1+r) = ( FV/PV ) 1/T
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The higher the price of any given bond the lower the yield
on that bond
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Bond’s Yield: Example
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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?
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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?
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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?
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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
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Higher risk, higher yield, lower price
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Why Do Bond Prices (and Bond Yields)
Differ?
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Riskiness is only one reason that bond prices and bond
yields differ
 Other reasons include
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Differences in maturity dates
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Differences in frequency of coupon payments
Because one bond is more widely traded (and
therefore easier to sell on short notice) than another
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Rating on Bonds
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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?
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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
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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
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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
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Important conclusions about factors that can affect a
stock’s value
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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
interest rates—decreases value of a share of stock
An increase in perceived riskiness of future profits
decreases value of a share of stock
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Gambling vs. Investing
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Expected return
Pi = probability that outcome i happens
Ri = Return when outcome i happens
C = investment costs
N outcomes
Probabilities add up to 1
N
Expected Return = Σ
Pi=1
i Ri - C
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Gambling vs. investing
Fair 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
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Gambling
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Unfair bet:
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Gambler: Expected return <0
Casino: Expected return >0
Example : slot machines pay 92¢ per $ bet
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Expected return for customer = -8¢
Expected return for Casino = 8¢
Lottery
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Expected return for customer = -50¢/$
Expected return for Lottery = 50¢/$
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Gambling
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Cards, Horses
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Gambler: Expected return depends on skill
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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
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What proportion of ISU college
students gamble?
Overall
Males
Females
56%
61%
49%
Gamblers spent
64% < $20/month
18% $20-$60/month
18% > $60/month
Average $33 per month
T. 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
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Future payment is not guaranteed sometimes
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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
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Or reduce the risk to the least given the same expected
return
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The Higher the Risk, the Higher the payoff
Probability
Payoff from A
Probability
Payoff from B
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0.2
0.8
0
100
0.8
0.2
0
600
Expected Return
80
Expected Return
120
Investment on A is less risky than investment on B,
but has a lower expected return from investment

tradeoff
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Diversification - Portfolio
Probability
0.2
0.3
0.5
Expected
Return
A
30
0
20
16
11.14
B
0
20
20
16
8.00
0.5A+0.5B
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10
20
16
4.36
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St Dev
Return
Holding several assets can lower risk without
sacrificing return
The mixed portfolio yields higher utility—same
expected return, lower variance
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Diversification
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1.
2.
3.
How can you low the risk?
Mutual fund
 Financial intermediary holds a portfolio of stock.
Individual investors buy shares of the portfolio
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
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