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# chapter03Introduction to Valuation(国际投资,英文版)

Introduction to Valuation

Chapter 3
Slides by: Pamela L. Hall, Western Washington University
Francis & Ibbotson Chapter 3: Introduction to Valuation

1

Background
? Determining current price of a security is easy
? Much more difficult to determine the value of an
investment
– How much is an investment worth?
? Need to know so you can determine if the investment is overor under-valued

– Ask the seller – Look in newspaper, television, Internet

? Chapter presents the discounted present value model
to estimate value of an investment
– Demonstrates examples of valuing stock, bond and rental property

Francis & Ibbotson

Chapter 3: Introduction to Valuation

2

Background
? Security price fluctuations may appear chaotic
? When you buy or sell a security you are part of
market ? Hedging is a technique that reduces risk
– One form of hedging is arbitrage – Responses to market’s reaction to random arrival of new information

? Informed buying, selling, hedging and arbitrage
tends to make a security’s price move closer to its value
Francis & Ibbotson Chapter 3: Introduction to Valuation

? Aligns prices with respect to law of one price

3

Time Value of Money
? One-period rate of return
Rate of Return ? Terminal Value - Present Value Present Value

? Rearranging this equation gives us the time value
model ?1 ? rate of return??Present Value ? ? Terminal Value ? The two models are equivalent because

?

The interest rate on the investment equals lender’s oneperiod rate of return
Terminal Value 1? r

? The present value of an investment is
Present Value ?
Francis & Ibbotson Chapter 3: Introduction to Valuation

4

Time Value of Money
?If the rate of return differs from the discount
rate, we can rewrite the equation as
Terminal Value 1? k

?Situations in which the discount rate (k)
differs from the rate of return (r) are common
? ? ?

Present Value ?

?If k > E(r) asset is over-priced
Present value of asset < its price Present value of asset > its price
Chapter 3: Introduction to Valuation

Different people have different opinions, different resources, etc.

?If k < E(r) asset is under-priced
Francis & Ibbotson

5

An Exchange
? Francois deposits 100 euros in a French bank ? An American has a required rate of return of 3%
– He receives a negotiable CD with a maturity value of 105 euros – Expects to earn 5% a year for one year – Economic conditions are not the same in U.S. as they are in France

? You and Francois are not concerned with exchange
rate risk
– Believe that exchange rate will remain constant over the next year

Francis & Ibbotson

Chapter 3: Introduction to Valuation

6

An Exchange
?Francois values the CD at
? You decide to offer to buy Francois’ CD today
?
What price are you willing to pay?
105 euros ? 101.94 euros 1 ? 0.03
105 euros ? 100 euros 1 ? 0.05

? Will Francois be willing to sell?
? He would get more than he thin

ks it is worth ? Are both parties pleased with the transaction?

?
?

Yes, because it is worth only 100 to him

Yes!
Chapter 3: Introduction to Valuation

Francis & Ibbotson

7

Valuing Coca-Cola at Different Discount Rates

?Coca-Cola (ticker symbol:
currently selling for \$54

KO) is

– You expect the selling price in one year to be \$64 and that KO will pay \$0.80 in dividends during the year – Based on that information, your expected rate of return would be
?\$64 - \$54 ? ? \$0.80 ? 20% or \$64 ? \$0.80 - 1 ? 20%
\$54 \$54

Francis & Ibbotson

Chapter 3: Introduction to Valuation

8

Valuing Coca-Cola at Different Discount Rates

?If your required rate of return were 19%, you
would think that KO was underpriced at \$54
\$64.80 ? \$54.45 1 ? 0.19
The most you are willing to pay, which is greater than the current price of \$54.

?If your required rate of return were 20%, you
would think that KO was correctly priced at \$54
\$64.80 ? \$54.00 1 ? 0.20
Francis & Ibbotson Chapter 3: Introduction to Valuation

9

Valuing Coca-Cola at Different Discount Rates

?If your required rate of return were
21%, you would think that KO was over-priced at \$54
\$64.80 ? \$53.55 1 ? 0.21
The most you are willing to pay, which is less than the current price of \$54.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

10

Time Value of Money: Multi-Period Models
? Present value model can value investments that span
multiple time periods
Present Value (PV) ?

? Since some cash flows can be expected to last
forever, sometimes the terminal time period is PV ? ? CF infinity ?1? k ? ? The value of a cash flow series is the discounted present value of all future cash flows
? t t ?1 t

CF ? CF ? ? ? CF ?1?k? ?1?k? ?1?k?
1 2 k 1 2

k

?

Where the discount rate, k, represents the cash flow’s appropriate required rate of return
Chapter 3: Introduction to Valuation

Francis & Ibbotson

11

Time Value of Money: Multi-Period Models

?Cash flows can be
– – – – Cash dividends Coupon interest Rent income from real estate Asset’s selling price, etc.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

12

Example: PV of a Bond
coupon payments and a principal repayment upon maturity
– For a three-year T-note this can be represented as
PVbond ?
Coupon1 Coupon3 ? Par

?1 ? YTM ?

? 1

Coupon2

?1 ? YTM ?

? 2

?1 ? YTM ?

3

Francis & Ibbotson

Chapter 3: Introduction to Valuation

13

Example: PV of a Bond
? The discount rate is the rate that equates the PV of all future cash flows to the bond’s current market value
– Yield to maturity

? Par value represents the principal, or face value, of the bond ? Coupon represent the periodic interest payment
– Coupon % × par value

Francis & Ibbotson

Chapter 3: Introduction to Valuation

14

Example: PV of a Bond
?If the bond has a coupon rate of 6%, a
yield t

o maturity of 5.5%, and a par value of \$1,000 the bond’s present value is
PV
? bond \$60

?1.055 ?

1

?

\$60

?1.055 ?

2

?

\$60 ? \$1,000

?1.055 ?

3

? \$56.872 ? \$53.907 ? \$902.710 ? \$1,013.489

If the bond can be purchased for less than this amount it is a good investment.
Francis & Ibbotson Chapter 3: Introduction to Valuation

15

Present Value of a Perpetuity
?Perpetual investments pay fixed cash flows
forever
– No principal repayment – Similar to buying a perpetual annuity that can be sold to another owner

?Perpetuities are valued using the following
formula
PV ? ?
t ?1 ? t t 1 1

CF ?1? k ? ? CF ? CF ? CF ? CF ? ? ?1? k ? ?1? k ? ?1? k ? ?1? k ?
2 3 4 2 3 4

?

CF k

Francis & Ibbotson

Chapter 3: Introduction to Valuation

16

Example: Valuing a Consol
?A Consol is a bond that pays a constant
coupon to infinity with no repayment of principal
– You are considering investing in a Consol with a yield to maturity of 5.9%
? The bond pays an annual coupon of ￡ 70 ? What price would you be willing to pay for the bond?
PV ?
Francis & Ibbotson

70 ? 1,186.44 pounds 0.059
Chapter 3: Introduction to Valuation

Most you are willing to pay.

17

Example: Estimating Value of Stock
– You think you should earn a required rate of return of 14.5% based on the stock’s risk level – You expect to sell the stock for \$40 in two years – You expect to receive \$2 in cash dividends each year for the next 2 years – What is the most you would be willing to pay for the stock?
PVstock ?
\$2

?1.145 ? ?1.145 ?

? 1

\$2

? 2

\$ 40

?1.145 ?

2

? \$1.7467 ? \$1.5255 ? \$30.510 ? \$33.783
Francis & Ibbotson Chapter 3: Introduction to Valuation

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Example: Stock With Constant Perpetual Growth Rate
? You are considering purchasing stock in a large
corporation with the following attributes
– The current price of the stock is \$51.50 – You believe the current dividend of \$3 will grow at a 3% rate in the foreseeable future – You think 13% is a fair discount rate for stock of its risk level
? What is the most you would be willing to pay for the stock?
PV = k ?g 0.13 ? 0.03 You should decide to not purchase the stock \$3.09 ? ? \$30.90 because it is priced far above the maximum 0.10 you are willing to pay.

Div ?1 ? g ?
1

?

\$3 ?1 ? 0.03?

Francis & Ibbotson

Chapter 3: Introduction to Valuation

19

Example: Estimating Value of Perpetual Preferred Stock

?The current market price of a share of
preferred stock is \$50
– The stock pays an annual cash dividend rate of 4.5% of its \$100 par value
? The annual cash dividend is fixed

– You believe the appropriate required rate of return on stock of this level of risk is 13% – What is the most you would be willing to pay for the stock? You should decide to not
PV ? CF \$4.5% x \$100 ? k 0.13 \$4.50 ? ? \$34.615

0.13

purchase the stock because it is priced far above the maximum you are willing to pay.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

20

Example: Valuing a Real Estate Investment

renting it
– The annual net rental income will be \$10,000 – You think you can sell the house for \$110,000 three years from now – What is the most you would be willing to pay for the house if the discount rate is 10%?
PVrental property ?
\$10,000

Should not pay more than this amount for the rental property.

?1.1?

1

?

\$10,000

?1.1?

2

?

\$10,000 ? \$110,000

?1.1?

3

? \$107 ,513

Francis & Ibbotson

Chapter 3: Introduction to Valuation

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?Professional investors use their value
estimates to make buy-sell decisions ?If an investor could compute the value of an investment with certainty, the following simplified buy-sell rules would apply
– If a security’s price < value it is underpriced and the investor should buy – If a security’s price = value it is correctly priced and the investor should not trade – If a security’s price > value it is overpriced and the investor should sell (or sell short)
Francis & Ibbotson Chapter 3: Introduction to Valuation

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?Selling overpriced securities brings
their price down ?Buying underpriced securities brings their price up ?Security prices are constantly changing as new information arrives ?In a world of uncertainty it is impossible to know the value of an asset with certainty
Francis & Ibbotson Chapter 3: Introduction to Valuation

23

? Some investors enjoy a competitive advantage over
other investors

? It is rational for investors to behave as though a
security’s price is equal to its value

? Security analysts are paid millions of dollars to
provide value estimates for a few securities

– Otherwise, you may be betting against anonymous experts with deep pockets

– Will develop a track record (professional reputation)
Francis & Ibbotson Chapter 3: Introduction to Valuation

24

Long Positions
?Simplest investment strategy
– Buy securities you think are underpriced and hold them in anticipation of a price increase
? Rate of return
r?

?P1 - P0 ? ? Cash Flows
P0

Francis & Ibbotson

Chapter 3: Introduction to Valuation

25

Short Positions
? A short sale would be used if an investor thought a
security were overpriced (and the investor did not currently own that security) and would fall in value
– Involves selling a security you do not own – Borrow the security from a third party
? Most brokerages are happy to lend shares to short sellers

– The short seller will eventually cover his position by buying the stock
? At a lower price than it was sold (hopefully)

– Short seller sells first and buys la

Francis & Ibbotson

Chapter 3: Introduction to Valuation

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Short Positions
?Rate of return ?Example:
? - ? - Cash Flows r ? P0 P1 P0

? Some time ago, you thought that at its
then-current price of \$64 the stock for ABC Company was overpriced. You sold the stock short at \$64.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

27

Example: Return from Short Position
? Now the stock is selling for \$66.50 and you think
that, unfortunately, the stock price will rise even more.
You decide to cover your short sale. Also, during the time that you had shorted the stock, the new owner received \$3.90 in dividends. You are required to reimburse the third party from whom you borrowed the shares by the amount of the dividends. What is your realized return from this transaction?
r?

? ?

?

?\$64 - 66.50 ? - \$3.90 ? -10%
\$64

Francis & Ibbotson

Chapter 3: Introduction to Valuation

28

Complications with Short Positions
?If common stock pays a dividend while on
loan to short seller, short seller must reimburse lender for the amount of cash dividends ?Short seller may be required to put up ‘margin money’

– Represents a good-faith deposit – May total as much as 100% of the value of the borrowed shares if you are a small individual investor

Francis & Ibbotson

Chapter 3: Introduction to Valuation

29

Gain-Loss Illustrations
? Mr. Optimist buys a long
position Gain \$0 -\$10 Loss
Slope of line is +1, meaning one dollar of profit (loss) is made for each dollar the market price rises (falls).
Francis & Ibbotson
Enjoys unlimited potential for gains.

? Mr. Pessimist sells short
Short sale price, \$50

\$40

\$ Market Price
Purchase price, \$50

\$10 \$0 Loss

Slope of line is -1, meaning one dollar of profit (loss) is made for each dollar the market price falls (rises).
Chapter 3: Introduction to Valuation

Gain \$40

\$ Market Price

Losses are unbounded (if price rises infinitely high).

30

Gain-Loss Illustrations
?The long buyer also enjoys limited
liability
– Most investor can lose is the amount of the invested funds (100%)

?The short seller can only gain a
maximum of 100%

– If the underlying asset become worthless and it costs the short seller nothing to cover his position
Francis & Ibbotson Chapter 3: Introduction to Valuation

31

A More Realistic Valuation And Investment Procedure

?In reality the valuation process is
complex
– For example, a security’s risk can change which affects its value – It is also never-ending

Francis & Ibbotson

Chapter 3: Introduction to Valuation

32

Figure 3-3: A Flowchart of the Endless Valuation Process

Francis & Ibbotson

Chapter 3: Introduction to Valuation

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How Price and Value Interact
?Consider two hypothetical groups of
investors
? Buy securities when they have excess liquidity
– Perhaps due to income tax refund, inheritance

? Sell securities when they need liq

uidity
– Buy a house, finance child’s education

? Usually do not buy or sell at times selected to be advantageous
– Often do not investigate whether a security is over-, under-, or correctly-priced

? Millions of liquidity traders, but their daily trading does not usually impact market prices
– Random transactions cancel out
Francis & Ibbotson Chapter 3: Introduction to Valuation

34

How Price and Value Interact
? Have resources to discover new information ? Form estimates of security values ? Recognize significant deviations of the market price away from the consensus estimate of a security’s value ? Make informed buy-sell transactions based on whether they think security is over- or under-valued ? Attempt to maximize their trading profits ? Volume of trading tends to align market price with its value

Francis & Ibbotson

Chapter 3: Introduction to Valuation

35

Comparing Differences Between Prices and Values

?Consensus value estimate
– Will be narrow if most security analysts have similar value estimates
? Security’s price will fluctuate in a narrow range around this value estimate

– Will be wide if there is a great deal of variability in security analysts’ value estimates
? Security’s price will fluctuate wildly
Francis & Ibbotson Chapter 3: Introduction to Valuation

36

Figure 3-4: Illustration of Three Different Hypothesized Price-Value Relationships
Price never deviates from value because numerous (all) investors are making rational, informed buy-sell decisions.

Only a moderate number of investors were making informed buysell decisions.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

37

Information Content of Prices
? Weakly efficient price
? Semi-strongly efficient price
– Reflects all historical information – Does not reflect current information or insider information – Reflects all historical information – Reflects all current information – Does not reflect inside information – Reflects all historical information – Reflects all current information – Reflects all inside information
Francis & Ibbotson Chapter 3: Introduction to Valuation

? Perfectly efficient price

38

Information Content of Prices
?If the market is inefficient with respect
to new information
– Securities analysts would earn huge profits from their buy-sell decisions

Francis & Ibbotson

Chapter 3: Introduction to Valuation

39

Passive Vs. Active Investment Management

?Evidence suggests that the U.S.
securities markets are not perfectly efficient
– Securities analysts can profit from finding under- and over-valued securities
? Encourages many investors to follow active management techniques

Francis & Ibbotson

Chapter 3: Introduction to Valuation

40

Active Investment Management
? Example:
Year 1998 (Actual) 1999 (Actual) 2000 (Est.) 2001 (Est.) 2002 (Est.) 2003 (Est.)

You estimate the following values for KO
Estimated EPS \$1.42 \$0.98 \$1.45 \$

1.64 \$1.85 \$2.09 Estimate d DPR 42% 65% 47% 44% 41% 38% Estimated Dividends \$0.60 \$0.64 \$0.68 \$0.72 \$0.76 \$0.80 PV of Estimated Dividend \$0 \$0 \$0.6018 \$0.5639 \$0.5267 \$0.4906

Sum = \$2.18

Francis & Ibbotson

Chapter 3: Introduction to Valuation

41

Active Investment Management

?You forecast a P-E ratio of 40 times
2003’s estimated EPS of \$2.09
– Your expected price in year 2003 is ? 40 x 2.09 = \$83.60 which has a present value (in 2000) of \$51.27

?Your estimate of KO’s value in 2000 is
– \$2.18 + \$51.27 = \$53.45

Francis & Ibbotson

Chapter 3: Introduction to Valuation

42

Passive Investment Management
?Many studies suggest that the market is
efficient in the semi-strong form
– Suggests that the search for incorrectlyvalued stocks may be too much trouble
? Many passive investors invest in index funds
– Mutual funds designed to track a particular market index ? S&P500 Composite Index is the most popular

Francis & Ibbotson

Chapter 3: Introduction to Valuation

43

Hedging
? Hedging is usually undertaken to reduce losses from
adverse price movements ? A perfect hedge is a combination of long and short positions with the objective of eliminating risk
If the price rises to \$70, the investor will win on his long position but lose the same amount on his short position, leaving him with a \$0 profit.

Gain

\$44 \$26 Long Profits at \$70 Market Price \$70 Short Losses at \$70

\$0

Loss

-\$26 -\$44

\$44

An investor takes a long (and a short) position in a stock with a purchase (sell) price of \$44. If the company goes bankrupt, investor will lose (win) \$44 on his long (short) position, leaving him with a \$0 loss.

Francis & Ibbotson

Chapter 3: Introduction to Valuation

44

Imperfect Hedges
?A hedge is imperfect if a profit or loss results
– Example: KO’s stock is selling for \$40 in London and \$41 on the NYSE.
? Arbitrageurs would buy the stock on the London exchange (because it is cheaper than the NYSE) and short sell the stock on the NYSE.
– This would bid up the price on the London exchange and drive down the price on the NYSE ? This would continue until the prices on both the London exchange and the NYSE were equal

Francis & Ibbotson

Chapter 3: Introduction to Valuation

45

Arbitrage
?Arbitrage involves buying a long position
and selling a short position
– In the same asset or different (but related) assets

?Enforces the economic law of one price
– Price of the same asset is the same in all free markets
? Prices may actually differ due to transaction costs
– – – –
Francis & Ibbotson

? To capitalize on unrealistic price differences

Brokers commissions Foreign exchange fees Governmental foreign exchange controls Telephone costs
Chapter 3: Introduction to Valuation

46

Arbitrage
?Who benefits from arbitrage?
– Everyone
? Arbitrage makes security prices respond rationally, efficiently and uniformly to new information
– Keeps the price of a good that is scarce in one location bu

t plentiful in another reasonable – Helps allocate resources geographically and through time

Francis & Ibbotson

Chapter 3: Introduction to Valuation

47

The Bottom Line
maximizing investment decisions ?Security prices fluctuate due to changing value estimates by investors ?Some investors follow an active investment strategy while others follow a passive one ?Market prices adjust to rapidly reflect new information ?Actions taken by profit-seeking speculators, short sellers, hedgers and arbitrageurs help allocate scarce resources Francis & Ibbotson Chapter 3: Introduction to Valuation 48

?Value estimates form the basis for wealth-