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Chapter 9
Stock Valuation
SLIDES
CHAPTER WEB SITES
Section Web Address
9.6 www.bloomberg.com
www.nyse.com
www.nasdaq.com
finance.yahoo.com
CHAPTER ORGANIZATION
9.1 The Present Value of Common Stocks
Dividends versus Capital Gains
9.1 Key Concepts and Skills
9.2 Chapter Outline
9.3 The PV of Common Stocks
9.4 Case 1: Zero Growth
9.5 Case 2: Constant Growth
9.6 Constant Growth Example
9.7 Case 3: Differential Growth
9.8 Case 3: Differential Growth
9.9 Case 3: Differential Growth
9.10 Case 3: Differential Growth
9.11 Case 3: Differential Growth
9.12 A Differential Growth Example
9.13 With the Formula
9.14 With Cash Flows
9.15 Estimates of Parameters
9.16 Where Does R Come From?
9.17 Using the DGM to Find R
9.18 Comparables
9.19 Price-Earnings Ratio
9.20 Enterprise Value Ratios
9.21 Valuing Stocks Using Free Cash Flows
9.22 The Stock Markets
9.23 Market and Limit Orders
9.24 Stop Orders
9.25 NASDAQ
9.26 Stock Market Reporting
9.27 Quick Quiz
Valuation of Different Types of Stocks
9.2 Estimates of Parameters in the Dividend Discount Model
Where Does g Come From?
Where Does R Come From?
A Healthy Sense of Skepticism
Dividends or Earnings: Which to Discount?
The No-Dividend Firm
9.3 Comparables
Price-to-Earnings Ratio
Enterprise Value Ratios
9.4 Valuing Stocks Using Free Cash Flows
9.5 The Stock Markets
Dealers and Brokers
Organization of the NYSE
Types of Orders
NASDAQ Operations
Stock Market Reporting
ANNOTATED CHAPTER OUTLINE
Slide 9.0 Chapter 9 Title Slide
Slide 9.1 Key Concepts and Skills
Slide 9.2 Chapter Outline
1. The Present Value of Common Stocks
Slide 9.3 The PV of Common Stocks
Stock valuation is more difficult than bond valuation because the cash
flows are uncertain, the life is (potentially) forever, and the required rate
of return is unobservable.
A. Dividends versus Capital Gains
The cash flows to stockholders consist of dividends plus a future selling
price. You can illustrate that the current stock price is ultimately the
present value of all expected future dividends:
P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)3 + …
Ethics Note: The importance of the components of the valuation model is
brought into sharp focus in a discussion of pension funding decisions.
Pension and Investments reports that in November, 1993 the Securities
and Exchange Commission issued a “new, unprecedented warning …to
use only ‘high-grade’ market rates for discounting” for valuing pension
assets. The article reports that many over-funded plans could “slip into
underfunded status.” A practical result of the use of inappropriate return
estimates is found in the case of Witco Chemical, which took large charges
against earnings in 1993 related to its use of an inappropriate rate for
computing its unfunded pension liability. Students might first be asked to
guess how one determines an “appropriate” return estimate for pension
funding purposes. Then,
ask them to whom the actuary owes greater responsibility – future pension
recipients, management, shareholders or the Pension Benefit Guaranty
Corporation? It is easy to see that the ethical issues underlying the
actuarial calculations can become quite complex.
Lecture Tip: Lively discussions can be generated in the area of stock
valuation and dividend cash flows. A stock that currently pays no
dividends may or may not have value; a stock that will NEVER pay a
dividend cannot have any value as long as investors are rational. For a
stock that currently pays no dividend, market value derives from (a) the
hope of future dividends and/or (b) the expectation of a liquidating
dividend. In the latter case, “never pays a dividend” really means “never
pays out cash in any form” to shareholders. Students will often argue
strenuously that a firm never has to pay a dividend because investors can
just rely on the increase in price. It’s important to emphasize that the price
won’t continue to increase forever. The company will eventually run out of
productive ways to use its cash. When this happens, it will need to begin
paying dividends. Another way to think of this is that a company that
never pays a dividend, including a liquidating dividend, is essentially a
perpetual zero-coupon bond. It is a big, black hole where you put money
in, but you never get anything back out.
B. Valuation of Different Types of Stocks
Slide 9.4 Case 1: Zero Growth
Zero growth implies that D0 = D1 = D2 … = D
Since the cash flow is always the same, the PV is a perpetuity:
P0 = D / R
Example: Suppose a stock is expected to pay a $2 dividend each period,
forever, and the required return is 10%. What is the stock worth?
P0 = 2 / .1 = $20
Slide 9.5 Case 2: Constant Growth
Slide 9.6 Constant Growth Example
Constant growth: Dividends are expected to grow at a constant percentage
rate each period.
D1 = D0(1+g)
D2 = D1(1+g)
in general, Dt = D0(1+g)t
Note that this is really just a future value.
Example: If the current dividend is $2 and the expected growth rate is 5%,
what is D1? D5?
D1 = $2(1+.05) = $2.10
D5 = $2(1+.05)5 = $2.55
An amount that grows at a constant rate forever is called a growing
perpetuity. The present value of all expected future dividends under this
scenario can be expressed as follows:
P0 = D1 / (R – g)
and more generally,
Pt = Dt+1 / (R – g)
Example: Consider the stock given above. If the required return is 10%,
what is the expected price today? In 4 years?
P0 = $2.10 / (.1 - .05) = $42
P4 = $2.55 / (.1 - .05) = $51
Lecture Tip: In his book, A Random Walk Down Wall Street, pp. 82 – 89,
(1985, W.W. Norton & Company, New York), Burton Malkiel gives four
“fundamental” rules of stock prices. Loosely paraphrased, the rules are
as follows. Other things equal:
-Investors pay a higher price, the larger the dividend growth rate
-Investors pay a higher price, the larger the proportion of earnings paid
out as dividends
-Investors pay a higher price, the less risky the company’s stock
-Investors pay a higher price, the lower the level of interest rates
If the required return, R, is viewed as a riskless rate of interest, Rf, plus a
risk premium, RP, (R = Rf + RP), it is easily shown that Malkiel’s rules
have counterparts in the dividend growth model.
Of course, the tricky part is estimating the growth rate and required
return. So, while the model is precise, its predictions may be substantially
different from observed stock prices depending on the values used.
Lecture Tip: If your students have had some calculus, you might find it
useful to derive the dividend growth model.
P0=D0(1+g)
(1+R)+D0(1+g)2
(1+R)2+D0(1+g)3
(1+R)3+. ..+D0(1+g)t
(1+R)t
Now multiply both sides by (1+R)/(1+g):
(1+R)
(1+g)P0=D0
[
1+(1+g)
(1+R)+(1+g)2
(1+R)2+...+(1+g)t−1
(1+R)t−1
]
Subtract the first equation from the second and you get:
[
(1+R)−(1+g)
(1+g)
]
P0=D0
[
1−(1+g)t
(1+R)t
]
The term 1 – (1+g)t/(1+R)t goes to one as t approaches infinity, assuming
R > g. If we solve for P0, we get the dividend growth model.
Lecture Tip: Students often ask:
1. “How can g ever be assumed to be constant?” The answer lies in the
competitive equilibrium model of classical macroeconomics. Since g
represents not only the growth rate in dividends but also in earnings
and sales, assuming no change in the firm’s cost structure, we are
simply assuming that the product market the firm operates in “settles
down” to a steady state in which competing firms earn sufficient
returns to remain in business, but not large enough to attract outside
capital. From a more practical standpoint, firms will often attempt to
manage their dividend policy so that there is a reasonably constant
growth in dividends.
2. “Why do we assume that R > g?” At least two answers are possible.
First, R may be less than g in the short-run. The supernormal growth
problem is an example of this situation. Second, in equilibrium, high
returns on investment will attract capital, which, in the absence of
technological change, will ensure that in succeeding periods, higher
returns cannot be earned without taking greater risk. But, taking
greater risk will increase R, so g cannot be increased without raising
R.
Slide 9.7 –
Slide 9.11 Case 3: Differential Growth
Assume that dividends will grow at different rates in the foreseeable future
and then will grow at a constant rate thereafter. This general type of model
is especially useful for valuing firms in the growth stage of their life cycle.
To value a Differential Growth Stock, we need to:
1. Estimate future dividends in the foreseeable future.
2. Estimate the future stock price when the stock becomes a Constant
Growth stock (case 2).
3. Compute the total present value of the estimated future dividends
and future stock price at the appropriate discount rate.
This can be accomplished by:
A) Using the formula
B) Or by finding the cash flows.
Slide 9.12 A Differential Growth Example
Slide 9.13 With the Formula
Slide 9.14 With Cash Flows
An example:
A common stock pays a current dividend of $2. The dividend is expected
to grow at an 8% annual rate for the next three years; then it will grow at
4% in perpetuity. The appropriate discount rate is 12%. What is the price
of this stock today?
R = 12% (required return)
g1 = g2 = g3 = 8%
P=C
R−g1
[
1−(1+g1)T
(1+R)T
]
+
(
DivN+1
R−g2
)
(1+R)N
D0 = $2
D1 = $2 × 1.08 = $2.16, D2 = $2.33, D3 = $2.52
g4 = gn = 4%
Constant growth rate applies to D4 –> use Case 2 (constant growth) to
compute P3
D4 = $2.52 × 1.04 = $2.62
P3 = $2.62 / (.12 – .04) = $32.75
Expected future cash flows of this stock:
0 1 2 3
| | | | (r = 12%)
||||
D1D2D3 + P3
$2.16 $2.33 $2.52 + $32.75
P0 = $2.16/1.12 + $2.33/1.122 + $35.27/1.123 = $28.89
We should note that to this point we have assumed that dividends are the
sole cash payout of the firm to its shareholders. However, in recent times
more firms have undertaken share repurchases, which can essentially be
thought of as a substitute for dividends and should, therefore, also be
included in the dividend valuation model.
2. Estimates of Parameters in the Dividend Discount Model
Slide 9.15 Estimates of Parameters
In addition to the current dividend, the growth rate and the required return
impact the stock price.
A. Where Does g Come From?
g can be found using a form of the sustainable growth rate:
g = (retention ratio) x (return on retained earnings)
B. Where Does R Come From?
