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T8.1 Chapter Outline
Chapter 8Stock Valuation
Chapter Organization
8.1 Common Stock Valuation
8.2 Common Stock Features
8.3 Preferred Stock Features
8.3 Stock Market Reporting
8.4 Summary and Conclusions
CLICK MOUSE OR HIT SPACEBAR TO ADVANCE
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 2
Common Stock Valuation - the theory
Investment theorists argue that the best measure of going - concern value for a common stock is the present value of expected future dividends
The basic approach is to : estimate the future earnings of the company make a judgment on the proportion of earnings that would be paid
out as dividends discount the future dividend stream at the appropriate discount rate
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 3
T8.2 Common Stock Cash Flows and the Fundamental Theory of Valuation
In 1938, John Burr Williams postulated what has become the fundamental theory of valuation:
The value today of any financial asset equals the present value of all of its future cash flows.
For common stocks, this implies the following:
D1 P1 D2 P2
P0 = + and P1 = + (1 + R)1 (1 + R)1 (1 + R)1 (1 + R)1
substituting for P1 gives
D1 D2 P2
P0 = + + . Continuing to substitute, we obtain (1 + R)1 (1 + R)2 (1 + R)2
D1 D2 D3 D4
P0 = + + + + … (1 + R)1 (1 + R)2 (1 + R)3 (1 + R)4
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 4
Common Stock Valuation - the theory
We ultimately lose the future value of the stock price in the equation given that it is assumed to be in the distant future and the present value of this distant price is essentially zero
this allows us to focus solely on the future dividend stream as the driver of the stock’s value
What happens if the firm does not pay dividends - does this mean the stock does not have any value?
The issue here is one of expectations of future dividends or some form of liquidating dividend
according to the theory - rational investors would never place a value on a stock that was never going to pay a dividend
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 5
Common Stock Valuation - the theory
3 situations where the model can be applied Zero Growth Case - no growth assumed for the dividends over
time - Constant Growth - steady growth in dividends is assumed -
constant or even Non-constant Growth - after a certain period of time dividends are
assumed to grow at a constant pace - but at some point in the future
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 6
T8.3 Common Stock Valuation: The Zero Growth Case
According to the fundamental theory of value, the value of a financial asset at any point in time equals the present value of all future dividends.
If all future dividends are the same, the present value of the dividend stream constitutes a perpetuity.
The present value of a perpetuity is equal to
C/r or, in this case, D1/R.
Question: Cooper, Inc. common stock currently pays a $1.00 dividend, which is expected to remain constant forever. If the required return on Cooper stock is 10%, what should the stock sell for today?
Answer: P0 = $1/.10 = $10.
Question: Given no change in the variables, what will the stock be worth in one year?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 7
T8.3 Common Stock Valuation: The Zero Growth Case (concluded)
Answer: One year from now, the value of the stock, P1, must be equal to the present value of all remaining future dividends.
Since the dividend is constant, D2 = D1 , and
P1 = D2/R = $1/.10 = $10.
In other words, in the absence of any changes in expected cash flows (and given a constant discount rate), the price of a no-growth stock will never change.
Put another way, there is no reason to expect capital gains income from this stock.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 8
T8.4 Common Stock Valuation: The Constant Growth Case
In reality, investors generally expect the firm (and the dividends it pays) to grow over time. How do we value a stock when each dividend differs from the one preceding it?
As long as the rate of change from one period to the next, g, is constant, we can apply the growing perpetuity model:
D1 D2 D3 D0(1+g)1 D0(1+g)2 D0(1+g)3
P0 = + + + … = + + + ... (1 + R)1 (1 + R)2 (1 + R)3 (1 + R)1 (1 + R)2 (1 + R)3
D0(1 + g) D1
P0 = = . R - g R- g
Now assume that D1 = $1.00, r = 10%, but dividends are expected to increase by 5% annually. What should the stock sell for today?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 9
T8.4 Common Stock Valuation: The Constant Growth Case (concluded)
Answer: The equilibrium value of this constant-growth stock is
D1 $1.00
= = $20
R - g .10 - .05
Question: What would the value of the stock be if the growth rate were only 3%?
Answer:
D1 $1.00
= = $14.29.
R - g .10 - .03
Why does a lower growth rate result in a lower value?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 10
T8.5 Stock Price Sensitivity to Dividend Growth, g
0 2% 4% 6% 8% 10%
50
45
40
35
30
25
20
Stock price ($)
Dividend growth rate, g
D1 = $1Required return, R, = 12%
15
10
5
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 11
T8.6 Stock Price Sensitivity to Required Return, r
6% 8% 10% 12% 14%
100
90
80
70
60
50
40
Stock price ($)
Required return, R
D1 = $1Dividend growth rate, g, = 5%
30
20
10
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 12
T8.7 Common Stock Valuation - The Nonconstant Growth Case
For many firms (especially those in new or high-tech industries), dividends are low or non existent but are expected to be paid at some point in the future. As product markets mature, the dividend growth rate is then expected to evolve to a “steady state” rate. How should stocks such as these be valued?
Answer: We return to the fundamental theory of value - the value today equals the present value of all future cash flows.
Put another way, the nonconstant growth model suggests that
P0 = present value of dividends in the nonconstant growth period(s)
+ present value of dividends in the “steady state” period.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 13
Common Stock Valuation - Non Constant Growth Case
Example
Assume:
company ABC pays a C/S dividend of $5.00 per share today
no growth is assumed for 3 years followed by constant growth of 4%
using a discount rate of 8% what is the value of the stock?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 14
ABC Company - answer
1st calculate the value of the stock at p3 using the constant
growth formula
D/r-g = $5.00/(.08-.04) = $125
Next discount this value back to p0
P3/(1+r)3 = $125/1.25971 = $99.22
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 15
Common Stock Valuation - other theories
Burton Malkiel in his book ‘ A Random Walk Down Wall Street’ gives his four ‘fundamental’ rules of stock prices:
investors pay a higher price the larger the dividend growth rate investors pay a higher price the larger the proportion of earnings
paid out in dividends investors pay a higher price per share the less risky the company’s
stock is investors pay a higher price per share the lower the level of interest
rates
.....there are other theories!!
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 16
T8.8 Chapter 8 Quick Quiz -- Part 1 of 3
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely. If the required return is 9%, then the price today is _____ ?
P0 = D1/(R - g)
= $5 ( ____ )/( ____ -____ )
= $5.25/.04
= $_____ per share
What will the price be in a year?
Pt = Dt+1/(R - g)
P1 = D___ /(R - g) = ($____ 1.05)/(.09 - .05) = $137.8125
By what percentage does P1 exceed P0? Why?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 17
T8.8 Chapter 8 Quick Quiz -- Part 1 of 3 (concluded)
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely. If the required return is 9%, then the price today is _____ ?
P0 = D1/(R - g)
= $5 ( 1.05 )/( .09 - .05 )
= $5.25/.04
= $131.25 per share
What will the price be in a year?
Pt = Dt+1/(R - g)
P1 = D 2 /(R - g) = ($5.25 1.05)/(.09 - .05) = $137.8125
By what percentage does P1 exceed P0? Why?
P1 exceeds P0 by 5% -- the capital gains yield.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 18
T8.9 Chapter 8 Quick Quiz -- Part 2 of 3
Find the required return:
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely.
If the stock sells today for $65 5/8, what is the required return?
P0 = D1/(R - g)
(R - g) = D1/P0
R = D1/P0 + g
= $5.25/$65.625 + .05
= dividend yield (_____) + capital gains yield (_____)
= ____
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 19
T8.9 Chapter 8 Quick Quiz -- Part 2 of 3
Find the required return:
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 5% per year indefinitely.
If the stock sells today for $65 5/8, what is the required return?
P0 = D1/(R - g)
(R - g) = D1/P0
R = D1/P0 + g
= $5.25/$65.625 + .05
= dividend yield ( .08 ) + capital gains yield ( .05 )
= .13 = 13%
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 20
T8.10 Summary of Stock Valuation (Table 8.1)
I. The General Case
In general, the price today of a share of stock, P0, is the present value of all of its future dividends, D1, D2, D3, . . .
D1 D2 D3
P0 = + + + … (1 + R)1 (1 + R)2 (1 + R)3
where r is the required return.
II. Constant Growth Case
If the dividend grows at a steady rate, g, then the price can be written as:
P0 = D1/(R - g)
This result is the dividend growth model.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 21
T8.10 Summary of Stock Valuation (Table 8.1) (concluded)
III. Supernormal Growth
If the dividend grows steadily after t periods, then the price can be written as:
D1 D2 Dt Pt
P0 = + + . . . + + (1 + R)1 (1 + R)2 (1 + R)t (1 + R)t
where
Dt+1 (1 + g) P0 =
(R - g)
IV. The Required Return
The required return, r, can be written as the sum of two things:
R = D1/P0 + g
where D1/P0 is the dividend yield and g is the capital gains yield (which is the same thing
as the growth rate in dividends for the steady growth case).
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 22
T8.11 Features of Common Stock
Features of Common Stock
The right to vote - including major events like takeovers
The right to share proportionally in dividends paid
The right to share proportionally in assets remaining after liabilities have been paid, in event of a liquidation
The preemptive right
Dividends
Not a liability until declared by the Board of Directors
Unlike interest on debt, dividends are not tax deductible to the firm
However, shareholder receipt of dividends does have preferential tax treatment (See Chapter 2)
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 23
T8.11 Features of Common Stock
Classes of Stock
Dual Class shares are becoming more commonplace
Usually classes divide into voting and non-voting shares
“Coattail” provisionally invoked at the time of a takeover
Some dual class shares allow foreign investment without foreign control
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 24
T8.12 Features of Preferred Stock
Features of Preferred Stock
Preferences over common stock - dividends, liquidation
Dividend arrearages
Cumulative and non-cumulative
Stated/liquidating value
Is preferred stock really debt?
Preferred stock and taxes
Tax treatment differs from debt
Differential tax treatment suggests a preferred stock clientele
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 25
Preferred Stock - why it looks like debt
Pref. Shareholders receive a stated dividend much like the stated coupon on a bond
Pref. Shares often carry credit ratings much like a bond issues
Pref. Stock is often callable by the issuer
Some pref. Share issues even have sinking funds
Floating rate pref. Shares are similar in concept to floating rate bond issues
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 26
Price Earnings and PEG Ratios
The P/E ratio is partially impacted by the net present value of growth opportunities
for a given level of earnings, two stocks can trade at much different P/E ratios - one reason being investors are willing to pay more (a higher multiple of earnings) for the firm that has the greater growth opportunities.
PEG ratio is the P/E ratio / earnings growth rate useful when comparing stocks which have high P/E ratios - to help
differentiate e.g
-two stocks may both be trading at high P/E’s of say 50
-one may be growing earnings at 25 times per year and the other at 10 times....the two firms have PEG’s of 2.5 and 5.
-all other things being equal - which one would be the better investment?
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 27
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 10% for the next two years, the 8% for one year, and then 6% indefinitely. The required return is 12%. What is the stock’s value?
TimeDividend
0 $ 5.00
1 $ ____ (10% growth)
2 $ ____ (10% growth)
3 $6.534 ( __% growth)
4 $6.926 ( __% growth)
T8.15 Chapter 8 Quick Quiz -- Part 3 of 3
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 28
Suppose a stock has just paid a $5 per share dividend. The dividend is projected to grow at 10% for the next two years, the 8% for one year, and then 6% indefinitely. The required return is 12%. What is the stock’s value?
TimeDividend
0 $ 5.00
1 $ 5.50 (10% growth)
2 $ 6.05 (10% growth)
3 $6.534 ( 8% growth)
4 $6.926 ( 6% growth)
T8.15 Chapter 8 Quick Quiz -- Part 3 of 3
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 29
T8.15 Chapter 8 Quick Quiz -- Part 3 of 3 (concluded)
At time 3, the value of the stock will be:
P3 = D4/(R - g) = $_____ /(.12 - .06) = $115.434
The value today of the stock is thus:
P0 = D1/(1 + R) + D2/(1 + R)2 + D3/(1 + R)3 + P3/(1 + R)3
= $5.5/1.12 + $6.05/1.122 + $6.534/1.123 + $115.434/1.12
= $96.55
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 30
T8.15 Chapter 8 Quick Quiz -- Part 3 of 3 (concluded)
At time 3, the value of the stock will be:
P3 = D4/(R - g) = $6.926/(.12 - .06) = $115.434
The value today of the stock is thus:
P0 = D1/(1 + R) + D2/(1 + R)2 + D3/(1 + R)3 + P3/(1 + R)3
= $5.5/1.12 + $6.05/1.122 + $6.534/1.123 + $115.434/1.123
= $96.55
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 31
T8.16 Solution to Problem 8.1
Green Mountain, Inc. just paid a dividend of $2.00 per share on its stock. The dividends are expected to grow at a constant 5 percent per year indefinitely. If investors require a 12 percent return on Favre stock, what is the current price? What will the price be in 3 years? In 15 years?
According to the constant growth model,
P0 = D1/(R - g) = $2.00(1.05)/(.12 - .05) = $30.00
If the constant growth model holds, the price of the stock will grow at g percent per year, so
P3 = P0 (1 + g)3 = $30.00 (1.05)3 = $34.73, and
P15 = P0 (1 + g)15 = $30.00 (1.05)15 = $62.37.
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 32
T8.17 Solution to Problem 8.10
Metallica Bearings, Inc. is a young start-up company. No dividends will be paid on the stock over the next 5 years. The company will pay a $6 per share dividend in six years and will increase the dividend by 5% per year thereafter. If the required return on this stock is 21%, what is the current share price?
The current market price of any financial asset is the present value of its future cash flows, discounted at the appropriate required return. In this case, we know that:
D1 = D2 = D3 = D4 = D5 = 0
D6 = $6.00
D7 = $6.00(1.05) = $6.30 . . .
Irwin/McGraw-Hill copyright © 2002 McGraw-Hill Ryerson, Ltd Slide 33
T8.17 Solution to Problem 8.10 (concluded)
This share of stock represents a stream of cash flows with two important features:
First, because they are expected to grow at a constant rate (once they begin), they are a growing perpetuity;
Second, since the first cash flow is at time 6, the perpetuity is a deferred cash flow stream.
Therefore, the answer requires two steps:
1. By the constant-growth model, D6/(r - g) = P5;
i.e., P5 = $6.00/(.21 - .05) = $37.50.
2. And, P0 = P5 1/(1 + .21)5 = $37.50 .3855 = $14.46.