choose a publicly-traded company, and then estimate your company’s common stock price, using one of the valuation models presented in the assigned readings or outside readings.

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Element 1: Calculation for: Stock Price Valuation-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Element 2a: Model Choice – Defends Choice of Model-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Element 2b: Model Choice – Comparison to Other Potential Models-Exemplary 5 (5%) points
Very Good 4.65 (4.65%) points
Proficient 4.25 (4.25%) points
Opportunity for Improvement 3.75 (3.75%) points
Unacceptable 0 (0%) points
Element 3: Valuation vs. Current Price-Exemplary 15 (15%) points
Very Good 13.95 (13.95%) points
Proficient 12.75 (12.75%) points
Opportunity for Improvement 11.25 (11.25%) points
Unacceptable 0 (0%) points
Element 4: Reasons and Rationales-Exemplary 20 (20%) points
Very Good 18.6 (18.6%) points
Proficient 17 (17%) points
Opportunity for Improvement 15 (15%) points
Unacceptable 0 (0%) points
Element 5: Critical Thinking, Analysis, and Synthesis-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Element 6: Written Communications-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Element 7: Relevance-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Element 8: Formal and Appropriate Documentation of Evidence, Attribution of Ideas
(APA Citations)-Exemplary 10 (10%) points
Very Good 9.3 (9.3%) points
Proficient 8.5 (8.5%) points
Opportunity for Improvement 7.5 (7.5%) points
Unacceptable 0 (0%) points
Chapter 9. Stocks and Their Valuation (Models)
This model is similar to the bond valuation models developed in Chapter 7 in that we employ
discounted cash flow analysis to find the value of a firm’s stock.
THE DISCOUNTED DIVIDEND MODEL (Section 9-4)
The value of any financial asset is equal to the present value of future cash flows provided by the
asset. Stocks can be evaluated in two ways: (1) by finding the present value of the expected
future dividends, or (2) by finding the present value of the firm’s expected future free cash flows,
subtracting the market value of the debt and preferred stock to find the total value of the common
equity, and then dividing that total value by the number of shares outstanding to find the value per
share. Both approaches are examined in this spreadsheet.
When an investor buys a share of stock, he/she typically expects to receive cash in the form of
dividends and then, eventually, to sell the stock and to receive cash from the sale. Moreover, the
price any investor receives is dependent upon the dividends the next investor expects to earn, and
so on for different generations of investors.
The basic dividend valuation equation is:
P0 =
D1
( 1 + rs )
+
D2
( 1 + rs ) 2
+
. . . .
Dn
( 1 + rs ) n
The dividend stream theoretically extends on out forever, i.e., n = infinity. It would not be feasible
to deal with an infinite stream of dividends, but if dividends are expected to grow at a constant
rate, we can use the constant growth equation as developed in the text to find the value.
CONSTANT GROWTH STOCKS (Section 9-5)
In the constant growth model, we assume that the dividend will grow forever at a constant growth
rate. This is a very strong assumption, but for stable, mature firms, it can be reasonable to
assume that the firm will experience some ups and downs throughout its life but those ups and
downs balance each other out and result in a long-term constant rate. In addition, we assume that
the required return for the stock is a constant. With these assumptions, the price equation for a
common stock simplifies to the following expression:
P0 =
D1
(rs−g)
The long-run growth rate (g) is especially difficult to measure, but one approximates this rate by
multiplying the firm’s return on equity by the fraction of earnings retained, ROE x
(1 – Payout ratio). Generally speaking, the long-run growth rate is likely to fall between 5% and
8%.
EXAMPLE
Allied Food Products just paid a dividend of $1.15, and the dividend is expected to grow at a
constant rate of 8.3%. What stock price is consistent with these numbers, assuming a 13.7%
required return?
D0
g
rs
$2.15
8.3%
13.7%
P0 =
D1
( rs − g )
P0 =
$43.12
=
D0 (1+g)
( rs − g )
$2.33
0.054
=
STOCK PRICE SENSITIVITY
One of the keys to understanding stock valuation is knowing how various factors affect the stock
price. We construct below a series of data tables and a graph to show how the stock price is
affected by changes in the dividend, the growth rate, and rs.
% Change
in D0
-30%
-15%
0%
15%
30%
Resulting
Price
Dividend, D0 $43.12
$0.81
$16.14
$0.98
$19.60
$1.15
$23.06
$1.32
$26.52
$1.50
$29.98
Last
Stock Price
Stock Price Sensitivity
$90
Div
r
g
$80
$70
$60
% Change
-30%
-15%
0%
15%
30%
rs
9.38%
11.39%
13.40%
15.41%
17.42%
$43.12
$215.60
$75.35
$45.66
$32.75
$25.53
% Change
-30%
-15%
0%
15%
30%
g
5.60%
6.80%
8.00%
9.20%
10.40%
$43.12
$28.03
$33.28
$40.74
$52.17
$71.93
$50
$40
$30
$20
$10
$0
-30%
-20%
-10%
0%
10%
20%
30%
% Change in Input
From the chart we see that the stock price increases with increases in the dividend and the growth
rate but decreases with increases in the required return. The dividend relationship is linear, while
price is a nonlinear function of the growth rate and the required return. Changes in r s and g have
especially strong effects on the stock price. This occurs because as rs declines or g increases,
the denominator approaches zero, and this leads to exponential increases in the stock price.
The constant growth assumption is reasonable only if we are valuing mature firms with a stable
history of growth and a likelihood that this stability will continue. There are some special
scenarios when the Gordon DCF constant growth model will not make sense, and this will be
discussed later.
EXPECTED RATE OF RETURN ON A CONSTANT GROWTH STOCK
Using the constant growth equation, we transpose the equation to solve for r s. In doing so, we are
now solving for an expected return. Here is the resulting equation:
D1
P0
rs =
+
g
This expression tells us that the expected return on a stock comprises two components, the
expected dividend yield, which is simply the next expected dividend divided by the current price,
and the expected capital gains yield, which is the expected annual rate of price appreciation, g.
This shows us the dual role of g in the constant growth rate model: It is both the expected
dividend growth rate and also the expected stock price growth rate.
EXAMPLE
You buy a stock for $23.06, and you expect the next annual dividend to be $1.245. Furthermore,
you expect the dividend to grow at a constant rate of 8.3%. What is the expected rate of return and
dividend yield on the stock?
P0
D1
g
$23.06
$1.245
8.3%
rs =
13.70%
Div Yield =
5.40%
Capital Gains Yield =
8.30%
EXTENSION
What is the expected price of this stock in 5 years?
N =
5
Using the growth rate we find that:
P5 =
$34.36
VALUING NONCONSTANT GROWTH STOCKS (Section 9-6)
For many companies, it is unreasonable to assume constant growth. Here valuation procedures
become a little more complicated, because we must estimate a short-run nonconstant growth rate,
then assume that after a certain point of time the firms will grow at a constant rate, and estimate
that constant long-run growth rate.
The point in time when the dividend begins to grow at a constant rate is called the “horizon date,”
and the value of the stock at that time is called the “horizon, or continuing, value,” and it is
calculated as follows:
HV =
PN =
DN+1
( rs − g )
EXAMPLE
A company just paid a $1.15 dividend, and it is expected to grow at 30% for the next 3 years. After
3 years the dividend is expected to grow at the rate of 8% indefinitely. If the required return is
13.4%, what is the stock’s value today?
D0
rs
gs
gL
$1.15
13.4%
30%
8%
Year
Dividend
0
$1.15
PV of dividends
$
1.3183
1.5113
1.7326
$
4.5622
34.6512
$
39.2135
Short-run g; for Years 1-3 only.
Long-run g; for Year 4 and all following years.
8%
1
2
3
4
1.495
1.9435
2.5266
2.7287
2.7287
50.5310
= Terminal value =
0.054
= P0
PREFERRED STOCK (Section 9-8)
A special case of the constant growth model is a stock with a zero growth rate. Such a stock is a
preferred stock, which pays a constant dividend in perpetuity. Perpetuity valuation was discussed
in Chapter 5, and the formula is simply V = Cash flow / Required return.
EXAMPLE
A perpetual preferred stock pays a $10 annual dividend and has a required return of 10.3%. What is
its value?
Vp =
Vp =
Vp =
Dp
$10.00
$97.09
/
/
rp
10.30%
= rs − gL
EXAMPLE
Consider another preferred stock that has a finite life of 50 years (a sinking fund preferred issue), a
$100 par value, and a $10 annual dividend. The required return is 10%. If the par value is repaid at
maturity in 50 years, what is the price of the stock?
N
I/YR
PMT
FV = Par value
Price
50
10%
$10
$100
$100.00
What would its value be if the required return declined to 8%?
N
I
PMT
Face value
Price
50
8%
$10
$100
$124.47
Had this been a perpetual preferred with a required return of 8%, what would be the stock price?:
Price
$125.00

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