09 Chapter modelChapter 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+D2+. . . .Dn( 1 + rs )( 1 + rs ) 2( 1 + rs ) nThe 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:P 0 =D 1( r s − 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%.EXAMPLEAllied 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$2.15g8.3%rs13.7%P0 =D1=D0 (1+g)=$2.33( rs − g )( rs − g )0.054P0 =$43.12STOCK PRICE SENSITIVITYOne 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. R ...

1. 09 Chapter modelChapter 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+D2+. . . .Dn( 1 + rs )(
1 + rs ) 2( 1 + rs ) nThe 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

2. simplifies to the following expression:P 0 =D 1( r s − 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%.EXAMPLEAllied 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$2.15g8.3%rs13.7%P0 =D1=D0 (1+g)=$2.33( rs − g
)( rs − g )0.054P0 =$43.12STOCK PRICE SENSITIVITYOne 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.
Resulting % ChangeLastPricein D0Dividend, D0$43.12-
30%$0.81$16.14-
15%$0.98$19.600%$1.15$23.0615%$1.32$26.5230%$1.50$29.9
8% Changers$43.12-30%9.38%$215.60-
15%11.39%$75.350%13.40%$45.6615%15.41%$32.7530%17.42
%$25.53% Changeg$43.12-30%5.60%$28.03-
15%6.80%$33.280%8.00%$40.7415%9.20%$52.1730%10.40%$
71.93From 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 rs 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

3. growth equation, we transpose the equation to solve for rs. In
doing so, we are now solving for an expected return. Here is
the resulting equation:rs =D1+gP0This 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 $23.06D1$1.245g8.3%rs
=13.70%Div Yield =5.40%Capital Gains Yield
=8.30%EXTENSIONWhat is the expected price of this stock in
5 years?N =5Using the growth rate we find that:P5 =$34.36
Christopher Buzzard: If growth is constant, we can use the
following formula to find the value after any number of years
(n):
Value (in year n) = Beginning value x (1+g)nVALUING
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
)EXAMPLEA 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

4. the required return is 13.4%, what is the stock's value
today?D0$1.15rs13.4%gs30%Short-run g; for Years 1-3
only.gL8%Long-run g; for Year 4 and all following years.<-----
----- 30% ----------
>8%Year01234Dividend$1.151.4951.94352.52662.7287PV of
dividends$ 1.31831.51131.73262.7287$ 4.562250.5310=
Terminal value =34.65120.054= rs − gL$ 39.2135 =
P0PREFERRED 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.EXAMPLEA perpetual preferred stock pays a $10 annual
dividend and has a required return of 10.3%. What is its
value?Vp =Dp/rpVp =$10.00/10.30%Vp
=$97.09EXAMPLEConsider 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?N50I/YR10%PMT$10FV = Par value
$100Price$100.00What would its value be if the required return
declined to 8%?N50I8%PMT$10Face
value$100Price$124.47Had this been a perpetual preferred with
a required return of 8%, what would be the stock price?:Price
$125.00
Stock price sensitivity
Div 1 1 r 1 1 g 1 1
% change in input
Stock Price
Stock Price Sensitivity
Div -0.3 -0.15 0 0.15 0.3 16.144722222222217
19.604305555555552 23.063888888888886

5. 26.523472222222214 29.983055555555548 r -
0.3 -0.15 0 0.15 0.3 215.5972222222224
75.354368932038838 45.65588235294117
32.748945147679329 25.531249999999993 g -
0.3 -0.15 0 0.15 0.3 28.029629629629625
33.278260869565216 40.73684210526315
52.173333333333318 71.927272727272722
% Change in Input
Stock Price
Week Four Application Assignment
As a manager, it is important to understand how decisions can
be analyzed in terms of alternative courses of action and their
likely impact on a firm's value. Thus, it is necessary to know
how stock prices can be estimated before attempting to measure
how a particular decision might affect a firm's market value.
To prepare for this Assignment, 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. (If you want to analyze a
dividend paying company, you can find a robust list
at http:/www.dividenddetective.com/big_dividend_list.htm.)
Defend your choice of model, and explain why it is appropriate
to use for your company's stock. Be sure to explain how you
arrived at any assumptions regarding values used in the model.
Determine whether your company appears to be correctly
valued, overvalued, or undervalued based on your company's
stock current price and model result. Check Yahoo Finance for
current stock prices. Finally, explain why your company's stock
appears to be over-, under-, or correctly valued.

6. Below isan example. You have to select another stock and go
through the process I have shown above. I posted information
on stock valuation in Discussions. Study text readings and
Weekly Dashboard supplementary information and provide
reasons for overvaluation or undervaluation of your chosen
stock. Address all questions for this assignment in your
explanation. Include key figures in explanation and show
calculations in Appendix. Show citations & references.
I chose Pfizer (PFE). I then went to finance.yahoo.com where I
entered PFE in the Search Finance slot. Below is the
information I received:
Pfizer Inc. (PFE)
NYSE
$34.25 Mar 20, 4:02PM EDT
Beta:
0.89
P/E (ttm):
24.09
EPS (ttm):
$1.42
Div & Yield:
$1.12 (3.30%)
Use the 10-year Treasury bond rate for the riskfree rate of
return = 1.93% at www.cnbc.com or search at google.com
S&P 500 Index return can be used for the market return =
11.93%. Check google.com for 2014 return.
r = 1.93% + [0.89 (11.93% - 1.93%)]
= 1.93% + 8.90% = 10.83%
Do = $1.12 – the dividend for last year
g = retention ratio x ROE

7. Payout ratio and ROE for Pfizer are given under Key
Statistics in cnbc.com or finance.yahoo.com
retention ratio = (1 – payout ratio) = (1 – 0.73) = 0.27 =
27%. Payout ratio was given in finance.yahoo.com
ROE = 12.30% (given)
g = 0.27 x 12.30% = 3.32%. As a decimal, g = 3.32/100 =
.0332
Po = [Do(1+g)]/(r-g) = [$1.12(1+.0332)]/(10.83% - 3.32%)
= ($1.12 x 1.0332)/(.1083 - .0332)
= 1.1572/.0751 = $15.48
Compare Po to current market price of $34.25. If the
intrinsic value is the fair value based on assumptions of
constant growth in dividends, the current market price shows
overvaluation of Pfizer stock.
Study text readings and Weekly Dashboard supplementary
information and provide reasons for overvaluation or
undervaluation.
This is an example. You have to select another stock and
go through the process I have shown above. Address all
questions for this assignment in your explanation. Include key
figures and show calculations in Appendix. Show citations &
references.