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FIN 501
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Edward Blinder
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Chapter 7

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Finance

FIN 501

Edward Blinder

Summer

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Chapter 7: Common Stock Valuation
7.1 Security Analysis:
Fundamental Analysis: examination of a firm’s accounting statements and other financial and
economic information to assess the economic value of a company’s stock
Numbers such as a company’s earnings per share, cash flow, book equity value, and sales are often
called fundamentals because they describe, on a basic level, a specific firm’s operations and profits (or
lack of profits)
7.2 The Dividend Discount Model:
A fundamental principle of finance holds that the economic value of a security is properly measured by
the sum of its future cash flows, where the cash flows are adjusted for risk and the time value of money
Dividend Discount Model (DDM): method of estimating the value of a share of stock as the present
value of all expected future dividend payments (where dividends are adjusted for risk and the time value
of money)
For example, suppose a company pays a dividend at the end of the year.
- Let D(t) denote a dividend to be paid t years from now
- Let V(0) represent the present value of the future dividend steam
- Let k denote the appropriate risk-adjusted discount rate
- Using the dividend discount mode, the present value of a share of this company’s stock is
measured as this sum of discounted future dividends:
( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
- Assumes that the last dividend is paid T years from now, where the value of T depends on the
specific valuation problem considered
Constant Dividend Growth Rate Model: a version of the dividend discount model that assumes a
constant dividend growth rate
- Letting a constant growth rate be denoted by g, then successive annual dividends are stated as:
( ) ( )( )
- If the number of dividends to be paid is large, calculating the present value of each dividend
separately is tedious and possibly prone to error
- Fortunately, if the growth rate is constant, some simplified expressions are available to handle
certain special cases
- The present value of the next T dividends, that is, D(1) through D(T), can be calculated using this:
( ) ( )( ) [ ( ( )) ]
( )
- Requires that the growth rate and the discount rate does not equal to each other ( ), since this
requires division to be zero
- When the growth rate is equal to the discount rate, that is, k=g, the effects of growth and discounting
cancel exactly, and the present value V(0) is simply the number of payments T times the current
dividend D(0):
( ) ( )
Constant Perpetual Growth:
- Where a firm will pay dividends that grow at the constant rate g forever
- Constant perpetual growth model: a version of the dividend discount model in which dividends
grow forever at a constant rate, and the growth rate is strictly less than the discount rate - Constant perpetual growth model:
( )( )
( ) ( )
- Since D(0)(1+g)= D(1), we could also write the constant perpetual growth model as:
( )
( ) ( )
Applications of the Constant Perpetual Growth Model:
- The constant perpetual growth model can be usefully applied only to companies with a history of
relatively stable earnings and dividend growth expected to continue into the distant future
Historical Growth Rates:
- In the constant growth model, a company’s historical average dividend growth rate is frequently
taken as an estimate of future’s dividend growth
- There are two ways to calculate a historical growth rate yourself:
1. Geometric Average Dividend Growth Rate: a dividend growth rate based on a geometric
average of historical dividends
( ) ⁄
[ ]
( )
D(0) is the earliest dividend and D(N) is the latest dividend to be used.
2. Arithmetic Average Dividend Growth Rate: a dividend growth rate based on an arithmetic
average of historical dividends
o We first calculate each year’s dividend growth rate separately and then calculate an
arithmetic average of these annual growth rates
o Example on page 195
The Sustainable Growth Rate:
- It is necessary to come up with an estimate of g, the growth rate in dividends
- In our previous discussions, we described two ways to do this: (1) using the company’s historic
average growth rate or (2) using an industry median or average growth rate
- We now describe a third way, know as the sustainable growth rate: a dividend growth rate that can
be sustained by a company’s earnings
- Retained Earnings: earnings retained within the firm to finance growth
- Payout Ratio: proportion of earnings paid out as dividends
- Retention Ratio: proportion of earnings retained for reinvestment
- If we let D stand for dividends and EPS stand for earnings per share, then the payout ratio is:
- The Retention Ratio:
( )
- Return on equity is commonly computed using an accounting-based performance measure and is
calculated as a firm’s net income dividend by stockholders’ equity:
( )
- Common problems with sustainable growth rates is that they are sensitive to year-to-year
fluctuations in earnings
- Security analysts routinely adjust sustainable growth rate estimates to smooth out the effects of
earning variations 7.3 The Two-Stage Dividend Growth Model:
Two-stage dividend growth model: dividend model that assumes a firm will temporarily grow at a rate
different from its long-term growth rate
Assumes that a firm will initially grow at a rate during a first stage of growth lasting T years and
thereafter grow at a rate during a perpetual second stage of growth
The present value formula for the two-stage dividend growth model is stated as follows:
( )( ) ( )( )
( ) [ ( ) ] ( )
( )
- The first term on the right-hand side measures the present value of the first T dividends and is the
same expression we used earlier for the constant growth model
- The second term then measures the present value of all subsequent dividends
The two-stage formula requires that the second-stage growth rate be strictly less than the discount rate,
that is,
However, the first- stage growth rate can be greater, smaller, or equal to the discount rate
In the special case where the first-stage growth rate is equal to the discount rate, that is, , the two-
stage formula reduces to this form:
( )( )
( ) ( )
The last case we consider is non-constant growth in the first stage
Using the dividend growth model, we can say that the price in 4 years will be:
( ) ( )
( ) ( ) ( )
( ) ( )
We can now calculate the total value of the stock as the present value of the first three dividends plus the
present value of the price at Time 3, V(3): total value of the stock today

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