Chapter 6
Valuing Stocks
Topics Covered
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Preferred Stocks and their valuation
Valuing Common Stocks
Simplifying the Dividend Discount Model
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No growth
Constant growth
Non-constant growth
Growth Stocks and Income Stocks
Preferred Stock Characteristics
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Unlike common stock, no ownership interest
Second to debt holders on claim on company’s assets
in the event of bankruptcy.
Annual dividend yield as a percentage of par value
Preferred dividends must be paid before common
dividends
If cumulative preferred, all missed past dividends
must be paid before common dividends can be paid.
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Preferred Stock Valuation
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Promises to pay the same dividend year after year
forever, never matures.
A perpetuity.
P0 = Div/r
Expected Return: r = Div/P0
Example: GM preferred stock has a $25 par
value with a 8% dividend yield. What price
would you pay if your required return is 9%?
The Financial Pages:
Preferred Stocks
52 weeks
Yld
Vol
Hi Lo
Sym
Div % PE 100s Close
27.88 25.06 GM pfG 2.28 8.4 … 86
27.00
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Dividend: $2.28 on $25 par value = 9.12%
dividend rate.
Expected return: 2.28 / 27.00 = 8.4%.
What do investors in common stock
want?
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Periodic cash flows: dividends, and…
To sell the stock in the future at a higher price
Management to maximize their wealth
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Valuing Common Stocks: Expected
Return
Expected Return - The percentage yield that an investor
forecasts from a specific investment over a set period
of time. Sometimes called the holding period return
(HPR).
Expected Return = r =
Div1 + P1 − P0
P0
Expected Return
The formula can be broken into two parts.
Dividend Yield + Capital Appreciation
Expected Return = r =
Div1 P1 − P0
+
P0
P0
Example
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Lisa Simpson buys Grease Gougers stock for
$20 per share. In a year she expects the
receive $1 in dividends and the price of the
stock to be $22.
What is Lisa’s expected return?
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Valuing Common Stocks
Dividend Discount Model - Computation of today’s
stock price which states that share value equals the
present value of all expected future dividends.
P0 =
Div1
Div2
Div H + PH
+
+...+
1
2
(1 + r ) (1 + r )
(1 + r ) H
H - Time horizon for your investment.
Stock Valuation
Infinite Holding Periods
Stock Value = PV of Future Expected
Dividends
P0 =
D3
D1
D2
D∞
+
+
+ ... +
1
2
3
(1 + r ) (1 + r ) (1 + r )
(1 + r )∞
Stock Valuation: Dividend Patterns
For Valuation: we will assume stocks fall into one of
the following dividend growth patterns.
† Constant growth rate in dividends
† Zero growth rate in dividends, like preferred stock
† “Supernormal” (non-constant) growth rate in
dividends
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Stock Valuation Case Study: Doh!
Doughnuts
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We have found the following information for Doh!
Doughnuts:
current dividend = $2 = Div0
Required return = 12% = r
Analysts Estimates for Doh!
Doughnuts
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NEDFlanders predicts a constant annual growth rate
in dividends and earnings of zero percent (0%)
Barton Kruston Simpson predicts a constant annual
growth rate in dividends and earnings of 7 percent
(7%).
Homer Co. expects a dramatic growth phase of 20%
annually for each of the next 3 years followed by a
constant 7% growth rate in year 4 and beyond.
Our Task: Valuation Estimates
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What should be each analyst’s estimated
value of Doh! Doughnuts?
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Valuing Common Stocks: No Growth
If we forecast no growth, and plan to hold out stock
indefinitely, we will then value the stock as a
PERPETUITY.
Perpetuity = P0 =
Div1
EPS1
or
r
r
Assumes all earnings are
paid to shareholders.
Ned Flanders’ Valuation
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Div0 = $2, r = 12% or 0.12, g = 0%
P0 = Div0/r = $2/0.12 = $16.67
Valuing Common Stocks: Constant
Growth
Constant Growth DDM - A version of the
dividend growth model in which dividends
grow at a constant rate (Gordon Growth
Model).
P0 =
Div (1 + g ) = Div
0
r-g
1
r-g
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Barton Kruston Simpson’s Valuation
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Div0 = $2, g = 7%, r = 12%
Expected Return of Constant
Growth Stocks
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Expected Rate of Return = Expected Dividend
Yield + Expected Capital Gains Yield
Div1/P0 = Expected Dividend Yield
g = Expected Capital Gains Yield
R = Div1/P0 + g = Div0(1+g)/P0 + g
Example
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Burns International’s stock sells for $40 and
their expected dividend is $4. The market
expects a return of 14%.
What constant growth rate is the market
expecting for Burns International?
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Homer Co. Valuation
“Supernormal” (non-constant) growth
Years 1-3 expect 20% growth
After year 3: constant growth of 7%
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Non-constant Growth Stock
Valuation
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Framework: Assume Stock has period of
non-constant growth in dividends and
earnings and then eventually settles into a
normal constant growth pattern (gn).
0 g1 1 g2 2 g3 3 gn 4 gn 5 gn ...
D1
D2
D3
Nonc-onstant Growth Period
Constant Growth
Non-constant Growth Valuation
Process
3 Step Process
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Estimate Dividends during non-constant growth
period.
Estimate Price, which is the PV of the constant
growth dividends, at the end of non-constant
growth period which is also the beginning of the
constant growth period.
Find the PV of non-constant dividends and
constant growth price. The total of these PVs =
Today’s estimated stock value.
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Back to Homer Co’s Valuation: Step 1
Homer Co’s Valuation: Step 2
Homer Co’s Valuation: Step 3
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