2. 2
Learning objectives
1. Distinguish between the intrinsic value and price
of a share of common stock.
2. Calculate the intrinsic value of a firm using
dividend discount models
Constant dividend growth model
Multistage dividend growth model
3. Use the constant growth model to relate growth
opportunities to stock value.
4. Calculate the P/E ratio for a constant growth firm.
5. Discuss the free cash flow valuation methods.
4. 4
Why equity valuation?
Identify mispriced equity securities.
How?
By calculating “intrinsic” or “true” value of a
stock using valuation models.
These valuation models make use of
information concerning current & future
profitability.
This approach of identifying mispriced
stocks is called fundamental analysis.
5. 5
Intrinsic value vs. market price (1)
Intrinsic value, V0
Present value of all expected future cash
flows to the stock investor. The cash
flows are discounted at the appropriate
required rate of return, k.
Expected future cash flows consist of:
1. cash dividends
2. sale price: proceeds from the ultimate sale
of the stock
6. 6
Intrinsic value vs. market price (2)
Intrinsic value is your (the analyst’s)
estimate of what a stock is really worth.
Intrinsic value (V0) can differ from the
current market price (P0).
If V0 > P0: stock is underpriced => buy
If V0 < P0: stock is overpriced => sell or don’t
buy.
7. 7
Market equilibrium
In market equilibrium,
Everyone has the same intrinsic value. So,
intrinsic value equals market price, i.e.,
V0 = P0.
Everyone also demands the same required rate
of return from the stock. So everyone has the
same k. In addition, expected HPR = k.
This common required rate of return is called the
market capitalization rate.
Market capitalization rate: required rate of return
which the market (i.e., everyone) uses to discount
future cash flows.
8. 8
Equity valuation models
Dividend discount models
Constant dividend growth model
Multistage (non-constant) dividend growth
model
Price-earnings ratio (P/E)
Free cash flow models
9. 9
Dividend discount models (DDMs)
Dividend discount models say that the
intrinsic value of a stock is equal to the
present value of all expected future
dividends.
What about cash flow from the ultimate sale of
the stock? Is that included?
Yes, because stock price at time of sale is
again determined by expected dividends at
the time of sale.
10. 10
Dividend discount model:
General formula
1 2 3
0 2 3
....
1 (1 ) (1 )
D D D
V
k k k
= + + +
+ + +
This formula cannot be implemented because it
requires dividend forecasts every year into the
indefinite future.
To implement the DDM, we make assumptions about
how dividends evolve over time.
11. 11
Two versions of DDM
We look at 2 assumptions:
Dividends grow at constant rate
Constant dividend growth model
Dividends grow at different rates over
different periods. At some future date,
dividend growth settles down to a
constant rate.
Multistage (non-constant) dividend
growth model
12. 12
Constant dividend growth model (1)
1. Assume that dividends grow at a
constant rate, g, per period forever.
2. Given this assumption, the intrinsic value
equals
0 1
0
(1 )
D g D
V
k g k g
+
= =
- -
D0 = Dividend
that the firm
just paid
Required rate
of return or
discount rate
Dividend
growth rate
Don’t panic.
D1 = D0(1 + g)
13. 13
Constant dividend growth model (2)
Warning: The model works only if k > g.
Useful properties.
All other things unchanged,
• If D1 increases (decreases), V0 increases
(decreases).
• If g increases (decreases), V0 increases
(decreases).
• If k increases (decreases), V0 decreases
(increases).
14. 14
Constant dividend growth model (3)
Suppose the market is in equilibrium. This
means that stock price is equal to intrinsic
value, i.e., P0 = V0.
Then, stock price is expected to grow at
the same rate as dividends.
That is, the expected rate of price
appreciation in any year will equal the
constant growth rate, g.
P1 = P0 ( 1 + g ) = V1 = V0 ( 1 + g )
15. 15
Expected HPR and k (1)
Continue to assume that P0 = V0 .
Then, expected HPR, E(r) is,
1 1 0
0 0
1
0
( )
D P P
E r
P P
D
g
P
-
= +
= +
Dividend yield Capital gains yield
16. 16
Expected HPR and k (2)
If stock is selling at intrinsic value, P0 = V0
Then required rate of return, k, must equal the
expected HPR. Therefore,
When everyone agrees on the same k (in equilibrium),
we can use the above formula to compute market
capitalization rate.
1
0
D
k g
P
= +
17. 17
Constant dividend stream
If g = 0, then dividends do not grow and
stay the same forever. We have a
constant dividend stream – a perpetuity.
The constant dividend stream assumption
is a special case of the constant growth
model with g = 0.
Implication: with constant dividend stream,
we continue to use the preceding
equations but set g to 0.
18. 18
Applying the constant growth DDM (1)
A common stock pays an annual dividend
per share of $2.10. The risk-free rate is
7% and the risk premium for this stock is
4%. If the annual dividend is expected to
remain at $2.10 forever, what is the value
of the stock? (to two decimal places)
Verify that V0 = $19.09
19. 19
Applying the constant growth DDM (2)
The risk-free rate of return is 10%, the
required rate of return on the market is
15%, and High-Flyer stock has a beta
coefficient of 1.5. If the dividend per share
expected during the coming year, D1, is
$2.50 and g = 5%, at what price should a
share sell?
Hint: use the CAPM to get the market
capitalization rate.
20. 20
Applying the constant growth DDM (3)
Big Oil Inc. just paid a dividend of $10 (i.e.,
D0 = 10.00). Its dividends are expected to
grow at a 4% annual rate forever. The
market capitalization rate is 15%. What is
the price of Big Oil’s common stock? (to 2
decimal places)
Verify that price = $94.55
21. 21
Applying the constant growth DDM (4)
The price of a stock in the market is $62.
You know that the firm has just paid a
dividend of $5 per share (i.e., D0 = 5). The
dividend growth rate is expected to be 6
percent forever. What is the market
capitalization rate for this stock (to 2
decimal places)?
22. 22
Applying the constant growth DDM (5)
A firm is expected to pay a dividend of
$5.00 on its stock next year. The current
price of this stock is $40 and investors
require a return of 20%. The firm’s
dividends grow at a constant rate. What is
the constant dividend growth rate (g)?
use k = (D1/P0) + g
Verify that g = 7.5%
23. 23
Applying the constant growth DDM (6)
In order to use the constant dividend growth
model to value a stock it must be true that:
a. The required rate of return is less than the expected
dividend growth rate.
b. The expected dividend growth rate is greater than zero.
c. The next dividend (D1) is expected to be greater than
$1.00.
d. The expected dividend growth rate is less than the
required rate of return.
Which statement is correct?
24. 24
Stock prices &
investment/growth opportunities
How do we figure out dividend growth rate, g ?
Growth rate depends on:
1. Investment opportunities embodied in return
on equity, ROE
2. Reinvestment of earnings, represented by
earnings retention ratio, b.
Earnings retention ratio is also called the plowback
ratio.
Growth rate, g = ROE x b
25. 25
Earnings retention ratio and
dividend payout ratio
Earnings retention rate
= reinvested earnings/ total earnings.
A related measure is the dividend payout
ratio.
Dividend payout ratio
= dividends paid/ total earnings
= 1 – retention rate
26. 26
Problem
Geoscience Corp. has a beta of 1.2 and its most
recent EPS is $10 per share. The company just paid
40% of its earnings in dividends. Geoscience Corp will
earn an ROE of 20% per year on all reinvested
earnings forever. The risk-free rate is 8% and the
expected return on the market portfolio is 15%.
a) What is the intrinsic value (V0) of a share of
Geoscience’s stock (to two decimal places)?
b) If the market price of a share is currently $100, and
you expect the market price to be equal to the intrinsic
value one year from now, what is your expected one-
year HPR on Geoscience Corp.’s stock?
27. 27
Earnings retention ratio
affects growth
Suppose ROE > 0 Growth
policy
No-growth
policy
Earnings retention ratio, b b > 0 b = 0
Growth rate, g g > 0 g = 0
Bottomline: If a company reinvests some portion of
earnings back into the business (b > 0), future earnings and
dividends will grow (i.e., g > 0). Otherwise, earnings and
dividends will not grow.
28. 28
Is growth always beneficial?
Does having positive growth always
increase stock price?
No. It depends on the attractiveness of the
firm’s investment opportunities, ROE.
Compared to a no-growth policy,
If ROE > k, then retaining earnings (i.e., b > 0)
will increase stock price.
If ROE < k, then retaining earnings will
decrease stock price.
29. 29
Consider two companies
Growth
Prospects,
Inc (GP)
Dead Beat,
Inc (DB)
No-growth earnings per share $5 $5
Market capitalization rate, k 12.5% 12.5%
No-growth price per share 5/0.125 = 40 5/0.125 = 40
ROE 15% 10%
30. 30
Suppose both companies reinvest
60% of next year’s earnings…
Growth Prospects,
Inc (GP)
Dead Beat, Inc
(DB)
Earnings retention ratio, b 0.6 0.6
Next year’s dividend per
share,
D1 = (1 – b) x 5
$2 $2
Dividend growth rate, g
= ROE x b
9% 6%
Constant dividend growth
model share price
2/(0.125 – 0.09)
= 57.14
2/(0.125 – 0.06)
= 30.77
31. 31
Compare GP and DB
Growth
Prospects, Inc
(GP)
Dead Beat,
Inc (DB)
ROE 15% 10%
Market capitalization rate, k 12.5% 12.5%
No-growth price per share (1) 40 40
Constant div. growth Price (2) 57.14 30.77
Present value of growth
opportunities, PVGO = (2) – (1)
17.14 -9.23
PVGO = Price per share – no-growth price per share
32. 32
Problems involving growth (1)
MF Corp. has an ROE of 16% and a
plowback ratio of 50%. If the coming
year’s earnings are expected to be $2
per share. The market capitalization rate
is 12%.
A. At what price will the stock sell today?
B. At what price do you expect MF shares
to sell for in 3 years?
33. 33
Problems involving growth (2)
Even Better Products has come out with a new
and improved product. As a result, the firm
projects an ROE of 20%, and it will maintain a
retention ratio of 0.30. Its earnings in one year
will be $2 per share. Investors expect a 12%
rate of return on the stock.
a) Calculate the stock price.
b) What is the present value of growth
opportunities (PVGO)?
c) What would be the stock price and PVGO if the
firm reinvests only 20% of its earnings?
34. 34
Multi-stage dividend growth 1
With this assumption, dividends grow at
different rates for different periods of time.
Eventually, dividends will grow at a
constant rate forever.
Time line is very useful for valuing this
type of stocks.
To value such stocks, also need the
constant growth formula.
Best way to learn is through an example.
35. 35
Multi-stage dividend growth 2
ABC Co. is expected to pay dividends at the end of the
next three years of $2, $3, $3.50, respectively. After
three years, the dividend is expected to grow at 5%
constant annual rate forever. If the market capitalization
rate for this stock is 15%, what is the current stock price?
T = 0
$2.00 $3.00 $3.50
Dividends grow
at 5% forever
T =1 T = 2 T = 3 T = 4
36. 36
What to do?
1. Place yourself at t = 3 and use the
constant growth formula to find PV of
dividend stream after year 3. Call this P3.
2. Find the PV of P3.
3. Find PV of dividends at t=1, t=2 and t=3.
4. Current stock price = sum of 2, 3 and 4.
38. 38
Another type of
multi-stage growth problem
Malcolm Manufacturing, Inc. just paid a $2.00
annual dividend (that is, D0 = 2.00). Investors
believe that the firm will grow at 10% annually for
the next 2 years and 6% annually forever
thereafter. Assuming a required return of 15%,
what is the current price of the stock (to 2 decimal
places)?
Use timeline to ‘see’ the problem better.
Verify that stock price = $25.29
39. 39
Price-earnings (P/E) ratios
P/E ratio is the ratio of current price per
share (P0) to next year’s expected
earnings per share (EPS).
How do we use P/E ratio to value a stock?
1. Forecast next year’s EPS, E1.
2. Forecast P/E ratio, P0/E1.
3. Multiple P/E by EPS to get current
estimate of price.
(P0/E1) x E1 = P0
40. 40
P/E ratio and
constant growth model
If a company has a constant dividend
growth rate and the market is in
equilibrium (i.e., V0=P0), then we have an
explicit formula for the P/E ratio!
Recall that b = retention ratio, k = market capitalization rate.
)
(
1
1
0
b
ROE
k
b
E
P
41. 41
P/E questions (1)
ABC Co. has an ROE of 25%, a CAPM
beta of 1.2 and a retention ratio of 40%.
The risk-free rate is 6% and the market
risk premium is 5%. What is ABC’s P/E
ratio?
42. 42
P/E questions (2)
Analog Electronic Corporation has an ROE =
9% and a beta of 1.25. It plans to maintain
indefinitely its traditional plowback ratio of 2/3.
The most recent earnings per share is $3 per
share. The expected market return is 14% and
the risk-free rate is 6%.
a) What is Analog’s stock price?
b) Calculate the P/E (P0/E1) ratio.
c) Calculate the PVGO.
43. 43
Free Cash Flow Valuation Approach
Dividend discount models don’t work for
companies which do not pay dividends.
For non-dividend paying companies, we
can use free cash flow valuation approach.
There are two versions:
Free cash flow to the firm (FCFF)
Free cash flow to equity holders (FCFE)
44. 44
Free Cash Flow to the Firm (FCFF) (1)
FCFF: cash flow that accrues from the firm’s
operations, net of investments in capital and net
working capital.
FCFF represent cash flows available to both
debt and equity holders.
FCFF = EBIT(1 – tc) + Depreciation – capital
expenditures – increase in NWC
EBIT = earnings before interest and taxes
tc = corporate tax rate
NWC (net working capital) = current asset – current
liability
45. Free Cash Flow to the Firm (FCFF) (2)
Capital expenditure includes:
1. acquiring fixed, and in some cases, intangible assets
2. repairing an existing asset so as to improve its useful
life
3. upgrading an existing asset if its results in a superior
fixture
4. preparing an asset to be used in business
5. restoring property or adapting it to a new or different
use
6. starting or acquiring a new business
45
46. 46
Free Cash Flow to the Firm (FCFF) (3)
Find the PV of the firm by discounting the year-
by-year FCFF plus some estimate of terminal
value, PT.
Firm Value=
where
Market value of equity = Firm value – market value of debt.
)
1
(
)
1
(
1 WACC
P
WACC
FCFF T
T
t
t
t
g
WACC
FCFF
P T
T
1
47. 47
Free Cash Flow to Equity Holders (FCFE)
FCFE: Free cash flow available to equity holders.
FCFE = FCFF – interest expense(1 – tc) + increases in
net debt
Find the market value of equity by discounting the year-
by-year FCFE plus some estimate of terminal value, PT.
is the cost of equity.
E
K
g
k
FCFE
P
where
k
P
k
FCFE
equity
of
value
market
E
T
T
T
E
T
T
t
t
E
1
1 )
1
(
)
1
(
48. 48
Summary
1. Distinguish between the intrinsic value and price.
2. Calculate intrinsic value using dividend discount
models
Constant dividend growth model
Multistage dividend growth model
3. Discuss the use of the P/E ratio to value common
stock.
4. Calculate the P/E ratio for a constant growth firm.
5. Discuss the free cash flow valuation methods.
