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Module 4.2
Stock Valuation
McGraw-Hill/Irwin
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
Cautionary Note
Stock valuation is often a topic dedicated to
one or more 3-credit elective courses.
 FINC852 at UD is a stock valuation and
portfolio theory course.


Think of this chapter as a “scratching the
surface” of the topic, or as the “tip of the
iceberg.”
9-1
9.1 The PV of Common Stocks


The value of any asset is the present value of its
expected future cash flows.
Stock ownership produces cash flows from:



Dividends
Capital Gains
Valuation of Different Types of Stocks



Zero Growth
Constant Growth
Differential Growth
Of course firms don’t announce their
“type” of stock. This is up to stock
analysts to consider – and of course most
stocks are “differential” growth.
9-2
Case 1: Zero Growth

Assume that dividends will remain at the same level
forever
Div1 = Div2 = Div3 =
 Since future cash flows are constant, the value of a zero
growth stock is the present value of a perpetuity:
Div1
Div 2
Div 3
P0 =
+
+
+
1
2
3
(1+ R) (1+ R) (1+ R)
Div
P0 =
R
9-3
Case 2: Constant Growth
Assume that dividends will grow at a constant rate, g,
forever, i.e.,
Div 1  Div 0 (1  g )
Div 2  Div 1 (1  g )  Div 0 (1  g ) 2
Div 3  Div 2 (1  g )  Div 0 (1  g )3
..
.
Since future cash flows grow at a constant rate forever,
the value of a constant growth stock is the present value
of a growing perpetuity:
Div
P0 =
1
R-g
9-4
Constant Growth Example
Suppose Big D, Inc., just paid a dividend of
$0.50. It is expected to increase its dividend by
2% per year. If the market requires a return of
15% on assets of this risk level, how much
should the stock be selling for?
 Use our (growing) perpetuity formula:
 P0 = .50(1+.02) / (.15 - .02) = $3.92

9-5
Case 3: Differential Growth
Assume that dividends will grow at different
rates in the foreseeable future and then will
grow at a constant rate thereafter.
 To value a Differential Growth Stock, we need
to:

Estimate future dividends in the foreseeable future.
 Estimate the future stock price when the stock
becomes a Constant Growth Stock (case 2).
 Compute the total present value of the estimated
future dividends and future stock price at the
appropriate discount rate.

9-6
Case 3: Differential Growth
 Assume that dividends will grow at rate g1 for N
years and grow at rate g2 thereafter.
 Estimating dividends using our FV tools:
Div 1  Div 0 (1  g1 )
Div 2  Div 1 (1  g1 )  Div 0 (1  g1 ) 2
..
.
Div N  Div N 1 (1  g1 )  Div 0 (1  g1 ) N
Div N 1  Div N (1  g 2 )  Div 0 (1  g1 ) N (1  g 2 )
..
.
9-7
Case 3: Differential Growth
We can value this as the sum of:
 a T-year annuity growing at rate g1
C é (1+ g1 )T ù
PA =
ê1T ú
R - g1 ë
(1+ R) û
 plus the discounted value of a perpetuity growing at
rate g2 that starts in year T+1
æ Div T+1 ö
ç
÷
è R - g2 ø
PB =
T
(1+ R)
9-8
Case 3: Differential Growth
Consolidating gives P0 = PA + PB:
æ Div T+1 ö
ç
÷
T
C é (1+ g1 ) ù è R - g2 ø
P=
+
ê1T ú
T
R - g1 ë (1+ R) û (1+ R)
Or, we can “cash flow” it out.
9-9
A Differential Growth Example
A common stock just paid a dividend of $2. The
dividend is expected to grow at 8% for 3 years, then it
will grow at 4% in perpetuity.
What is the stock worth? The discount rate is 12%.
9-10
With the Formula
 $2(1.08)3 (1.04) 



.12  .04
$2  (1.08)  (1.08)3  

P

1 
3
3
.12  .08  (1.12) 
(1.12)

$32.75
P  $54  1  .8966 
3
(1.12)
P  $5.58  $23.31
P  $28.89
9-11
With Cash Flows
$2(1.08)
0
1
$2.16
0
$2(1.08)
1
P0 =
2
$2(1.08)3
…
2
$2.33
2
$2(1.08)3 (1.04)
3
$2.62
$2.52 +
.12 -.04
3
4
The constant
growth phase
beginning in year 4
can be valued as a
growing perpetuity
at time 3.
$2.16 $2.33 $2.52 + $32.75
+
+
= $28.89
2
3
1.12 (1.12)
(1.12)
9-12
Same
example
with
spreadsheet
9-13