A Model of the Forward P/E
Value of savings account =
Capitalized forward earnings + No extra value
•
Extra value is added if abnormal earnings growth is forecasted
The model:
Value of equity = Capitalized forward earnings + Extra value for
abnormal earnings growth
The intrinsic P/E
is given by dividing through by Earn
1
6-44
3
4
2
3
2
1
0
1
1
1
E
E
E
E
E
E
AEG
AEG
AEG
Earn
V
3
4
2
3
2
1
1
1
E
E
E
E
AEG
AEG
AEG
Earn
1
E
0
Earn
V

Measuring Abnormal Earnings Growth for Equities:
Dell and Nike, 2010
Abnormal earnings growth
t
(AEG
t
) = Cum-dividend earn
t
- Normal earn
t
= [Earn
t
+ (ρ
E
– 1) d
t-1
] – ρ Earn
t-1
Dell:
Required return =
9%
Eps 2009 = $1.25
Nike: Required return =
9%
Eps 2009 = $3.07
Dell Inc.
Nike, Inc.
Eps 2010
Dps 2009
Earnings on reinvested 2009 dividends
Cum-dividend earnings 2010
Normal earnings from 2009:
Dell: 1.25 x 1.09; Nike: 3.07 x 1.09
Abnormal earnings growth (AEG) 2010
$0.00
$0.73
$0.00
0.73
1.363
-$0.633
$0.98
$3.93
0.088
4.018
3.346
$0.672
6-45
0.98*0.09

Cum-dividend Earnings Growth Rate
Cum-dividend earnings
growth rate (plus one):
Note: This is not
6-46
1
t
t
t
Earnings
earnings
dividend
Cum
G
1
t
t
earnings
dividend
Cum
earnings
divided
Cum

Alternative Calculation of AEG
Abnormal earnings growth
t
= [G
t
– ρ
E
] x Earnings
t-1
Where
G
t
= Cum-dividend earnings growth rate (plus one)
For Nike:
G
2010
= 4.018/3.07 = 1.3088 (a 30.88% growth rate)
AEG
2010
= [1.3088 – 1.09] x 3.07
= $0.672
6-47
(Cum-dividend earnings 2010 / EPS 2009)

Steps in Applying the Model
1.
Forecast earnings and dividends up to a forecast horizon.
2.
Calculate AEG after the forward year from the forecasts of earnings and
dividends.
3.
Discount the AEG to present value at the end of the forward year.
4.
Calculate a continuing value at the forecast horizon.
5.
Discount the continuing value to present value at the end of the forward
year.
6.
Add 3, 5, and forward earnings
7.
Capitalize this total at the required rate of return.
6-48
)
(
1
1
1
1
3
4
2
3
2
1
0
g
AEG
AEG
AEG
AEG
Earn
V
T
T
E
E
E
E
E

Applying the Model: A Simple Example and a Simple Model
Forecast for a firm with expected earnings growth of 3 percent per year (in dollars).
Required return is 10%
per year.
Residual earnings valuation:
AEG valuation:
6-49
Normal Earnings = Earnings * 0.10 (Required
rate of Return) = 12.36*(1+0.1) = 13.596
Cum Dividend Earning Growth 2002
=
(13.667/12.36)
-1
71
.
133
03
.
1
10
.
1
36
.
2
100
V
E
2000
71
.
133
03
.
1
10
.
1
071
.
0
36
.
12
10
.
0
1
2000
E
V

A Case 1 Valuation: General Electric
Required return is 10%
In this case, abnormal earnings growth is expected to be zero after 2004
Same as residual earnings valuation
6-50
13.07
0.017
1.29
10
0
1
V
1999
.
E

A Case 2 Valuation: Nike, Inc.
Required return is 9%
In this case, abnormal earnings growth is expected to grow at a 4.5 percent rate after 2012
Same as residual earnings valuation
6-51
* 1.045
18
.
53
495
.
1
332
.
0
96
.
2
09
.
0
1
2006
E
V

Converting Analysts’ Forecasts to a Valuation: Google Inc., 2010
Price, early 2011 =
$
624
Required return
= 11%
Consensus eps forecasts:
2011
$
33.83
2012
$
39.47
5-year growth rate forecasted = 17.4%
6-52

Abnormal Earnings Growth is Equal to the Change in
Residual Earnings
AEG
t
=
[
earn
t
+ (ρ
E
– 1)d
t-1
]
- ρ
E
earn
t-1
By the stocks and flows equation for accounting for the book value of equity (Chapter 2),
B
t-1
= B
t-2
+ earn
t-1
–
d
t-1
, so earn
t-1
– d

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