penman 5ed chap005
DESCRIPTION
penman - financial statements analysis and security valuation 5edTRANSCRIPT
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LINKS
Link to previous chapters
Chapter 4 showed
how accrual accounting
modifies cash accounting
to produce a balance
sheet that reports
shareholder
s'
equity.
However, Chapter 2
expl
ai
ned that book
value is not the value
of
shareholders' equity,
so firms typically trade
at price-to-book rat ios
different from 1.0.
0
This chapter
This chapter shows how to
estimate the value omitted
from the balance sheet and
thus how to estimate
intrinsic price-to-book
ratios.
9
Link to next chapter
Chapter 6 complements
this chapter. While
Chapter 5 shows how to
price the book value
of
equity, the bottom lin
e
of the balance sheet,
Chapter 6 shows how to
price earnings, the
bottom line
of
the
income statement.
Link to Web page
Go to the Web page
supplement for more
applica
ti
ons
of
the
techniques
in
this chapter.
ll
Accrual ccounting
and luation
Pricing
Book
Values
0 0
How are
How is a
firm
How are
premiums
va
lu
ed by
business
overbook
forecasting
strategies
value
income
evaluated?
determined? statements
and balance
sheets?
ll
How does
accrual
accounting
valuation
compare with
cash
flow
valuation?
Firms typically trade at a price that differs from book value. Chapter 2 explained why:
While some assets and liabilities are marked to market in the balance sheet, others are
recorded at historical cost, and yet others are excluded from the balance sheet. Conse
quently, the analyst
is
left with the task
of
estimating the value that
is
omitted from the
balance sheet. The analyst asks: What
is
the premium over book value at which a share
should trade?
This chapter lays out a valuation model for calculating the premium and intrinsic value.
t also models strategy analysis, and provides directions for analyzing firms to discover the
sources of value creation.
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Chapter 5 Accrual Accounting and a luation: Prici
ng
Book a lues 4
After reading this chapter you should understand :
What residual earnings
is.
How forecasting residual earnings gives the premium
over book value and the P/B ratio.
ow residual earnings are driven by return on common
equity
ROCE)
and growth in book value.
The difference between a Case
1,
2, and 3 valuation.
ow the residual earnings model captures value added
in a strategy.
The advantages and disadvantages
of
using the resid
ual
earnings model and how it contrasts to dividend
discounting and discounted
cash
flow
analysis.
How residual earnings valuation protects the investor
from pay ing too much for earnings added by investment.
ow residual earnings valuation protects the investor
from paying for earnings that
are
created by account
ing methods.
After reading this chapter you should be able to:
Calculate residual earnings.
Calculate the value of equities and strategies from
forecasts of earnings and book value.
Calculate
an
i ntrinsic price-to-book ratio.
Calculate
value
added in a strategy.
Convert an analyst's earnings forecast into a valuation.
THE CONCEPT BEHIND THE PRICE TO BOOK RATIO
Book value represents shareholders investment
in
the firm. Book value is also assets minus
liabilities, that is, net assets. But, as Chapter 2 explained, book value typically does not
measure the value
o
the shareholders investment. The value
o
the shareholders
investment- and the value
o
the net assets-
is
based on how much the investment (net as
sets) is expected
to
earn in the future . Therein lies the concept
o
the P/B ratio: Book value
is worth more or less, depending upon the future earnings that the net assets are likely to
generate. Accordingly, the intrinsic P/B ratio is determined by the expected return on book
value.
This concept fits with our idea that shareholders buy earnings. Price, in the numerator o
the P/B ratio, is based on the expected future earnings that investors are buying. o , the
higher the expected earnings relative to
book value, the higher the P/B ratio. The rate of
return on book value sometimes
referred to as the
profitability is
thus a measure that
features strongly in the determination
o
P/B ratios.
This chapter supplies the formal valuation model to implement this concept
o
the P/B
ratio, as well as the mechanics to apply the model faithfully. The formality is important, for
formality forces one to be careful. In evaluating P/B ratios, one must proceed formally
because one can pay too much for earnings i one is not careful.
Beware o Paying Too Much for Earnings
A basic precept
o
investing is that investments add value only i they earn above their
required return. Firms may invest heavily- in an acquisition spree, for example- but that
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42 Part One
inancial S
t
tements and l
u ti
on
investment , while producing more earnings, adds value only if it delivers earnings above
the required return on the investment. This maxim refines the P/B concept: The P/B ratio
prices expected return on book value, but
it
does not price a return that just yields the re
quired return on book value.
The analysis in this chapter is designed to prevent you from making the mistake
of
pay
ing for earnings that
do
not add value.As you apply the model and methods in this chapter,
you will see that P/B ratios should increase only if earnings from investments yield a return
that
is
greater than the required return on book value . Indeed, with the tools in this chapter,
you can assess whether the market is overpaying (or underpaying) for earnings and so
detect cases where the P/B ratio is too high or too low.
PROTOTYPE VALUATIONS
Fundamental analysis anchors valuation in the financial statements. Book value provides an
anchor. The investor anchors his valuation with the value that is recognized
in
the balance
sheet- the book value- and then proceeds
to assess
value that is not recognized- the pre
mium over book value:
Value = Book value + Premium
Two prototypes introduce you to the methods.
Valuing a Project
Suppose a firm invested 400 in a project that is expected to generate revenue
of
440 a
year later. Think of it as buying inventory and
selling
it a year later. After subtracting the
400 cost
of
the inventory from the revenue, earnings are expected to be 40, yielding a
rate
of
return
of
10 percent on the investment. he required rate
ofreturn
for the project is
10 percent. Following historical cost accounting, the asset (inventory) would be recorded
on the balance sheet at 400. How much value does this project add to the book value? The
answer,
of
course, is zero because the asset is expected to earn a rate
of
return equal to its
cost
of
capital. And the project would be worth its book value.
A measure that captures the value added to
book
value is
residual earnings
r
residual
income
For the one period for this project (where the investment is at time 0) ,
Residual earnings
1
=Earnings, - (Required return x Investment
0
For earnings
of
40, residual earnings is calculated as
Residual earnings= 40 - (0.10 x 400) = 0
f he project were
to
generate revenues of 448 and so earn 48, a rate ofreturn
of 12
percent
on the investment of 400, residual earnings would
be
calculated as
Residual earnings= 48 - (0.10 x 400) =
8
The required dollar earnings for this project is 0.10 x 400 = 40. Residual earnings is
the earnings in excess
of
these required dollar earnings. f he project earns 40, residual
earnings is zero; if the project earns 48, residual earnings is
8
. Residual earnings is
sometimes referred
to
as
abnormal earnings
or excess
profit
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EXHIBIT 5 1
Forecasts for a
Savings Account with
100 Invested at the
End of 2012, Earning
5 percent
per
Year.
Chapter
5
ccrual ccou
nt
in
g
an
d
Valua ti
o
n
P
ricin
g Bo
ok Va
l
ues
143
A model that measures value added from
forecasts
of residual earnings is called the
residual earnings model:
Value Book value + Present value o expected residual earnings
The one-period project with an expected rate ofreturn of
1
percent earns a residual earn
ings of zero. So the value of the project is
0
Value 400 + 400
1.10
This project is worth its historical cost recorded on the balance sheet; there is no value
added.
f
the project were expected to earn at a 12 percent rate, that is, earn residual
earnings of 8,
8
Value== 400 + 407 .27
1.10
In
this case the project
is
worth more than its historical-cost book value because it is anticipated
to generate positive residual earnings; there is value added, a premium over book value.
The residual earnings value for a terminal project is always the same
as
that calculated with
discounted cash
flow
methods. For the project yielding 448
in
sales, the DCF valuation is:
448
Value (DCF) 407.27
1.10
Valuing a Savings ccount
How much is a simple savings account worth? Well, surely it is worth its book value- the
balance on the bank statement- because that is the amount you would get out of the ac
count if you cashed it in. The book value is the liquidation value. But it is also the going
concern value
of
the account.
Exhibit 5.1 lays out forecasts of book values, earnings, dividends (withdrawals), and
free cash flows for 2013- 2017 for a 100 investment in a savings account at the end
of
Forecast Year
2012
2013
2014
2015
2016 2017
Scenario 1: Earnings withdrawn e ch year full payout)
Earnings
5
5
5
5 5
Dividends
5 5
5
5 5
Book va lue
100
100 100
100
100 100
Residual earnings
0 0
0 0
0
Free
cash
flow
s
5
5
5 5
5
Scenario 2:
No withdrawals zero payout)
Earnings
5
5.25
5.51 5.79
6.08
Dividen ds
0
0
0 0 0
Book value
100
105
110 .25
115.76 121 .55
127.63
Re
sidual earnings
0
0
0
0 0
Free
cash
flo
ws
0
0
0 0 0
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44
Part One
i
nancia
l Statements and
al it
at
ion
2012, under two scenarios. In the first
s e n r i o
earnings are paid out each year
so
that
book value does not change. The required retur:n for this savings account
is
5 percent
that is , the opportunity cost
of
the rate available at another bank across the street in an
account with the same risk. So, forecasted
residual
earnings for each year is
5
- (0.05 x
100) 0. As this asset
is
expected to yield no residual earnings, its value
is
equal to its
book value, 100.
In the second scenario in Exhibit 5.
1,
no withdrawals are taken from the account. As a
result, both earnings and book values grow
as earnings
are reinvested in the book values
to
earn within the account (numbers are rounded
to
two decimal places) . But residual earn
ings
is
still zero for each year. For 2013,
residual
earnings
is
5 - (0 .
05
x 100) 0; for
2014, residual earnings
is 5
.
25
- (0.05 x
105) =
0; for 2015 , residual earnings
is
5
.5125 - (0.05 x 110.25) 0, and
so on.
In
all
years, the rate
of
return on book value
is
equal to the required return. As expected residual earnings are zero, the value
of
this asset
at the end
of
2012 is its book value, 100.
Note that in Scenario 1, forecasted dividends are 5 and, with no investment back into
the account, free cash
flows
are also
5
each
year.
In Scenario
2,
cash generated
is
rein
vested
in
the account, so forecasted dividends
are
zero, and free cash
flows
(cash flows
minus investment back into the account) are
zero
.
Yet
the two scenarios have the same
va lue.
These examples from the savings account
bring
out some important principles that also
apply to the valuation of equities:
I . An asset
is
worth a premium or discount
to
its book value only
if
the book value
is
expected
to
earn nonzero residual earnings.
2. Residual earnings techniques recognize that earnings growth does not add value
if
that
growth comes from investments earning
the
required return. In the second scenario,
there
is
more earnings growth than in the first scenario, but that growth comes from
reinvesting earnings in book
va
lu
es to
earn
at
the required return
of
5 percent. After
charging earnings for the required return on
the
investment, there
is
no
addition
to
resid
ual earnings, even though there is
growth in earnings. Accordingly, the value
of
he asset
is the same for the case with no earnings growth.
3.
Even though
an
asset does not pay dividends, it can be valued from its book
va
lue and
earnings forecasts. Forecasting zero dividends in the second scenario will not work, but
we have been able to value it from earnings
and
book values.
4.
The valuation
of
the savings account does
not
depend on dividend payout. The two
scenarios have different expected dividends,
but
the same value: The va
lu
ation based on
book values and earnings is insensitive
to
payout. This
is
desirable if, indeed, dividends
are irrelevant to va lue,
as
discussed in Chapter 3.
5.
The valuation
of
the savings account
is
unrelated
to
free cash
flows.
The two scenarios
have different free cash flows but the
same
value. Even though the account for
Scenario 2 cannot be valued by forecasting free cash flows over
five
years- they are
zero-it
can be valued from its book value.
The Normal Price to Book Ratio
The value
of
the savings account
is
equal to its book value. That
is
, the price-to-book
ratio is equ
al
to 1.
0.
A P/B ratio
of
1.0
is
an important benchmark case, for it is the case
where the balance sheet provides the complete valuation . t is also the case where the
forecasted return on book value is equal to the required rate
of
return, and forecasted
residual earnings
is
zero- as with both the savings account and the project earning a
10
percent return.
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Chapter 5 Accrua
lAcco
unting
andVa lua tion
Pricing
Book Va l
ues
45
The required return is sometimes referred to as
the
normal return for the level of risk in
the investment. Accordingly, as an investment
with
a P/B of 1.0 earns a normal return, a
P/B of 1.0 is sometimes referred to as a normal P B ratio.
A MODEL OR ANCHORING VALUE ON BOOK VALUE
The prototypes show us how to value assets by anchoring on their book value and then
adding extra value by forecasting future residual earnings. The anchoring principle is
clear:
Anchoring principle: f one forecasts that an asset
will
earn a return on its book value equal
to its required return, it must
e
worth its book value.
Correspondingly, if one forecasts that an asset will
earn
a return on book value greater than
its required
return-positive
residual earnings- it
must
be worth more than book value;
there is extra value to be added. The valuation
model
that captures the extra value for the
equity
of
a going-concern is
E REI RE2
RE
3
Value of common equity (V
0
) = B
0
+ + -
2
- + -
3
- +
PE PE PE
5.1)
where RE is residual earnings for equity:
Residual earnings = Comprehensive earnings - (Required return for equity
x Beginning-of-period book value)
RE
1
= Earn1- (PE- l
11
Bo
is the current book value of equity on the balance sheet, and the residual earnings for
each period in the future is the comprehensive earnings available to common equity for the
period less a charge against the earnings for the book value
of
common equity at the
beginning of the period, B
1
_
1, earning at the required return, pE -
1.
This required return for
equity is also called the equity cost of capital.
We
w ll
deal with the issue of the required
return in Chapter 7. For the moment, see it as the return supplied by a beta technology like
the capital asset pricing model (CAPM) (discussed
in
the appendix to Chapter 3), or just as
your own hurdle rate for investing in equities.
We
saw in Chapter 2 that Nike, Inc
.,
reported 1,754 million
of
comprehensive income
in 2010 on book value (assets minus liabilities)
of 8,693 million.
If
Nike 's shareholders
require a 9 percent return, then its 2010 residual earnings was 1 ,754 - (0.09 x 8,693) =
971.6 million. Nike added 971.6 million in earnings over a 9 percent return on the share
holders' investment in
book
value.
We calculate the value of equity by adding the present value of forecasted residual earn
ings to the current book value in the balance sheet. The forecasted residual earnings are dis
counted to present value at
1
plus the equity cost of capital, PE
We
calculate the intrinsic
premium over
book
value, - B
0
as the present value of forecasted residual income. This
premium is the missing value in the balance sheet. The intrinsic price-to-book ratio is
B
0
.
This makes sense:
Ifwe
expect a firm to earn income for shareholders over that re
quired on the book value
of
equity (a positive
RE ,
its equity will be worth more than its
book value and should trade at a premium. And the higher the earnings relative to book
value, the higher will be the premium.
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146
Part ne
inancial
tatements andVal
uation
TABLE 5.1
Price-to-Book Ratios
and Subsequent
Residual Earnings
1965- 1995.
High-P/B firms yield
high residual earnings,
on average, and
low-P/B firms yield
low residual earnings.
Residual earnings for
P/B ratios close to 1.0
(in Levels 14 and 15)
are close to zero.
Source: Company: Standard
&
Poor's Compusta
t
data.
Residual Earnings Each Year
after
P B Groups
Are
Formed Year O
P/B Level P/B
0
1
2 3
4
5
1 (high) 6.68 0.181 0.230 0 .223 0.221 0.226 0.236
2
3.98
0.134 0.155
0 .144 0.154 0.154 0.139
3
3.10
0.109 0.113
0 .106 0.101 0.120 0.096
4
2.59
0.090 0.089
0 .077
0.093
0.100 0.099
5
2.26
0.076 0.077
0 .069
0.068 0.079
0.071
6
2.01
0.066 0.067
0 .059
0.057 0.076 0.073
7
1.81 0.057
0.048
0 .043 0.052 0.052 0.057
8
1.65 0.042
0.039
0 .029 0.039 0.
050
0.044
9
1.51 0.043
0.034
0 .031 0.038 0.046 0.031
10
1.39 0.031 0.031
0 .028 0.
036
0.047
0.028
11
1.30
0.024 0.026
0 .023
0.035
0.036 0.030
12
1.21 0.026
0.028
0 .023
0.036 0.
039
0.
038
13
1.12 0.
016 0.021
0 .012 0.031 0.039 0.026
14 1.05 0.009 0.008 0 .009 0.
026
0.034 0.032
15
0.97 0.006 0.005
0 .011
0.018 0.
031
0.017
16 0.89
-0.007
-0.011
- 0 .004
0.
008
0.029 0.015
17
0.80
-0 .017
-0.018
- 0 .004 0.
006
0.023 0.008
18
0.70
-0.031 0.030
- 0 .030 - 0.010 0.015
-0 .
001
19 0.58
- 0.052 -0.054
- 0 .039 -0 .015
-0.003
-0 .008
20(1ow)
0.42
- 0.090
- 0.075
- 0 .066
-0.037
-0.020 -0 .039
Table
5.1
shows that P/B ratios forecast subseq
ue
nt residual earnings. This table groups all
NYSE and AMEX firms into one of 20 groups based on their P/B ratio. The first group
(Level
l
includes the firms with the highest 5 percent ofP/B ratios, while the bottom group
(Level 20) includes those with the lowest 5 percent. The median P/B for Level 1 is 6.68, while
that for Level 20 is 0.42, as indicated in the P/B
column
of
the table. The table gives the me
dian RE for each level for the year that firms are grouped (Year 0) and for the subsequent five
years. The RE is standardized by book value in Year
0. You
can see that the RE entries
in
Years
1 to 5 are related to the P/B ratios in Year
0:
High-P/B firms pay high RE, on average, while
low-P/B firms pay low RE. Levels 14 and 15 have P /B close to 1.0 inYear 0 (a zero premium)
and, correspondingly, their RE payoffs are close
to
zero. Price-to-book ratios higher than
1.0
yield positive RE and low P/B ratios yield negative RE. In short, the data for actual firms be
have jus t as the model says.
1
The residual earnings model always yields
the
same value that we would get from
forecasting dividends over an infinite forecasting horizon. This is important to appreciate,
so that you can feel secure about the valuation, because share value is based on the divi
dends that the share is ultimately expected to pay. The residual earnings model substitutes
earnings and book values for dividends. That substitution means that we are really fore
casting dividends; however, we get an appreciation
of he ultimate dividends that a firm will
pay using forecasts
of
earnings and book values over forecast horizons that are typically
shorter than those required for dividend discounting methods. This is what we want for a
practical valuation method. The savings account example makes this abundantly clear. In a
zero-payout case where dividends might not be paid out for 50 years (say), we would have
to forecast dividends very far into the future .
But
using a residual earnings method, the val
uation is immediate- it is given by the current book value.
1
The
s m
e requi
red
return
for
equity of 1O perce
nt
is used
fo
r a
ll
firms in the table . B
ut
using a CAPM
cost
of
capital (and thus adjusting fi rms required returns
for
their betas) giv
es
simi
l
r patterns.
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Return on common equity,
ROCE, is
comprehensive earnings
to common earned during a period relative to the book value
of net
assets put in place at the beginning of the period. For
period
1,
ROCE,
= Comprehensive earnings to common
1
Book valueo
Comprehensive earnings to common are after preferred divi
dends and the book value is (of course) the book va lue of com
mon shareholders' equity. Sometimes thi s measure is referred
to as return on equity ROE), but we will use ROCE to be clear
that it
is the return to common shareholders whose shares
we
are pricing. The
ROCE
is also referred
to
as a book r te o
-
turn or an ccounting r te
o
return to distinguish it from the
rate of return earned in the market from holding the shares.
Comprehensive income for Nike,
Inc.
, for
2010
was
1,754 million, and the book value of common shareholders'
equity at the beginning of the year was 8,693 million . So
Nike's
ROCE
for
2010
was
1,754/ 8,693 = 20.18%. This is
quite high . But of course, most of Nike's assets-customer re
lationships, brand, supply chain-are
not
on its balance sheet,
but the earnings from those assets are coming through com
prehensive income. The high ROCE explains why Nike traded
at a relatively high P/B
of
3.67.
Earnings are earned throughout the period and will
change with changes in book va lues through share
issues,
stock repurchases,
or
dividends. But book value
is
measured at
a point in time.
For
short periods, like a fiscal quarter, this does
not
matter much . But
for
longer periods, like a full fiscal year,
it might.
So ROC
E for a year
is
often calculated
as
ROC E, = Comprehensive earnings
1
1
/i 81
+Bo
The denominator is the average of beginning and ending
book value
for
th e year.
Th
is calculation is approximate. More
strictly, the
denominator
should be a weighted average
of
book values during the year. Significant errors will occur only
if there are large share issues or stock repurchases near the
beginning or
end
of a
year.
The calculation can be done on a per-share basis:
ROCE
= PS1
1
BPSo
(with EPS based on comprehensive income).
BPS is
book value
of common
equity
divided by sha res outstanding (and shares
outstanding is issued shares minus shares in treasury). The EPS
are weighted down
for
share
issues
and repurchases during
the yea r by the weigh ted-average calculation . So this calcula
tion keeps the numerator and denominator on the same per
share basis .
The three calculations typically give different ans
we
rs but
the difference is usually small. It
is,
however, dangerous
to
compare ROCE over time with calculations based on per
share amounts because share issues and repurchases affect
EPS and BPS differently.
Residual Earnings Drivers and Value Creation
Residual earnings is the return on common equity, expressed as a dollar excess return
rather than a ratio. For every earnings period t we can restate residual earnings as
Residual earnings = (ROCE - Required return on equity) 5.2)
x Book value o common equity
Earn, - (p
-
1)8
1 1 =
[ROCE1 - (p
- l ]B1
- 1
1) 2)
where ROCE
1
=
Earn/ B
1
_
1
is the rate
o
return on common equity. Box
5.1
takes you
through the calculation ofROCE. Thus residual earnings compares ROCE to the required
return,
PE- 1
and expresses the difference as a dollar amount by multiplying it by the
beginning-of-period book value. Nike's (comprehensive) ROCE for 2010 was 20.18 per
cent (from Box 5.1).
f
ts required return on equity (the equity cost o capital) was 9 per
cent, then its residual earnings was (0.2018 - 0.09) x 8,693 = 971.6 million, which is
the same number as we got before (adjusted for rounding error).
f
ROCE equals the
required return, RE will be zero. f we forecast that the firm will earn an ROCE equal to
its cost o capital indefinitely in the future , intrinsic price will be equal to book value . f
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48 Part One inancial Statements and
Va
lua tion
we forecast that ROCE will be greater than the
cost of
capital, the equity should sell at a
premium.
Ifwe
forecast that ROCE will be less
than
the cost of capital, the equity should
sell at a discount.
RE is determined by two components, (1) and (2) in expression 5.2. The first is ROCE
and the second is the amount of the book
value
of the equity investment (assets minus
liabilities, or net assets) that are put in place in each period. These two components are
called residual earnings drivers. Firms increase their value over book value by increasing
their ROCE above the cost of capital. But they rther increase their value by growth in
book value
net
assets) that will earn at this
ROCE.
For a given ROCE (greater than the
cost
of
capital), a firm will add more value with
more
investments earning at that ROCE.
Indeed these two drivers are sometimes
referred
to as value drivers Determining the
premium or discount at which a share should
sell
involves forecasting these two drivers.
Figure 5.1 depicts how forecasts of he two drivers , along with the current book value, yield
current value.
You
can see how this model can be a strategy analysis tool: Increase value by
adopting strategies that increase ROCE above
the
required return and grow book values
(net assets) that can earn at an ROCE above
the
required return. That,
of
course, is what
business
is
all about And that will drive the financial statement analysis in Part Two of the
book to discover the value in a business.
On the next page selected firms ranked by their P/B ratios in 2010, along with the ROCE
they earned
in
2010 and their book value growth
rates
for the year.
FIGUR 5.1 The Drivers of Residual Earnings and the Calculation of
the
Value of Equity
Residual earnings is driven by return on common equity (ROCE a
nd
the book
va
lue of investments put in place. Valuation
involves forecasting future
RO
CE and the growth
in
the book values of net
assets,
discounting the residual earnings that they
produce to present va lue , and adding
th
e current book value.
Current
book value
PVofRE
1
PV
of
RE
2
PV
ofRE
3
I Current data I Forecasts
~
Current year
Year I ahead
Current
L book value
Residual
earnings
Year 2 ahead
I OCE
2
IBook value
1
Residual
earnings
2
Discount byp2
Year 3 ahead
I OCE
3
IBook value
2
Residual
earnings
3
Discount b p3
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Demutualization
of
Insurance Companies
re These Firms Worth More Than Book Value?
5 2
A number
of
large insurance companies, including
John
Hancock Mutual Life Insurance and Metropolitan
Life
Insur
ance,
have
converted from mutual companies owned
by
policy
holders to companies owned
by shareholders. The process
of
dem
utualization in
volves
issuing shares to policyholders
and new investors
in an
initial public offering .
When these
two
firms demutualized,
analysts
conjectured
that they would
be
priced at book value.
They
we re earning
9 percent-12 percent return on equity
and analysts
did
not
expect this rate
of
return to improve. Why might they trade at
H.
J.
He
inz Co.
Coca-Cola Company
Kimberly-Clark Corp.
Dell, Inc.
Nike, Inc.
Ex
xon
Mobil
Corp.
Cisco Systems, Inc.
Macy's, Inc.
General Electric Co.
Kraft Food
s
Inc.
J
P Morgan Chase & Co.
Banco Santander,
S.A.
Sony Corp.
Panasonic Corp.
Bank
of
America Corp.
book
value? Well,
if the return that investors require
to
buy
the initial
share
issue
is also
9 percent-12 percent, the firms
would be expected to generate zero residual earnings from
their book values,
and so
should
be
priced at book value.
John Hancock's
in
itial public offering was on January 27,
2000, when it became John Hancock Financial
Services
Inc.
The
firm's
ROC
E was
12
percent. It issued
331
.7 million
shares
229.7 million
to
policyholders.
These
shares traded
at $17
:1
per share, a little above book value
of
$15 per
share.
Book Value
P/B
RO E rowth
Rate
6.1
42 .
3%
55%
5.1
41.9% 25%
4.5
32.7% 10%
3
.8
39.3%
38%
3.7
20.2%
12%
2 .9
23.4% 33%
2.1
17.4%
15%
1.9
16.6% 19%
1.8
10.6%
1%
1.6
8.1% 38%
1.1
10.2%
7%
1.0
11
.
8%
10%
0.9
3.6% 6%
0.8 -
0.9%
6%
0
.6
- 1
.0%
-1
You
can see that P/B is related to ROCE and growth in book value. Banco Santander, S.A. and
J P Morgan Chase have a P/B close to l O and correspondingly earned an ROCE of 11.8 and
10.2 percent, roughly equal to what is considered to be the typical required return on equity.
Thus residual earnings for these firms were roughly zero, appropriate for a normal P/B ratio
of 1.0. Other firms have considerably higher P/B and, correspondingly, higher ROCE and
growth rate in book value. Sony, Panasonic, and
ank
of
America have P/B less than 1.0 and
also have low ROCE and book value growth rates. Now look at Box 5.2.
A few firms do not give the full story,
of
course, so look at Figure 5.2. This figure plots
2010 ROCE for the S P 500 firms on their P/B
The
regression line through the plots shows
that higher P B is associated with higher ROCE on average. The plot is typical of most years.
Of course, many firms do not fall on the regression line and it is the task of financial analysis
to explain why Is it growth in book value, the second driver? Or is it because ROCE in the
fu-
tme will be different from the present?
For a historical picture of ROCE and book value growth, Figure 5.3 plots percentiles
of
ROCE over the years 1963- 2010 for U.S. firms. The median ROCE over all years is
149
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150 P t One inancial
Statements and Valuation
FIGURE
5.2
Price-to-Book Ratios
for
S P 500 Firms
and
Subseq
u
ent
Return on Common
Equity (ROCE).
The figure plots ROCE
in 2010 on price-to-
book ratios (P/B) at the
end
of2010.
The
line
through the dots is the
regression line for the
relationship between
ROCE and P/B: ROCE
is positively related to
P/B.
Source: Standard Poor's
COMPUSTAT 'data.
F
IGUR 5.3
Percentiles of ROCE
for
all U.S. Traded
Firms with Market
Capitalization over
$200 million,
1963- 2010.
The median ROCE
over all years is
13.7 percent.
Source: Standard & Poor
s
O M P U S T T
data.
ROCE on J>/B Rat
io
0.8
.6
0.4
8
0.2
0
~
0
0
c:i:::
- 0.2
- 0.4
0.6
- 0.8
- 1
0
2
3
4
5
6
7
8 9
JO
Price-to-book ra tio (20 JO)
0.4
-+--plO --+-p25 ~ e d i a n 75 __,._p90
0.3
0.2
0.1
u
0
c:i:::
0
- 0.1
-0.2
- 0.3
1963
1973 1983 1993
2003
13
.7 percent, but there is considerable variation. Accordingly, there
ha
s been consider
able variation in P/B ratios, as indicated in Figure 2.2 in Chapter 2. The average ROCE
for the S&P 500 over the 30 years to 2010 (based on a market-value weighting
of
stocks
in the index) has been 18 percent (and the average S&P 500 P/B ratio has been 2.5).
Simple Demonstration and a Simple Valuation Model
Exhibit 5.2 presents forecasts
of
comprehensive earnings and dividends over five years for a
firm with $100 million in book value at the end
of
he current year, Year
0.
The required equity
return is
10
percent and we must value the equity at time 0.
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EXHIBIT 5 2
Forecasts for a
Simple Firm
In
millions
of
dollars.
Required return is
10 percent.
Chapter
5
ccr
ual
A cc
oun
ting
a
nd Va lu
atio
n:
P
ric
ing
Book
Va
lues 151
Forecast Year
0
1
2
3
4
5
Earnings
12
.00 12.36
12.73
13.11 13.
51
13.
91
Dividends
9.09
9.36
9 64 9.93
10.23 10.53
Book value
100.00 103.00 106.09
109 .27
112.55 115.93
R (10%
charge
2.36
2.43
2.50
2.58 2.66
R growth
rate
3/o
3
3 3
Future book values are forecasted using the stocks and flows equation of Chapter 2:
Ending book value= Beginning book value Comprehensive income - Net dividend
The expected book value at the end
of Year
1, in millions, is 103 = 100 12.36 - 9.36.
Residual earnings for Year 1 is 12.36 - (0.10 x 100) = 2.36 million, and similiarly for
subsequent years. You can see that forecasted residual earnings is growing at a 3 percent
rate per year after Year 1, so a simple valuation capitalizes the residual earnings forecasted
for Year l
as
a perpetuity with growth:
RE
o
= Bo
P
g
With
g
=
1 03
and PE= 1 10 , the valuation is
V= 100
2
.
36
= 133.71 million
1.10 - 1 03
The intrinsic price-to-book ratio (P/B) is 133.71/ 100 = 1 34 This is a simple valuation
model: A constant growth rate is applied to the forecast for the forward year. The forecast
horizon is very short, just one year ahead.
This simple example demonstrates that the RE model gives the same valuation that would
result from forecasting dividends indefinitely into the future. Dividends are expected to
grow at 3 percent per year in this example, so
E di
9.36 .
.
V
0
= =
=133.7 lm1 ion
p
g
1.10-1.03
This is a stylized case in which the dividend discount model works because the payout is
tied directly to earnings with a fixed payout ratio, and growth in dividends is the same as
growth in residual earnings . As we saw in Chapter 4, this is not usually the case, as the sav
ings account with zero payout makes abundantly clear. However, the accrual accounting
model supplies the desired valuation.
APPLYING THE
MO EL TO
EQUITIES
The forecasting long-run (to infinity) that is required for the going-concern model (5.1) is
a challenge. The criteria for a practical valuation technique in Chapter 3 require finite fore
cast horizons, the shorter the better. For a forecast over a T-period horizon,
RE RE
RE RE F -B
VE
B 1 2 3 + T T
0 0 2 3
T T
PE PE PE PE PE
5.3)
where - BT is the forecast of the intrinsic premium at the forecast horizon.
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152
Part One inanc ial Sta
cemems a
nd
Va lua on
Current book value is of course in the current balance sheet, leaving us with the task
of forecasting residual earnings and the horizon premium. We also need to choose a fore
cast horizon . The horizon premium
th
stock's expected value relative to book value T
periods from now- appears
to
be a particular
challenge
. Indeed, the model appears cir
cular:
To
determine the current premium, we need to calculate a premium expected in the
future. The calculation of this premium is the
problem of
determining a continuing value
at the horizon. This section focuses on the
problem.
Here are the steps to follow for a residual earni
ngs
valuation:
1.
Identify the book value in the most recent balance sheet.
2. Forecast earnings and dividends up to a foreca s t horizon.
3. Forecast future book values from current book v alues and your forecasts of earnings and
dividends.
Book value = Beginning Book valu e Earnings - Dividends
4. Calculate future residual earnings from the fo r ecasts of earnings and book values.
5.
Discount the residual earnings to present value .
6.
Calculate a continuing value at the forecast
horizon.
7. Discount the continuing value
to
present value.
8. Add 1, 5, and 7.
Case 1 applies these steps to Flanigan's Enterprises, Inc., a firm operating chain restaurants and
beverage stores.The first two lines give the firm's basic earnings per share (EPS) and dividends
per share (DPS) for 2000 through 2003. Let's play th same game as in Chapter 4 and pretend
that
we
are forecasting at the end of 1999 but know for sure what the subsequent earnings and
dividends are going to be. From forecasts of EPS a nd DPS
we
can compute successive book
values per share (BPS) by adding EPS
to
beginning-of-period BPS and subtracting DPS. So
the forecast
of
BPS for the end of2001, for example, is 4.76,
as
shown below the valuation.
With a forecast
of
EPS and BPS
we
can forecast
RE
.The cost
of
capital
is
9 percent, so RE
for 2001 is 0.80 - (0 .09 x 4.20) = 0.422 or, calculating
it
from the forecasts ofROCE and book
value, RE is (0 .1905 - 0.09) x 4.20 = 0.422, as
also
shown below the valuation.
Now suppose we wished to value this finn at th e end of 1999.We would take the present
value of the RE forecasts (the discount factors are 1.09
1
,
sum them, and add the sum
to
the
1999 book value of 3 .58 per share. This gives
us
a valuation of 4.53 per share, as shown.
The calculated premium over book value is 4.53 - 3 .58
=
0.95. Is our valuation correct?
Well
,
it would be
if
we forecasted RE after 2003 to be zero.
You
see the RE are declining over the
years toward zero. Although the book value driver o RE is increasing, the ROCE driver is de
clining, and in 2003 it is 9.0 percent, equal to the cost
of
capital. t looks as ifRE from 2003
and onward might be zero. If so , we have completed the valuation.
We
can write
it
as
RE RE RE
VE=
B
+ - -
Case 1
0 0 2 3
PE PE PE
5.4)
where, in this case, Year 0 is 1999 and Year
T
three years ahead) is 2002.
Compare this calculation with model 5.3. The ho1izon premium is missing in the calcula
tion here and this makes sense: IfRE after the forecast hmizon is forecasted
to
be zero, then
the forecast of
th
e premium at that point must be zero. We have forecasted Vf B
7
0.
The Forecast Horizon and th Continuing Value Calculation
How typical is a Case 1 valuation? Well, let 's ret urn to General Electric (GE), the firm for
which discounted cash flow analysis failed in Chapter 4. Case 2 displays the same five years
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Chapter 5 Accrual ounting and
Valuation
Pri
ing Book
Values 153
CASE
Flanigan s
Enterprises, Inc.
999
Required rate ofreturn
EPS
is 9 percent. In this DPS
case, residual earnings
BPS
3.58
is expected to be zero
after 2003. ROCE
CASE 2
General Electric Co.
Required rate ofreturn
is I 0 percent. In this
case, residual earnings
is
expected to e
constant , but nonzero,
RE
(9 charge)
Discount
rate
(1.09
1
Present
va
lue of RE
Total
present va lue of
RE
to 2003 0.95
Value
per
share 4.53
Ho
w the
forecasts
are developed (for 2001 ):
Forecasting Book Value per Share BPS)
Beginning
BPS
a)
4.20
Forecasted EPS b)
0.80
Forecasted DPS O 24)
Ending
BPS 4.76
EPS
DPS
BPS
999
4.32
after 2004. ROCE
RE (10 charge)
Discount
rate
(1.10
1
Present value
of RE
Total present v
alue
of
RE
to 2004
Continuing
value
CV)
Present value of CV
Value per share
The continuing value :
0.882
CV=
Q 10 =
8.82
3.27
5.48
13 .07
Forecast Year
2
2001 2002
0 .73 0.80
0.71
0 . 11
0.24 0.25
4.20
4.76 5.22
20 .
4
19 .0 14.9
0 .408
0.422 0.282
1 .09
1.188
1.295
0.374 0.355 0.217
Forecasting Residual Earnings
Forecasted
ROCE
b/a)
Cost
of equity capital
Excess ROCE
c)
RE (ax c)
Alternatively,
2003
0.47
0.27
5.42
9.0
0.000
1.412
0.000
19.05
-9.00
10.05
0.422
RE = 0.80 - 0 .09 x 4.20) 0.422
Forecast Year
2000
2001 2002 2003 2004
1.29
1.38
1.42 1.50 1.60
0.57
0.66
0.73 0.77 0.82
5.
04
5.76 6.45
7.18 7.96
29.
9
27.4 24.7
23
.3
22 .3
0.858
0.876 0.844
0.855
0.882
1.100
1.210 1.331
1.464 1.6 11
0.
780
0.724 0.634 0.584 0.548
8.
82
Present value of continuing value= =
5.48
No
te: Allow for
rounding
errors
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54 Part One
Financial
Statements
and
Valuation
as
earlier, but now the EPS, DPS, and BPS are giv en. Again pretending these actual num
bers are numbers forecasted in 1999, forecasted
RE
and ROCE have been calculated. We
charge GE a
10
percent cost for using equity capit al. The sum
of
the present values
of
the
RE up
to
2004
3
.27 per share), added to the 1999 b ook value
of
4.32 per share, yield a val
uation of 7 59 per share. But this is not correct
bec
a use GE is earning a positive
RE
in 2004
and will probably continue with positive RE in sub
sequent
years. GE has a declining ROCE
driver, but its growth in book value more than
offsets
this to maintain its RE. The valuation
of
7.59 per share is missing the continuing value the continuing premium in model 5.3.
The continuing value is the value of residual ea rn ings beyond the horizon. Look at the se
ries
of
RE forecasts for GE up to the 2004 horizo
n .
You can see that RE is fairly constant.
Suppose we forecast that RE beyond 2004 is going to be the same
as
the 0.882 in 2004: The
subsequent RE will be a perpetuity. The value
of the
perpetuity is the capitalized amount
of
the perpetuity: 0.882/0.
10
= 8.82, as shown below the valuation. And as this is the value of
expected REs after 2004, it is also the value of the expected premium at the end of 2004. So
we can replace model 5.3 with
RE RE
RE (RE )
= + _ _ +__ +
..
.+ +
-1:: : ..
I
PT
0 0 2 T
J
E
PE PE PE pE -
Case 2
5.5)
where, in GE s case, is five years ahead.
So
the 1999 valuation is 13.07
=
4.32 + 3.27 +
8.82/1.6105. The calculated premium is 13.07 - 4
.3
2 = 8.75. The RE forecasts for 2005 and
beyond supp
ly
the continuing value (CV) at the end of 2004 and this is the expected
premium in 2004: Vf
-
Bs = 8.82.
We refer to the case of constant RE after the forecast horizon as Case 2.
You
might ex
pect Case 1 to be typical: A firm might earn a positive RE for a while (ROCE greater than
the cost
of
capital), but eventually competition will drive its profitability down so its ROCE
will equal the cost of capital. High ROCE do decl ine,
as
illustrated by both Flanigan s En
terprises and GE, but it is more common
fo
r ROCE and RE
to
level offat a positive amount.
f
so, Case 2 applies.
Note that
we
are able to value General Electric, even though its free cash flows are
negative. By applying accrual accounting, we have dealt with the problem that haunted us
in Chapter 4. Exercise E5 .l l looks at GE in 2004.
As there is no expected growth in RE after the forecast horizon, we can refer to Case 2
as
the no-growth valuation. Case 3 is a growth
va
luation, demonstrated with Nike, for the
fiscal years 2006 to 2011. With the exception
of
the recession year, 2009, Nike s residual
earnings are growing, with declining ROCE but growing book values.
It
is probably unrea
sonable to expect
RE to
be constant or zero after 2011.
f
he growth is forecast to continue,
the continuing value calculation can be modified
by
adding a growth rate:
RE RE RE RE
( RE )
E +__ +
__
+__ + ... + + _..I .J . . I
PT
0 0 2 3
T E
PE PE PE PE pE
- g
Case3
5.6)
where g is I plus the rate of growth.
2
Nike s RE growth rate in 2011is2.108/2.017, that is
about 4.5 percent (g = 1.045).
f
his rate were expected to continue after 2011 , the fore
casted RE for 2012 would be 2.108
X
1.045 = 2.203.
So
the continuing value is 48.95, and
2
The growth rate has to be less than t
he
cost of capita l or the terminal value calculat ion b lows up. It is
unreasonable
to
expect a firm s R
to grow
at a rate greater than t
he
cost of capital indefinitely an d so
have an infinite pr ice). Growth cou
ld
be negative at a hor izon (g < 1 . This is typica lly a
case
of a positive
R declining toward zero.
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C SE
3
Nike,
Inc
.
Required rate
of
return
is 9 percent. In this
case, residual earnings
is
expected to grow at
a 4.5 percent rate after
2011.
hapter
5 ccrua
l
cco
unting and Valuation: Pricing Book Values 55
EPS
DPS
PS
ROCE
R (
9
charge )
Di
scount rate (1.09
1
)
Present
value
of
R
Total present v
alue
of R to 2011
Continuing v
alue CV)
Pre
se
nt v
alue
of CV
V
al
ue per share
The continuing
value
:
C
V=
2.108
x
1.045 =
48
.
95
1.09 - 1.045
2006
14.00
7.37
31 .81
53
.18
2007
2.
96
0.71
16 .25
21.1
1
.7
00
1.090
1.560
f
. . I 48.95
3
resent va lue o con
t1nu
1ng va ue
=
1
.
539
=
1.81
Note Allow for roun
ding
errors.
Forecast Year
2008 2009
2010 2011
3.80 3.07 3.93 4.28
0.88 0.98 1.06 1.20
19 .17 21.26 24.13
27.21
23.4 16.0
18.5 17.7
2.338 1.345
2.017 2.108
1.188 1.295
1.412 1.539
1.968 1.039
1.429 1.370
48.95
its present value at the end
of
2006 is 31.81 , as indicated at the bottom
of
the case study.
The value at the end
of
2006 is = 14 .00 + 7.37 + 31.81 =
53
.
18.
Case 3, along with Cases 1 and 2, completes the set
of
cases
we
are likely to meet in
practice. The long-term level
of
RE and its growth rate are sometimes referred to as the
steadystate condition for the firm. The growth
rate
distinguishes the growth
of
Case 3 from
the no-growth
of
Case
2.
(For Case 2, g = 1.0.)
Look
at Box
5.3
for some technical issues
when calculating continuing values.
Beware
of
Paying
Too
Much for rowth
You probably get the feeling that determining a long-term growth rate is the most uncertain
part
of
a valuation. In our examples, we extrapolated growth rates from what we saw up to
the forecast horizon- no-growth for GE based on the constant residual earnings and posi
ti
ve growth for Nike based on the growth rate in the horizon year. Growth up to the forecast
horizon gives some infonnation about long-term growth, but
it
is unwise to extrapolate
even worse to assume a rate. Rather we should investigate th e information that informs
about the growth rate. Accordingly, analyzing and forecasting growth will be a focus
of
our
financial statement analysis in Part
Two of
the text.
At this point, we might well remind ourselves
of
the fundamentalist dictum in Chapter
1:
Beware
of
paying too much for growth
Fundamental investors see growth as risky; unless
the firm has barriers to entry - maybe due to a protected brand, like Nike- growth can
easily be competed away. The stock market tends to get overexcited about growth prospect
s
with most bubbles forming around exaggerated growth expectations. Fundamental investors
are thus careful about buying growth. Th
e risk
in
investing
is th
e risk
of
paying
to
o much
and
that often comes down to paying too much for growth. It is easy to plug in a growth rate to
a formula but that can be dangerous.
Once
we
have our valuation
fr
amework in place in
thi
s and the next chapter, we proceed in
Chapter 7 to the task
of
applying the framework in a way that protects us from paying too much
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A continuing value
is
always calculated at the end
of
a period
on the
basis
of
a forecast for the following period.
So
a con-
tinuing value at the end
of Year
T is
based on
a forecast
of
residual earnings for T + 1:
Calculation
1)
dr a ws the continuing value at the end
of Year
1
based on
residu a l earnings for
Year
2 growing at the rate,
g
Calculation
2)
d
r
ws the continuing value at the end
of
Year
2 based on
resid
u al earnings
for Year
3, but also
has
residual
earnings in Year
2
growing at the rate,
g
into
Year
3
CV = REr 1
Pc
This continuing value
is
discounted
to
present value at the d
is
-
count rate for
Year T
pf.
The
following v aluations for Home Depot illustrate with a
required return
o f
1O percent and a 4 percent growth rate).
Home Depot,
the
warehouse retailer,
has
a book value
of
$12.67
per
sha
r
e
with residual earnings
of 1 .713
and
$1. 755
forecaste d for
Year 1
and
Year 2
ahead respectively.
The
following calculations give the same
va
lue:
56
1)
vl
= 12.67+
1
713
+
1
755
= $40.82 (1)
1 .10 1.10X(1.10-1.04)
2)
,,E_
1267
1 .713 1.755 1.755X1.04
(2)
v .
1 .10 1.
21
1.21
x
(1.10 - 1.04)
=$40.82
for growth. At this stage you should have some assurance that the methods here are helpful. We
saw in Chapter 4 that discounted cash
flow
valuation often leaves us with a high proportion
of the calculated value in the speculative continuing value. Indeed, for General Electric we saw
that over 100 percent
of
the value was in the continuing value. In contrast, our Case 2 valua
tion for GE here captured a considerable part of the value in the book value and short-term
forecasts about which we are more confident. That is the result
of
using accrual accounting
income statements and balance sheets rather
than
cash flows- which typically brings the
future forward in time. Nevertheless, there remains a continuing value calculation
to
take care
of.
Converting Analysts Forecasts t a Valuation
Analysts typically forecast earnings for one or two years ahead and then forecast
intermediate-term growth rates for subsequent years , usually three to five years. These fore
casts are available on Yahoo and Google Finance Web sites. The forecasts for one and two
years ahead are somewhat reliable (but buyer beware ); however, analysts' growth rate fore
casts are often not much more than a guess. In any case, given the forecasts, the investor
asks: How can the forecasts be converted to a valuation?
Table 5.2 gives consensus analysts' forecasts for Nike, Inc., made after fiscal 2010
financial statements were published. A consensus forecast is an average of forecasts made
by sell-side analysts covering the stock. The forecasts for 2011- 2012 are point estimates,
and those for 2013- 2015 are the forecasts implied by the analysts' five-year intermediate
term EPS growth rate
of
11
percent per year. Analysts typically do not forecast dividends,
so one usually assumes that the current payout ratio- DPS/EPS- will be maintained in the
future . Nike paid $1.06 per share in dividends during 2010 on EPS of$3.93 ,
so
its payout
ratio was 27 percent. You can see from the table that Nike's residual earnings, calculated
from the analysts' forecasts, are growing. Analysts
do
not forecast earnings for the very
long run, but if we were to forecast that RE after 2015 were to grow at a rate equal to the
typical rate of growth in Gross Domestic Product (GDP) of 4 percent,
we
would establish
a continuing value of $70.62, as indicated in the table. The value implied by the analysts'
forecasts is $77.24 per share. At the time, Nike's shares traded at $74 each. So, on these cal
culations, Nike is reasonably priced.
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5/19/2018 Penman 5ed Chap005
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Chapter
5 Accrual ounting
and
Valuation
ricing
Book
Values
157
T BLE
5.2 Converting Analysts' Forecasts to a
Valuation:
Nike, Inc. (NKE)
Analysts forecast EPS two years ahead ( 4.29 for
2011
a
nd
4.78 for 2012) and also forecast a five
year EPS growth rate of percent. Forecasts for 2013-
2015
apply this consensus EPS growth rate
to the 2012 estima
te
.
Di
vidends per share (DPS) are set
t
the 2010 payout rate
of27
percent
of
earnings. Required rate of return is 10 percent.
Years
labeled A are actual numbers, years labeled E
are expected numbers.
2 1 A
2 11 E
2 1 2 E
2 13 E
2 14 E 2 15 E
PS
3.93
4.29
4 .78
5.31 5.89 6.54
DPS
1.06
1.16
1-29
1.43 1.59 1.77
BPS
20.15 23 .28 26 .77
30.65 34.95 39.72
ROCE
21.3%
20 .
5
19.8% 19.2%
18.7%
R
(9% charge) 2.477
2.
685
2.901 3.132 3.395
Discount rate (1.09)t 1.090
1- 188
1.295 1.412 1.539
Present
value
of R
2.272
2 .
260
2.240 2.218 2.206
Total PV
to
2015
11
.20
Continuing
value
CV)
70.62
Present
value
of CV
45.89
Value per
share
77 .24
The continuing v
alue
based on the
GDP
growth rate:
CV=
3.395
x
1.04
= 70 .62
1.09 - 1.04
Note: All
ow
for rounding error
s.
In this Nike valuation, we used the average historical GDP growth rate of 4 percent as
the long-run growth rate. With the calculated value of 77 .24 close to the market price
of
74,
we
have learned something else: Given that the analysts' forecasts are reasonable, the
market is pricing Nike on the basis of a 4 percent GDP growth rate in the long run. This
makes some sense: In the long run, we expect residual earnings for all firms to grow at the
GDP growth rate . Box 5.4 provides more justification for using a GDP growth rate, at least
as a first guess and also gives you a feel for how well the valuation model of this chapter
works on average.
Although the GDP growth rate may work well
on
average, it is probably not appropriate
for all firms. While we might expect all firms to
grow
at the GDP rate in the long run, some
(including Nike) may be able to sustain a higher growth rate for a considerable period of
time.
Yet
others may never achieve growth at the GDP rate.
We
have more work to
do
in in
vestigating growth and Chapter 7 takes up the task.
BUILD YOUR
OW
V LU TION ENGINE
The mechanics of the valuations in Cases 1, 2, 3, and Table 5 2 can easily be handled in a
spreadsheet. The spreadsheet requires the following inputs: (1) current book value,
(2) earnings and dividend forecasts up to a given forecast horizon, (3) a required return,
and (4) a long-term growth rate to calculate the continuing value. You then build in the
spreadsheet calculations to forecast future book values, residual earnings, a continuing
value, and finally the present value of the forecasts. The standard spreadsheet has forecasts
for two years ahead (that's what analysts forecast) and applies a growth rate for years there
af
ter. A more flexible engine allows for different forecast horizons.
-
5/19/2018 Penman 5ed Chap005
19/37
Value-to-price ratios compare calculated value to the current
market price . If a V/P ratio is more than 1.0, a buy recommen
dation is implied . If the V/P ratio is less than 1.0, a sell recom
mendation is implied.
The
graph below tracks median V/P ratios for all U.S. listed
firms from 1975 to 2001. Value is estimated using analysts'
consensus forecasts
for two
years ahead, converting them
into a residual earnings forecast
(as
in
Table 5.2 ), and then ap
plying a
GDP
growth rate of 4 percent for growth in residual
earnings thereafter. That is,
The
required return, p, is
set
at the
risk
-free rate (on U.S.
government 10-year obligations) for each year plus a 5 per
cent risk premium. This valuation is only approximate
as
the
continuing value and the required return will be different for
different firms.
Even though the valuati
on
is approximate, you
can
see
that V/P ratio oscillates around 1.0. When the VIP ratio is
2.5
1
Median
VIP Ratio
I
above 1 0- indica ting prices are too low i t tends to revert to
1.0
as
prices adju s t
to
fundamentals. When
V/P
is
below
1.0
indicating prices a re too high i t tends to revert back to 1.0.
The
pattern
co
u Id
be
due to discount rates changing
as
market-wide risk c hanges, so one does have to be careful. We
have
used a
risk
p remium of 5 percent at
all
points
in
time in
calculating V here . But
in
bad times, like the 1970s, investors
might require a h igher risk premium, pushing prices down . In
good times, like the 1990s, the
risk
premium declines, so
prices
rise
.
This
is t he efficient markets interpretation of the
graph.
The
graph of t he
V/P
ratio
also
tells us that the
GDP
long
term growth rate t hat we used for Nike
in
Table 5.2 also works
for the average
rm
It is a good first guess at the growth rate.
But
guesse
s are not sufficient; what works on average
may not work fo r firms that are different from average.
The
challenge is to
identify
superior (or inferior) growth . That chal
lenge is taken u p in the financial statement
analysis
of
Part Two of this t ext.
2 ~
58
.s
1.5
0 5
0
V
t--
t-- t--
'
V
t--
t--
00 00 00
00
-
'
V
t--
0
8
-
N
Sour
ce
:
Pr
ices
are
from Sta
ndard
&
Poor's
COMPUST
AT.
Analysts'
earni
ngs forecasts
are
fro m Tho
ms
on F
nancia
l l/B/
E S
data.
With these inputs you can calculate a value at the press of a button. Further
to
under
stand your uncertainty about the valuation the engine can show how the value changes
with different inputs. For example you might be comfortable with inputting your own hur
dle rate for the required return 9 percent say- but you are unsure of the long-term
growth rate. The GDP growth rate was applied in Table 5 .2 but you might look at the sen
sitivity
of
the valuation to a 3 percent or 2 percent rate: What is the stock worth
if
it deliv
ers only 2 percent growth?
I f
you believe 2 percent is conservative and the stock is trading
below the calculated value you may feel comfortable in buying the stock.
I f
,
on the other
-
5/19/2018 Penman 5ed Chap005
20/37
Chapter 5 Accrual Accounting
and
Valuat
i
on Pricing oo
k
Values 159
hand, you see that, by experimenting with alternative growth rates, a 6 percent growth rate
is required to justify the market price , then you mi ght see the stock
as
too expensive.
With such scenario experimentation, you are focusing on the most important aspect of
valuation: understanding your uncertainty.
We
will
build on this theme in Chapter 7, with
the spreadsheet engine developed further for the
purpose.
The engine will then be expanded
by
building in the financial statement analysis
of
Part
Two of
the book until you have devel
oped a full analysis and valuation product. The
BuildYour
Own Analysis Product (BYOAP)
on the book's Web site will be your guide.
You
might be tempted to appropriate an off-the-shelf valuation spreadsheet.
You
can do
this- it's available within BYOAP in fact- but nothing helps your learning more than
building the product yourself.
You
will be proud o the results.
You
will be more secure in
using the product to value firms and to challenge market prices. You will find yourself
adding bells and whistles. And you will find yourself taking the product into your profes
sional life and using it for your personal investing.
APPLYING THE
MODEL TO
PROJECTS
ND
STRATEGIES
The RE method also can be used to value projects within the firm . At the beginning
of
the
chapter
we
demonstrated this for a simple one-
period
project. Multiperiod project evaluation
is
typically done using NPV ana
ly
sis of cash flows),
as
for the project in Figure 3.4 in Chap
ter 3 that required an investment
of
1,200. Table 5 .3 accounts for that project using accrual
accounting. The revenue is from the cash inflow but depreciation has been deducted to get
the net income from the project. The depreciation is calculated using the straight
-l
ine method,
that is, by spreading cost le
ss
estimated salvage value (the depreciation base) over the
five
years. The book value of the project each year
is
its original cost minus accumulated depreci
ation. And this book value follows the stocks and flows equation, similar
to
equities:
Book value
1
=Book value
1
_ 1 + Income
1
- Cash
fl.ow
1
So
the book value in Year 1 is 1 ,200
+
214 -
430
= 984, and similiarly for subsequent
years. (The cash
fl.ow
comes from the revenues.) At the end ofYear 5, the book value is zero
as
the assets in the project are sold for estimated salvage value. This is standard accrual
accounting.
TABLE 5 3 Project Evaluation: Residual Earnings Approach.
Hurdle rate: 12 percent.
Revenues
Depreciation
Project
income
Book value
Book
rate
of return
Residual project income 0 .12)
Discount rate (1.12t)
PV of
R
Total
PV of R
Value
of project
0
1,200
330
1,530
430
216
214
984
17 .8
70
1.120
62.5
Forecast Year
2
3
460 460
216
216
244
244
768
552
24.8
31 .8
126
152
1.254
1.405
100.5
108.2
Value added = 330
4
5
380 250
216 216
164 34
336 0
29 .7 10.1%
98
6)
1.574 1.762
62 .3
(3.4)
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5/19/2018 Penman 5ed Chap005
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160 Part One inancial
tatements
and Valuation
TABLE 5.4 Strategy Evaluation.
Hurdle rate: 12 percent.
Fore c ast Year
0 1 2
3
4
5 6
Residual Earnings Approach
Revenues
430 890 1,350
1,730
1,980
1,980
Depreciation 216 432 648
864 1,080
1,080
Strategy
income
214 458 702
866 900
900 .
Book
value
1,200 2,184 2,952 3,504
3,840 3,840
3,840
Book rate of return
17.8% 21.0% 23.8%
24.7%
23.4% 23.4%
Residual strategy income (0 .12) 70.0
195.9 347.8
445.5
439.2
439.2 .
PV
of R 62.5 156.2 247.5
283.0
249.3
Total PV of R
999
Continuing
value
1
3,660
PV
of CV
2,077
Value
of
strategy
4,276
Value
added:
3,076
Discounted
Cash
Flow Approa
ch
Cash inflow
Investment
Free cash flow
PV
of FCF
Total PV
of
FCF
Continuing va l
ue
2
PVof CV
Value
of
strategy
1
CY = 439.2/0.12 = 3,660.
2
CY
= 900/0.12 = 7,500.
430
(1,200) (1,200)
(1,200) (770)
(687.5)
20
890
(1,200)
(
31
O)
(247.
2)
1,350
(1,200)
150
106.8
Net prese
nt
value :
3,076
1
,730
(1,200)
530
336.7
2
,100
(1,200)
900
510.7
7,500
2, 100 .
(1,200)
900 . . .
The value of the project is its book value plus th e present value of expected residual in-
come calculated from the forecasts of net income and book values. This value of 1 ,530 is
the same as the discounted cash flow valuation in Chapter 3. The forecasts of RE have cap-
tured the value added over the cost
of
the investment: The present value of the forecasts
of
RE of
3
30 equals the NPV we calculated
in
Chapter 3.
Strategy involves a series of ongoing investment
s.
Table 5.4 evaluates a strategy which
(to keep it simple) requires investing 1,200
in
the same project as before but
in
each
year indefinitely. The revenues are those from all overlapping projects in existence in a
given year: The revenue
in
Year 1 is 430 from the project begun in Year 0, the revenue in
Year 2 of 890 is the second year's revenue
( 460)
from the project begun in Year O plus
th
e first yea
r'
s revenue from the project begun
in
Year 1 (430), and so on. Depreciation
is the same as before ( 216 per year for a project), so total depreciation is 216 times the
number of projects operating at a time. By the fifth year into the strategy there are five
projects operating each year with a steady stream
of
1,980 in revenues and 1,080 in
depreciation . Book value at all points is accumulated net investment less accumulated
depreciation.
You
see from the calculations that the strategy adds 3,076 of value to the initial investment
of 1
,2
00 if the required return is
12
percent, and this value added is the present value of
expected residual income from the project. You also see from the second panel that this value
added equals the NPV of the strategy calculated using discounted cash
flow
analysis.
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5/19/2018 Penman 5ed Chap005
22/37
ADVANTAGES
Focus
on value drivers:
Focuses
on
profitability of investment
in
net
assets
and
growth
in
net
assets,
which dr
ive
value;
directs
strateg
ic
thinking to these driv
ers.
Incorporates the financial
statements
appropriately:
Incorporates the value
already
recogn
ized
in t
he
balance sheet the book value); to add
value to the
balance sheet,
it forecasts the income
statemen
t, which typically
is
a better
measure
of
va lu
e
added
than the
cash
flow statement.
Uses
accrual accounting:
Forecast horizon:
Versatility:
Uses the properties of accrua l accounting that recognize value added ahead of cash
flows, matches value added to value given up, and treats investment as an
asset
rather
than a oss of value .
Forecast horizons can be shorter than for
DCF analysis and more
v
alue is
typically
re
c-
ognized in the immediate future.
Aligned with what
people
forecast:
Can be used
with awi
de variety
o accounting principles see text
be
low and
Chapte
r
17).
Analysts forecast
earnings from which fore
casts
of
residual earnings can
be calculated).
Protects from pay ing too much for growth.
rotection:
Reduces
reliance on speculation:
The
valuation
relies
l
ess
on
the uncertain continuing
value
calc
ulati
on and speculation
about long-run growth.
DISADVANTAGES
Accounting complexity:
Suspect accounting:
Requires
an
understanding of how accrual accounting works see Chapters 2
and
3
).
Relies
on
accounting numbers, which can be suspect must be applied along with an
accounting quality ana lysis; see Chapter 8).
Many
of
the strategic planning products marketed by consulting
firms with
such
names as economic profit models, economic value-added models, value driver models, and
shareho
ld
er value-added
models are
variations
on
the residual earnings mode
l To
guide
strategy analysis, they focus on the two drivers
of
residual income and
of
value added:
return
on
investment and growth in investment. They direct management to maximize
return on investment and to grow investments that can earn a rate of return greater than the
required return. These value-added measures are used, in turn, to evaluate and reward man
agement on the success
of
their strategies.
FEATURES OF THE RESIDUAL EARNINGS
V LU TION
Box 5.5 lists the advantages and disadvantages
of
the residual earnings approach. Compare
it to summaries for the dividend discount and discounted cash
flow
DCF) models in
Chapter 4. Some
of
the features listed will
be
discussed in more detail later in the book as
indicated) . Some are discussed below.
Book Value Captures Value and Residual Earnings
Captures Value Added
to
Book Value
The residual earnings approach employs the properties of accrual accounting that typi
cally) bring value recognition forward in time. More value is recognized earlier within a
forecasting period, and less value is recognized
in
a continuing value about which we usu
ally have greater uncertainty.
Residual earnings valuation recognizes the value in the current book value on the
balance sheet, for a start; in addition, value is usually recognized in RE forecasts earlier
6
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62 Part One Financial Statemen
ts and
al
ua
tion
than for free cash flow forecasts.
You
can see
this
by comparing the value captured in
forecasts for one and two years ahead with the
tvv
methods in the strategy example we
just went through: Free cash flows forecasts are
negative
for Years 1 and 2 but RE fore
casts are positive. Scenario 2 for the savings
account
, earlier in the chapter, provides an
extreme example: Forecasted free cash flows
are
zero, yet a savings account can be
valued immediately from the current book
value
without forecasting at all. The com
parison
of
the General Electric valuation here with the attempt to apply DCF valuation
to
its negative free cash flows in Chapter 4 drives the point home. In short, RE valuation
honors the fundamentalist's dictum
to
put less
weight
on speculation, particularly about
a continuing value.
Protection from Paying
oo
Much or Earnings Generated
by Investment
The stock market is often excited by earnings
growth
, and it rewards earnings growth with
a higher price. Analysts tend
to
advocate
growth
firms. Momentum investors push
up
stock prices
of
growth firms, anticipating even more growth. However, growth
in
earnings
does not necessarily imply higher value. Firms can grow earnings simply
by
investing
more.
f
hose investments fail
to
earn a return
above
the required return, they wi
ll
grow
earnings but they will not grow value. So, growth
comes
with a caveat: An investor should
not pay for earnings growth that does not add
value
.
A case in point is a firm that grows earnings dramatically through acquisitions.The mar
ket often sees acquisitive firms
as
growth firms and gives them high PI multiples. But,
if
an acquirer pays fair value for an acquisition, it
may
not add value
to
the investment: Even
though the acquisition adds a lot
of
earnings, the investment just earns the required return.
Or worse, should
an
acquirer overpay for the acquisition- as
is
often the case with empire
builders-he
may actually destroy value while
adding
earnings growth.
During the 1990s, a number
of
firms went on acquisition sprees. Some acquisitions were
for strategic reasons, while others appeared
to
be growth for growth's sake.
Tyco
Interna
tional, a firm with 8 ,471 million in assets in 1996, grew to become a conglomerate with
111,287 million in assets by 2001. Its businesses included electronic components, under
sea cables, medical supplies, fire suppression equipment, security systems, and flow control
products, and it also ran a financing arm.
t
became a darling of the market, with its stock
price increasing from
53
per share in 1996
to
236 (split-adjusted) in 2001. In 2002,
much
of
its market value evaporated, with the
price
falling
to
68,
as
the value
of
the
acquisitions- and the accounting employed in reporting earnings from the acquisitions
came into question. WorldCom grew from a small Mississippi firm to the number
two
telecommunications firm in the United States, acquiring (among others) MCI. Its stock price
rose to over 60, but by 2002, due
to
an accounting scandal, it was trading at
25
cents per
share and ultimately went bankrupt. Both Tyco
and
WorldCom were led by aggressive em
pire builders (who subsequently resigned under doubtful circumstances), both borrowed
heavily
to
make acquisitions , and both ultimately
ran
into difficulties in servicing that debt.
General Electric,
on
the other hand, made many acquisitions that significantly added value.
The residual earnings model has a built-in safeguard against paying too much for
earnings growth: Value
is added only
if
the investment earns over and above its required
return. Look at Exhibit 5.3 .This
is
the same simple example
as
in Exhibit 5.2 except that, in
addition to paying a dividend
of
9.36 million, the firm issues shares in Year 1 for 50 mil
li
on, giving it a net dividend in Year 1 of - 40.64 million. Book value at the end ofYear
is
thus 153.00 million. The investment, earning at a
10
percent rate, is expected
to
con
tribute 5 million additional earnings in Year 2, and earnings for Years 3
to
5 also increase.
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Chapter 5
ccrual ccounting
and
Valuation
Pricing
Book Values 163
EXHIBIT 5 3
Forecasts
for a Simple Firm with
dded
Investment
In millions of dollars. This is the same firm as that in Exhibit 5.2 except the firm is expected to
make a share issue of 50 million in Year l,
to
be inve
sted
in assets earnings I 0 percent per year.
Required return
is
I 0 percent per year.
Forecast Year
0
2
3
4
5
Earnings
12.00 12.36
17.73
18.61 19.