Chapter 5
Accrual Accounting and Valuation:
Pricing Book Values
GROUP MEMBERS
1.SHONHIWA ARMSTRONG
2.OTTILIA MATANHIRE
3.MAPA INNOCENT
R133923R
R186653H
R1812767E
• Previous presenters showed how accrual
accounting modifies cash accounting to produce a
balance sheet that reports shareholders' equity.
However, they explained that book value is not
the value of shareholders' equity, so firms typically
trade at price-to-book ratios different from 1.0. 0.
• This presentation shows how to estimate the
value omitted from the balance sheet and thus
how to estimate intrinsic price-to-book ratios. 9
• Firms typically trade at a price that differs from
book value. Previous presentations 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.
• Consequently, 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 presentation lays out a valuation
model for calculating the premium and intrinsic
value. It also models strategy analysis, and
provides directions for analyzing firms to discover
the sources of value creation
• 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.
• • How 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.
• • How the residual earnings model captures value
added in a strategy.
• • The advantages and disadvantages of using the
residual earnings model and how it contrasts to
dividend discounting and discounted cash flow
analysis.
• How residual earnings valuation protects the
investor from paying too much for earnings added
by investment.
• How residual earnings valuation protects the
investor from paying for earnings that are created
by accounting 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 intrinsic price-to-book ratio.
• Calculate value added in a strategy.
• 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. However, book value typically does not
measure the value of the shareholders' investment. The
value of the shareholders' investment- and the value of
the net assets- is based on how much the investment
(net assets) is expected to earn in the future. Therein
lies the concept of 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 of the P/B ratio, is based on the expected
future earnings that investors are buying. So, 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 of P/B ratios. This
presentation supplies the formal valuation model to
implement this concept of 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 if
one is not careful
• Beware of Paying Too Much for Earnings
• A basic precept of investing is that investments add
value only if they earn above their required return.
Firms may invest heavily- in an acquisition spree, for
example- but that
• 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 required
return on book value. The analysis in this presentation
is designed to prevent you from making the mistake of
paying for earnings that do not add value.
• As you apply the model and methods in this
presentation, 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 presentation, 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
Anchoring valution
• 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 recognizedthe premium over book value:
• Value = Book value + Premium
• 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. The
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
Valuing a One-Period Project (1)
Investment
Required return
Revenue forecast
Expense forecast
Earnings forecast
$400
10%
$440
$400
$ 40
Residual earnings1  Earnings 1  (Required return x Investment)
 40 - (0.10 x 400)
0
 400 
Value
0
1.10
 400
This is a zero-residual earnings project
This is a zero NPV project:
DCF Valuation:
V
440
 400
1.10
Valuing a One-Period Project (2)
Investment
Required return
Revenue forecast
Expense Forecast
Earnings forecast
$400
10%
$448
$400
$ 48
Residual earnings1  48 - (0.10 x 400)
8
Value Project
 400 
 407.27
The project adds value
448


DCF
value


407
.
27


1.10


8
1.10
Valuing a Savings Account
Forecast Year
________________________________________
2000
2001
2002
2003
2004
2005
5
5
100
5
5
100
5
5
100
5
5
100
5
5
100
Earnings withdrawn each year (full payout)
Earnings
Dividends
Book value
100
Residual earnings
0
0
0
0
0
______________________________________________________________________________________
No withdrawals (zero payout)
Earnings
Dividends
Book value
100
Residual earnings
5
0
105
0
5.25
0
110.25
0
5.51
0
115.76
5.79
0
121.55
6.08
0
127.63
0
0
0
______________________________________________________________________________________
Value = Book Value + Present Value of Residual Earnings
= 100 + 0
= 100
The Normal Price-to-Book Ratio
Normal P/B = 1.0
(Price = Book Value)
The Normal P/B firm earns a rate of return on
its book value equal to the required return
Lessons from the Savings Account
1. 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
investment earning at the required return.
3. Even though an asset does not pay dividends, it can be
valued from its book value and earnings forecasts.
4. The valuation of the savings account does not depend
on dividend payout. The two scenarios have different
expected dividends, but the same value.
5. The valuation of a savings account is unrelated to free
cash flows: The two accounts have the same value,
but different free cash flow.
A Model for Anchoring Value on Book Value
 
Value of common equity V0E  B0 
RE 1 RE 2 RE
 2  3  ...
ρE
ρE
ρE
where RE is residual earnings for equity :
Residual earnings  comprehens ive earnings - (required
return for equity x beginning -of-period book value )
RE t  Earn t  (ρ E  1)B t 1
Derivation of the Equity Valuation Model:
One Period
Valuing a one-period payoff equation:
P0 
P1  d1 
ρE
Substitute for the expected dividend
d1  Earnings 1  (B1  B0 )
to get
P0 
Earnings 1  (B1  B0 )  P1
ρE
or
Earnings 1  (ρ E  1)B 0 P1  B1
P0  B0 

ρE
ρE
The amount, Earnings 1  ρ E  1B0 is called
Residual Earnings
Derivation of the Equity
Valuation Model: Multiperiod
Substituting comprehensive earnings and book value for
dividends in each period,
P0  B0 
Earnings 1  ρ E  1B0 Earnings 2  ρ E  1B1

 ...
2
ρE
ρE
Earnings T  ρ E  1BT 1 PT  BT
... 

T
ρE
ρ TE
If we set
RE t  Earnings t  ρ E  1Bt 1 ,
RE 1 RE 2
RE T PT  BT
P0  B0 
 2  ....  T 
ρE
ρE
ρE
ρ TE
The Equity Valuation Model:
Infinite Horizon
The model can be extended for
infinite horizons
P0  B 0 
Earnings1  ρ E  1B 0 Earnings
2  ρ E  1B1

 ...
ρE
ρ 2E
... 
EarningsT  ρ E  1B T 1
ρ TE
 ...
or
P0  B0 
RE 1 RE 2 RE 3 RE 4 RE 5
 2  3  4  5  .....
ρE
ρE
ρE
ρE
ρE
Relation Between P/B Ratios and
Subsequent RE
_____________________________________________________________________________________
Residual Earnings for
Years After P/B Groups Are Formed (Year 0)
P/B
_____________________________________________________________
0
1
2
3
4
5
6
_____________________________________________________________________________________
P/B
Group
1 (High)
6.20
.173
.230
.218
.213
.211
.200
.204
2
3.66
.121
.144
.142
.140
.148
.149
.139
3
2.82
.101
.112
.108
.108
.101
.103
.116
4
2.33
.089
.100
.099
.096
.097
.108
.123
5
2.00
.076
.082
.080
.088
.085
.086
.094
6
1.76
.064
.066
.064
.058
.066
.071
.076
7
1.58
.057
.058
.058
.056
.061
.059
.073
8
1.43
.047
.052
.047
.049
.053
.060
.068
9
1.31
.040
.040
.041
.044
.046
.055
.056
10
1.22
.035
.036
.035
.040
.047
.054
.054
11
1.13
.032
.034
.035
.040
.045
.051
.055
12
1.05
.028
.027
.028
.032
.040
.043
.046
13
.98
.023
.023
.025
.031
.035
.037
.045
14
.94
.018
.019
.025
.029
.035
.037
.039
15
.85
.009
.008
.013
.020
.028
.033
.041
16
.79
-.001
-.001
.006
.015
.023
.024
.024
17
.72
-.011
-.015
-.005
.008
.011
.021
.022
18
.64
-.024
-.024
-.012
-.003
.008
.010
.017
19
.54
-.042
-.044
-.028
-.015
-.007
-.007
-.006
20 (Low)
.39
-.068
-.070
-.041
-.028
-.020
-.017
-.014
_____________________________________________________________________________________
Residual income is deflated by book value at the beginning of year 0, the year the P/B groups are formed.
Ingredients of the Model
For finite horizon forecasts we need three ingredients,
besides the cost of capital:
1. The current book value
2. Forecasts of residual earnings (earnings and book
values) to horizon
3. Forecasted premium at the horizon
Component 3 is called the continuing value
As efficient prices equal intrinsic values, then
E
RE
RE
RE
V
B
1
V0E  B0 
 2 2  .....  TT  T T T
ρE
ρE
ρE
ρE
Return or Common Shareholders’
Equity (ROCE)
Comprehens ive earnings to common t
ROCE t 
Book value t 1
Alternative Measure of Residual
Earnings
Residual earnings is the rate of return on equity, ROCE,
expressed as a dollar excess return on equity rather than a
ratio. But it can also be expressed in ratio form:
Earnings t  E  1Bt 1  ROCE t  E  1Bt 1
Drivers of Residual Earnings
Two Drivers:
1. ROCE
•
If forecasted ROCE equals the required return, then
RE will be zero, and V = B
•
If forecasted ROCE is greater than the required
return, then V > B
•
If forecasted ROCE is less than the required return,
then V < B
2. Growth in book value (net assets) put in place to
earn the ROCE
RE will change with change with ROCE and growth in
book value
P/B, ROCE and Growth in Book
Value
P/B in 2003
The Gap Inc.
General Electric Co.
Verizon Comm. Inc.
Citigroup Inc.
Home Depot Inc.
General Motors Corp.
Federated Dept. Stores
4.23
4.16
3.32
2.79
2.62
1.19
0.92
ROCE in 2004
28.1%
22.3%
23.4%
17.4%
19.2%
11.1%
12.0%
Growth Rate for
Book Value in 2004
30.7%
39.3%
12.2%
11.5%
13.2%
9.7%
3.1%
How the Residual Earnings Model Works
Current Data
Current year
Forecasts
Year 1 ahead
ROCE1
Current book
value
Current book
value
PV of RE2
PV of RE3
Year 3 ahead
Book value1
ROCE2
ROCE3
Book
value2
Current book
value
Residual earnings1
PV of RE1
Year 2 ahead
Discount by 
Discount by 2
Discount by 3
Residual earnings2
Residual earnings3
A Simple Demonstration
In millions of dollars. Required return is 10% per year.
Forecast Year
0
1
2
3
4
5
13.51
13.91
Earnings
12.00
12.36
12.73
13.11
Dividends
9.09
9.36
9.64
9.93
10.23
10.53
103.00 106.09
109.27
112.55
115.93
2.43
2.50
2.58
2.66
3%
3%
3%
Book value 100.00
RE (10% charge)
2.36
RE growth rate
RE1
.  g
V0E  B0 
With g = 1.03 and ρ = 1.10, the valuation is:
V0E  $100 
$2.36
$133.71 million
1.10  1.03
The intrinsic price-to-book ratio (P/B) is $133.71 / $100 = 1.34.
3%
Buying Residual Earnings: Flanigan’s
Enterprises Inc.
Case 1: Zero RE after T
Required rate of return is 9 percent.
Forecast Year
Eps
Dps
Bps
1999
2000
2001
2002
2003
3.58
0.73
0.11
4.20
0.80
0.24
4.76
0.71
0.25
5.22
0.47
0.27
5.41
20.4%
0.408
1.09
0.374
19.0%
0.422
1.188
0.355
14.9%
0.282
1.295
0.217
9.0%
0.000
1.412
0.000
ROCE
RE (9% charge)
Discount rate (1.09)t
Present value of RE
Total present value
of RE to 2003
0.95
Value per share
4.53
Assuming zero RE after period T (zero premium at T):
V0E  B0  PV of RE for T periods
V0E  4.53  3.58  0.95
Continuing Value
Case 1: Zero RE after T
RE is forecasted to be zero in perpetuity at the horizon
So
CVT  0
The forecasted premium at the horizon is
VTE  BT  0
Buying Residual Earnings: General
Electric (GE)
Case 2: Constant RE after T
Required rate of return is 10 percent.
Forecast Year
Eps
Dps
Bps
1999
2000
2001
2002
2003
2004
4.32
1.29
0.57
5.04
1.38
0.66
5.76
1.42
0.73
6.45
1.50
0.77
7.18
1.60
0.82
7.96
29.9%
0.858
1.100
0.780
27.4%
0.876
1.210
0.724
24.7%
0.844
1.331
0.634
23.3%
0.855
1.464
0.584
22.3%
0.882
1.611
0.548
ROCE
RE (10% charge)
Discount rate (1.10)t
Present value of RE
Total present value
of RE to 2004
3.27
Continuing value (CV)
Present value of CV 5.48
Value per share
13.07
8.82
The continuing value:
CV =
0.882
= 8.82
0.10
Present value of continuing value =
8.82
= 5.48
1.6105
Assuming constant RE after period T:
V0E  13.07  4.32  3.27  5.48
Continuing Value
Case 2: Constant RE after T
RE is forecasted to be constant in perpetuity at the horizon
So
CVT 
RE T +1
 E 1
The forecasted premium at the horizon is
VTE  BT  CVT
For GE, CVT =
0.882
 8.82
0.10
Buying Residual Earnings: Dell Inc.
Case 3: Growing RE after T
Required rate of return is 11 percent.
Forecast Year
Eps
Dps
Bps
2000
2001
2002
2003
2004
2005
2.06
0.84
0.0
2.90
0.48
0.0
3.38
0.82
0.0
4.20
1.03
0.0
5.23
1.18
0.0
6.41
40.8%
0.613
1.110
0.553
16.6%
0.161
1.232
0.131
24.5%
0.568
1.518
0.374
22.6%
0.605
1.685
0.359
ROCE
RE (11% charge)
Discount rate
PV of RE
Total PV
of RE to 2005 1.75
CV
PV of CV
8.50
Value
12.31
2 4.3%
0.448
1.368
0.328
14.32
The continuing value (growth at 6.5%):
0.605  1.065
CV = 1.11  1.065 = 14.32
14.32
Present value of continuing value =
1.685 = 8.50
1  RE T 1 

V  B  PV of RE for T periods  T 
 E   E  g 
Assuming growing RE after period T :
E
0
0
V0E  12.31  2.06  1.75  8.50
Continuing Value
Case 3: Growing RE after T
RE is forecasted to grow at constant rate in perpetuity at the
horizon
So
RET +1
CVT 
ρE  g
The forecasted premium at the horizon
CVT  VTE BT
0.605  1.065
For Dell, CVT 
1.11  1.065
 14.32
Forecasting Target Prices
Target Price T  BT  CVT
Case 1 (Flanigan’s)
E
V2003
 B2003  5.41
Case 2 (GE)
E
V2004
 B2004  CV2004  7.96  8.82  16.78
Case 3 (Dell)
E
V2005
 B2005  CV2005  6.41  14.32  20.73
Converting an Analyst’s Forecast to a
Valuation: Nike Inc.
Forecasts:
$4.45
2006
$5.04
Five-year eps growth rate: 14%
2005
Eps
Dps
Bps
ROCE
RE (10%)
Discount rate
PV of RE
Total PV
to 2009
CV
PV of CV
Value
2004A
2005E
2006E
3.59
0.74
18.17
4.45
0.92
21.70
5.04
1.04
25.71
24.49%
2.633
1.110
2.394
23.23%
2.870
1.210
2.372
2007E
5.75
1.18
30.27
22.36%
3.175
1.331
2.386
2009E
6.55
1.35
35.47
7.47
1.54
41.40
21.64%
3.523
1.464
2.406
21.06%
3.920
1.611
2.434
11.99
67.95
42.19
72.35
The continuing value (4% growth = GDP growth rate):
CV =
2008E
3.920  1.04
= 67.95
1.10  1.04
Project Evaluation: Residual Earnings
Approach
Project evaluation: residual earnings approach.
Forecast year, t
0
Revenues
1
2
3
4
5
$430
$460
$460
$380
$250
Depreciation
216
216
216
216
216
Net Income
214
244
244
164
34
984
768
552
336
120
17.8%
24.8%
31.8%
29.7%
10.1%
70
126
152
98
(6)
Discount rate (1.12t)
1.120
1.254
1.405
1.574
1.763
PV of RE
62.5
100.5
108.2
62.3
(3.4)
Book value
$1,200
ROCE
RE (.12)
Total PV of RE
330
Value of project
$1,530
Value added: PV of RE = 330
(same as NPV)
Strategy Evaluation: Residual Earnings
Approach and DCF Approach
Hurdle rate: 12%
Forecast Year
1
2
0
Residual Earnings Approach
Revenues
Depreciation
Strategy income
Book value
Book rate of return
Residual Income (0.12)
PV of RE
Total PV of RE
1
Continuing value
PV of CV
Value of strategy
$1,200
2
CV= 439.2/0.12=$3,660.
CV=900/0.12=$7,500.
$890
432
458
2,956
21.0%
195.9
156.2
3
4
5
6…
$1,350
648
702
3,504
23.8%
347.8
247.5
$1,730
864
866
3,840
24.7%
445.5
283.0
$1,980
1,080
900
3,840
23.4%
439.2
249.3
$1,980 …
1,080 …
900 …
3,840 …
23.4%
439.2 …
999
3,660
2,077
$4,276
Discounted Cash Flow Approach
Cash inflow
Investment
$(1,200)
Free cash flow (FCF)
(1,200)
PV of FCF
Total PV of FCF
20
2
Continuing value
PV of CV
4,256
Value of Strategy
$4,276
1
$430
216
214
2,184
17.8%
70
62.5
,t
Value add: $3,076
$430
(1,200)
(770)
(687.5)
$890
(1,200)
(310)
(247.2)
$1,350
(1,200)
150
106.8
$1,730
(1,200)
53 0
336.7
$2,100
(1,200)
900
510.7
7,500
Net present value: $3,076
$2,100 …
(1,200)
900…
Advantages and Disadvantages of the
Residual Earnings Model
Advantages
Focus on
value drivers:
focuses on profitability of investment and growth in investment
that drive value; directs strategic thinking to these drivers
Incorporates the
financial
statements:
incorporates the value already recognized in the balance sheet (the
book value); forecasts the income statement and balance sheet
rather than the cash flow statement
Uses accrual
accounting:
uses the properties of accrual 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 loss of value
Versatility:
can be used with a wide variety of accounting principles (Chapter
16)
Aligned with what
people forecast:
analysts forecast earnings (from which forecasted residual
earnings can be calculated)
Validation:
forecasts of residual earnings can be validated in subsequent
audited financial statements
Disadvantages
Accounting
complexity:
requires an understanding of how accrual accounting works
Suspect
accounting:
relies on accounting numbers that can be suspect (Chapter 17)
Forecast horizon:
forecast horizons can be shorter than for DCF analysis and more
value is typically recognized in the immediate future; also,
forecasts up to the horizon give an indication of profitability and
growth for a continuing value calculation; but the forecast horizon
does depend on the quality of the accrual accounting (Chapter 16)
Protection from Paying Too Much for
Earnings Generated by Investment
Invest $50 million in Year 1 with proceeds from a share
issue:
Forecast Year
0
1
2
3
4
5
Earnings
12.00
12.36
17.73
18.61
19.56
20.57
Net dividends
9.09
(40.64)
9.64
9.93
10.23
10.53
100.00
153.00
161.09
169.77
179.10
189.14
2.36
2.43
2.50
2.58
2.66
3%
3%
3%
3%
Book value
RE (10% charge)
RE growth rate
Beware!
V0E  $100 
$2.36

1.10  1.03
$133.71 million.
Protection from Paying Too Much for
Earnings Created by the Accounting:
the Project
Project (1): Write down book value to $360
Book Value
Required Return
Revenue
Earnings
$360
10%
$440
80
($440 – 360)
Earnings have been created
Residual Earnings = 80 – (0.10 x 360)
= 44
Value = 360 + 44
1.10
= 400
The valuation is unchanged.
Beware!
Protection from Paying Too Much for
Earnings Created by the Accounting:
the Simple Example
Writing inventory down by $8 million in Year 0 creates lower
cost-of-goods sold in Year 1:
Forecast Year
0
1
2
3
13.11
13.51
13.91
9.93
10.23
10.53
112.55
115.93
Earnings
4.00
20.36
12.73
Dividends
9.09
9.36
9.64
Book value
92.00
RE (10% charge)
RE growth rate
103.00 106.09
1.16
2.43
109.27
4
2.50
3%
 2.43


11.16 1.10  1.03
= $133.71 million.
V0E  $92 


1
.
10
1.10 



2.58
3%
5
2.66
3%
Beware!
Reverse Engineering the Growth Rate:
A Simple Demonstration
P0  $133.71 = $100  $2.36
1.10  g
g = 1.03
The market is forecasting a growth rate for residual
earnings of 3% per year
Reverse Engineering the Expected
Return: A Simple Demonstration
P0  $147.2 = $100 
RE1
  1.03
RE1 = $12.36 – [(ρ – 1) × 100.0]
Solution: ρ = 1.0936
You expect a 9.36% return from buying the stock at the
current market price.
The formula for ρ is:
P0  B0 Earn1
  1  g  1

P0
P0
Reverse Engineering the S&P 500
S&P 500 Index, beginning of 2005 =1200
S&P 500 P/B ratio = 3.0
S&P 500 ROCE for 2004 = 16%
Required return = Risk-free rate + risk premium
= 4.6% + 5%
= 9.6%
P2004  B2004 
RE 2004 x g
g
(0.16  0.096) x g
$3.0  $1.0 
1.096  g
g  1.062 (6.2% growth rate)