Accrual Accounting and
Valuation: Pricing Book
Values----
Residual Earnings Model
权责发生制与价值评估:
账面价值定价--剩余收益模型
C
h
a
p
t
e
r
5
公司在进行交易时,价格并非是账
面价值。资产负债表中的资产和负债有
的是公允价值,有的是历史成本,还有
一些则被从资产负债表中删除。这就导
致分析家们忽略了从资产负债表中删除
的价值。分析家们会问:到底在账面价
值的基础上增加多少才是固有的价值?
每支股票在交易时基于账面价值的溢价
到底是多少?本章提出的剩余收益模型
解决了分析家们的困惑。
C
h
a
p
t
e
r
5
结
构
P/B
简单模型
剩余收益模型 复杂模型
Equities
剩余收益模型的应用 Prijects
Stategies
剩余收益模型的优点、缺点
剩余收益模型对投资者的提醒
总结
本本
章章
重重
要要
专专
业业
英英
文文
词词
汇汇
• residual earnings or residual income: 剩余收益
• residual earnings model: 剩余收益模型
• premium:溢价
• price-to-book ratio(P/B):市净率
• rate of return on common equity(ROCE): 普通股本
回报率
• terminal investment:终端投资
• going concern investment:持续投资
• withdrawl: 撤回;提款
• forecast horizon:预测期间
• fiscal years:会计年度
• share issue:发行股票
• earnings per share(EPS):每股收益
• dividends per share(DPS):每股股利
• discounted cash flow method(DCF):现金流量折现法
• continuing value(CV): 持续价值
PP
//
BB
rr
aa
tt
ii
oo
P/B 公式:
P/B与剩余收益、剩余收益模型的两个驱动因
素都有密切的联系。同时,提醒投资者:
Beware of paying too much for earnings!
剩余收益模型剩余收益模型((简单简单))
1.什么是剩余收益?
定义:Residual earnings is the earnings in
excess of these required dollar earnings.
公式:
2.剩余收益模型是什么?
定义:A model that measures value added
from forecasts of residual earnings is called
the residual earnings model.
公式:
value=Book value+Premium
=Book value +present value of expected residual earnings.
Example:Example:Valuing a One-Period Project (1)Valuing a One-Period Project (1)
Investment $400
Required return 10%
Revenue forecast $440
Forecasted earnings $ 40
DCF Valuation:
A rate of return of 10 percent on the investment of $400.
EE
xx
aa
mm
pp
ll
ee
::
VV
aa
ll
uu
ii
nn
gg
aa
OO
nn
ee
--
PP
ee
rr
ii
oo
dd
PP
rr
oo
jj
ee
cc
tt
((
22
))
Investment $400
Required return 10%
Revenue forecast $448
Earnings forecast $ 48
A rate of return of 12 percent on the investment of $400.
The project adds value
Example:Example:Valuing a Savings AccountValuing a Savings Account
Forecasts for a Savings Account with $100 invested at the
end of % per year.
Value = Book Value + Present Value of Residual Earnings
= 100 + 0
= 100
TT
hh
ee
NN
oo
rr
mm
aa
ll
PP
rr
ii
cc
ee
--
tt
oo
--
BB
oo
oo
kk
RR
aa
tt
ii
oo
Normal P/B =
(Price = Book Value)
The Normal P/B firm earns an expected rate of return on its
book value equal to the required return
The Normal P/B firm earns expected residual earnings of zero.
LL
ee
ss
ss
oo
nn
ss
ff
rr
oo
mm
tt
hh
ee
SS
aa
vv
ii
nn
gg
ss
AA
cc
cc
oo
uu
nn
tt
从储蓄账户这个例子得到一些准则,这些准则在将要介绍的模型
中也是适用的。
1. An asset is worth a premium or discount to its book value only if the book
value is expected to earn non-zero 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.
EE
xx
aa
mm
pp
ll
ee
::
aa
SS
ii
mm
pp
ll
ee
MM
oo
dd
ee
ll
In millions of dollars. Required return is 10% per year.
Forecast Year
0 1 2 3 4 5
Earnings
Dividends
Book value
RE (10% charge)
RE growth rate 3% 3% 3% 3%
.
$ million
The intrinsic price-to-book ratio (P/B) is $ / $100 = .
剩余收益模型(复杂)剩余收益模型(复杂)
An equity investment is a going concern, and a going
concern goes on indefinitely.
We calculate the intrinsic premium over book
value, ,as the present value of forecasted
residual premium is the missing
value in the balance sheet.
P/B与RE的关系(见下表)
High P/B firms pay high RE,on average,while
low P/B firms pay low RE.
Relation Between P/B Ratios and Subsequent RERelation Between P/B Ratios and Subsequent RE((有问题有问题))
Alternative Measure of Residual EarningsAlternative Measure of Residual Earnings
Residual earnings is the return on common equity,
expressed as a dollar excess return rather than a
ratio. We also restate residual earnings as:
剩剩
余余
收收
益益
模模
型型
的的
驱驱
动动
因因
素素
DD
rr
ii
vv
ee
rr
ss
oo
ff
RR
ee
ss
ii
dd
uu
aa
ll
EE
aa
rr
nn
ii
nn
gg
ss
Two Drivers:
• 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
RE will change with change with ROCE and growth in book value
PP
//
BB
,,
RR
OO
CC
EE
aa
nn
dd
GG
rr
oo
ww
tt
hh
ii
nn
BB
oo
oo
kk
VV
aa
ll
uu
ee
P/B in 2003 ROCE in 2004 Growth Rate for
Book Value in 2004
The Gap Inc. % %
General Electric Co. % %
Verizon Communications Inc. % %
Citigroup Inc. % %
Home Depot Inc. % %
General Motors Corp. % %
Federated Department Stores % %
ROCE is positively related to P/ growth in book value is
also positively related to P/B.
RR
OO
CC
EE
aa
nn
dd
PP
//
BB
RR
aa
tt
ii
oo
ss
::
SS
&&
PP
55
00
00
FF
ii
rr
mm
ss
Ingredients of the ModelIngredients of the Model
1. The current book value
2. Forecasts of residual earnings
3. Forecasted premium at the horizon
Component 3 is called the continuing value.
As efficient prices equal intrinsic values, then
Steps in Applying the ModelSteps in Applying the Model
1. Identify the book value in the most recent balance sheet.
2. Calculate future residual earnings from the forecasts of
earnings and book values.
3. Discount the residual earnings to present value.
4. Calculate a continuing value at the forecast horizon.
5. Discount the continuing value to the present value.
6. Add 1, 3, and 5.
How the Residual Earnings Model Works How the Residual Earnings Model Works
ROCE1
Current
book value ROCE2
Book
value1 ROCE3
Book
value2
Year 3 aheadYear 2 aheadYear 1 ahead
Residual earnings1 Residual earnings2 Residual earnings3
Current
book value
Current year
PV of RE1 Discount by
Forecasts
PV of RE2
PV of RE3
Current
book value
Discount by 3
Discount by 2
Current Data
剩余收益模型的应用剩余收益模型的应用------Equities ------Equities
Case 1: Zero RE after TCase 1: Zero RE after T
Flanigan’s Enterprises Inc. Required rate of return is 9 percent. In this case,residual earnings is
expected to be zero after 2003.
Forecast Year
1999 2000 2001 2002 2003
Eps
Dps
Bps
ROCE % % % %
RE (9% charge)
Discount rate ()
Present value of RE
Total present value of RE to 2003
Value per share
Case 1: Zero RE after TCase 1: Zero RE after T--------Continuing Value Continuing Value
RE is forecasted to be zero in perpetuity at the horizon
So
The forecasted premium at the horizon is
Case 2: Constant RE after TCase 2: Constant RE after T
General Electric rate of return is 10 percent. In this case ,residual earnings is expected to be
constant,but nonzero after that RE beyond 2004 is going to be the same as the in 2004.
Forecast Year
1999 2000 2001 2002 2003 2004
Eps
Dps
Bps
ROCE % % % % %
RE (10% charge)
Discount rate ()
Present value of RE
Total present value of RE to 2004
Continuing value (CV)
Present value of CV
Value per share
The continuing value:
CV = =
Present value of continuing value = =
Assuming constant RE after period T:
RE is forecasted to be constant in perpetuity at the horizon
So
Case 2: Constant RE after TCase 2: Constant RE after T----------Continuing ValueContinuing Value
For GE, CVT =
Case 3: Growing RE after TCase 3: Growing RE after T
Dell Inc. Required rate of return is 11 percent. In this case ,residual earnings is expected to grow at a
percent
rate after 2005. Forecast Year
2000 2001 2002 2003 2004 2005
Eps
Dps
Bps
ROCE % % 2 % % %
RE (11% charge)
Discount rate ()t
Present value of RE
Total present value of RE to 2005
Continuing value (CV)
Present value of CV
Value per share
The continuing value (with growth at %):
CV = =
Present value of continuing value = =
Assuming growing RE after period T :
Case 3: Growing RE after TCase 3: Growing RE after T----------Continuing ValueContinuing Value
RE is forecasted to grow at constant rate in perpetuity at the horizon
So
Forecasting Target Prices
Case 1 (Flannigan’s)
Case 2 (GE)
Case 3 (Dell)
剩余收益模型应用剩余收益模型应用------------Project Project
Value added: PV of RE = 330 (same as NPV)
剩余收益模型应用剩余收益模型应用------------Strategy EvaluationStrategy Evaluation
Residual Earnings Model and DCF Residual Earnings Model and DCF ApproachApproach
(!!!)(!!!)
在前面的例子中,我们看到剩余收益模型计
算的价值与现金流量折现法计算的价值是相同的。
The foercasts of RE have captuerd the value
added over the cost of the investment.
��
剩剩
余余
收收
益益
模模
型型
的的
优优
点点
、、
缺缺
点点
��
AdvantagesAdvantages
• 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)
• 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
• Predictability: dividends are usually fairly stable in
the short run so dividends are easy to forecast (in the
short run)
DisadvantagesDisadvantages
• 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)
剩余收益模型对投资者的提醒:
((11))Protection from Paying Too Much for Earnings Protection from Paying Too Much for Earnings
Generated by InvestmentGenerated by Investment
The firm is expected to make a share issue of $50 in Year 1 .Required return is 10 percent per year.
Forecast Year
0 1 2 3 4 5
Earnings
Net dividends ()
Book value
RE (10% charge)
RE growth rate 3% 3% 3% 3%
$ million.
Beware!
剩余收益模型对投资者的提醒:剩余收益模型对投资者的提醒:
((22))Protection from Paying Too Much for Earnings Protection from Paying Too Much for Earnings
Created by the Accounting: the Simple ExampleCreated 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 4 5
Earnings
Dividends
Book value
RE (10% charge)
RE growth rate 3% 3% 3%
= $ million.
Beware!
剩剩
余余
收收
益益
模模
型型
对对
投投
资资
者者
的的
提提
醒醒
::
��
((
33
))
CC
aa
pp
tt
uu
rr
ii
nn
gg
VV
aa
ll
uu
ee
NN
oo
tt
oo
nn
tt
hh
ee
BB
aa
ll
aa
nn
cc
ee
SS
hh
ee
ee
tt
--
--
--
--
ff
oo
rr
AA
ll
ll
AA
cc
cc
oo
uu
nn
tt
ii
nn
gg
MM
ee
tt
hh
oo
dd
ss
Residual earnings valuation solves the problem of the
imperfect balance sheet,adding a premium by foercasting the
earnings that the book values will higher
residual earnings compensate for the lower book values,to
produce a valuation that corrects the low book value. This
makes sense:If assets are missing from the balance sheet,the
P/B ratio should be higher,and a higher P/B means that
residual earnings are expected to be higher.
剩剩
余余
收收
益益
模模
型型
对对
投投
资资
者者
的的
提提
醒醒
::
��
((
44
))
RR
ee
ss
ii
dd
uu
aa
ll
EE
aa
rr
nn
ii
nn
gg
ss
AA
rr
ee
nn
oo
tt
AA
ff
ff
ee
cc
tt
ee
dd
bb
yy
DD
ii
vv
ii
dd
ee
nn
gg
dd
ss
,,
SS
hh
aa
rr
ee
II
ss
ss
uu
ee
ss
,,
oo
rr
SS
hh
aa
rr
ee
RR
ee
pp
uu
rr
cc
hh
aa
ss
ee
ss
• Valuing a Savings Account
• Protection from Paying Too Much for Earnings Created
by Investment.
这两个例子就说明了这个问题!
SS
uu
mm
mm
aa
rr
yy
本章提出的剩余收益模型可以应用于股票、项目、
战略等。该模型利用了资产负债表中的信息,但它指出
了剩余收益的价值,这是报表所忽略掉的。
剩余收益模型的核心就是剩余收益这个概念。当一
项投资的预期收益是按所要求的回报率计算的,那么剩
余收益为0,并且没有使价值增加。剩余收益不受股利
分配、股票的发行、股票的回购等地影响,所以用该模
型计算的价值不受股东交易的影响。该模型并且提醒投
资不要为了追求收益的增长而支付太多,因为收益的增
长可能是由于过多的投资所致也可能是会计方法的不同
所致。
总之,剩余收益模型给我们提供了一种思考价值的
方法,尤其要关注的是ROCE和 Growth in book
value。
BEWARE OF PAYING TOO MUCH FOR GROWTH!