Earnings, Book Values, And Dividends

8/6/2019 Earnings, Book Values, And Dividends

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Labeling of x, and y, is obviously arbitrary andgratuitous unless the model exploits structuralattributes inherent in accounting. Of interest areat least two closely related attributes. F First, thechange in book value between two dates equalseamings minus dividends, that is, the model

imposes the clean surplus relation. Second,dividends reduce current book value, but notcurrent eamings.


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To formalize these two aspects of owners' equityaccounting, we introduce the following

mathematical restrictions:

yt-1 =yt+ dt xt (A2a)

and

(A2b)

0

1

=

=

t

t

t

t

dx

d

y


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0110

1

+=

+

=

t

t

t

t

t

t

t

t

dx

dd

dy

dy

Though (A2b) does not follow from (A2a), (A2b) isconsistent with (A2a) in the sense that

We distinguish between (A2a) and (A2b) because many

conclusions depend only on (A2a). One can apply theclean surplus relation (A2a) to expressPt, in terms in

terms of future (expected) earnings and book values inlieu of the sequence of dividends in the PVED

formula.


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Define:

earnings and book values in lieu of the sequence of

Using this expression to replace dt+1 ,dt-2 , in the

PVED formula yelds the equation

(1)

1)1( tfta

t yRxx

1+ tftatt yRyxd

][1

~

=

+

+=

a

ttftt xERyP


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provide that

as

We assume that the last regularity condition in

satisfied. That the clean surplus equationimplies equivalence of equation (l) and PVEDhas long been known in the accountingliterature. See, for example, Edwards and Bell

(1961), and Peasnell (I981), (1982).

0][

~

+

f

a

tt

R

xE


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We will refer to as abnormal earnings. Theterminology is motivated by the concept that normal

earnings should relate to the normal retum on the

capital invested at the beginning of the period, that is,netbook value at date t-1 multiplied by the interest rateThus one interprets as eamings minus a charge for

the use of capital.

a

tx

a

tx

A positive indicates a profitable period since the bookrate of return,

exceeds the firms cost of capital,t

t

y

x 1+

.1fR


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Relation (1) has a straightforward and intuitively appealing interpretation: afirm's value equals its book value adjusted for the present value of

anticipated abnormal eamings. In other words, the future profitability asmeasured by the present value of the anticipated abnonnal earnings

sequence sequence reconciles the difference between market and book

values.

While relation (l) may appeal to one's intuition, its equivalence to. PVEDdepends only on relatively trite algebra. As Peasnell (1982) notes, thisformula is peculiar because one interprets it by referring to accountingconcepts, yet the formula works regardless of the accounting principles

that measure book values and eamings. Accounting constructs eyond theclean surplus restriction are irrelevant, and (1) does not even rely on

assumption (A2b). The third and final assumption concemsthe time-seriesbehavior of abnormal earnings. Since any analysis of the valuation

function generally depends critically on various aspects of thisassumption, it demands careful elaboration An analytically simple linear

model formulates the information dynamics. Two variables enter thespecification: abnormal earnings, , and information other than

abnormal earnings, .a

txtv


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Assume (A3)

satisfies the sthocastic process

(2a)

(2b)

1

~

}{

a

tx

11

~

1

~

++ ++= tta

t

a

vxx

12

~

1

~

++ ++= ttvv


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(3)

(4)

(5)

where,

ttf

a

tt dyRxy += 1

t

a

ttftt vxyRxE ++=+ )1(][ 1~

t

t

att vxyP 21 ++=

0))(/(

0)/(

2

1

>=

=

fff

f

RRR

R


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ttttfttt PPRPdP //)1(/)( 12~

211~

11~

1~

++++ +++=+

Straightforward manipulations yield:

(6)

(7)

where

ttttt vykdxkP 2)1()( ++=

)/()1()1()1/(

1

===

fff

ff

RRRkRR

T k h i i l ( l ) b


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To make the point we simply (w.l.o.g) byputting vt=0. As the first special, let

(8)

(9)

(10)

(11)

.1== k

ttt dxP =

~

111

~

)1( +++=

ttftft dRxRx

tt yP =

~

111

~

)1( ++ += ttft yRx

T k h i i l ( l ) b


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To make the point we simply (w.l.o.g) byputting vt=0. As the first special, let

(8)

(9)

(10)

(11)

.1== k

ttt dxP =

~

111

~

)1( +++=

ttftft dRxRx

tt yP =

~

111

~

)1( ++ += ttft yRx


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, ,, ,Dividends in Equity ValuationDividends in Equity Valuation

((OHLSON, 1995)OHLSON, 1995)

As is well-known, PVED and CSR imply the RIV model:o introduce the RIV model, assume the following:

where defines residual (or abnormal) income(eamings). In fact, one can make the slightly strongerstatement that, given the clean surplus relation CSR,

PVED implies RIV, and conversely. This equivalence hasbeen much noted in recent literature, including DHS.

=

+

+=1

~

)(

tttt xERbP

1

tt

a

tr bxx


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((OHLSON, 1995)OHLSON, 1995)

Having established RIV, it appears reasonable that one nextimposes a time-series stochastic process related to residual

income in lieu of dividends. The particularly simple first-orderauto-regressive (AR(1)) process suggests itself. Suppose that

in which case

The derivation that yields (2), given RIV and (1), is of courseelementary.

1

~

1

~

++ + ta

t

a

t xx

a

ttt xR

bP

+=


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((OHLSON, 1995)OHLSON, 1995)The EBD model adds no significant analytical complications. It extends the

simple AR(1) dynamic by introducing information other than current residualincome. Such information influences forecasts of subsequent residualincomes. A scalar variable v, represents "other information", and two

stochastic dynamic equations specify the evolution of :

1

~

1

~

++ + ta

t

a

t xx

a

ttt xR

bP

+=

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Earnings, Book Values, And Dividends