Earnings, Book Values, And Dividends
-
Upload
ivonegluiz -
Category
Documents
-
view
220 -
download
0
Transcript of Earnings, Book Values, And Dividends
-
8/6/2019 Earnings, Book Values, And Dividends
1/16
-
8/6/2019 Earnings, Book Values, And Dividends
2/16
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.
-
8/6/2019 Earnings, Book Values, And Dividends
3/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
4/16
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.
-
8/6/2019 Earnings, Book Values, And Dividends
5/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
6/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
7/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
8/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
9/16
Assume (A3)
satisfies the sthocastic process
(2a)
(2b)
1
~
}{
a
tx
11
~
1
~
++ ++= tta
t
a
vxx
12
~
1
~
++ ++= ttvv
-
8/6/2019 Earnings, Book Values, And Dividends
10/16
(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
-
8/6/2019 Earnings, Book Values, And Dividends
11/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
12/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
13/16
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
-
8/6/2019 Earnings, Book Values, And Dividends
14/16
, ,, ,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
-
8/6/2019 Earnings, Book Values, And Dividends
15/16
, ,, ,Dividends in Equity ValuationDividends in Equity Valuation
((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
+=
-
8/6/2019 Earnings, Book Values, And Dividends
16/16
, ,, ,Dividends in Equity ValuationDividends in Equity Valuation
((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
+=