Employee Stock Option Accounting in a Residual Income Valuation Framework Wayne R. Landsman Kenan-Flagler Business School University of North Carolina at Chapel Hill Chapel Hill, NC 27599 Ken Peasnell Management School Lancaster University Lancaster, LA1 4YX England Peter Pope Management School Lancaster University Lancaster, LA1 4YX England Shu Yeh Department of Accounting National Taiwan University Taipei, Taiwan, R.O.C. September 2003 We are grateful to Jack Ciesielski of R.G. Associates, Inc., for providing employee stock option data used in this study, and to the Center for Finance and Accounting Research, University of North Carolina, and the Financial Services Exchange for providing financial support. Corresponding author: Wayne R. Landsman, Kenan-Flagler Business School, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3490, (919) 962-3221, [email protected]
Transcript
Employee Stock Option Accounting in a Residual Income Valuation
Framework
Wayne R. Landsman Kenan-Flagler Business School
University of North Carolina at Chapel Hill Chapel Hill, NC 27599
Ken Peasnell
Management School Lancaster University Lancaster, LA1 4YX
England
Peter Pope Management School Lancaster University Lancaster, LA1 4YX
England
Shu Yeh Department of Accounting
National Taiwan University Taipei, Taiwan, R.O.C.
September 2003
We are grateful to Jack Ciesielski of R.G. Associates, Inc., for providing employee stock option data used in this study, and to the Center for Finance and Accounting Research, University of North Carolina, and the Financial Services Exchange for providing financial support. Corresponding author: Wayne R. Landsman, Kenan-Flagler Business School, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599-3490, (919) 962-3221, [email protected]
2
Employee Stock Option Accounting in a Residual Income Valuation Framework
Abstract
We use the Ohlson (1995, 1999) valuation framework to compare the extent to which four alternative approaches to accounting for employee stock options (ESOs) that reflect variations of current and proposed accounting standards best capture the economic effects of employee stock options on current equity market value. The ESO accounting methods are APB 25, the FASB’s 1993 Exposure Draft, SFAS 123, and an extension of the IASB’s ED-2. We explicitly model the dilution effects on shareholder value of employee stock options using a dividend discount model and then use the Ohlson residual income framework to derive the implied equity value amounts associated with each ESO accounting method. Findings from the modeling indicate that only the ED-2 extension method results in recognized balance sheet amounts that accurately reflect the economic dilution effects of ESOs on current shareholder equity value by recognizing an ESO asset and liability at grant date, and subsequently recognizing gains and losses on the liability in income. That is, only the ED-2 extension employs super clean surplus accounting, whereby income reflects all gains and losses attributable to existing shareholders. The other accounting methods all result in balance sheet amounts that overstate the value of current shareholder equity. Based on the modeling analysis and employing cross-sectional valuation equations we then test two predictions. First, for the APB 25 and Exposure Draft methods, we predict and find that the equation is better specified, in terms of relative explanatory power, when the estimating equation is adjusted by including option fair value as a regressor, restricting its coefficient to be −1, because a valuation based on equity book value and residual income should equal equity value of current shareholders plus option fair value. Although we have no clear prediction for the SFAS 123 method, we find the similarly adjusted equation is also better specified. We also predict and find that the SFAS 123 estimating equation exhibits lower relative explanatory power than that associated with the adjusted APB 25 and Exposure Draft methods and the ED-2 extension method, although the result only obtains for the ED-2 extension when we permit the change in the ESO liability to have a different coefficient from that on other aggregate income components.
1. Introduction
Current accounting rules for employee stock options (ESOs) for firms filing in the
U.S. are governed by Statement of Financial Accounting Standards No. 123: Accounting for
disclose in footnotes to the financial statements the pro forma effects on earnings of
employee compensation expense attributable to amortizing the fair value of employee stock
options at the grant date.1 If firms were required to recognize ESO expense, Bear Stearns
(Accounting Issues, July 2002) reports that 2001 diluted EPS for S&P 500 including effect of
fair value of ESO grants is 20% lower than reported EPS. The sheer magnitude of this effect
on income, as well as the recent political fallout associated with corporate managers cashing
in on their employee stock options before large price declines, has raised the question of
whether firms should be required to recognize ESO expense to ensure that investors get a true
picture of corporate performance.
The pressure on the FASB in the U.S. to revisit SFAS 123 with a look at mandating
recognition of ESO expense in income is being largely driven by the International
Accounting Standards Board (IASB), who recently issued an exposure draft, ED-2, Share
Based Payment (IASB, 2002) mandating recognition of employee stock option expense using
grant date fair value. Although there are some minor differences between ED-2 and SFAS
123, the key point is that all European Union firms would be required to expense employee
stock options using grant date fair value if, as is likely to be the case, the ED is adopted as a
standard.
Corporate preparers, particularly those in high tech industries that use stock options as
a major component of their compensation packages, are not keen on the requirement to
1 SFAS 123 permits firms to use Accounting Principles Board Opinion 25: Accounting for Stock Issued to Employees (AICPA 1972, hereafter APB 25), which allows firms to avoid recognizing employee stock compensation expense if the options that are granted have a zero intrinsic value at the date of grant.
2
expense ESOs. They raise two potentially valid criticisms. First, firms that issue stock
options to their employees do so because they get something in return, an intangible asset, in
the form of the employees’ intellectual capital, that is not recognized under SFAS 123 nor
ED-2. The FASB acknowledged this in their exposure draft that preceded SFAS 123,
Exposure Draft: Accounting for Stock-Based Compensation (FASB, 1993, hereafter,
Exposure Draft). The Exposure Draft would have required employers to recognize as an
intangible asset the fair value of stock options at the grant date, to amortize this asset, and to
record the asset’s amortization as employee compensation expense. Second, the total
compensation expense recognized using grant date ESO fair value may bear no relation to the
firm’s total economic debt to its employees at date of exercise. Thus, accounting that treats
the firm’s obligation to its employees as an offsetting liability to the intangible asset at grant
date, and includes the effects of changes in the firm’s obligation to employees after grant date
better captures the economic impact of ESOs on the firms’ equity-holders. Although
marking-to-market this obligation appears to be at odds with the ways in which other
liabilities are treated in financial statements, this is exactly the way the IASB and FASB
propose to treat the liability when settlement takes the form of cash rather than the issuance
of stock. It is also commonplace in accounting to regularly update the amounts shown for
long-term liabilities, such as site restoration costs.
The purpose of this study is to use the Ohlson (1995, 1999) valuation framework to
compare the extent to which the various approaches to accounting for employee stock options
best reflect the economic effects of employee stock options on current equity market value.
We do this in two steps. First, we explicitly model the dilution effects on shareholder value
of employee stock options using a dividend discount model. Then, using the Ohlson residual
income framework, we derive the implied equity value amounts associated with four ESO
accounting methods that reflect variations of current and proposed accounting standards, viz.
3
APB 25, SFAS 123, the Exposure Draft, and an extension of ED-2 (hereafter the ED-2
extension) that recognizes changes in the fair value of firm’s obligation to employees after
grant date.
Findings from the modeling analysis indicate that only the ED-2 extension results in
recognized balance sheet amounts that accurately reflect the economic dilution effects of
ESOs on current shareholder equity value. The reason for this result is that of the four
methods, only the ED-2 extension adopts what Christensen and Feltham (2003, ch. 9) refer to
as “super clean surplus accounting,” whereby income reflects all gains and losses attributable
to existing shareholders. The findings also indicate that the APB 25 and Exposure Draft result
in balance sheet amounts that overstate the value of current shareholder equity value. In
particular, these two methods result in balance sheet measures that reflect the sum of current
equity market value and the value of the stock options granted to employees. Although both
methods satisfy “clean surplus” in that all gains and losses arising from transactions not
involving equity claimants pass through income, Christensen and Feltham label these
methods as “mixed surplus” accounting because the accounting amounts reflect the value of
the claims of existing and future equity holders. Finally, we find that the SFAS 123
accounting method results in balance sheet amounts that also overstate the equity value of
existing shareholders, although the overstatement is less than that associated with the APB 25
and the Exposure Draft. The reason for this is that the SFAS 123 accounting method is
neither super-clean nor mixed.
We test the empirical validity of our residual income valuation models by estimating
two separate cross-sectional equity valuation models relating to each accounting method in
which equity book value and residual income are adjusted to reflect the accounting treatment
applicable to each of the four methods. Both equations within each pair have equity market
value as the dependent variable, but the second “adjusted” equation includes option fair value
4
as an explanatory variable with the restriction that its coefficient equals negative one. The
effect of this restriction is to restate the dependent variable as the sum of equity market value
and option fair value. Based on our modeling, we make two predictions. First, for the APB
25 and Exposure Draft methods, we predict that the adjusted equation will be better specified
than the unadjusted model—i.e., the one that excludes option fair value—because a valuation
based on equity book value and residual income should equal equity value of current
shareholders plus option fair value. We cannot make a similar prediction for the SFAS 123
method, because a valuation based on equity book value and residual income should equal
equity value of current shareholders plus a fraction of option value. Finally, because a
valuation based on equity book value and residual income should equal equity value of
current shareholders under the ED-2 extension method, there is no reason to expect the
adjusted equation will be better specified than the unadjusted equation. We test our
predictions by assessing each model’s relative goodness-of-fit using the Vuong (1989) Chi-
square test.
Second, we predict that the estimating equation based on SFAS 123 equity book value
and residual income amounts should be dominated by each of the other three models,
appropriately adjusted to reflect whether option fair value should be included as an implicit
addition to equity market value. This prediction is based on the observation in our residual
income valuation modeling which shows that the gradual recognition of equity under SFAS
123 gives rise to measures of equity book value and residual income that equal neither equity
market value nor the sum of equity market value an option fair value.
We test our predictions using a sample of S&P 500 firms with available data from
1996-2001, and estimate annual cross-sectional valuation models and pooled models with
year fixed-effects. We estimate option fair value using the Black-Scholes option pricing
formula. However, because of the endogeneity problem arising from regressing stock prices
5
on option fair values (Aboody, 1996), we estimate our option fair value measure using an
instrument for equity market value constructed from a two-stage regression. The results
from our tests are consistent with our predictions. In particular, we find that the adjusted
estimating equations are better specified than the unadjusted ones for the APB 25 and
Exposure Draft models, but there is no difference in relative explanatory power between the
adjusted and unadjusted ED-2 extension estimating equations. In addition, the SFAS 123
estimating equation exhibits less relative explanatory power than those associated with the
other three methods.2
The remainder of this paper is organized as follows. Section 2 derives how the four
different methods of accounting for employee stock options affect the relation between
market values and future accounting numbers. Section 3 describes the empirical estimating
equations, section 4 discusses sample data, and section 5 presents the empirical findings.
Section 6 summarizes and concludes the study.
2. Accounting for ESOs
There are at least four ways of accounting for ESOs:3
1. APB 25 method: ignore it, i.e. measure at intrinsic value. If the option is exercised, “paid-
in capital” is credited with the cash received.
2. SFAS 123 method: credit “paid-in capital – employee stock options” (PIC – options) as
and when ESO expense is recognized. Add the balance on this account to the cash
2 In a related study, Li (2002) also models the dilution effects of employee stock options, and provides empirical evidence that the fair value of outstanding ESOs is negatively associated with equity market value. However, the paper does not address how current and proposed ESO accounting methods reflect ESO dilution effects. In another related study, Li and Wong (2003) estimate equity valuation equations, including an estimate of ESO fair value as a regressor in addition to equity book value and residual income, each of which is based on reported book amounts. The study finds that equity market value reflects the dilution of ESOs, providing evidence that investors take into account that such options dilute the claim to future dividends of current shareholders. However, as with Li (2002), Li and Wong (2003) does not address accounting for the effects of ESO dilution. 3 Most ESOs are granted at-the-money. What follows ignores the issue of whether the options have an exercise price that is different to the market value of the underlying shares at grant date since incorporating this possibility merely complicates the analysis without adding anything significant.
6
received and include in paid-in capital as when the option is exercised. If not exercised,
leave balance on PIC – options as a dirty surplus component of equity.
3. 1993 FASB ED rejected method: recognize asset at grant date equal to the fair value of
the ESO and amortize over the vesting period as ESO expense. PIC – options is set equal
to the value shown for the asset (pre-paid compensation) and left unchanged thereafter.
As with the SFAS 123 method, the balance on PIC – options is added to the cash received
and included in paid-in capital as and when the option is exercised and if not exercised
left as a component of equity.
4. Options as a liability method: as under method 3, recognize asset and amortize it but treat
the recognized fair value of the option as a liability. Mark-to-market the liability with the
value adjustments being included in income. If the option is exercised, the value of the
option plus the cash proceeds will equal the fair value of the equity issued to employees.
Either way, the liability will be extinguished.
Methods 1 and 4 conform with “clean surplus” in that all gains and losses pass through
income. Method 1 is an example of what Christensen and Feltham (2003, ch. 9) label “mixed
surplus” accounting. Method 4 is accounted for on what they call a “super-clean surplus”
basis. Income reflects all gains and losses attributable to existing shareholders. Methods 2 and
3 appear to contain an element of “dirty surplus” accounting absent from methods 1 and 4,
since if the options are not exercised, a gain to existing shareholders bypasses income.
There are several implications for the residual income model of the different ways of
accounting for ESOs. The impact, in methods 3 and 4, of the recognition of an asset that is
subsequently amortized is straightforward. Ignoring for the moment the treatment of the
associated credit entry, the recognition of the pre-paid compensation asset simply changes the
balance between current book value and future residual income. All we need to ensure, as is
7
done in Bell, Landsman, Miller and Yeh (2002), is that the two components are treated
consistently.
Under method 4, the credit arising from recognition of the asset at grant is treated as a
liability account, meaning that the book value of equity at that date is the same as under
method 1, where nothing is recognized. The difference between the two methods appears in
the streams of future residual incomes and (we shall see) in their resultant present values.
Methods 2 and 3, on the other hand, treat the option account as a form of paid-in capital. The
only difference between the two methods is that the “equity” builds up slowly under method
2 (with nothing being recognized at grant date) whereas it is all recognized at grant date
under method 3. Therefore, the book value of equity differs at grant date from the book value
under methods 1 and 4, reflecting the fact that future incomes are to be shared between
existing and new (i.e. option holding) shareholders. Under certain (no-exercise) states of
nature, gains will arise to existing shareholders that will not be recognized until the firm is
dissolved.
2.1 Example
To gain further insight, it is helpful to consider a very simple three-period scenario. A
firm issues an ESO at time 1 exercisable after two periods on payment of X. No new
information appears in period 1.4 At time 1, the existing shareholders get all of the (certain)
dividend ( 11 dd e = ). At time 2, the state of nature is revealed. Payoffs in period 3 are
conditional on the state of nature at time 2 and the firm is liquidated at time 3. As in period 1,
the existing shareholders get all the dividends in period 2 ( ses dd 22 = ), regardless of whether
the state is “good” (s = g) or “bad” (s = b). If s = g, the option is exercised because the
present value of the new shares exceeds the strike price: .2 XMV ng > In that case, existing
4 This extra period is included in the model simply in order to have two periods over which option expense can be charged in methods 2-4.
8
shareholders would receive egd3 in period 3 and the new shareholders would get n
gd3 such that
ng
egg ddd 333 += . Conversely, if s = b, the option would lapse unexercised because the new
shares would be worth less than the employees would have to pay for them: .2 XMV nb < In
that case, the existing shareholders would get all the dividends in period 2: .33 beb dd = All
agree that the probability of a good state at t = 2 is p and of a bad one is 1−p. We assume that
employees and investors alike are risk-neutral. All expectations of dividends are after
incorporation of incentive effects arising from the compensation contract.5
The fair value of the ESO at t = 0 is
+−
+=
+
−= 23
32
20 )1()1()1(
)(
rX
r
dp
r
XMVpOPV
ng
ng (1)
where r is the riskless rate of interest.6 The market value of existing shares can be therefore
be written as
+
++
−+
+
−+
++
+=
+−
++
++
=
++
++
+=
33
22
333
221
3330
2201
330
2201
0
)1()1()1(
)1()1(1
)1(][
)1(][
1
)1(][
)1(][
1
rd
rdp
rdd
rd
pr
d
rddE
rdE
rd
rdE
rdE
rdMV
bbnggg
n
eeee
(2)
Making use of (1), (2) can be re-arranged and redefined in terms of dividends accruing to
current and future shareholders adjusted for the expected market value of any shares
subsequently issued to employees (the dilution effect):
5 The simple three period model ignores the effects of options that might be granted in future periods. Such complications are ignored since consideration of these potential effects adds no obvious valuation or accounting insights and cannot be modeled empirically. In particular, in contrast to Li (2002) and Li and Wong (2003), we treat future option grants as an unmodeled source of “other information” in the empirical analysis, since all estimating equations based on the different accounting treatments of ESOs are similarly affected by this omitted variable.
9
330
220201
0 )1(][
)1(][][
1 rdE
rMVEdE
rd
MVn
e
++
+−
++
= (3)
where .][ 220ng
n pMVMVE = Consistent with Christensen and Feltham, the period 2 net
dividends is arrived at after deducting the fair value of any new shares expected to be issued
in the future, not the cash proceeds, X, received by the firm from the exercise of options. A
price per share can be computed by dividing by current shares in issue, without any
adjustment for the existence of potentially dilutive securities. This is important when working
with super-clean surplus residual incomes.
A measure of equity value can also be derived that mixes together the claims of
existing and future shareholders:
.)1(][
)1(][)1(][
1
)1(][
)1(][
1
00
330
220
20201
330
2201
0
OPVMVrdE
rMVErOPVdE
rd
rdE
rXdE
rdMV
e
n
m
+=
++
+−++
++
=
++
+−
++
=
(4)
Equations (3) and (4) reveal that the way future dilution is measured affects
directly the valuation of current claims. Furthermore, identifying the appropriate net dividend
stream is central to the choice of a suitable residual income concept. The direct method of
valuing existing shares requires subsequent share issues to third parties (in this case,
employees) to be measured at fair value. The indirect method does not distinguish between
the value of equity in issue and possible new shareholders in the future. Any such share
issues are therefore measured at the resources flowing to the enterprise at time of issue.
These two bases correspond to the super-clean and mixed bases for accounting purposes.
6 The assumption of risk neutrality is made simply to avoid having to specify risk-neutral probabilities, with the problems they entail for empirical work.
10
2.2 Residual Income Valuation
Let itsBV represent the book value of equity using method i at time t under state s.7
Under methods 2, 3 and 4, option expense will be based on the fair value of the option at
grant date ( 0OPV ), to be spread over the two-year vesting period, with 0OPVδ to be charged
in period 1 and 0)1( OPVδ− in period 2. No asset or option credit is initially recognized at
time 0 under method 2, whereas it is under methods 3 and 4. The amount initially recognized
as asset value under methods 3 and 4 equals ,0OPV with the corresponding credit treated as
equity under method 3 and as a liability under method 4.
Method 1
Net incomes with this (base-case) method are:
).,(
)(
123
13
11
122
12
11
122
12
10
111
11
bgsBVdNI
BVBVdNI
BVBVXdNI
BVBVdNI
sss
bbb
ggg
=−=
−+=
−+−=
−+=
(5)
The value obtained by converting these incomes to residual incomes, 10
11
11 rBVNIRI −= and
1,1
11sttsts rBVNIRI −−= , and discounting is
7 The state subscript is suppressed in what follows either when only one state can occur or when dealing with probability-weighted expectations.
11
.)1()1(
)1(
)1()1(1
)1()1()1(
)1()1(1
3
12
13
2
11
12
3
12
13
2
11
12
10
111
0
3
13
2
12
3
13
2
12
111
01
0
+−
++−
−
+
+
−+
+
−+
+−
+=
+
++
−+
++
++
++=
rrBVNI
rrBVNIp
rrBVNI
rrBVNI
prrBVNIBV
rRI
rRIp
rRI
rRI
pr
RIBVMV
bbb
ggg
bbgg
(6)
Substituting (5) into (6), canceling and collecting terms yields:
330
22011
0 )1(][
)1(][
1 rdE
rXdE
rdMV
++
+−
++
= , (7)
which is exactly the same value obtained using the mixed surplus dividend model given by
equation (4):
.00010 OPVMVMVMV em +== (8)
Since 0OPV must be positive, the use of method 1 will result in an over-estimate of the value
of current equity.
Method 2
The initial book value of equity under method 2 is the same as under method 1:
.10
20 BVBV = Method 2 net income contains a charge for option expense in the first two
periods, but it is the same in period 3, regardless of the state:
.
)1(13
23
012
22
011
21
ss
ss
NINI
OPVNINI
OPVNINI
=
−−=
−=
δ
δ
(9)
However, since the credit associated with the option expense is included in paid-in capital,
the two entries cancel and the equity book value under method 2 is always the same as equity
book value under method 1: 11
21 BVBV = and 12
tsts BVBV = (t = 2,3; s = g,b). This means that
the capital charge levied to arrive at residual income is the same under the two methods. It
therefore follows that method 2 residual incomes will be less than their method 1 counterparts
12
by an amount equal to the option expense: 011
21 OPVRIRI δ−= and
.)1( 012
22 OPVRIRI ss δδ−−= The residual income-based value obtained by method 2 must
therefore equal
.)1(
11
)1(1
11
)1(1
1
020
020
021
02
0
OPVrrMV
OPVrr
MV
OPVrr
MVMV
e
e
++
−+=
+−
−+
−+=
+−
++
−=
δ
δδ
δδ
(10)
Method 2 recognizes option equity slowly, as a by-product of recognizing option
expense. The result is a measure of equity value that is neither super-clean nor mixed. For
,0=r ,02
0eMVMV = i.e., the equity value per model 2 equals that of current equity holders.
For ,0>r .02
0eMVMV > Moreover, for any feasible amortization rate, ,10 ≤< δ 2
0MV is
closer to eMV0 than to 00 OPVMV e + since
r
r 1)1( 2
2
1−+
>δ .
Method 3
Net incomes are the same as under method 2: ;21
31 NINI = 23
tsts NINI = (t = 2,3; s = g,b). On
the other hand, the recognition of an asset immediately gives rise to a credit that is treated as
equity under method 3 such that
.0100
20
30 OPVBVOPVBVBV +=+=
At time 1, the extra opening equity is reduced by the additional period expense to give
.)1( 01
13
1 OPVBVBV δ−+=
13
At time 2, a further amortization charge will have ensured that ,12
32 ss BVBV = regardless of
the state of nature. In other words, all the additional option equity, ,0OPV recognized at the
outset will by now have been completely offset through the completion of the amortization of
the corresponding asset. The residual income stream will incorporate both the amortization
charges and the extra (but diminishing) equity. In period 1, the full effects are felt:
.)(
)(
011
01
0011
30
31
31
OPVrRI
OPVBVrOPVNI
rBVNIRI
+−=
+−−=
−=
δ
δ (11a)
In period 2, the capital charge diminishes regardless of the state of nature (s = g,b):
.)1)(1(
])1([)1(
012
01
1012
31
32
32
OPVrRI
OPVBVrOPVNI
rBVNIRI
s
s
ss
δ
δδ
−+−=
−+−−−=
−=
(11b)
Finally, in period 3 there are no additional expenses and the capital charge is the same as
under method 1 (regardless of state):
.13
10
13
32
33
33
s
s
sss
RI
rBVNI
rBVNIRI
=
−=
−=
(11c)
Putting this altogether, we have:
.)1(
][)1(
])1)(1([1
])([)(
)1(][
)1(][
1
3
130
20
120
0110
01
0
3
330
2
320
313
03
0
rRIE
rOPVrRIE
rOPVrRIE
OPVBV
rRIE
rRIE
rRIBVMV
++
+−+−
+
++−
++=
++
++
++=
δ
δ (12)
Collecting terms, we have:
14
.
)1()1)(1(
11
00
10
0210
30
OPVMV
MV
OPVr
rrrMVMV
e +=
=
+−+
−++
−+=δδ
(13)
The result is the same as with method 1. Method 3 provides an over-estimate of the value of
existing equity.
Method 4
Under method 4, an asset is recognized immediately but the associated credit is
treated as debt. Opening equity is therefore the same as it is under method 1: .10
40 BVBV =
The asset is amortized in the same way as under method 3. However, there are two
differences in the way incomes are calculated: net income contains gains and losses on
marking-to-market the option liability; and since accumulated prior valuation adjustments are
included in beginning-of-period equity, capital charges differ accordingly. After 1 period, no
uncertainty has been resolved and the option is now worth ),1(01 rOPVOPV += resulting in
01 rOPVOPV =∆ being charged to income. In the next period, if the good state occurs, the
option will increase in value to ,22 XMVOPV ngg −= the option will be exercised and there
will be a further charge of .122 OPVXMVOPV ngg −−=∆ In the bad state, the option will
lapse unexercised and a gain will be recorded of .12 OPVOPV b =∆
Combining these amortization charges and fair value adjustments,8 the residual
income in the first period is:
.)( 011
1011
41
OPVrRI
OPVOPVRIRI
+−=
∆−−=
δ
δ (14)
15
If the good state follows, the method 4 residual income contains an amortization charge, a
gain in the value of the option liability and an adjustment to the capital charge to in period 2:
).())(1(
)()1(
2012
02012
42
XMVOPVrrRI
OPVrrOPVOPVRIRIngg
ggg
−−+++=
++∆−−−=
δ
δδ (15)
The book value of equity at the beginning of (good) period 3 includes option expenses and
pricing adjustments from the two previous periods, plus the new share capital that has been
issued (recorded at market value):
.
][][
])1([
12
221
0012
42
g
ngg
gg
BV
XMVOPVOPV
OPVOPVBVBV
=
−+∆+∆−
−+−= δδ
(16)
The final period residual income is therefore unchanged: .13
43 gg RIRI = If the bad state
occurs, period 2 residual income will be:
.))(1(
)()1(
012
02012
42
OPVrrRI
OPVrrOPVOPVRIRI
b
bbb
+++=
++∆+−−=
δ
δδ (17)
Again, .13
43 bb RIRI =
As with the other cases, we can define method 4 value by reference to method 1
value:
.)1())(1(
)1(
)1(
)())(1(1
)(
20
220
010
40
+
++−+
+
−−+++
++
−=
rOPVrr
p
r
XMVOPVrrp
rOPVr
MVMV
ng
δ
δ
δ
(18)
Using (1), this simplifies to
8 Since opening equity is the same as under method 1, there is no incremental capital charge in period 1.
16
.0
010
40
eMV
OPVMVMV
=
−= (19)
Method 4 is the only one that provides an unbiased estimate of the value of existing
equity. Equity is recognized if (and only if) new shares are issued, and these are then
recorded in the books at market value. Such super-clean accounting guarantees that residual
income is on a “proprietary” basis relevant to the valuation of shares in issue.9
3. Empirical Specification and Predictions
3.1 Estimating Equations
The residual income valuation models in section 2 suggest that for models 1 and 3,
equity market valuation equations based solely on equity book value and residual income
applicable to each method will be incorrectly specified unless an estimate of the option fair
value is added to equity market value. The adjustment for method 2 is more complex, since a
valuation based on equity book value and residual income should equal equity market value
and a fraction of option value, rendering it difficult to make any clear prediction. Because a
valuation based on equity book value and residual income should equal equity market value
under method 4, no adjustment should be necessary.
To test these predictions, we estimate the following four pairs of equations, and
compare the relative explanatory power of each set of regressors based on the Vuong (1989)
likelihood ratio test, which permits comparison of the explanatory power of two alternative
9 An interesting aside is that our modeling provides a clear answer to the question of how best to reflect the dilution effects of potential shareholders in the computation of earnings per share, EPS. Procedures that reject super clean surplus accounting for ESOs in favor of mixed surplus accounting will misstate diluted EPS unless adjustments are made to the denominator so that it reflects the fair value of options outstanding. In particular, EPS computed using methods 1 and 3 will equal EPS computed using method 4 only by setting the denominator equal to the number of existing shares plus a multiple, φ , times the maximum number of potential new shares arising from exercise of ESOs outstanding. By comparing equations (13) and (19), it is straightforward to show that the additional shares, mφ , must equal neMVOPV )0/0( , where n is the number of existing shares, and m is the number of possible new shares. Current GAAP accounting for EPS makes an adjustment based on option intrinsic values instead of their fair values. As a result, EPS fully diluted will be biased upwards. Core, Guay, and Kothari (2002) make a similar observation. The same basic observation applies to method 2, except that the function for the additional new shares is more complicated in that it is based on the rate at which ESOs are amortized.
17
non-nested models without assuming under the null that either model is the correct model.
Following the standard Ohlson framework, each estimating equation includes a measure of
equity book value and current period residual income applicable to each method of
accounting for ESOs.10
For model 1, that based on accounting for ESOs under APB 25, we have:
112
110 itititit BVRIMVE εααα +++= (20)
'112
110 ititititit OPVBVRIMVE εααα +−++= ( 02 ′ )
where 1itRI is abnormal earnings under model 1 and equals NI rBVEt t− −1 ; itNI equals net
income before extraordinary items and discontinued operations for fiscal year t;11 itBVE is the
book value of common equity at the end of fiscal year t; itMVE is the market value of
common shares outstanding at the end of fiscal year t; itOPV is an estimate of ESO option fair
value (described below) at the end of fiscal year t; and 1itε and '1
itε are error terms; and the i
and t subscripts denote firms and years, respectively.12 Following Dechow et al. (1999),
Barth, Beaver, Hand, and Landsman (1999), and Bell, Landsman, Miller, and Yeh (2002), we
set the expected rate of return on book value of common equity, r, at 12 percent, the long-
term return on equities, in these and all subsequent valuation equations. The error terms
reflect other information as well as random error. For ease of exposition, we use the same
notation for coefficients across alternative pairs of valuation equations. Note that by
10 Our primary concern is with the relative explanatory power of regressors associated with different methods of accounting for ESOs Although we expect the equity book value and residual income coefficients to be positive, we make no predictions regarding the magnitudes of their coefficients across the various specifications. 11 Bell, Landsman, Miller, and Yeh (2002) point out that although defining residual income based on net income before extraordinary items and discontinued operations violates the clean surplus assumption in Ohlson (1995), it eliminates potentially confounding effects of large one-time items and is consistent with prior empirical research (e.g., Barth et al. 1999, 2000; Dechow et al. 1999; Hand and Landsman, 2000). Ohlson (1999, 160) concludes that this approach is justified in empirical work because one-time items are likely to have limited forecasting ability. 12 Following prior research (e.g., Barth, Beaver, Hand, and Landsman, 1999), each valuation equation we consider includes intercepts and error terms to allow for the valuation effects of unmodeled other information.
18
restricting the coefficient on OPV to be −1 in equation ( 02 ′ ), the dependent variable in that
equation is implicitly the sum of MVE and OPV. Based on the residual income valuation in
section 2.2, we predict that equation ( 02 ′ ) will be better specified than equation (20) because
a valuation based on equity book value and residual income should equal equity value of
current shareholders plus option fair value.
For model 2, which is based on the SFAS 123 method of accounting for ESOs, we
have:
222
210 itititit BVRIMVE εααα +++= (21)
,'222
210 ititititit OPVBVRIMVE εααα +−++= ( 12 ′ )
where 12tt BVBV = and ttt NSEOPTIONEXPERIRI −= 12 . Similar to other earnings
components, OPTIONEXPENSEt is an after-tax measure of ESO expenses, measured as
tNI less after-tax SFAS 123 Pro Forma Earnings, which is taken from the SFAS 123
disclosures. tNSEOPTIONEXPE corresponds to 0OPVtδ in equation (10). As in equation
( 02 ′ ), the coefficient on OPV is restricted to be −1 in equation ( 12 ′ ), and the dependent
variable in that equation is implicitly the sum of MVE and OPV. Based on the residual
income valuation in section 2.2, we hesitate to predict whether equation ( 12 ′ ) will be better
specified than equation (21).
For model 3, which is based on the FASB Exposure Draft, we have,
332
310 itititit BVRIMVE εααα +++= (22)
'332
310 ititititit OPVBVRIMVE εααα +−++= ( 22 ′ )
where
,1
13ts
t
stt TYOPTIONEQUINSEOPTIONEXPEBVBV +∑−=
=
).(1
11
13s
t
stttt NSEOPTIONEXPETYOPTIONEQUIrNSEOPTIONEXPERIRI
−
=− ∑−−−=
19
∑=
t
stNSEOPTIONEXPE
1is the accumulated amortizations of the ESO asset at time t and
)(1
11 s
t
st NSEOPTIONEXPETYOPTIONEQUIr
−
=− ∑− is the additional capital charge arising from
amortizing the ESO asset. tTYOPTIONEQUI is the sum of amounts credited to equity as of
time t resulting from ESO grants. Note that TYOPTIONEQUI is fixed at date of grant and is
therefore measured at historical cost, whereas OPV is marked-to-market every accounting
period. As in equation ( 02 ′ ), the coefficient on OPV is restricted to be −1 in equation ( 22 ′ ),
and the dependent variable in that equation is implicitly the sum of MVE and OPV. Based on
the residual income valuation in section 2.2, we predict that equation ( 22 ′ ) will be better
specified than equation (22) because a valuation based on equity book value and residual
income should equal equity value of current shareholders plus option fair value.
Finally, for model 4, which is based on the ED-2 extension method of accounting for
ESOs, we have,
442
410 itititit BVRIMVE εααα +++= (23)
'442
410 ititititit OPVBVRIMVE εααα +−++= ( 32 ′ )
where
)__(
)(
1
111
14
s
t
ss
ss
t
ss
t
stt
EXERCISEDOPTIONSESOFV
OPTIONLIABOPTIONLIABNSEOPTIONEXPEBVBV
×
+−−∑−=
∑
Σ
=
−==
and
)( 114
−−−−= ttttt OPTIONLIABOPTIONLIABNSEOPTIONEXPERIRI
)]([ 1
1
1
1
1−
−
=
−
=−−∑− Σ ss
t
ss
t
sOPTIONLIABOPTIONLIABNSEOPTIONEXPEr ,
20
tOPTIONLIAB is the sum of amounts recognized as liabilities as of time t resulting from
ESO grants. Note that OPTIONLIAB is simply OPV; we adopt the convention of referring to
it as a liability to reinforce the notion that under the ED-2 extension method, the credit at
grant date is to a liability account, and the liability is then marked-to-market. The amount
sOPTIONLIAB 1−− sOPTIONLIAB is a gain or loss item resulting from changes in the fair
values of ESO liability subsequent to the grant date. sESOFV _ is the weighted average fair
value of ESOs exercised at time s, and sEXERCISEDOPTIONS _ is the number of ESOs
exercised at time s. When ESOs are exercised, equity book value under Method 4 increases
by fair market value of the shares issued, which equals the balance of OPTIONLIAB and the
cash received (which is already included in method 1 equity book value). In contrast to the
first three models, including OPV as on an explanatory variable in equation ( 32 ′ ) should not
improve upon the correct residual income specification given by equation (23). In fact, it
may worsen things by adding noise to the estimating equations. Thus, we predict no
difference in model explanatory power between equations (23) and ( 32 ′ ).
It is important to note that
ttt OPTIONLIABBVBV −= 34 . (24)
This follows because, prior to exercise, tOPTIONLIAB and tTYOPTIONEQUI differ by the
amount of the sum of the changes in tOPTIONLIAB that are included in income under
Method 4; when ESOs are exercised or expire, tOPTIONLIAB is closed into book equity and
equation (24) still holds. Thus, equation (24) permits measurement of equity book value
under Method 4 without having to calculate all of its components, particularly the number of
options exercised or expired.
In addition to the pairwise comparisons of the estimating equations corresponding to
each of the four methods for accounting for ESOs, we make the further prediction that the
21
estimating equation based on SFAS 123 should be dominated by each of the other three
methods, appropriately adjusted to reflect whether option fair value should be included as an
implicit addition to the dependent variable, MVE. This prediction is based on the observation
in our residual income valuation modeling which shows that the gradual recognition of equity
under SFAS 123 gives rise to measures of equity book value and residual income that equal
neither MVE nor MVE plus OPV. Thus, we also predict that equations ( 02 ′ ), ( 22 ′ ), and (23)
will each be better specified than either equation associated with model 2, equations (21) and
( 12 ′ ).
We estimate cross-sectional regressions for equations (20) through (23) for 1997
through 2001, as well as pooled regressions for each equation using year fixed-effects. We
report regression t-statistics using White- (1980) corrected standard errors and consider t-
statistics with associated two-sided p-values less than 0.05 as statistically significant. We do
not report constants from either the pooled fixed-effects or the annual regressions. All
equations are estimated using unscaled data (Barth and Kallapur (1996)).13
3.2 Measurement issues
Unlike NSEOPTIONEXPE , which can be deduced as the net of reported net income
and SFAS 123 pro forma net income, the other option value-based variables,
)(OPTIONLIABOPV and TYOPTIONEQUI , must be estimated. tTYOPTIONEQUI is the
sum of grant date ESO fair values, which is computed as the accumulation since 1995 of the
number of ESOs granted in each year multiplied by the weighted-average fair value per share
at grant date. A complication is that SFAS 123 pro forma ESO expenses and related
13 Although Barth and Kallapur (1996) provide convincing reasons to estimate cross-sectional equity valuation models similar to ours using unscaled data, there are several additional reasons to avoid estimating our equations on a per share basis. First, our theoretical analysis suggests that equations using different accounting methods for ESOs require different share amounts as scalars. This would amount to throwing away the baby with the bath water in that we could no longer carry out any meaningful tests of the valuation effects of different methods of accounting for ESOs. Second, as noted in footnote 9, deflation for all but method 4 would require estimating additional shares relating to ESOs based on OPV. This would needlessly introduce the potential of additional measurement error in the affected models.
22
disclosures are based on ESOs granted from 1995 and forward but the disclosures do not
provide separate totals for the number of options outstanding arising from grants before and
after 1995. Because we estimate the option value-based variables using the total number of
options granted and outstanding as of a particular balance sheet date, there is an inconsistency
between measurement of the income statement variable, NSEOPTIONEXPE , and the
measurement of equity book value under Methods and 4.14
We use the Black-Scholes (1973) option pricing model to estimate fair value of ESOs
outstanding at each balance sheet date so that we can construct )(OPTIONLIABOPV using
disclosed parameter amounts taken from the SFAS 123 disclosures. The related parameters
we use are:
1. Exercise price of the option: the current year’s weighted exercise price for all
outstanding ESOs.
2. Expected stock-return volatility: reported expected stock-return volatility for options
issued in the current year, taken from the SFAS 123 disclosures.
3. Risk-free interest rate: reported risk-free interest rate for options issued in the current
year, taken from the SFAS 123 disclosures.
4. Expected dividend yield: reported expected dividend yield for options issued in the
current year, taken from SFAS 123 disclosures.
14 There are two additional inconsistencies in the measurement of equity book value and residual income for all but Methods 1 and 2. The first arises from the fact that NSEOPTIONEXPE is on an after-tax basis, and we ignore income effects in our measurement of equity book value under Methods 3 and 4. In principle, equity book value under these two methods should reflect accumulated the same before-tax NSEOPTIONEXPE charge. The second is that NSEOPTIONEXPE reflects adjustments for anticipated forfeitures, but book equity under Methods 3 and 4 cannot be adjusted appropriately because we do not have details of the forfeitures. We do not expect these sources of measurement error to have a material affects on inferences concerning the validity of our predictions because all the relevant models are affected similarly.
23
5. Time to maturity: reported expected life for options issued in the current year,
adjusted for the time lapses since issuance by using half of expected life of newly
granted options.15
Because the SFAS 123 disclosures do not provide detail on these input variables for different
tranches of options, we assume the option grants are issued evenly across years, and no
options are exercised before the end of their expected lives. Thus, the average life for all
options outstanding is equal to half of expected life of newly granted options. In addition, for
firm years with missing input data, we substitute the average values from the available years.
The final key parameter used as an input to the Black-Scholes option pricing model is
the price of the underlying stock. Option pricing theory would suggest that we use the stock
price at fiscal year end. However, Aboody (1996) notes that because ESO values increase
with prices of underlying stocks, regressing stock prices on ESO values creates an
endogeneity problem as stock price would appear in both the dependent and independent
variables. Thus, failure to take account of this endogeneity would result in estimated ESO
values that are positively correlated with regression error terms, and the resulting coefficients
on the option fair value-based variables would be biased. In particular, contrary to the
predictions of our theoretical analysis, findings from untabulated regressions relating to
Method 4 reveal a positive relation between OPTIONLIAB and equity market value. To
address the endogeneity problem, we estimate OPV andOPTIONLIAB using the predicted
stock price from the benchmark Ohlson model (on a per share basis) that excludes all ESO-
related measures, i.e., equation (20). By construction, the estimated ESO fair values obtained
from this first-stage procedure are not correlated with the error terms in the second-stage
valuation equations (21) through (23). When predicted stock prices from the first-stage
regression are negative, we set them to zero.
15 Because we do not have the data related to all options outstanding, we use the current year’s. We are currently conducting sensitivity tests using the simple average of individual years’ data.
24
4. Sample and Data
The sample comprises 1,354 firm-year observations drawn from the S&P Industrial
Index. The sample period includes fiscal years 1996-2001, with 1996 being the first year for
which SFAS 123 data are available and 2001 being the most recent available sample year.
The potential sample for use in our cross-sectional regression is 2,500 observations, which
reflects the fact that lagged equity book value is used to compute abnormal earnings. We
require firms to have earnings, equity market value, (non-negative) equity book value, and
employee stock option data necessary to estimate equity book value and residual income
under all four ESO accounting methods.16 To mitigate the effects of outliers, for each
variable appearing in the estimating equations, by year, we treat as missing observations that
are in the extreme top and bottom one percentile (Kothari and Zimmerman, 1995; Collins,
Maydew and Weiss, 1997; Fama and French; 1998; Barth, Beaver, Hand, and Landsman,
1999). After imposing this requirement but before imposing the ESO data availability
requirement, the potential sample ranges from a low of 440 firm-year observations in 1996 to
a high of 467 in 2000. Earnings, equity book value and equity market value data are drawn
from the Compustat database, and employee stock option data are from a database provided
to us by Jack Ciesielski of R.G. Associates, Inc.
Table 1, panels A and B, presents sample descriptive statistics and correlations. Panel
A reveals that, on average, equity market value far exceeds equity book value for all four
ESO accounting methods, with mean (median) ratios of the two amounts of roughly 4.5 (3.5).
In addition, mean and median residual income for all four methods are positive. Although
the positive median residual income contrasts with findings in prior research, e.g., Barth,
Beaver, Hand, and Landsman (1999), the earlier study’s sample period ends in 1997—our
first sample year—and the remaining sample years were highly profitable for large U.S.
25
firms. The sample mean and median amounts for the option liability under method 4 are of
same order of magnitude as residual income. Panel B reveals that all of the variables are
correlated with each other. Notably, equity market value is highly correlated with each of the
equity book value and residual income amounts, as well as with the ESO liability. Table 2
presents regression summary statistics corresponding to the first-stage equity valuation
equation used to estimate predicted stock price, which is an input to the Black-Scholes
formula-based estimate of option fair value. As described in section 3, the estimating
equation is essentially the same as that associated with APB 25—in which equity book value
and residual income are reported amounts that exclude effects of ESOs—although the
equation is estimated on a per share basis so that the fitted value from the regression can be
used directly in the option valuation formula. Table 2 reveals that equity book value and
residual income are significant regressors in every sample year, and produce high R2 values.
5. Results
Panels A and B of Tables 3 through 6 present regression summary statistics
corresponding to the equity valuation equations for each of the four ESO accounting
methods, i.e., equations (20) through ( 32 ′ ). Panel A (panel B) in each table corresponds to
the equation that excludes (includes) option fair value as an additional regressor whose
coefficient is restricted to equal negative one. Each panel includes pooled fixed effects
coefficients, t-statistics and adjusted R2 values, mean coefficients, t-statistics and adjusted R2
values from the five annual cross-sectional estimations, maximum and minimum coefficients,
number significantly positive coefficients, and Z1 and Z2 statistics based on the annual
16 Following Bell, Landsman, Miller, and Yeh (2002), we require positive beginning owner’s equity to ensure that the firm’s cost of capital in calculating abnormal earnings ( rBVEt−1 ) is positive.
26
regressions.17
The overall picture provided by the four tables is very similar. All eight models have
high R2 values, and all unrestricted regressor coefficients are significant positive in the
pooled and in all five annual estimations. For example, Table 3, panel A, which reports the
findings relating to the APB 25 method of accounting for ESOs (i.e., method 1) reveals R2
values exceed, 80 percent, on average, and mean across years residual income and equity
book value coefficients of 26.32 and 3.01, respectively. Inspection of the remaining tables
suggests that different methods of accounting for ESOs results in equity coefficients book
value and residual coefficients of similar magnitudes.
Table 7 summarizes the key results of the study. Panel A presents the Vuong t-
statistics corresponding to the pairwise comparisons, for any given method of accounting for
ESOs, of model explanatory power for equations that do or do not include option fair value as
a regressor, i.e., those between equations (20) and ( 02 ′ ), (21) and ( 12 ′ ), (22) and ( 22 ′ ), and
(23) and ( 32 ′ ). Panel B presents the Vuong t-statistics corresponding to the comparisons of
model explanatory power between those relating to the SFAS 123 method of accounting for
ESOs and those relating to the three ESO accounting methods. Although, based on our
predictions, comparisons should be limited to between equation (21) and equations ( 02 ′ ) ,
( 22 ′ ) and (23), we tabulate statistics comparing estimations for methods 1, 3, and 4 to both
estimations for method 2.
Panel A reveals findings consistent with our predictions. In particular, the Vuong t-
statistic comparing equations (20) and ( 02 ′ ) for the APB 25 accounting method is 3.18,
17 Throughout we use a five percent level of significance level under a two-sided alternative. Mean t-statistics for regression parameters from the year estimations are simple year averages and are included for descriptive purposes. Two Z-statistics, Z1 and Z2, are used to test for significance of the t-statistics from the five annual estimations. Z1 equals )2/(/1 /1 −∑ = jkjkN N
j jt , where tj is the t-statistic for year j, kj is the degrees of
freedom, and N is the number of years. Z2, which equals )1(/)(/( −Ntstddevt , corrects for potential upward bias in Z1 arising from lack of independence of parameters across years. See Barth (1994) for further details.
27
indicating that the equation including option fair value as an implicit part of the dependent
variable is better specified. Similarly, the Vuong t-statistic comparing equations (22) and
( 22 ′ ) for the Exposure Draft accounting method is 3.15, also indicating that the equation
including option fair value as an implicit part of the dependent variable is better specified.
We predict and find that the two estimating equations corresponding to the ED-2 extension
ESO accounting method are statistically equivalent in terms of explanatory power (t-statistic
= 1.64). Finally, although we have no predictions for the SFAS 123 equations, the t-statistic
of 2.80 suggests that the model that includes option fair value is better specified, which is
consistent with the fraction of option value (see equation (10)) being closer to one than to
zero.18
Panel B reveals that, as predicted, the relevant estimating equations corresponding to
the APB 25 and Exposure Draft methods of accounting for ESOs, i.e., equations ( 02 ′ ) and
( 22 ′ ), are better specified than the one relating to SFAS 123, equation (21). The Vuong t-
statistics are 5.87 and 5.13, respectively. However, the Vuong t-statistic of 0.32 relating to
comparison of explanatory power of equations (23) and (21) suggests that the equation for the
ED-2 extension method of accounting for ESOs is not significantly better specified than that
for the SFAS 123 method. One explanation for this null result is that equation (23) is
empirically misspecified in that the change in option value, which is implicitly a negative
component of residual income, is restricted to have the same coefficient as the other
components of income. It is likely that change in option value is entirely transitory because
stock prices follow a random walk, which suggests it should have a coefficient of negative
18 One alternative and simple explanation for the superiority in terms of model specification of the adjusted models for methods 1,2 and 3 is the fact that an important variable, option fair value, is included as an additional regressor. To test this conjecture directly, we re-estimated each of the adjusted equations )02( ′ through )32( ′ with option fair value but without imposing the restriction that its coefficient equals −1. Untabulated findings indicate that for all four accounting methods, the adjusted and unadjusted equations have statistically indistinguishable model explanatory power. This finding refutes the alternative explanation and provides additional support for the inclusion of option liability but with the coefficient restriction implied by our theory.
28
one, or at least a smaller coefficient than other income components.
To determine whether this explanation is correct, we re-estimate equation (23),
permitting the change in the ESO liability to have a different coefficient from other income
components. Untabulated findings from this regression reveal that as predicted, the
coefficient on the change in ESO liability is significantly lower than the coefficient on the
other aggregated components of residual income, and its coefficient is statistically
indistinguishable from −1. In addition, panel B of table 7 indicates that this expanded version
of equation (23) is better specified than equation (21) (t-statistic = 4.77). That is, the ED-2
extension method of accounting for ESOs appears to be better specified from a valuation
perspective if the change in ESO liability coefficient is permitted to differ from other
aggregate income components.
6. Summary and Concluding Remarks
We use the Ohlson (1995, 1999) valuation framework to compare the extent to which
four alternative approaches to accounting for employee stock options that reflect variations of
current and proposed accounting standards best reflect the economic effects of employee
stock options on current equity market value. We explicitly model the dilution effects on
shareholder value of employee stock options using a dividend discount model and then use
the Ohlson residual income framework to derive the implied equity value amounts associated
with each ESO accounting method. Findings from the modeling indicate that the only
method that results in recognized balance sheet amounts that accurately reflect the economic
dilution effects of ESOs on current shareholder equity value is that which recognizes an asset
and liability at grant data, and subsequently recognizes gains and losses on the liability in
income. That is, only the ED-2 extension employs super clean surplus accounting, whereby
income reflects all gains and losses attributable to existing shareholders. The other
accounting methods all result in balance sheet amounts that overstate the value of current
29
shareholder equity, whereby the APB 25 and Exposure Draft result in balance sheet amounts
that reflect the sum of the value of current shareholder equity value and the value of the stock
options granted to employees, and the SFAS 123 accounting method results in balance sheet
amounts that reflect the sum of the value of current shareholder equity value and a fraction of
the value of the stock options granted to employees.
Based on the modeling analysis and employing cross-sectional valuation equations we
then test two predictions. First, for the APB 25 and Exposure Draft methods, we predict and
find that the adjusted equation is better specified, in terms of relative explanatory power, than
the unadjusted model—i.e., the one that excludes option fair value—because a valuation
based on equity book value and residual income equal equity value of current shareholders
plus option fair value. Although we have no clear prediction for the SFAS 123 method, we
find the adjusted equation is also better specified. We also predict and find that the SFAS 123
estimating equation exhibits less relative explanatory power than those associated with the
other three models, although the result only obtains for the ED-2 extension when we permit
the change in the ESO liability to have a different coefficient from that on other aggregate
income components.
30
References
Aboody, D. (1996). “Market Valuation of Employee Stock Options.” Journal of Accounting
and Economics 22, 357-391.
Aboody, D., M.E. Barth and R. Kasznik (2000). “Stock-Based Employee Compensation and
Equity Market Values.” Working paper, Stanford University.
Accounting Principles Board (1972). Opinion No. 25: Accounting for Stock Issued to
Employees. American Institute of Certified Public Accountants, New York.
Barth, M.E. (1994). “Fair Value Accounting: Evidence from Investment Securities and the
Market Valuation of Banks.” The Accounting Review 69, 1-25.
Variable definitions = market value of common shares outstanding at fiscal year-end.= book value of common equity as of fiscal year-end.= book value of common equity as of fiscal year-end, which is identical to .= plus the value of ESOs grants summed since 1996, minus ESO expense accumulated since 1996; the value of ESO grants is
measured as the number of ESOs granted times the weighted fair value of ESOs at grant date; ESO expense is measured as reported net icome minus pro forma net income per SFAS No. 123 disclosure.
= , is defined as below.= abnormal earnings measured as net income before extraordinary items and discontinued operations, minus 0.12 x (lagged one year). = abnormal earnings after ESO expense measured as net income before extraordinary items and discontinued operations, minus
ESO expense, minus 0.12 x (lagged one year).= abnormal earnings after ESO expense measured as net income before extraordinary items and discontinued operations, minus
ESO expense, minus 0.12 x (lagged one year).= abnormal earnings after ESO expense and gain or loss resulting from changes in the fair values of ESO liability, measured as net income
before extraordinary items and discontinued operations, plus (minus) gain (loss) from changes in OPTIONLIAB , minus ESO expense, minus 0.12 x (lagged one year).
= fair value of options oustanding at fiscal year-end, measured as the number of options oustanding at fiscal year-end times the estimatedyear-end fair value per option. The fair value per option is estimated using the Black-Scholes option pricing model. To control for theendogenity noted by Aboody (1996), predicted prices from a first-stage regression of a benchmark Ohlson model (on a per share basis) is employed in the fair value estimation. The detailed estimation procedure is described in Section 3.2.
MVE
MVEMVE
BV 1
BV 1
BV 1
BV 2
BV 2
BV 3
BV 3
BV 3
BV 4
BV 4
BV 4
RI1
RI1
RI1
RI 2
RI 2
RI2
RI 3
RI 3
RI3
RI 4
RI 4 ESLIAB
C E S O L I A B
C E S O L I A B
RI 4
MVEBV 1
BV 2
BV 3
BV 4
RI1
RI 2
RI 3
RI 4
OPTIONLIABC E S O L I A B
BV 1
BV 1
BV 3
BV OPTIONLIAB3 − OPTIONLIAB
OPTIONLIAB
OPTIONLIAB
OPTIONLIAB
BV 4
BV 2
BV 1
BV 2
33
Table 2First Stage Regressions of Equity Market Value on Residual Income and Equity Book Values,
*All variables except CONSTANT are as defined in Table 1, but are stated on a per share basis by dividing by the number of shares outstanding at the fiscal year end,CONSTANT is the inverse of number of shares oudtanding at the fiscal year end.
BV 1
B V 1
MVE RI BV uit it it it= + + +α α α0 11
21
M V E R I B V E S O L I A B ui t i t i t i t i t= + + − +α α α0 1 2
RI1
R I 1
34
Table 3Regressions of Equity Market Value under APB 25 Method, for a Sample
of S&P 500 Firms, with 1,354 Firm-Year Observations, 1997-2001*
Panel A: Summary statistics from regressions of equity market value on residual income and equity book value
Pooled fixed-effects 23.06 30.58 3.34 30.56 0.810Mean across years 26.32 16.04 3.01 13.68 0.842Maximum 34.45 3.58Minimum 17.27 2.20# significantly positive 5 5# significantly negative 0 0Z1 35.73 30.47Z2 9.86 5.43
Panel B: Summary statistics from regressions of equity market value on residual income, equity book valueand ESO liability whose coefficient is restricted to equal negative one
Pooled fixed-effects 23.10 30.71 3.35 30.74 0.811Mean across years 26.39 16.11 3.02 13.77 0.843Maximum 34.54 3.59Minimum 17.26 2.21# significantly positive 5 5# significantly negative 0 0Z1 35.90 30.67Z2 9.85 5.41* See Table 1 for the definitions of all variables All regressions are estimated with year fixed-effect, the associated coefficients and t-statistics are not reported.Z1 equals , where t j is the t-statistic for industry j , k j is the degrees of freedom, and N is the number of years.
Z2 equals .)2/(/1 /1 −∑ = jkjkN N
j jt)1(/)(/( −Ntstddevt )1(/)(/( −Ntstddevt
BV 1
BV 1
MVE RI BV uit it it it= + + +α α α0 11
21
MVE RI BV OPTIONLIAB uit it it it it= + + − +α α α0 11
21
RI1
RI1
35
Table 4Regressions of Equity Market Value under SFAS 123 Method, for a Sample
of S&P 500 Firms, with 1,354 Firm-Year Observations, 1997-2001*
Panel A: Summary statistics from regressions of equity market value on residual income and equity book value
Pooled fixed-effects 21.90 26.82 3.58 31.78 0.791Mean across years 25.45 14.13 3.24 14.09 0.823Maximum 34.39 3.85Minimum 16.35 2.36# significantly positive 5 5# significantly negative 0 0Z1 31.48 31.39Z2 9.12 5.66
Panel B: Summary statistics from regressions of equity market value on residual income, equity book valueand ESO liability whose coefficient is restricted to equal negative one
Pooled fixed-effects 21.94 26.92 3.59 31.96 0.791Mean across years 25.51 14.19 3.25 14.17 0.824Maximum 34.48 3.87Minimum 16.33 2.37# significantly positive 5 5# significantly negative 0 0Z1 31.62 31.57Z2 9.11 5.64* See Table 1 for the definitions of all variables All regressions are estimated with year fixed-effect, the associated coefficients and t-statistics are not reported.Z1 equals , where t j is the t-statistic for industry j , k j is the degrees of freedom, and N is the number of years.
Z2 equals .)2/(/1 /1 −∑ = jkjkN N
j jt)1(/)(/( −Ntstddevt
)2/(/1 /1 −∑ = jkjkN Nj jt
)1(/)(/( −Ntstddevt
MVE RI BV uit it it it= + + +α α α0 12
22
MVE RI BV OPTIONLIAB uit it it it it= + + − +α α α0 12
22
RI 2
RI 2 BV 2
BV 2
36
Table 5Regressions of Equity Market Value under Exposure Draft Method, for a Sample
of S&P 500 Firms, with 1,354 Firm-Year Observations, 1997-2001*
Panel A: Summary statistics from regressions of equity market value on residual income and equity book value
Pooled fixed-effects 20.48 25.55 3.74 35.60 0.801Mean across years 23.89 13.50 3.43 15.70 0.831Maximum 32.98 4.02Minimum 15.65 2.44# significantly positive 5 5# significantly negative 0 0Z1 30.07 34.98Z2 8.18 6.02
Panel B: Summary statistics from regressions of equity market value on residual income, equity book valueand ESO liability whose coefficient is restricted to equal negative one
Pooled fixed-effects 20.51 25.65 3.75 35.81 0.802Mean across years 23.95 13.56 3.44 15.80 0.831Maximum 33.06 4.03Minimum 15.63 2.46# significantly positive 5 5# significantly negative 0 0Z1 30.20 35.19Z2 8.17 6.00* See Table 1 for the definitions of all variables All regressions are estimated with year fixed-effect, the associated coefficients and t-statistics are not reported.Z1 equals , where t j is the t-statistic for industry j , k j is the degrees of freedom, and N is the number of years.
Z2 equals .)2/(/1 /1 −∑ = jkjkN N
j jt)1(/)(/( −Ntstddevt
)2/(/1 /1 −∑ = jkjkN Nj jt
)1(/)(/( −Ntstddevt
MVE RI BV uit it it it= + + +α α α0 13
23
BV 3
MVE RI BV OPTIONLIAB uit it it it it= + + − +α α α0 13
23
BV 3RI 3
RI 3
37
Table 6Regressions of Equity Market Value under ED2-extension (Option as a Liability)
Method, for a Sample of S&P 500, with 1,354 Firm-Year Observations, 1997-2001*
Panel A: Summary statistics from regressions of equity market value on residual income and equity book value
Pooled fixed-effects 19.17 23.66 3.74 33.42 0.793Mean across years 22.81 12.43 3.40 14.43 0.821Maximum 33.79 4.27Minimum 14.03 2.46# significantly positive 5 5# significantly negative 0 0Z1 27.69 32.15Z2 8.26 5.88
Panel B: Summary statistics from regressions of equity market value on residual income, equity book valueand ESO liability whose coefficient is restricted to equal negative one
Pooled fixed-effects 19.20 23.73 3.75 33.56 0.793Mean across years 23.49 13.06 3.46 15.05 0.832Maximum 32.92 4.15Minimum 15.25 2.45# significantly positive 5 5# significantly negative 0 0Z1 29.10 33.53Z2 8.94 5.79* See Table 1 for the definitions of all variables All regressions are estimated with year fixed-effect, the associated coefficients and t-statistics are not reported.Z1 equals , where t j is the t-statistic for industry j , k j is the degrees of freedom, and N is the number of years.
Z2 equals .)2/(/1 /1 −∑ = jkjkN N
j jt)1(/)(/( −Ntstddevt
)2/(/1 /1 −∑ = jkjkN Nj jt
)1(/)(/( −Ntstddevt
MVE RI BV uit it it it= + + +α α α0 14
24
R I 4 BV 4
RI 4 BV 4
MVE RI BV OPTIONLIAB uit it it it it= + + − +α α α0 14
24
38
TABLE 7Model Explanatory Power of ESO accounting Methods, for a Sample
of S&P 500 Firms, with 1,354 Firm-year Observations, 1997 - 2001
Panel A: Intra-model pairwise comparisons, for any given method of accounting for ESOs, of model explanatory power for equations that do or do not include option fair value as a regressor with coefficientrestricted to equal -1
*The reported Vuong ststistic has a t-distribution, a positive (negative) number indicates the equation includesoption fair value is better (worse) specificed than the equation does not include option fair value as a regressor **The reported Vuong statistic in each cell has a t-distribution, a positive (negative) number indicates the column method is better (worse) specified than the row model. ***modified ed-2 extension is based on the ed-2 extension method, but permits change in eso liability to have a coefficient different from other residual income components.
