the value relevance of alternative methods of …assets.csom.umn.edu/assets/22269.pdf · the value...

The Value Relevance of Alternative Methods of Accounting for Employee Stock Options

Wayne R. Landsman,1 Ken Peasnell,2 Peter F. Pope2 and Shu Yeh3

April 2004 1. Kenan-Flagler Business School, University of North Carolina at Chapel Hill, Chapel Hill, NC

27599. 2. The Management School, Lancaster University, Lancaster, LA1 4YX, UK. 3. Department of Accounting, National Taiwan University, Taipei, Taiwan, R.O.C.

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. We also thank workshop participants at the 2004 European Accounting Association Congress, the University of North Carolina, and the Ohio State University for helpful comments. Corresponding author: Wayne Landsman, Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599-3490, 919-962-3221, [email protected].

The Value Relevance of Alternative Methods of Accounting for Employee Stock Options

Abstract

We use the residual income valuation framework to compare four approaches to employee stock options (ESOs) accounting proposed by regulators. Only an extension of the IASB’s ED-2 method treating the fair value of ESOs as a liability and employing mark-to-market accounting, results in accounting numbers that accurately reflect the dilution effects of ESOs on current shareholder value. The other accounting methods (APB-25, FASB Exposure Draft and SFAS-123) lead to overstatement of current equity value. Empirical value-relevance results are consistent with two predictions. First, estimating equations for methods that do not account for ESO dilution effects are better specified after controlling for option fair value. Second, SFAS-123 accounting numbers have relatively low explanatory power for equity values, when compared with APB-25 and Exposure Draft specifications including option fair value and an IFRS 2 extension specification where the valuation weight on the change in the ESO liability differs from other 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 Stock-

Based Compensation (FASB 1995, hereafter, SFAS 123). SFAS 123 requires firms to 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, Credit Suisse First Boston (2004) reports that for

S&P 500 firms diluted EPS including the effects of fair value of ESO grants is 8%, 19% and 20%

lower than reported EPS in 2003, 2002, and 2001, respectively. 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 and to consider mandating

recognition of ESO expense in income has been largely driven by the International Accounting

Standards Board (IASB), which issued in February 2004 International Financial Reporting

Standard No. 2, Share Based Payment (IASB, 2004). IFRS 2 requires recognition of employee

stock option expense using grant date fair value. Although there are some minor differences

between IFRS 2 and SFAS 123, the key point is that all adopters of IAS (e.g., all European Union

firms beginning in 2005) would be required to expense employee stock options using grant date

fair value beginning on January 1, 2005. One month after passage of IFRS 2, the FASB issued

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

an Exposure Draft, Share Based Payment (FASB, 2004), that closely parallels the international

standard. If the Exposure Draft is enacted as a standard, it will require recognition of employee

stock option expense using grant date fair value.

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 expense

ESOs. They raise two potentially valid criticisms. First, firms that issue employee stock options

do so because they get something in return, an intangible asset, in the form of the employees’

intellectual capital.2 This asset is recognized neither under SFAS 123 nor IFRS 2. The FASB

acknowledged this in the 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. In effect, SFAS 123 and IFRS 2 recognize an expense that relates to an

off-balance sheet asset, which creates the impression that ESOs impose a cost without providing

any attendant benefit to the firm. Critics contend that a more appropriate accounting treatment

would be to record an asset at grant date, as is the case in the Exposure Draft.

Second, critics argue that 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, i.e., the difference between the cash proceeds, if any, and the cash the firm would

receive if the shares were issued at market price. Similarly, if the options lapse unexercised, the

current shareholders enjoy a gain at the expense of the option holders that is not recognized in

SFAS 123 and IFRS 2. An accounting policy that (1) recognizes at grant date the firm’s

2 Consistent with this, Hanlon, Rajgopal, and Shevlin (2003) find a positive empirical relation between ESO grants to the firm’s top five executives and future earnings.

3

obligation to its employees as a liability, rather than as a component of equity, and (2) includes

the effects of changes in a firm’s obligation to employees after grant date, would better capture

the economic impact of ESOs on a firm’s 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 in IFRS 2 and FASB in the March 2004 Exposure

Draft treat the liability when ESO settlement takes the form of cash rather than the issuance of

stock. It is also commonplace in accounting regularly to update the amounts shown for long-term

liabilities, such as site restoration costs.

The purpose of this study is to examine how these substantially different approaches to

accounting for employee stock options reflect the economic effects of employee stock options on

current equity market value. First, we explicitly model the dilution effects on shareholder value

associated with employee stock options using a dividend discount model. We then use the

residual income framework to derive the implied equity values in terms of accounting variables

associated with four ESO accounting methods. The methods we examine reflect variations of

current and proposed accounting standards, i.e., APB 25, SFAS 123, the Exposure Draft, and an

extension of IFRS 2 (hereafter the IFRS 2 extension) that recognizes an ESO asset and an ESO

liability at grant date, and changes in the fair value of the ESO liability after grant date.

Findings from the modeling analysis indicate that only the IFRS 2 extension results in

recognized balance sheet and net income 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 IFRS 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 methods

4

result in balance sheet and net income amounts that overstate the value of current shareholder

equity value. In particular, these two methods result in accounting 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

both existing and potential future equity holders. Finally, we find that the SFAS 123 method

results in balance sheet and net income amounts that when used in valuation would also lead to

the equity value of existing shareholders being overstated, although to a lesser extent than in the

cases of the APB 25 and Exposure Draft methods. The reason for this is that SFAS 123

accounting amounts reflect the value of the claims of existing shareholders and a fraction of the

claim of potential future equity holders.

We test the value relevance of the four accounting methods by estimating two separate

cross-sectional equity valuation models for each accounting method in which the measures of

equity book value and residual income are adjusted to reflect the applicable accounting treatment.

Both equations within each pair have equity market value as the dependent variable, but the

second “adjusted” equation includes option fair value 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, we make predictions concerning the importance of

including option fair value in the adjusted equation. For the two mixed surplus accounting

methods, APB 25 and Exposure Draft, 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

5

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 analysis shows that a valuation based on equity book value and residual income

should equal equity value of current shareholders plus a fraction of option value. Finally, under

the IFRS 2 extension method, because a valuation based on equity book value and residual

income should equal equity value of current shareholders, there is no reason to expect the

adjusted equation will be better specified than the unadjusted equation.

Second, we predict that the estimating equation based on SFAS 123 equity book value and

residual income amounts should be less well specified than the adjusted estimating equation for

the APB 25 and Exposure Draft methods, and the unadjusted estimating equation for the IFRS 2

extension method. This prediction is based on our valuation modeling showing that the gradual

recognition of equity under SFAS 123 gives rise to measures of equity book value and residual

income that do not combine to correctly value either equity market value or the sum of equity

market value and option fair value.

We test our predictions using a sample of S&P 500 firms with available data from 1997-

2001, and estimate annual cross-sectional valuation models and pooled models with year fixed-

effects. We estimate option fair value using the Black-Scholes (1973) option pricing formula.

To address the endogeneity problem arising from regressing stock prices on option fair values

(Aboody, 1996), we estimate option fair value 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 IFRS 2 extension estimating

6

equations. In addition, the SFAS 123 estimating equation exhibits less relative explanatory power

than those associated with the other three appropriately adjusted methods.

Our study builds on prior research examining the relation between ESO expenses and

equity market values. Using an estimate of ESO fair values in the period before SFAS 123,

Aboody (1996) shows a negative relation between his estimate and equity market values.

Chamberlain and Hseih (1999) and Aboody, Barth, and Kasznik (2004) find a negative relation

between ESO expense and equity market values, where the former is based on SFAS 123

disclosures. A study that relates more closely to the current one, Bell, Landsman, Miller and

Yeh (2002), compares the value relevance of accounting amounts based on two accounting

methods, SFAS 123 and APB 25, for a sample of computer software firms.

In a concurrent study, Li (2002) extends the work of Chamberlain and Hseih (1999) and

Aboody, Barth, and Kasznik (2004) by incorporating the dilution effects of employee stock

option grants, both current and expected future, and provides empirical evidence of a negative

association between equity market values and both outstanding ESOs and expected future ESO

expenses. In another concurrent 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, neither

Li (2002) nor Li and Wong (2003) addresses how current and proposed ESO accounting methods

reflect ESO dilution effects.

The remainder of this paper is organized as follows. Section 2 presents analysis of how

the four different methods of accounting for employee stock options affect the relation between

7

market values and future accounting numbers. Section 3 describes the empirical estimating

equations. Section 4 describes the sample data. Section 5 presents the empirical findings.

Finally, section 6 summarizes and concludes the study.

2. Analysis

2.1 Accounting for ESOs

There are at least four ways of accounting for ESOs:3

1. APB 25 method: ignore them, i.e., measure them at intrinsic value. If the options are

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

received and include in paid-in capital as when the option is exercised. If the options are

not exercised, leave the balance in PIC – options as a dirty surplus component of equity.

3. 1993 FASB Exposure Draft method: recognize an asset at grant date equal to the fair

value of the ESOs granted and amortize the asset 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 (IFRS 2 extension) method: as under method 3, recognize an asset

and amortize it but treat the recognized fair value of the option as a liability. Mark-to-

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.

8

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.

Figure 1 shows the accounting journal entries under each of the four methods. Method 1

conforms to the “clean surplus” principle, since all recognized gains and losses pass through

income. Method 4 shares this property. However, gain and loss recognition differs under the two

methods. Method 1 is an example of what Christensen and Feltham (2003, ch. 9) label “mixed

surplus” accounting, whereby gains and losses are accounted for from the perspective of the

aggregate equity claims including existing and prospective equity holders. Method 4 is accounted

for on what Christensen and Feltham call a “super-clean surplus” basis. Under this method,

income reflects all gains and losses attributable only to existing shareholders.

We now develop a model showing the consequences of the alternative accounting

treatments of ESO’s and the related implications for accounting-based valuation.

2.2 Model

2.2.1 Model setup

Consider a firm that has granted an ESO to a manager at date 0 that is exercisable at date T on

payment of the exercise price, X. No further ESO contracts are expected to be granted in the

future.4 At grant date 0, the net incomes in future periods, tNI , t = 1,2,…, are uncertain, but the

market’s net income forecasts incorporate the anticipated motivational and retention benefits that

led the firm to choose the manager’s compensation contract. Dividends in future periods t =

1,2,…, will be shared between existing shareholders (e) and the manager (m), 4 We make this assumption to simplify the exposition. Since none of the accounting methods under consideration involves immediate recognition of options that might be granted in the future, nothing is gained by introducing such complications. We return to the valuation implications of this simplification at the end of sub-section 2.2.2.

9

,mt

ett ddd += (1)

with the existing shareholders receiving etd and the manager getting m

td . Until date T+1, all the

dividends flow to the existing shareholders, i.e., .,...,2,1, Ttdd ett == If the ESO subsequently

lapses unexercised, the manager gets nothing, i.e., ,...2,1,0 ++== TTtd mt We assume that the

value of the firm and the claims of e and m do not depend on the exercise price, X.5 Cash flows

and non-ESO components of accounting accruals are assumed to be unaffected by the choice of

accounting treatment of the ESO.

The manager’s net ESO compensation at exercise date T is

),,min()0,max( XMVMVXMV mT

mT

mT −=− (2)

where the (currently uncertain) market value of the shares that might be issued to m at that date is

∑+

=∞

=

+

1 )1(][

t t

mtTTm

T rdE

MV , (3)

where [.]TE is the expectations operator evaluated using risk-neutral probabilities based on

information available at date T and r is the (assumed constant) risk-free rate of interest. The

value of the ESO at grant date at date 0, 0OPV , can be expressed in terms of the discounted

expected value of (2):

,)1(

)()(

)1()],min([0

0

TX

mT

mTX

mT

T

mT

mT

rMVdFXMVdFMV

rXMVMVE

OPV

+∫−∫=

+−

=

∞∞ (4)

5 The exercise proceeds are a source of capital to the firm. To avoid irrelevant complications, we make the standard Modigliani-Miller type of assumption that the firm is following an optimal investment strategy such that an additional dollar of X results in a dollar increase in dividends, leaving the total value of the firm unchanged. We make an equivalent assumption regarding m’s employment contract. An increase in X will result in the ESO being worth less to m, but we assume that this would be offset by an increase in straight salary such that both m’s utility and the value of e’s shares are unchanged.

10

where )( mTMVF is the cumulative risk-neutral probability density function associated with

mTMV . By the law of iterated expectations, we can use (3) to rewrite (4) as

,)1(][

)1(][ 0

1

00 TTt t

mt

rXE

rdEOPV

+−∑

+=

∞

+= (5)

where ∫= ∞X

mTMVdFXXE )(][0 is the exercise price multiplied by the probability of the option

being exercised. As long as there is some probability that the option will be exercised, the ESO

will have a positive value, i.e., .00 >OPV

2.2.2 Dividend-based valuation

The date 0 value of the existing shareholders’ claim can be expressed as:

.)1(][

1

00 ∑

+=

∞

=t t

ete

rdE

MV (6)

Consistent with Christensen and Feltham (2003), expression (6) can be redefined, using (1) and

(3), in terms of the aggregate dividend flow expected to accrue to both current and future

shareholders, adjusted for the dilution effect associated with the ESO grant. The ESO will only

be exercised by m if XMV mT > and the economic cost incurred by e will exceed X, the cash

proceeds received by the firm from the exercise of options. The correct dilution adjustment is the

expected market value of any shares subsequently issued to employees. This can be captured

explicitly by writing eMV0 in terms of total dividends expected to be paid to e and m, recognizing

that the subsequent issuance of new shares to m will dilute the claim of e by an amount equal to

the expected market value of those shares, i.e., by ][0m

TMVE :

.)1(

][)1(][ 0

1

00 T

mT

tt

te

rMVE

rdEMV

+−

+= ∑

∞

=

(7)

11

Value per share can be computed by dividing 0eMV by the number of current shares outstanding,

without any further adjustment for the dilution effects of the ESO.

A measure of equity value that “mixes” or “combines” the claims of existing and future

shareholders, cMV0 , can also be derived. This measure discounts the projected net dividend flow

between the firm and all current and prospective equity claimants, treating new capital

contributions as negative dividends:

.)1(][

)1(][ 0

1

00 T

tt

tc

rXE

rdEMV

+−∑

+=

∞

= (8)

It follows from (1) and (5) that this combined value is equal to the sum of the market values of

existing shares and the ESO:

.

)1(][

)1(][

)1(][

00

1

00

1

00

OPVMV

rXE

rdE

rdE

MV

e

Tt Tt

mt

t t

etc

+=

∑

+−

++∑

+=

∞

+=

∞

= (9)

The valuation expression equation (9) can be used to obtain an indirect estimate of eMV0 ,

by valuing both cMV0 and 0OPV and taking the difference, but this is a cumbersome procedure.

Another way is to compute value on a diluted per share basis. However, the applicable dilution

correction to be used in per share calculations is equivalent to assuming that the proportion of

new shares to be issued under the ESO relative to existing shares is equal to 0 0/ .eOPV MV 6 The

direct method of valuing existing shares in equation (7) requires subsequent share issues to third

parties, in this case m, to be measured at fair value. The indirect method of equation (8) does not

6 Let en and mn denote the number of shares held by existing shareholders and employee shareholders,

respectively, upon exercise of the ESOs. We can see from equation (9) that this requires 0 0 0 .e e

e e m

MV MV OPVn n n

+=

+

This implies that 0

0

m

e e

OPVnn MV

= .

12

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, i.e., the exercise price, X. Equations (7) and (8) reveal the importance of clarity in the

treatment of future dilution in the valuation of current equity claims. We show below that the

issue of identifying the appropriate net dividend stream has implications for the choice of ESO

accounting method.

Our analysis assumes that no new ESO contracts will be issued in the future. However,

future ESO grants at dates can easily be accommodated in our analysis. To see this, assume the

firm is expected to issue additional ESOs at dates ,...),2,1( =≥ iTTi with projected values

][0future

TiOPVE . Dividends payable to non-current shareholders, ,m

td will be shared between the

holders of the current and future ESOs. Suppose the valuation is carried out as in equation (8),

based on the forecast net cash flows to and from all equity claimants., It can be shown by

induction that the value of that dividend stream will equal the present value of all claims,

including those not yet written, i.e.,

.)1(

][0000 ∑

∞

⊆ +++=

iTtt

futuretec

rOPVEOPVMVMV (10)

One reason we ignore this aspect of valuation is that no proposed ESO accounting method

involves recognition of future ESOs. We treat future option grants as an unmodeled source of

“other information” in the empirical analysis, omitting the .)1(

][0∑∞

⊆ +iTt

t

futuret

rOPVE term in (10), since

all our estimating equations based on the different accounting treatments for ESOs are similarly

affected by this omitted variable. In the remainder of our modeling, we therefore continue to

assume that no further ESO contracts will be written.

13

2.3 Residual income valuation

The residual income valuation model allows the value of the firm to be written in terms of

accounting fundamentals related to the creation of shareholder wealth rather than dividends,

which reflect the distribution of wealth (Preinreich, 1938; Edwards and Bell, 1961; Peasnell,

1982; Ohlson, 1995). If the clean surplus accounting relation holds then the dividend discount

model can be expressed in terms of current equity book value and future residual incomes, as

follows:

∑∞

= ++=

1

000 )1(

][t

t

itii

rRIEBVMV (11)

where itBV 0 and i

tRI are the book value of equity at time 0 and the residual income for period t,

respectively, using ESO accounting method i. Residual income is a random variable, defined as

it

it

it rBVNIRI 1−−= . i

tNI is net income for period t using accounting method i. If accounting

violates the clean surplus relation, future residual income flows would have to be adjusted by

expected dirty surplus flows in order to ensure articulation between equation (11) and the

relevant dividend discount model.

The four alternative accounting methods described in section 2.1 establish different

measures for (components of) equity book value and accrued ESO-related expenses. We now

consider the implications of applying the residual income valuation model to items measured

under the accounting alternatives. Specifically, given that the alternative accounting treatments

adopt different perspectives on the inclusion of ESO-related accounting items, we consider the

relation between value estimates based on the residual income valuation model and the value of

14

the underlying claims of owners and managers. This analysis has implications for the

specification of the empirical tests that follow in section 3.

Differences in residual income-based value estimates may arise because of differences in

the magnitude of recognized equity book value, or differences in the timing or magnitude of

income, or both. Option expense is not charged in arriving at net income under method 1. Option

expense under accounting methods 2, 3 and 4 is based on the fair value of the ESO at grant date

( 0OPV ) apportioned over the T-year vesting period. We assume option expense is computed on

a straight-line basis, with TOPV0 being allocated to each period.

Equity book value differences arise depending on whether the accounting method

recognizes an ESO-related pre-paid compensation asset and because of differences in the

classification of the associated option as an equity account or a liability. No asset or option credit

is recognized at date 0 under method 2 (SFAS 123), in contrast to methods 3 and 4 (Exposure

Draft and IFRS extension). The amount initially recognized as a pre-paid compensation asset

under methods 3 and 4 equals .0OPV The corresponding credit is treated as equity under method

3 and as a liability under method 4.

There are several implications for the residual income model of the different ways of

accounting for ESOs. In methods 3 and 4, the impact of the recognition of an asset that is

subsequently amortized is straightforward. The recognition of the pre-paid compensation asset

simply changes the balance between current book value and future residual income. Under

method 4, the credit arising from recognition of the asset at grant date is treated as a liability,

implying that equity book value at that date is identical to method 1 (APB 25), where no asset or

liability is recognized. The difference between the two methods appears in the streams of future

residual incomes and (we shall see later) in the resulting present values. Methods 2 and 3, on the

15

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, equity book

value under methods 2 and 3 differ at grant date from the equity book value amounts reported

under methods 1 and 4.

We now examine the consequences of applying the residual income valuation model (11)

to equity book value and projected residual income flows obtained under the four accounting

alternatives. Our main objective in this section is to show how estimated value obtained from the

residual income model relates to the value of current equity outstanding.

Method 1

Method 1 is the benchmark model where the accounting system recognizes no ESO

expense, asset or liability, i.e., APB 25. The other three accounting alternatives can be related to

the relevant accounting numbers obtained under method 1. We assume that the net income flows

are linked to the underlying dividend flows and equity book values by assuming that the clean

surplus relation holds in this base accounting system, i.e., changes in equity book value equal net

income less dividends paid. However, note that for valuation purposes dividend policy

irrelevance is assumed to hold. Any exogenous change in the timing of dividend payments will

not affect the value of the firm because the firm and equity claimants are assumed to be able to

borrow and lend at the same cost of capital.

The value of the firm obtained by applying expression (11) to the residual income flows

under method 1 is as follows:

∑∞

= ++=

1

101

01

0 )1(][

tt

t

rRIEBVMV (12)

16

where

11

11−−= ttt rBVNIRI and .

(()(

11

1

11

11

≠−+=−+−

=−

−

TtforBVBVdTtforBVBVXdNI

ttt

tttt Substituting the net

income and equity book value values for method 1 into equation (12) and canceling and

collecting terms gives:

Tt tt

rXE

rdE

MV)1(][

)1(][ 0

1

010

+−∑

+=

∞

=. (13)

Valuation expression (13) is identical to the value obtained using the mixed surplus dividend

discount model in equation (8). We therefore know from (9) that .00010 OPVMVMVMV ec +==

Since 0OPV must be positive, applying the residual income valuation model to accounting

numbers prepared under method 1 over-estimates the value of current equity. This is obvious,

given that method 1 ignores stock options in recognized net income and equity book value. Note

that method 1 applies what Christensen and Feltham (2003, p.294) label as “mixed surplus”

because the accounting reflects dividends flowing to existing and potential future equity holders.

Method 2

In the first T periods, net income under method 2 differs from net income under method 1

by an amount equal to the recognized option expense. However, as can be seen in Figure 1, the

credit associated with the option expense is included in paid-in capital. The two entries therefore

cancel and the equity book value under method 2 is always the same as equity book value under

method 1,i.e., 12tt BVBV = (t =0,1, …). This implies that the capital charge levied to arrive at

residual income is the same under the two methods. It therefore follows that method 2 residual

17

incomes will be less than their method 1 counterparts by an amount equal to the option expense:

.012T

OPVtt RIRI −= As a result, use of ESO method 2 accounting numbers in (11) yields:

.)1(11

)1(

00

1

010

20

OPVrT

rMV

rTOPVMVMV

Te

T

tt

+−−+=

+−=

−

=∑

(14)

ESO accounting method 2 recognizes option equity over time, as a by-product of recognizing

option expense. Generally, the resulting valuation provides an estimate of neither the eMV0 nor

00 OPVMV e + . Only in the special case where 0r = will 20 0 .eMV MV= For r > 0, .0

20

eMVMV >

More generally, 20MV is an increasing function of both r )0/( 2

0 >∂∂ rMV and T )0/( 20 >∂∂ TMV

and falls within the range, .002

00 OPVMVMVMV ee +<≤ . The boundary to which 20MV is closest

will vary from case to case. However, for option grants where T = 5 (a typical option grant

vesting period), 20MV will be closer to eMV0 than to 00 OPVMV e + as long as r is less than

28.6%. Thus, empirically we expect method 2 to yield a value estimate closer to eMV0 .

Method 3

Net income under method 3, the Exposure Draft method, is the same as under method 2.

On the other hand, the immediate recognition of an asset gives rise to a credit that is treated as

equity under method 3, thus giving rise to a difference in equity book value at date 0 under the

two methods, i.e., .200

10

30 BVOPVBVBV =+= This difference in book values diminishes with

time, as the ESO asset is amortized, such that ( ).10

13TtT

tt OPVBVBV +−+= At time T, the asset is

18

fully amortized and .13TT BVBV = The residual income stream reflects both the amortization

charges and the extra (but diminishing) equity book value. Applying valuation expression (11) to

the equity book value and residual income flows, yields:

.

)1(11)1(11

)1(1

10

001

0

1

020

30

MV

OPVrT

rOPVrT

rMV

rtT

TOPVrMVMV

TT

T

tt

=

+−−−

+−−+=

++−

−=

−−

=∑

(15)

The result is the same as with method 1, i.e., .003

0 OPVMVMV e += Method 3 results in an over-

estimate of the value of existing equity but correctly values the total of the claims of e and m. As

with method 1, method 3 is a form of mixed surplus accounting because it reflects dividends

flowing to existing and potential future equity holders.

Method 4

Under method 4, the IFRS 2 extension method, an asset is recognized immediately and the

associated credit is treated as a liability. As a consequence, date 0 equity book value is the same

as under method 1 because the asset and liability fully offset each other. The asset is amortized

in the same way as under method 3, but net income also includes gains and losses on marking-to-

market the liability:

,

)(

01

41

44

tt

tttt

OPVT

OPVNI

BVBVdNI

∆−−=

−+= −

(16)

19

where 1−−=∆ ttt OPVOPVOPV represents the change in the market value of the liability. The

equity book values of methods 1 and 4 diverge during the vesting period by the accumulated

charges against net income:

,1

014 ∑

=

∆−

−=

t

sstt OPV

TtOPVBVBV t =1,2,…,T-1. (17)

As shown in Figure 1, at date T, the marked-to-market book value of the ESO liability

plus the exercise proceeds will equal the market value of the shares issued to m:

.1

0 ∑=

∆+=

=T

tt

Tm

T

OPVOPV

OPVMV (18)

It can be seen from (17) and (18) that equity book values under methods 1 and 4 are equal at

vesting date T and thereafter:

.11

14

sT

mTt

T

tTsTsT

BV

MVOPVOPVBVBV

+

=++

=

+∆−−= ∑ s = 0,1, … (19)

The residual income valuation rule can be applied, using equations (16), (17) and (19), as

follows:

∑

∑

∑

∞

+=

=

−

∞

=

++

+

−−

−

−−∆−−+=

++=

1

10

1

01001

01

0

1

404

04

0

.)1(

][)1(

)(1][

)1(][

Ttt

t

T

tt

ttt

tt

t

rRIE

r

OPVOPVT

tOPVrOPVT

OPVRIEBV

rRIEBVMV

(20)

Collecting terms in (20), we know from our results for method 1 that

20

.)1(][

)1(][

01

0

10

101

04

0

OPVrdE

OPVr

RIEBVMV

tt

t

tt

t

−+

=

−+

+=

∑

∑∞

=

∞

= (21)

Insight into this result can be obtained by recalling that all the ESO expenses and gains and losses

on the ESO liability are accounted for on what Christensen and Feltham (2003) refer to as the

“super-clean surplus” accounting basis, whereby the accounting reflects dividends flowing only

to existing equity holders. In which case, it follows that method 4 will yield an estimate of value

that is a function of td and mTMV . Equation (21) implies that .0

40

eMVMV =

Method 4 is the only one of the four accounting methods considered 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 accounted for at market value. Such super-clean accounting

guarantees that residual income is on a “proprietary” basis relevant to the valuation of shares in

issue.

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 plus a fraction of option

value, rendering a precise prediction difficult. Because a valuation based on equity book value

21

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 using an F-test because each of the

pairwise comparisons is between nested models. Following the standard residual income

valuation framework, each estimating equation includes a measure of equity book value and

current period residual income applicable to the relevant ESO accounting method.7

For model 1, based on accounting for ESOs under APB 25, we have the following

empirical models:

11

21

10 itititit BVRIMVE εααα +++= (22)

,'112

110 ititititit OPVBVRIMVE εααα +−++= (22*)

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;8 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

7 Because our primary concern is with the relative explanatory power of regressors associated with different methods of accounting for ESOs, we make no predictions regarding the magnitudes of equity book value and residual coefficients across the various specifications. However, in our discussion of the results, we assess their reasonableness, including their signs, and compare their magnitudes with those from extant research. We note that the Ohlson residual income valuation model suggests that “other information” will generally be relevant in explaining equity values when prices lead earnings. 8 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.

22

firms and years, respectively.9 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 restricting the coefficient on OPV to be −1 in equation (21*)

the dependent variable in that equation is implicitly the sum of MVE and OPV. Based on the

residual income valuation in section 2.3, we predict that equation (22*) will be better specified

than equation (22) because equity book value and residual income equal equity value of current

shareholders plus option fair value.

For accounting method 2, based on the SFAS 123 method of ESO accounting, we have:

22

22


,'222


where 12tt BVBV = and 2 1 .t t tRI RI OPTIONEXPENSE= − 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 T

OPV0 in the model. As in equation (22*), the coefficient on

OPV is restricted to be −1 in equation (23*), and the dependent variable in that equation is

implicitly the sum of MVE and OPV. Based on the residual income valuation in section 2.3, we

hesitate to predict whether equation (23*) will be better specified than equation (23).

9 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.

23

For model 3, based on the FASB Exposure Draft, we have the following estimating

equations:

332


,'332


where

,1

13ts

t

stt TYOPTIONEQUINSEOPTIONEXPEBVBV +∑−=

=

13 1

11

( ).t

t t t t ss

RI RI OPTIONEXPENSE r OPTIONEQUITY OPTIONEXPENSE−

−=

= − − − ∑

∑=

t

stNSEOPTIONEXPE

1

is the accumulated amortization of the ESO asset at time t and

)(1

11 s

t

st NSEOPTIONEXPETYOPTIONEQUIr

−

=− ∑− is the additional capital charge arising from the

unamortized 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. In contrast, OPV is marked-to-market every accounting period. As in

equations (22*) and (23*), the coefficient on OPV is restricted to be −1 in equation (24*), and the

dependent variable in that equation is implicitly the sum of MVE and OPV. Based on the residual

income valuation in section 2.3, we predict that equation (24*) will be better specified than

equation (24) because equity value of current shareholders plus option fair value depend on

equity book value and residual income.

Finally, for model 4, based on the IFRS 2 extension method of ESO accounting, we have,

442


,'442


24

where

4 11

1 1

1

( )

( _ _ ),

tt

t t s s ss s

t

s ss

BV BV OPTIONEXPENSE OPTIONLIAB OPTIONLIAB

FV ESO OPTIONS EXERCISED

−= =

=

= − ∑ − − +

×

Σ

∑

)( 114

−−−−= ttttt OPTIONLIABOPTIONLIABNSEOPTIONEXPERIRI

)]([ 1

1

1

1

1−

−

=

−

=−−∑− Σ ss

t

ss

t

sOPTIONLIABOPTIONLIABNSEOPTIONEXPEr ,

and tOPTIONLIAB is the sum of amounts recognized as liabilities as of time t resulting from

ESO grants. Note that OPTIONLIABis simply OPV; we adopt the convention of referring to it

as a liability to reinforce the notion that under the IFRS 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 the 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 (25*) should not improve upon

the correct residual income specification given by equation (25) and could lead to a deterioration

in specification by adding noise to the estimating equation. Thus, we predict no difference in

model explanatory power between equations (25) and (25*).

It is important to note that:

ttt OPTIONLIABBVBV −= 34 . (26)

25

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 ESO are exercised or expire, tOPTIONLIAB is closed into book equity and equation (24)

still holds. Thus, equation (26) 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 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 (22*), (24*) and (25) will each be

better specified than either equation associated with model 2, equations (23) and (23*). To test

these predictions, we 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 non-nested models, without assuming under the null that either model is the

correct model.

We estimate cross-sectional regressions for equations (22) through (25) 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

26

constants from either the pooled fixed-effects or the annual regressions. All equations are

estimated using unscaled data (Barth and Kallapur, 1996).10

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, 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 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 3 and

4.11

10 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 13, 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. 11 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

27

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.

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.12

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

of measurement error to have a material affects on inferences concerning the validity of our predictions because all the relevant models are affected similarly. 12 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.

28

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 1 reveal a positive relation between OPV and

equity market value. To address the endogeneity problem, we estimate OPV

andOPTIONLIABusing the predicted stock price from the benchmark residual income valuation

model (on a per share basis) that excludes all ESO-related measures, i.e., equation (21). 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 equation (21). When predicted stock

prices from the first-stage regression are negative, we set them to zero.

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

29

methods.13 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 on a per share basis, 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. firms. The sample

mean and median amounts for the option liability under method 4 (OPV) 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 OPV. 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

13 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.

30

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

(22) through (25*). 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 2R 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 regressions.14

The overall picture provided by the four tables is very similar. All eight models have high

2R values, and all unrestricted regressor coefficients are significantly positive in the pooled and

in all five annual estimations. For example, Table 3, panel A, containing findings relating to the

APB 25 ESO accounting method (i.e., method 1) reveals that R2 values exceed 80 percent, on

14 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.

31

average, and across years mean residual income and equity book value coefficients are 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 F-statistics

corresponding to the pairwise comparisons, for any given method of ESO accounting, of model

explanatory power for equations that do or do not include option fair value as a regressor, i.e.,

those between equations (22) and (22*), (23) and (23*), (24) and (24*), and (25) and (25*). Using

a 5% significance level, we can reject the null of equivalence in model explanatory power for F-

statistics exceeding 3.84. Panel B presents the Vuong t-statistics corresponding to the

comparisons of model explanatory power between those relating to the SFAS 123 method of ESO

accounting and those relating to the other three ESO accounting methods. Based on our

predictions, we tabulate Vuong t-statistics corresponding to comparisons between equations (22*),

(24*), and (25), and equations (23) and (23*).

Panel A reveals findings co22*) for the APB 25 accounting method is 6.23, indicating that

the equation including option fair value as an implicit part of the dependent variable is better

specified. Similarly, the F-statistic comparing equations (24) and (24*) for the Exposure Draft

accounting method is 6.08, 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 IFRS 2 extension ESO accounting method are

statistically equivalent in terms of explanatory power (F-statistic = 3.42). Finally, although we

have no predictions for the SFAS 123 equations, the F-statistic of 5.21 suggests that the model

32

that includes option fair value is better specified, which is consistent with the fraction of option

value (see equation (14)) being closer to one than to zero.

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 (22*) and (24*), are

better specified than that relating to SFAS 123, equation (23). 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 (25) and (23) suggests that the equation for the IFRS 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 (25) is empirically misspecified in

that the change in option value (the ESO liability), 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 one (Ohlson, 1999), or at least a

smaller coefficient than other income components.

To determine whether this explanation is valid, we re-estimated equation (25), permitting

the change in the option value to have a different coefficient from other income components.

Untabulated findings from this regression reveal that as predicted, the coefficient on the change

in option value 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 (25) is better specified than equation

(24) (t-statistic = 4.77). That is, the IFRS 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.

33

6. Summary and Concluding Remarks

We use the residual income 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 capture 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 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

accounting 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 IFRS 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

and net income amounts that overstate the value of current shareholder equity, whereby the APB

25 and Exposure Draft result in balance sheet and net income 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 and net income 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

34

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 IFRS 2 extension when we permit the change in the ESO

liability to have a different coefficient from that on other aggregate income components.

35

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.

Barth, M.E., W.H. Beaver, J.M. Hand, and W.R. Landsman (1999). “Accruals, Cash Flows, and

Equity Values.” Review of Accounting Studies 4, 205-229.

Barth, M.E., W.H. Beaver, J.M. Hand, and W.R. Landsman (2000). “Accrual Components,

Earnings Forecasting, and Equity Values.” Working paper, University of North Carolina and

Stanford University.

Barth, M.E, and S. Kallapur (1996). “Effects of Cross-Sectional Scale Differences on Regression

Results in Empirical Accounting Research.” Contemporary Accounting Research 13, 527-

567.

Bell, T.B., W.R. Landsman, B.L. Miller, and S. Yeh, (2002). “The Valuation Implications of

Employee Stock Option Accounting for Profitable Computer Software Firms.” The

Accounting Review 77, 971-996.

Black, F., and M. Scholes, (1973). “The Pricing of Options and Corporate Liabilities.” Journal of

Political Economy 81 (3), 637-654.

36

Christensen, P.O., and Feltham, G.A. (2002). Economics of Accounting. Volume 1 – Information

in Markets. Kluwer Academic Publishers, Hingham, MA.

Collins, D.W., Maydew, E.L., and I.S. Weiss. (1997). “Changes in the Value-Relevance of

Earnings & Equity Book Values Over The Past Forty Years.” Journal of Accounting and


Core, J., and W. Guay, and S. P. Kothari (2002). “The Economic Dilution of Employee Stock

Options: Diluted EPS for Valuation and Financial Reporting.” The Accounting Review 77,

627-652.

Credit Suisse First Boston (2004). “Expensing Stock Options: The Impact on S&P 500

Earnings.” Accounting & Tax, March.

Dechow, P.M., A.P. Hutton, and R.G. Sloan (1999). “An Empirical Assessment of the Residual

Income Valuation Model.” Journal of Accounting and Economics 26, 1-34.

Edwards, E.O., and P.W. Bell (1961). The Theory and Measurement of Business Income.

University of California Press, Berkeley and Los Angeles.

Fama, E.F., and K.R. French. (1998). “Taxes, Financing Decisions, and Firm Value.” Journal of

Finance 53, June.

Feltham, g., and J.A. Ohlson (1995). “Valuation and Clean surplus Accounting for Operating and

Financial Activities.” Contemporary Accounting Research, 689-731.

Financial Accounting Standards Board (1993). Exposure Draft: Accounting for Stock-Based

Compensation. FASB, Norwalk, CT.

Financial Accounting Standards Board (1995). Statement of Financial Accounting Standards No.

123: Accounting for Stock-Based Compensation. FASB, Norwalk, CT.

37

Financial Accounting Standards Board (2004). Exposure Draft: Share Based Payment. FASB,

Norwalk, CT.

Hand, J.R.M., and W. Landsman (2004). “The Pricing of Dividends and Equity Valuation.”

Journal of Business Finance and Accounting, forthcoming.

Hanlon, M., S. Rajgopal, and T. Shevlin (2003). “Are Executive Stock Options Associated with

Future Earnings?” Journal of Accounting and Economics 36, 3-43.

International Accounting Standards Board (2004). International Financial Reporting Standard,

Share-Based Payment. IASB, London.

Kothari, S.P., and J. Zimmerman. (1995). “Price and Return Models.” Journal of Accounting and


Li, F., and M.H.F. Wong. (2003). “Investor Valuation of Employee Stock Option Dilution.”

Working paper, University of Chicago.

Li, H. (2002). “Employee Stock Options, Residual Income Valuation, and Stock Price Reaction

to SFAS 123 Footnote Disclosures.” Working paper, University of Iowa.

Miller, M.H., and F. Modigliani (1961). “Dividend policy, Growth and the Valuation of Shares.”

Journal of Business 4, 411-433.

Ohlson, J.A. (1995). “Earnings, Equity Book Values, and Dividends in Equity Valuation.”

Contemporary Accounting Research, 66-687.

Peasnell, K.V. (1982). “Some formal Connections Between Economic Values and yields and

Accounting Numbers.” Journal of Business Finance and Accounting 9, 361-381.

Penman, S.H. (2003). Financial Statement Analysis and Security Valuation. McGraw-Hill.

Preinreich, G.A.D. (1938). “Annual survey of Economic Theory: The Theory of Depreciation.”

Econometrica 6, 219-241.

38

Ohlson, J.A. (1999). “On Transitory Earnings.” Review of Accounting Studies 4, 145-162.

Vuong, Q.H., 1989, Likelihood ratio tests for model selection and non-nested hypotheses,

Econometrica 57, 307–333.

White, H. (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct

Test for Heteroskedasticity.” Econometrica 48: 817–38.

39

Figure 1: Journal Entries Under Alternative ESO Accounting Treatments

Method 1: APB 25

1. At time of granting the option: no entry

2. Each year during the vesting period: no entries

3. At exercise date:

If the option is exercised, record receipt of cash

Dr Cash $XXX Cr Paid-in capital $XXX If the option lapses unexercised, no entry.

Method 2: SFAS 123

1. At time of granting the option: no entry

2. Each year during the vesting period: record ESO expense

Dr ESO expense $XXX Cr Paid-in capital – employee stock options $XXX 3. At exercise date:

If the option is exercised, record receipt of cash and close out PIC – options account

Dr Cash $XXX Dr Paid-in capital – employee stock options $XXX Cr Paid-in capital $XXX

If the option lapses unexercised, no further entry.

Method 3: 1993 FASB Exposure Draft

1. At time of granting the option: recognize fair value of ESO as an asset and as a component of equity

Dr Pre-paid compensation expense $XXX Cr Paid-in capital – employee stock options $XXX


Dr ESO expense $XXX Cr Pre-paid compensation expense $XXX

40

Figure 1: Journal Entries Under Alternative ESO Accounting Treatments, Continued

3. At exercise date:

If the option is exercised, record receipt of cash and close out PIC – options account

Dr Cash $XXX Dr Paid-in capital – employee stock options $XXX Cr Paid-in capital $XXX If the option lapses unexercised, no further entry.

Method 4: “option as a liability” IFRS 2 Extension

1. At time of granting the option: recognize fair value of ESO as an asset and as a liability

Dr Pre-paid compensation expense $XXX Cr Obligation to issue shares to employees $XXX


Dr ESO expense $XXX Cr Pre-paid compensation expense $XXX and mark-to-market the ESO. In the case of a rise in the fair value of ESO options, record loss

Dr Loss on increase in value of ESO obligation $XXX Cr Obligation to issue shares to employees $XXX And record a gain if the options decline in value

Dr Obligation to issue shares to employees $XXX Cr Gain on increase in value of ESO obligation $XXX 3. At exercise date:

If the option is exercised, record receipt of cash and cancel the liability

Dr Cash $XXX Dr Obligation to issue shares to employees $XXX Cr Paid-in capital $XXX

If the option lapses unexercised, no further entry is required since the liability will have been marked

to-market to zero.

TABLE 1Descriptive Statistics for Equity Market Value, Equity Book Values, Residual Incomes,

and Option Fair Value, for a Sample of S&P 500 Firms,with 1,354 Firm Year Observations, 1997-2001

Panel A: Distributional statistics (in $ millions)

Variable Mean Median Std. Dev.MVE 17,592.90 7,370.68 31,256.90BV 1 3,573.59 2,001.14 4,647.57BV 2 3,573.59 2,001.14 4,647.57BV 3 3,806.92 2,157.81 4,840.10BV 4 3,626.41 1,980.49 4,771.37RI 1 237.79 91.58 670.49RI 2 196.05 75.42 639.59RI 3 177.15 68.34 631.32RI 4 205.56 68.42 652.21OPV 180.51 117.71 218.46

Panel B: Correlations, with Pearson (Spearman) correlations above (below) the diagonal

Variable MVE BV 1 BV 2 BV 3 BV 4 RI 1 RI 2 RI 3 RI 4 OPVMVE 1.00 0.76 0.76 0.78 0.78 0.76 0.71 0.69 0.71 0.21BV 1 0.73 1.00 1.00 1.00 1.00 0.52 0.50 0.48 0.53 0.32BV 2 0.73 1.00 1.00 1.00 1.00 0.52 0.50 0.48 0.53 0.32BV 3 0.76 0.99 0.99 1.00 1.00 0.54 0.50 0.48 0.53 0.33BV 4 0.75 0.99 0.99 0.99 1.00 0.53 0.49 0.47 0.53 0.29RI 1 0.62 0.34 0.34 0.35 0.32 1.00 0.99 0.99 0.96 0.27RI 2 0.57 0.32 0.32 0.31 0.29 0.98 1.00 1.00 0.96 0.26RI 3 0.55 0.31 0.31 0.30 0.28 0.97 1.00 1.00 0.95 0.25RI 4 0.56 0.33 0.33 0.33 0.32 0.88 0.89 0.89 1.00 0.23OPV 0.23 0.29 0.29 0.30 0.24 0.33 0.30 0.29 0.22 1.00

Variable definitions MVE = market value of common shares outstanding at fiscal year-end.

BV 1 = book value of common equity as of fiscal year-end.

BV 2 = book value of common equity as of fiscal year-end, which is identical to BV 1.

BV 3 = BV 1 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.

BV 4 = BV 3 – OPV , OPV is defined as below.

RI 1 = abnormal earnings measured as net income before extraordinary items and discontinued operations, minus 0.12 x BV 1 (lagged one year).

RI 2 = abnormal earnings after ESO expense measured as net income before extraordinary items and discontinued operations, minus

ESO expense, minus 0.12 x BV 2 (lagged one year).

RI 3 = abnormal earnings after ESO expense measured as net income before extraordinary items and discontinued operations, minus

ESO expense, minus 0.12 x BV 3 (lagged one year).

RI 4 = 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 OPV , minusESO expense, minus 0.12 x BV 4 (lagged one year).

OPV = fair value of options oustanding at fiscal year-end, measured as the number of options oustanding at fiscal year-end times the estimated

year-end fair value per option. OPV is referred as OPTIONLIAB , ESO liability under Method 4.The fair value per option is estimatedusing the Black-Scholes option pricing model. To control for the endogenity noted by Aboody (1996), predicted prices from a first-stageregression 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.

ESLIAB

C E S O L I A B

C E S O L I A B

C E S O L I A B

41

Table 2First Stage Regressions of Equity Market Value on Residual Income and Equity Book Value,

for a Sample of S&P 500 Firms, 1996-2001*

CONSTANT __

Yaer No of Obs CoefficientWhite t-statistic Coefficient

White t-statistic Coefficient

White t-statistic Adj. R-Square

1996 440 338.70 3.44 9.59 10.34 1.83 22.66 0.851997 446 613.36 3.94 9.88 9.16 2.09 20.69 0.831998 450 1,048.00 6.62 10.50 9.55 2.03 19.41 0.741999 454 1,310.91 4.40 10.80 7.40 1.84 13.06 0.642000 467 1,013.79 4.53 8.87 9.40 1.83 17.68 0.712001 455 1,146.86 6.63 3.40 5.31 1.83 23.46 0.76

*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

MVE RI BV uit it it it= + + +α α α0 11

21

RI1

42

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

__

CoefficientWhite t-statistic Coefficient


Pooled fixed-effects 23.06 10.54 3.34 14.03 0.810Mean across years 26.32 7.42 3.01 7.60 0.842Maximum 34.45 3.58Minimum 17.27 2.20# significantly positive 5 5# significantly negative 0 0Z1 16.53 16.92Z2 5.84 8.52

Panel B: Summary statistics from regressions of equity market value on residual income, equity book valueand option fair value, with the option fair value coefficient restricted to equal negative one

_ __



Pooled fixed-effects 23.10 10.59 3.35 14.17 0.811Mean across years 26.39 7.43 3.02 7.63 0.843Maximum 34.54 3.59Minimum 17.26 2.21# significantly positive 5 5# significantly negative 0 0Z1 16.56 17.01Z2 5.86 8.67* 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 . )1(/)(/( −Ntstddevt )1(/)(/( −Ntstddevt

BV1

BV1


21

RI1

RI1MVE RI BV OPV uit it it it it= + + − +α α α0 1

12

1

)2/(/1 /1 −∑ = jkjkN Nj jt

)1(/)(/( −Ntstddevt )1(/)(/( −Ntstddevt

BV1

BV1


21

RI1

RI1MVE RI BV OPV uit it it it it= + + − +α α α0 1

12

1

43

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*


__





_ __




Z2 equals .)2/(/1 /1 −∑ = jkjkN N

j jt)1(/)(/( −Ntstddevt

)2/(/1 /1 −∑ = jkjkN Nj jt

)1(/)(/( −Ntstddevt


22

RI 2

RI 2 BV 2

BV 2

MVE RI BV OPV uit it it it it= + + − +α α α0 12

22

44

Table 5of Equity Market Value under Exposure Draft Method, for a SampleP 500 Firms, with 1,354 Firm-Year Observations, 1997-2001*

tics from regressions of equity market value on residual income and equity book value

__



20.48 9.69 3.74 16.45 0.80123.89 6.32 3.43 8.43 0.83132.98 4.0215.65 2.44

5 50 0

14.09 18.796.54 7.63

tics from regressions of equity market value on residual income, equity book valueh the option fair value coefficient restricted to equal negative one

_ __



20.51 9.75 3.75 16.60 0.80223.95 6.34 3.44 8.47 0.83133.06 4.0315.63 2.46

5 50 0

14.13 18.887.72 6.56

ll variables ear fixed-effect, the associated coefficients and t-statistics are not reported

, where t j is the t-statistic for industry j , k j is the degrees of freedom, and N is the number of years.)2/( −jkjk )2/( −jkjk


23

BV 3

BV 3RI 3

RI 3


23

45

Table 6Regressions of Equity Market Value under IFRS 2-extension (Option as a Liability)Method, for a Sample of S&P 500, with 1,354 Firm-Year Observations, 1997-2001*


__





__ __




Z2 equals .)2/(/1 /1 −∑ = jkjkN N

j jt)1(/)(/( −Ntstddevt

)2/(/1 /1 −∑ = jkjkN Nj jt

)1(/)(/( −Ntstddevt


24

RI 4 B V 4

RI 4 B V 4


24

46

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*

Method APB 25 SFAS 123 Exposure Draft IFRS2 extension

F-stat 6,23 5.21 6.08 3.42

Panel B: Inter-model comparisons of model explanatory power between method SFAS 123 and methods APB25, Exposure Draft , and IFRS 2 extension**

Method*** APB 25 (22*) Exposure Draft (24*) IFRS 2 extension (25) Modified IFRS 2 extension****

SFAS 123 (23) 5.87 5.13 0.32 4.77SFAS 123 (23*) 5.60 4.65 0.19 4.41

*The reported statistic tests incremental contribution of an explantory variable and has a F-distribution with degreeof freedom (1,1347), a number exceeding critical value indicates the equation includes option fair value is better 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 (less well) specified than the row model. ***Numbers in parentheses next to method refer to estimating equation number.****modified IFRS 2 extension is based on the IFRS 2 extension method, but permits change in option fair value to have a coefficient different from other residual income components.

O I aN I a

47

the value relevance of alternative methods of …assets.csom.umn.edu/assets/22269.pdf · the value...

Documents