Should Intangibles Be Measured: What Are the Economic ...qc2/BA532/2004 JAR kanodia sapra... ·...

Journal of Accounting ResearchVol. 42 No. 1 March 2004

Printed in U.S.A.

Should Intangibles Be Measured:What Are the Economic Trade-Offs?

C H A N D R A K A N O D I A , ∗ H A R E S H S A P R A , †A N D R A G H U V E N U G O P A L A N †

Received 11 December 2002; accepted 19 May 2003

ABSTRACT

We investigate whether a firm’s intangible investments should be measuredand separated from operating expenses. We find that the information ex-tracted from accounting reports of investments and earnings is different whenintangibles are measured and identified separately from operating expensesthan when intangibles are left commingled with operating expenses. This dif-ference in the market’s information causes a change in the behavior of marketprices, inducing changes in the firm’s investments and cash flows. Thus, froma real effects perspective, measuring intangibles is not unambiguously desirable.We identify the conditions under which providing information on intangiblesmay be desirable. This study also shows the inadequacy of statistical associ-ations between accounting numbers and prices as a basis for evaluating thedesirability of measuring intangible investments. We show that the measure-ment of intangibles alters the very distribution of cash flows about which themeasurement regime is seeking to provide information.

∗University of Minnesota; †University of Chicago. We appreciate the helpful commentsof David Aboody, Ray Ball (the editor), Tim Baldenius, Qi Chen, Sidney Davidson, JenniferFrancis, Frank Gigler, Milt Harris, Jack Hughes, Karim Jamal, Jing Liu, Per Olsson, ShivaRajgopal, Stefan Reichelstein, Jack Simms, Michael Smith, Sri Sridharan, Andy Spero, MohanVenkatachalam, Ram Venkataraman, and an anonymous referee. This paper has also benefitedfrom the comments of workshop participants at Alberta, Duke, Houston, Minnesota, Stanford,UCLA, and the 2002 Chicago-Minnesota Theory Conference held at Chicago. Sapra andVenugopalan gratefully acknowledge financial support from the University of Chicago,Graduate School of Business.

89

Copyright C©, University of Chicago on behalf of the Institute of Professional Accounting, 2004

90 C. KANODIA, H. SAPRA, AND R. VENUGOPALAN

1. Introduction

The last decade has witnessed an explosive growth in intangible invest-ments. Currently, it is believed that such investments frequently constitutethe most valuable assets of firms. Despite the enormity and value of theseassets, the appropriate accounting treatment of intangibles remains an un-settled issue, with ongoing debate in the Financial Accounting StandardsBoard (FASB), the academic literature, and the popular press. Critics ofcurrent accounting practice argue that “R&D outlays generate some of themost prized economic assets in the economy, and that accountants’ refusalto recognize these expenditures as assets seriously impairs the credibil-ity and relevance of financial reporting” (Healy, Myers, and Howe [2002,p. 678). Lev and Zarowin [1999] argue that nonrecognition of intangi-bles on the balance sheet has caused a significant decline in the relevanceand usefulness of accounting reports. In a 1996 symposium on “FinancialAccounting and Reporting of Intangible Assets,” organized by the Securi-ties and Exchange Commission (SEC), many speakers expressed the viewthat enhanced disclosure of intangible investments is highly desirable. Inthe popular press there are concerns that “arcane” accounting rules de-vised for a brick-and-mortar economy may be ill-suited to an economy inwhich many firms derive their competitive advantage from investments inintangibles.

Most of the debate regarding the accounting treatment of intangibles hascentered on whether expenditures on intangibles should be reported in theincome statement or in the balance sheet. Under current accounting rules,R&D outlays are disclosed as a line item in the income statement but arenot allowed to be capitalized on the balance sheet. However, many otherintangible investments are not even identified in the financial statements.For example, investments that create brand value, increase customer base,enhance a firm’s information technology, or improve product and processdesign are not distinguished from operating expenditures. Thus, there is amore primitive question that must precede the issue of whether intangiblesshould be reported in the income statement or the balance sheet: Shouldexpenditures on intangibles be measured and reported separately, or leftunmeasured and commingled with operating expenditures? In this paperwe investigate this more primitive informational question and ignore issuesregarding the balance sheet or income statement disclosure of intangibles. Ifexpenditures on intangibles are not measured and identified separately, theyare accounted for in the same way as operating expenditures because theyremain commingled with such expenses. Hence, we refer to this disclosureregime as the “expensing regime.” If intangibles are measured and identifiedseparately, there is the additional issue of whether these expenditures shouldbe capitalized and reported on the balance sheet or reported as a line-itemexpense on the income statement. We do not distinguish between thesetwo accounting treatments and refer to both forms of disclosure as the“intangibles measurement regime.”

SHOULD INTANGIBLES BE MEASURED 91

It appears that the FASB’s reluctance to account for intangibles separatelyfrom operating expenditures is due to two concerns: (1) impairment ofthe reliability of reported accounting numbers because of errors associatedwith measuring intangibles, and (2) expansion of opportunities for earningsmanagement by unscrupulous managers. Our model incorporates FASB’sconcerns by assuming that the measurement of intangibles is necessarilynoisy. We model three sources of noise and show that each of these sourcesof noise plays an important role in determining whether intangibles shouldbe measured and reported. The first kind of noise arises from random er-rors in discriminating between operating expenses and expenditures onintangible investments. The boundaries between operating expendituresand intangible investments are often so fuzzy that separation of the twowould require many subjective judgments by accountants and auditors. Forexample, what portion of product design and product engineering costsshould be treated as operating expenses and what portion should be re-ported as intangible investments? What proportion of an employee’s time isdevoted to normal production, what proportion to process and product de-velopment, and what proportion to human capital development? Even thebest intentioned accountant would make random errors in sorting throughthis maze. A second source of noise arises from the difficulty of discrimi-nating between productive and unproductive components of expenditureson intangibles. Not all expenditures on intangibles are productive; somerandom unforeseeable component is inevitably unproductive and wasteful.This is most apparent in R&D but is likely true of all kinds of intangibles.We think it is unlikely that accountants can accurately discriminate betweenthe productive and unproductive components of intangibles at each pointin time. This inaccuracy would precipitate random errors in accounting re-ports. We think a third source of noise arises because the measurement ofintangibles (and the implicit claim that they are assets) induces error inthe measurement of tangible investments. Attempts to classify the totalityof investments into tangible and intangible is prone to manipulation andclassification errors.

Informationally, the noise associated with measuring intangibles is a majordifference between the intangibles measurement regime and the expens-ing regime. The expensing treatment is relatively free of noise because itrequires no measurement of intangibles at all. Any outlay that is not clearlyin the nature of tangible investments is immediately charged to the incomestatement as an expense.

It may appear that even a crude estimate of intangibles would be betterthan providing no information on intangibles. Although true in a gameagainst nature, this claim is false in a situation where intangibles are pur-posefully chosen to optimize some well-specified objective function. In suchsituations, noisy estimates of intangibles contain no information on the in-tangibles themselves and are ignored by the market. What does changeas a result of intangibles measurement is the structure and informationcontent of the reported operating earnings of the firm. The separation of


intangibles removes the contamination of earnings caused by the unobserv-ability of intangibles in an expensing regime but introduces random errorsbecause of the shifting of transactions among operating expenses, intangi-ble investments, and tangible investments. This is akin to a noisy accrualprocess. Given noisy accruals, a firm’s cash flows acquire information con-tent incremental to the information contained in the reported operatingincome. Thus, in the intangibles measurement regime both reported op-erating earnings and reported net cash flow have information content. To-gether, they convey strictly more information to the market about the firm’strue operating earnings than the reports in an expensing regime. However,in this process, some information about the firm’s tangible investments islost.

Because observed net cash flow acquires information content in the in-tangibles measurement regime, capital market prices assign positive weightsto both earnings and cash flows. We show that a positive weight on earningsstimulates investment, but a positive weight on net cash flow deters invest-ment. This deterrence arises from a subtle endogenous informational cost.When the capital market cannot perfectly observe the firm’s investments,it is forced to anticipate those investments and incorporate these anticipa-tions into its pricing rule. Given these anticipations, higher net cash flowsignals good news and induces upward revisions in the market’s assesseddistribution of future earnings, causing an increase in the market price ofthe firm. This informational factor makes the firm reluctant to take unobserv-able actions, such as investment in intangibles, that decrease current cashflows, even though the decrease is more than offset by expected increases infuture cash flows. The incentive to cut back investments from first-best levelsto increase current cash flow is fully anticipated by the market and built intoits pricing rule. Thus, there is no deception, but the firm is trapped in a badequilibrium.

Such informational costs are also present in the expensing regime be-cause the firm’s intangible investments are unobservable in this regime,too. The observability of tangible investments in the expensing regime par-tially alleviates this cost. But, more important, we show that the informa-tional cost in the expensing regime is independent of noise in accountingmeasurements and is determined solely by the technological parametersthat govern the relative weight on intangibles in the tangibles-intangiblesmix that constitutes the firm’s capital stock. On the other hand, the infor-mational cost in the intangibles measurement regime depends critically onthe extent of noise in the earnings report caused by random misclassifica-tions of operating expenses and intangible investments. As this noise in-creases, the equilibrium price in the capital market assigns relatively lessweight to the firm’s earnings report and more weight to the firm’s ob-served cash flow, causing an increase in the informational cost to investment.This shift in the assigned weights on earnings and cash flow deters invest-ment in intangibles, which in turn reduces the firm’s incentives to invest intangibles.


Our main result is that separate disclosure of intangibles is preferred ifand only if intangibles can be measured with sufficient precision and thefirm’s technology is such that the relative weight on intangibles in the firm’scapital stock is sufficiently high. In all other cases, immediate expensing ofintangibles is preferred. This result is consistent with the FASB’s intuitionthat there is a trade-off between reliability and relevance that must be takeninto account in the determination of accounting standards. Our analysismakes this trade-off precise, albeit in a stylized setting, and underscores theimportance of the real effects of accounting in understanding the natureof the trade-off. Our analysis also identifies a hitherto ignored aspect ofdisclosure. The totality of information about the firm’s current earnings thatis revealed to the capital market is insufficient to rank disclosure policies;how that information is conveyed to the capital market is also important.Information about earnings that is conveyed through cash flows comes withhidden costs. These costs can be decreased by accruals, provided the accrualsare appropriately designed and relatively free of noise.

Empirically, it has been found that stock prices correlate better with ac-counting income and book values when intangibles are estimated, capi-talized, and amortized than when they are expensed (Lev and Sougiannis[1996], Aboody and Lev [1998]). The policy implication of these findings issummarized by Lev and Zarowin [1999], who explicitly state, “Accountingstandards which improve the alignment of reported book value with thefirm’s intrinsic value (usually proxied by market value) and/or improve theprediction of earnings should be preferred over standards which do not”(p. 378). This value-relevance approach to accounting policy suggests thatthe measurement and capitalization of intangibles is unambiguously pre-ferred to the expensing of intangibles. Our approach, and our conclusions,differs sharply from this value-relevance approach. Statistical associationsand alignments do not by themselves identify economic consequences. If thestatistical associations between accounting reports and stock prices changedepending on the accounting treatment of intangibles but nothing else inthe economy changes, such as capital market prices and firms’ investmentsand cash flows, these statistical associations are of purely academic interestand must surely lack policy significance. We believe that accounting policyon intangibles is better guided by a clear identification of changes in eco-nomic decisions, and their consequences, that are caused by a change inthe accounting treatment of intangibles. We assume that intangible invest-ments are value relevant and show that the value relevance of intangibles,the magnitude and growth of these investments, or their profitability do notby themselves imply that measurement and disclosure of intangibles is thepreferred accounting policy.

The results in our paper depend on explicit differences in the informationcontent of accounting reports, disclosed to the capital market, because ofthe accounting treatment of intangibles. We study how these informationaldifferences induce the firm’s investments to change. The firm is assumed tochoose its investments in tangibles and intangibles to maximize its price in


the capital market. The price in the capital market is endogenously deter-mined and depends on inferences made by traders from publicly observedaccounting reports and from prior knowledge of the firm’s technology andexpectations of profitability. The beliefs of traders are rational, in the sensethat these beliefs are consistent with the firm’s equilibrium choices, evenwhen these choices are not fully observed, and all assessed distributions offuture cash flows coincide with the distributions realized in equilibrium.This extreme rationality (market efficiency) rules out, by fiat, any form ofmispricing in the capital market. However, rational pricing does not implythat firms’ incentives for investment are unaffected. Informational differ-ences caused by the accounting treatment of intangibles induces a changein the behavior of market prices, which in turn induces changes in thefirm’s investments and cash flows. These real effects have clear implicationsfor accounting policy. We find that from such a real effects perspective, themeasurement and disclosure of intangibles is not unambiguously preferredto expensing. We identify conditions under which such measurements aredesirable and conditions under which expensing is the preferred account-ing treatment.

Stein [1989] and Kanodia and Mukherji [1996] are important an-tecedents to this paper. Stein shows how managers acquire an incentiveto borrow at unfavorable terms from the future to inflate current earningswhen such borrowings cannot be observed by the capital market. The no-tion of informational cost is implicit in Stein’s analysis but is more fullydeveloped in Kanodia and Mukherji, who use it to show why it is fundamen-tally important for accounting to separate investments from operating cashflows.1 Our analysis also exploits the results in Kanodia and Lee [1998], whoshowed how interim earnings reports that precede a firm’s final cash flowsprovide discipline for the firm’s investment decisions, via the pricing of thefirm in the capital market. Kanodia [1980] first formulated the real effectsof accounting by developing a general model of how accounting disclosuresand firms’ decisions are interrelated through the pricing of firms in thecapital market.

The remainder of the paper is organized as follows. Section 2 describesthe model and the assumptions underlying our analysis. In sections 3, 4,and 5, we characterize equilibrium investments and market prices for eachof three informational regimes: the regime where full information is avail-able, the regime where intangibles are expensed, and the regime whereintangibles are measured and disclosed. In section 6, we construct welfarecomparisons and develop the implications of our analysis for accounting pol-icy. Section 7 provides some insights suggested by our analysis regarding theinterpretation of empirical findings concerning the capitalization of intan-gibles. Finally, in section 8 we indicate some limitations to our analysis anddescribe possible extensions. Proofs of formal propositions are containedin the appendix.

1 Dutta and Reichelstein [2003] investigate a similar issue in an agency setting.


2. The Model

Consider a firm that needs both tangible and intangible investments toproduce future returns. Let K denote the firm’s tangible investments andN + γ denote the firm’s expenditures on intangible investments. We assumethat the expenditures required to build intangible investments are uncer-tain, in the sense that some random component of these expenditures turnsout to be wasteful and unproductive. For example, inevitably only some ofthe numerous R&D projects undertaken by a firm will be successful; hence,ex ante the cost of achieving an innovation is a random variable. We cap-ture this real-world feature by the additive term γ , which represents the ran-dom unproductive component of expenditures on intangible investments,whereas N represents the productive component. Tangible investments andproductive intangible investments combine to form the firm’s capital stock,q (K , N). The future returns to investment are determined by the firm’scapital stock rather than directly by its tangible and intangible investments.We assume:

A1. qK > 0.

A2. q N > 0.

A3. qKN > 0.

A4. qKK < 0, qNN < 0, qKK · qNN − q 2K N > 0.

Assumption A3 implies that the marginal effect of each investment on thefirm’s capital stock is increasing in the magnitude of the other investment.This specification captures the idea that tangible and intangible investmentscomplement each other. Assumption A4 is a standard concavity assumption.Though many of our results are established more generally, to obtain closed-form solutions, we assume a Cobb Douglas–like technology:

q (K , N) = K α Nβ, α > 0, β > 0, α + β < 1. (1)

The specification in (1) satisfies assumptions A1 through A4; α + β < 1guarantees strict concavity.

There are three dates in the economy: dates 0, 1, and 2. The firm acquiresits tangible and intangible investments, K and N, at date 0. The returns,x1, x2, to these investments are stochastic and are realized at dates 1 and 2,respectively. We assume that (x1, x2)is joint normally distributed with:

E (x1) = E (x2) = q (K , N)µ,

where µ > 0 is a known constant, describing the expected per period returnper unit of the firm’s capital stock,

Var(x1) = σ 2x ,


and

Cov(x1, x2) = ρ > 0.

A positive covariance implies there is some persistence, or growth compo-nent, in returns, making current returns informative about future returnsto the investment undertaken.

We assume that the firm’s manager makes all decisions in the best in-terests of the firm’s current shareholders. However, current shareholdersdo not hold the firm until all of the returns to the firm’s investments havebeen realized. At some interim date, there is a change in ownership, andcurrent shareholders are replaced by a new generation of shareholders.Specifically, we assume that current shareholders sell their shares inelasti-cally in a competitive capital market at date 1, after realization of x1 butbefore the realization of x2. Thus, although there is no source of conflictbetween the firm’s manager and current shareholders, there is a conflict ofinterest between current and prospective shareholders. This specificationallows us to abstract away from contracting issues and focus entirely on con-flicts that are mediated by capital market prices, accounting measurements,and disclosures.

We assume that all current and prospective shareholders are risk neutral.Thus, the date 1 equilibrium price in the capital market is:

P = x1 − K − N − γ︸︷︷︸cash assets at date 1

+ E (x2 | information)︸︷︷︸expectation of future cash flows

that is, the price in the capital market is the firm’s cash assets at date 1 plusthe expectation of its future cash flows. The firm’s current shareholdersconsume P , obtaining their entire return through market prices while futureshareholders consume the firm’s net cash flows less the price they pay toacquire the firm.

The accounting system provides a report on the firm’s investments, earn-ings and net cash flows before the transfer of ownership occurs. We ana-lyze three disclosure regimes: the full information regime, an expensingregime where intangibles are not measured, and an intangibles measure-ment regime. The primitive variables describing the state of the firm at date1 are: (1) the firm’s investment in tangibles K , (2) the firm’s productiveintangibles investment N , (3) the total expenditure on intangibles N + γ ,and (4) the date 1 true operating profits x1. The true operating profit ofthe firm at any date should be thought of as a summary statistic that netsout the revenues from goods sold during the period from those productionand marketing expenses that depend directly on the goods sold during thatperiod. For example, the expenses included in true operating profits wouldconsist of direct labor, direct materials, manufacturing overhead, and mar-keting and administrative expenses that support current-period revenueswith no direct effect on future cash flows. It is this true operating profitthat has persistence and covaries over time. In the full-information regime,


the capital market directly and perfectly observes all of the four primitivesthat describe the state of the firm at date 1. Full information is an unattain-able ideal but serves as a useful benchmark to evaluate the efficiencies ofthe other regimes. In the two other regimes, the primitives describing thestate of the firm are not directly observable; the capital market receives itsinformation from accounting measurements and reports. In principle, theaccountant seeks to measure each of the four primitives but makes errors(and is subject to managerial manipulation) because the boundaries be-tween true investments and true operating profits are fuzzy. We explicitlymodel three reporting errors that are associated with the measurement andtreatment of intangibles.

1. Errors due to misclassifications of operating expenses and intangibleinvestments. These errors arise because of the inherent fuzziness ofthe boundaries between these two types of expenditure. For example,it is extremely difficult to determine what portion of total market-ing expenditures increases future revenues by enhancing customerloyalty for the firm’s products and what portion of the expendituremerely increases current-period revenues. Such errors affect both re-ported operating profits and reported intangibles in the same direc-tion. Thus, if some operating expenditures are mistakenly identifiedas intangible investments, the report on investment is overstated andso is the report on earnings. We capture this measurement error by arandom variable ω.

2. Errors due to an inability to discriminate between productive and un-productive components of intangible investments. As discussed ear-lier, it is inevitable that some random component γ of the expendi-tures on intangible investments will turn out to be wasteful, in thesense that it benefits neither the present nor the future. In principle,this wasteful component of investment is different from operating ex-penses, even intangible operating expenses such as those marketingexpenses that support the revenues earned in the current period andthat are included in the firm’s true operating profit. We assume thatthe inability to discern the unproductive component will result in theentire expenditure of N + γ being accounted the same way.

3. Errors due to misclassifications of tangible and intangible invest-ments. Such misclassifications must be offsetting in the sense thatthey affect reported tangibles and reported intangibles in oppositedirections. We capture this misclassification error by a random vari-able η.

In the intangibles measurement regime, the reports provided by the ac-counting system consist of a measurement of tangible investments IK , ameasurement of intangible investments IN , earnings (or operating profits)yc , and date 1 net cash flow zc . We assume these reports are of the form:


IK = K + η,

IN = N + γ − η + ω,

zc = x1 −K − N − γ ,

yc = zc + IK + IN = x1 +ω.

As discussed earlier, these specifications incorporate the classification er-rors and noise associated with the measurement of intangibles. The randomvariable η, which represents errors that arise from attempts to classify a firm’sinvestments as tangible or intangible, appears in both IK and IN but withopposite signs. Because the accounting system cannot perfectly discrimi-nate between productive and unproductive expenditures associated withthe acquisition of intangible investments, the entire expenditure on intan-gibles N + γ is reported as intangibles investment. The presence of ω in thereported intangibles and in reported earnings reflects the fact that errorsdue to misclassifications of operating expenses and intangibles affect bothmeasurements in the same direction. Consistent with standard accountingprinciples, periodic (operating) earnings yc is obtained by adjusting thefirm’s net cash flow by adding back measured investments. We assume thatthe measurement errors η, γ , and ω are independent of each other andare normally distributed with zero means and variances of σ 2

η , σ 2γ , and σ 2

ω ,respectively.

In the expensing regime, the accounting system measures and capitalizesthe firm’s tangible investments only and treats all other cash outflows asoperating expenses for the period. The reports provided by the accountingsystem consist of a measurement of tangible investments IK , earnings ye ,and net cash flow ze (we use the subscript e to denote measurements inthe expensing regime and the subscript c to denote measurements in theintangibles measurement regime). Because the expensing regime makes noattempt to separate intangibles from operating expenses, it is clear that therandom variable ω will not appear in the accounting reports. We assume theaccounting reports produced in an expensing regime are of the form:

IK = K

ye ≡ x1 −N − γ

ze ≡ x1 −K − N − γ

We now give two examples to illustrate the error structure in these report-ing regimes. Suppose the only expenditures on intangibles in a firm consistof R&D. The total cash outflow on account of R&D is N + γ , where N isthe productive component and γ is the random unproductive componentof R&D. Suppose that a significant amount of R&D expenditures consists ofsalaries paid to engineers and that, in addition to R&D, engineering servicesare also supplied for routine production. In the expensing regime there isno need to separate the cost of engineering services supplied for routineproduction from engineering for R&D because they are both expensed.


This is what produces the earnings report ye ≡ x1 −N − γ . However, whenR&D is accounted separately from operating income, as in the intangiblesmeasurement regime, the accountant needs to separate the two compo-nents of engineering salaries and will likely make errors in doing so. Thisis what produces the error ω that affects both reported operating incomeand reported intangible investment. Additionally, suppose that some of theR&D results in tangible investments and some in intangible investments.Attempts to separate the two types of investments produces the error η.

Similar to the R&D example, total marketing expenditures generally sup-port both the routine production and sale of goods and the brand buildingand expansion of the customer base that benefit future sales. The first com-ponent (call it xm) is contained in x1 (because it is in the nature of anoperating expense and will covary with next period’s operating income),whereas the second component is what we call N + γ (because it is in thenature of an intangible expenditure). The total marketing expenditure isM = xm + N + γ . In the expensing regime, there is no need to separatexm from N + γ , but in the intangibles measurement regime, attempts toseparate the two will precipitate the error that we call ω.

The presence of η in the intangibles reporting regime and its absencein the expensing regime warrants additional explanation. Expensing of in-tangibles is inherently a regime where the measurement of investments isextremely conservative. The operational guideline here is “when in doubt,expense.” This is why intangibles are expensed, and only observed cash out-flows that are unambiguously in the nature of investment are measured andreported separately. Strictly speaking, this extreme conservatism implies thatthe measurement of tangibles in the expensing regime would be stochasti-cally downward biased; that is, IK would be a random variable with support[0, K ], where K is the true investment in tangibles and IK is the accountingmeasurement of tangibles. Clearly, the only information conveyed by sucha report is that K ≥ IK . In this spirit, the expensing regime as modeled,where I K = K is an approximation to a measurement regime with such astochastic downward bias, where the downward bias is small.2 An intangiblesmeasurement regime, however, is a more permissive regime where the samestrict standards of doubt are not applied. In this more permissive regime,shifting of transactions among operating expenses, intangible investments,and tangible investments becomes feasible.

In both the expensing regime and the intangibles measurement regime,the firm’s true operating profit x1 as well as its productive intangible in-vestment N cannot be detected, and capital market traders must make in-ferences on the basis of noisy information. Even though the intangiblesmeasurement regime provides a noisy estimate of the firm’s intangible in-vestment N , such noisy measurements contain no information on the in-tangibles themselves (see Bagwell [1995], Kanodia and Mukherji [1996]).

2 We show later that equilibrium investments in the intangibles measurement regime areunaffected by the magnitude of the variance of η.


However, we show that the intangibles measurement regime does providestrictly more information on the firm’s operating profit x1 than the expens-ing regime, precisely because of its noisy measurement of intangible invest-ments. This feature is a key difference between the two disclosure regimes. Asecond key difference is that the conservative aspect of the expensing regimeprovides a sharp measurement of the firm’s tangible investments, whereasthe absence of this property in the intangibles measurement regime in-troduces classification errors between tangible and intangible investments.Taken together, these two differences make the expensing regime moreinformative about the firm’s tangible investments while making the intan-gibles measurement regime more informative about the firm’s operatingprofits. Given these informational differences, it is unclear, a priori, whichdisclosure regime is better from a welfare perspective.

3. Equilibrium Investments in the Full-Information Regime

In the full-information regime, the firm’s date 1 operating profit, its in-vestment in tangibles, and its productive intangibles are all observable andavailable to the capital market for assessing the distribution of future cashflows. Thus, the equilibrium date 1 capital market price is:

P (x1, K , N) = x1 − K − N − γ + E (x2 | x1, K , N).

Given the market’s prior expectations, E (x1 | K , N) = E (x2 | K , N) =q (K , N)µ, this price reduces to:

P (x1, K , N) = x1 − K − N − γ + q (K , N)µ + ρ

σ 2x

[x1 − q (K , N)µ].

At date zero, when the firm chooses its investments, the date 1 operatingprofit x1 and the unproductive intangibles γ are random variables. Thefirm maximizes the expectation of the date 1 capital market price. Thus,the firm’s objective function is:

MaxK ,N

2q (K , N)µ − K − N. (2)

Optimal investments are characterized by the first-order conditions,

2µ qK = 1. (3)

2µ q N = 1. (4)

The objective function described in (2) and the optimal investments charac-terized in (3) and (4) are identical to those that would obtain if the currentshareholders did not liquidate their holdings at all and actually held thefirm until the terminal date. This is because a fully informed capital marketprice makes the current shareholders bear the full consequences of theiractions even though they liquidate their holdings early. In this sense, cap-ital market prices fulfill a perfect governance role in this full-informationeconomy.


Using the parametric technology q (K , N) = K α Nβ , we obtain closed-form expressions for the firm’s optimal investments. The first-order condi-tions become:

2µαK α−1 Nβ = 1, (5)

and

2µβK α Nβ−1 = 1, (6)

which implies that the efficient way to build capital stock is to combinetangible and intangible investments in the fixed proportion,

KN

= α

β(7)

Inserting this relationship between K and N into the first-order conditions(5) and (6), yields the following characterizations of the firm’s optimalinvestments:

PROPOSITION 1. Assuming that q (K , N) = K α Nβ , equilibrium investmentsin the full information regime are characterized by:

N1−α−β = 2µααβ1−α (8)

K 1−α−β = 2µα1−βββ.

4. Equilibrium Investments in the Expensing Regime

In the expensing regime, the accounting system reports the firm’s tangibleinvestments K , date 1 earnings, ye = x1−N−γ , and date 1 net cash flow, ze =x1 − K − N − γ . The information available to the market is summarized bythe tuple {K , ye } because clearly the firm’s net cash flow is equivalent to ze =ye −K and therefore contains no incremental information. The equilibriumprice in the capital market, as a function of the market’s information, is,

P (K , ye ) = ye − K + E (x2 | K , ye ).

It is not immediately apparent how the market would assess the conditionaldistribution E (x2 | K , ye ) because the firm’s reported income ye containsthe unknown intangible investment of N . Although N is unobservable bymarket participants, it is not a random variable and therefore has no de-fined statistical distribution that can be used to assess the joint distributionof (x2, y e ) unless N is first specified in some way. Because the quantity N isan endogenous choice for the firm, the market must rationally anticipate thefirm’s equilibrium choice of N , given its understanding of the firm’s incen-tives, and build this anticipation into its pricing rule (see Bagwell [1995],Kanodia and Mukherji [1996], and Kanodia, Singh, and Spero [2002] foradditional discussion). Because the firm’s tangible investment K is observedand because the firm’s incentives for choosing intangibles depends, in somefashion, on its choice of tangible investments, it seems reasonable to posit


that the market’s anticipation of intangibles is described by some scheduleN(K ), to be determined endogenously. Given these assessments, the marketperceives reported date 1 earnings as:

y e = x1 −γ − N(K )

with

E ( y e | K ) = q (K , N(K ))µ − N(K )

and

Cov(x2, y e ) = Cov(x2, x1) = ρ.

Moreover, the market’s prior expectation of x2 given its observation of K isq (K , N(K ))µ. Using these facts, the equilibrium date 1 price in the capitalmarket is:

P (K , ye ) = ye − K + q (K , N(K ))µ+ ρ

σ 2x + σ 2

γ

[ye − q (K , N(K ))µ+ N(K )]

(9)The firm chooses its investments to maximize its expectation of the date 1market price P (K , y e ). From the vantage of the firm, E ( y e ) = q (K , N)µ −N . It is important to distinguish between the firm’s true intangible invest-ment, which is N , and the capital market’s assessment of the firm’s intangibleinvestment, N(K ). In equilibrium, true and assessed intangibles coincide, butin choosing N the firm takes the market’s pricing rule as given and there-fore implicitly takes the market’s assessment N(K ) as given. Thus, the firm’sobjective function is:

MaxK ,N

q (K , N)µ − K − N + q (K , N(K ))µ

+ ρ

σ 2x + σ 2

γ

[q (K , N)µ − N − q (K , N(K ))µ + N(K )]. (10)

Differentiating (10) with respect to N yields the first-order condition:

µ∂q (K , N)

∂N− 1 + ρ

σ 2x + σ 2

γ

[µ∂q (K , N)

∂N− 1] = 0,

which simplifies to:

µ∂q (K , N)

∂N= 1. (11)

Comparing (4) with (11), the difference between the full-informationregime and the expensing regime is stark. The popular sentiment that thenonobservability of intangibles diminishes the firm’s incentive to invest inintangibles is confirmed. The nonobservability of intangibles results in aninformational cost that decreases the perceived marginal return to intan-gibles. When the date 1 operating profits of the firm cannot be observed,the market is forced to update its beliefs of future operating profits on the


basis of current earnings net of the expenditure on intangibles, that is, onthe basis of ye rather than x1. But, because Cov(x2, ye ) > 0, lower reportedearnings are rationally interpreted by the capital market as bad news, de-creasing the market’s expectation of future operating profits and depressingthe firm’s market value. This effect is purely informational and would disap-pear if the market were to directly observe the firm’s true earnings of x1. Thenonobservability of intangible investments creates an incentive for the firmto window dress its reported earnings by cutting back on these unobservableinvestments. From the firm’s perspective E ( ye ) = E (x1)− N ; therefore, anyexpenditure on intangibles beyond the amount that maximizes this quantityis harmful. Such window-dressing does not deceive the capital market. Thefirm’s diminished incentive to invest in intangibles is rationally anticipatedand the firm is priced accordingly.

Using the parametric form, q (K , N) = K α Nβ , the first-order condition(11) becomes

µβK α Nβ−1 = 1. (12)

Equation (12), and more generally equation (11), defines a relationshipbetween N and K that is consistent with the firm’s incentives and that thecapital market can anticipate. Thus, the schedule N(K ) that describes mar-ket anticipations must satisfy (11) and (12).

We now examine the firm’s choice of tangible investments. Differentiatingthe objective function, described in (10), with respect to K yields the first-order condition:

µ∂q (K , N)

∂K

[1 + ρ

σ 2x + σ 2

γ

]− 1

+ µ

[∂q (K , N(K ))

∂K+ ∂q (K , N(K ))

∂NN ′(K )

] [1 − ρ

σ 2x + σ 2

γ

]

+ ρ

σ 2x + σ 2

γ

N ′(K ) = 0.

Now, at the equilibrium value of K , the market’s assessment of intangiblesN(K ) coincides with the firm’s actual choice of N . Therefore, the firm’sequilibrium choice of (K , N) must satisfy:

2µ∂q (K , N)

∂K+ N ′(K )

[µ

(1 − ρ

σ 2x + σ 2

γ

)∂q (K , N)

∂N+ ρ

σ 2x + σ 2

γ

]= 1.

Inserting the firm’s first-order condition with respect to N , described in(11), the preceding equation reduces to,

2µ∂q (K , N)

∂K+ N ′(K ) = 1. (13)

The firm’s equilibrium investments are described by (12) and (13).


Closed-form characterizations of these equilibrium investments are ob-tained in Proposition 2.

PROPOSITION 2. Assuming that q (K , N) = K α Nβ , equilibrium investmentsin the expensing regime are described by:

KN

=(

1 + 11 − β

)α

β, (14)

K 1−α−β =(

1 + 11 − β

)1−β

µα1−βββ, (15)

N1−α−β =(

1 + 11 − β

)α

µααβ1−α. (16)

The equilibrium ratios, in which tangible and intangible investmentsare combined to produce capital stock, can be compared across the full-information regime and the expensing regime. In the full-informationregime we found that K/N = α/β. Comparing this with (14) yields theresult that in the expensing regime capital stock is built inefficiently be-cause of an excess reliance on tangible investments. Two factors contributeto this inefficiency: (1) there is an informational cost associated with intangi-bles but no informational cost associated with tangible investments, and (2)tangible investments acquire additional value because they communicateinformation about the firm’s intangibles.

5. Equilibrium Investments in the Intangibles Measurement Regime

As discussed earlier, attempts to measure intangible investments precipi-tate several kinds of measurement error. These errors preclude the perfectobservation of intangible investments as well as tangible investments. Similarto the expensing regime, such noisy measurements of endogenous decisionsdo not contain information on the decisions themselves. Thus, neither thereport on intangibles, IN = N + γ − η + ω, nor the report on tangibles,IK = K +η, is used to assess the firm’s investments. However, these measure-ments do strongly affect the structure and information content of the date1 earnings report of the firm. The earnings report is arrived at by addingthe measured investments to the publicly observed net cash flow of the firm,that is, yc = zc + IN + IK . Thus,

yc = (x1 − K − N − γ ) + (N + γ − η + ω) + (K + η) = x1 + ω.

Contrast this with the earnings report in the expensing regime, y e =x1 −N − γ . The contamination of earnings caused by the unknown invest-ment in intangibles that was present in the expensing regime is completelyeliminated in the intangibles measurement regime. However, measurementof intangibles introduces two new measurement errors, described by ω andη that were not present in the expensing regime. The error captured byω arises because it is often unclear whether some observed cash outflow


is an intangible investment with future benefits or an operating expensethat affects only the current period. The error captured by η arises frommisclassification of tangible and intangible investments. The latter error isoffsetting in nature; therefore, it is washed out in the earnings report.

In the expensing regime, the nonobservability of intangibles caused themarket to price the firm on the basis of anticipated intangible investments.In the intangibles measurement regime, the market anticipates both tan-gible and intangible investments because neither can be observed directly.Let K , N denote the market’s anticipations. Given these anticipations, themarket perceives the observed net cash flow of the firm as arising from:

z c = x1 − K − N − γ .

Thus, the market infers x1 −γ from the observed date 1 net cash flow ofthe firm, making this net cash flow incrementally informative relative to theearnings report. In fact, the net cash flow in the intangibles measurementregime contains the same information as the earnings report in the expens-ing regime because in both cases x1 − γ is inferred. But, additionally, theintangibles measurement regime conveys x1+ω through its earnings report.Thus, the intangibles measurement regime conveys strictly more informa-tion about current-period earnings than does the expensing regime. Is itpossible to obtain even more information in the intangibles measurementregime by reversing the measurement of either intangibles or tangibles?Expensing the reported intangibles yields y c −IN = x1 −N − γ + η; there-fore, the information here is strictly dominated by the information con-tained in the firm’s net cash flow. Expensing the reported tangibles yieldsyc − IK = x1 − K − η + ω, which is strictly dominated by the informationcontained in the earnings report.

The preceding arguments imply that the information available to the cap-ital market, in the intangibles measurement regime, is summarized by thetuple {z c , y c } describing the firm’s net cash flow and its reported earnings.Thus, the equilibrium date 1 price in the capital market is:

P (zc , yc ) = zc + E (x2 | zc , yc ).

Given anticipated investments of K , N , the market’s prior expectation of x2

is q(K , N)µ, and the assessed joint distribution of (x2, z c , y c ) is multivariatenormal. Using standard statistical formulae,

E (x2 | zc , yc ) = q (K , N)µ + b1[zc − E (z c )] + b2[yc − E ( y c )],

where the coefficients b1 and b2 are:

b1 ≡ cov(x2, z c ) var( y c ) − cov(x2, y c ) cov( y c , z c )var( y c ) var(z c ) − cov2( y c , z c )

, (17)

b2 ≡ cov(x2, y c ) var(z c ) − cov(x2, z c ) cov( y c , z c )var( y c ) var(z c ) − cov2( y c , z c )

. (18)


Now, as perceived by the market:

cov(x2, z c ) = cov(x2, x1 −K − N − γ ) = cov(x2, x1) = ρ

cov(x2, y c ) = cov(x2, x1 + ω) = ρ

cov( y c , z c ) = cov(x1 + ω, x1 − K − N − γ ) = σ 2x

var( y c ) = σ 2x + σ 2

ω

var(z c ) = var( x1 −K − N − γ ) = σ 2x + σ 2

γ .

Inserting the preceding equations into (17) and (18), and simplifying yields,

b1 = ρ σ 2ω

σ 2x

[σ 2

ω + σ 2γ

] + σ 2ωσ 2

γ

, (19)

b2 = ρ σ 2γ

σ 2x

[σ 2

ω + σ 2γ

] + σ 2ωσ 2

γ

. (20)

Additionally, the market’s expectations of net cash flow and earnings are,

E (z c ) = q (K , N)µ − K − N

E ( y c ) = q (K , N)µ

Using the preceding specifications, the equilibrium date 1 capital marketprice is,

P (zc , yc ) = zc +q (K , N)µ+b1[zc −q (K , N)µ+ K + N]+b2[yc −q (K , N)µ].

The firm chooses its investments to maximize the expectation of the pre-ceding price, where the expectation is over the random variables z c and y c .Noting that the firm takes the market’s pricing rule and, therefore, the mar-ket’s anticipation of investments K and N as given, the first-order conditionsfor a maximum are:

[1 + b1]∂ E (z c )

∂K+ b2

∂ E ( y c )∂K

= 0

and

[1 + b1]∂ E (z c )

∂N+ b2

∂ E ( y c )∂N

= 0.

Because, from the vantage of the firm, E (z c ) = q (K , N)µ − K − N andE ( y c ) = q (K , N)µ, these first-order conditions reduce to:

µ∂q (K , N)

∂K[1 + b1 + b2] = 1 + b1 (21)

and

µ∂q (K , N)

∂N[1 + b1 + b2] = 1 + b1. (22)


The market’s anticipation of the firm’s investments is rational if K , N satisfy(21) and (22). The market is perfectly capable of forming these anticipationsrationally because the parameters µ, b1, and b2 and the firm’s technologyq (K , N), are common knowledge.

To see how disclosures in the intangibles measurement regime affect thefirm’s investments, we now compare these investments with those obtainedin the first best economy. From (19) and (20):

b1 + b2 = ρ

σ 2x + σ 2

ωσ 2γ

σ 2ω + σ 2

γ

.

Because, in general, var(x1) ≥ cov(x1, x2), that is, σ 2x ≥ ρ, it follows that

b1 + b2 < 1. Additionally b1 > 0; therefore, it is clear that the firm underin-vests in both tangibles and intangibles, relative to first best. However, tangi-bles and intangibles are combined efficiently to build the firm’s capital stock

because (21) and (22) imply that∂q∂K∂q∂N

= 1, as in the full-information setting.

The reason for underinvestment in the intangibles measurement regime issimilar to that in the expensing regime, that is, the presence of informationalcosts.3 Higher net cash flows, which serve the same informational role hereas reported earnings in the expensing regime, are interpreted as good news,making the firm reluctant to decrease its date 1 net cash flow by increas-ing its investments toward the full-information levels. This informationalcost applies to both tangible and intangible investments, whereas in the ex-pensing regime it applies only to intangible investments. In the intangiblesmeasurement regime, investments are not treated as operating expensesand therefore do not contaminate earnings. Thus, the informational cost ofnet cash flow is partially offset by the earnings report. This offsetting effectis described by the weight b2 on the firm’s reported earnings, whereas theweight b1 on the firm’s net cash flow captures the informational cost. Tosee this more clearly, suppose σ 2

ω → 0, making the earnings report moreinformative about true date 1 operating earnings of x1 . In this case, b1 → 0and b1 + b2 becomes larger, moving the firm’s investments toward the full-information levels.

Inserting the Cobb Douglas–like technology into first-order conditions(21) and (22) yields the closed-form solutions described as follows.

PROPOSITION 3. Assuming that q (K , N) = K α Nβ , equilibrium investmentsin the intangibles measurement regime are described by:

KN

= α

β

K 1−α−β =(

1 + b2

1 + b1

)µα1−βββ, (23)

3 Bushee’s [1998] empirical findings are consistent with this result.


N1−α−β =(

1 + b2

1 + b1

)µααβ1−α. (24)

6. Welfare Comparisons and Policy Implications

Having characterized the equilibrium for each of the three disclosureregimes, we can now ask the policy question of whether intangible invest-ments should be measured or left commingled with operating expenses.We begin with the observation that it is vacuous to ask this question withouttaking into account the change in the equilibrium investments of the firminduced by changes in the disclosure regime. From a policy perspective,any disclosure regime must be evaluated ex ante to the actual release ofaccounting reports. The ex ante value of the firm, given that capital marketparticipants form their beliefs rationally, is always 2q (K , N)µ − K − N inall three disclosure regimes. Thus, if it is assumed that the firm’s investmentsare fixed, say at the first-best levels of K ∗, N∗ regardless of the disclosureregime, it is moot whether intangibles are expensed or identified separately.Expensing or measuring and reporting intangibles separately will, of course,produce different book values and earnings that correlate differently withrealized returns and prices in the capital market. But these are mere statisti-cal facts with no economic significance. We show that the firm’s equilibriuminvestments are not the same across disclosure regimes. In fact, in both theexpensing regime and the intangibles measurement regime, if capital mar-ket participants cling to the belief that the firm invests at first best levels, thefirm can actually increase its value by decreasing its investments below firstbest.

We evaluate disclosure regimes in terms of two criteria. First, we comparethe equilibrium investments of the firm across disclosure regimes. Second,we compare the expected payoff to the firm’s current shareholders acrossdisclosure regimes. The expected payoff to prospective shareholders is al-ways zero because, in each disclosure regime, the price paid by prospectiveshareholders equals the total expected cash flows of the firm. Hereafter, allof the analysis is conducted under the assumption that q (K , N) = K α Nβ.

6.1 COMPARISON OF INVESTMENT LEVELS

We use K ∗, N∗, q ∗ to denote first-best investments and capital stock,K E , NE , q E to denote equilibrium investments and capital stock in the ex-pensing regime, and Kc , Nc , qc to denote equilibrium investments and cap-ital stock in the intangibles measurement regime.

PROPOSITION 4. In both the expensing regime and the intangibles measurementregime, the firm’s equilibrium investments in tangibles and intangibles are below firstbest.

We now compare investments in the expensing regime to investments inthe intangibles measurement regime. Because 1 − β > α, there are onlythree cases to consider:


(i) 1 + b21 + b1

≤(

1 + 11 − β

)α

(ii) 1 + b21 + b1

≥(

1 + 11 − β

)1 − β

(iii)(

1 + 11 − β

)α

< 1 + b21 + b1

<(

1 + 11−β

)1 − β

In case (i) it follows from Propositions 2 and 3 that Kc < K E , Nc ≤ NE

(with strict inequality if the inequality in (i) is strict), and therefore qc < q E .Thus, in case (i) the intangibles measurement regime results in strictly lowerinvestments and capital stock than the expensing regime.

In case (ii), Nc > NE , Kc ≥ K E (with strict inequality if the inequalityin (ii) is strict), and therefore qc > q E . Thus, in this case the intangiblesmeasurement regime results in strictly higher investments and capital stockthan the expensing regime.

In case (iii), Nc > NE , but Kc < K E ; therefore, we compare the two regimesin terms of their overall equilibrium capital stocks. In the intangibles mea-surement regime, Proposition 3 implies,

K αc =

((1 + b2

1 + b1

)µα1−ββB

) α1−α−β

,

Nβc =

((1 + b2

1 + b1

)µααβ1−α

) β

1−α−β

so that

qc =(

1 + b2

1 + b1

) α+β

1−α−β

µα+β

1−α−β αα

1−α−β ββ

1−α−β .

Similar calculations for the expensing regime, based on Proposition 2, yield,

q E =(

1 + 11 − β

) α1−α−β

µα+β

1−α−β αα

1−α−β ββ

1−α−β .

Therefore, qc > q E if and only if (1 + b21 + b1

)α+β

1−α−β > (1 + 11 − β

)α

1−α−β or,

equivalently, if and only if (1 + b21 + b1

) > (1 + 11−β

)α

α+β . Because α < αα+β

<

1 − β, all three cases are summarized in the following proposition.

PROPOSITION 5. The firm’s capital stock is higher (lower) in the intangiblesmeasurement regime than the expensing regime if and only if:(

1 + b2

1 + b1

)> (<)

(1 + 1

1 − β

) αα+β

. (25)

The right-hand side of (25) depends only on the technological parametersthat determine the relative weight of tangible and intangible investmentsin forming the firm’s capital stock, whereas the left-hand side depends onlyon the measurement noise in the firm’s accounting system. Because the


profitability parameter µ does not appear in this inequality, the magnitudeof the firm’s investment in intangibles or its profitability, or both, is irrele-vant to the issue of whether intangibles should be measured or expensed.Capitalization must be preceded by measurement and separation of intan-gibles from operating expenses. This finding therefore questions populararguments advocating the capitalization of intangible investments on thegrounds that the investment in intangibles is very large and highly profitable.The profitability of intangible investments affects both disclosure regimesin the same way and therefore does not determine the relative advantage ofone over the other.

To better understand the forces that drive a preference for measurementor expensing of intangibles, examine each side of (25). The coefficient b2

1 + b1

can be calculated from (19) and (20) yielding,

b2

1 + b1= ρ

[ρ

σ 2ω

σ 2γ

+ σ 2x

(1 + σ 2

ω

σ 2γ

)+ σ 2

ω

]−1

.

Clearly, b21 + b1

is strictly decreasing in σ 2ω , strictly increasing in σ 2

γ , and strictlyincreasing in ρ. Recall that σ 2

ω represents the degree of noise in separatingintangible investments from operating expenses. Our analysis indicates thatsuch misclassifications between operating expenses and intangible invest-ments are extremely damaging to the case for the measurement of intangi-bles. An increase in σ 2

ω causes an increase in the value of b1 and a decreasein the value of b2; that is, the market puts more weight on the firm’s net cashflow and less weight on reported earnings in pricing the firm. This in turnincreases the informational cost of investment, decreasing the firm’s incen-tives to invest in both tangibles and intangibles. Perhaps this is a key factorunderlying the FASB’s reluctance to permit the capitalization of intangibles.Lev and Sougiannis [1996] remark, “Apparently, U.S. standard setters areconcerned with the reliability and objectivity of the estimates required forR&D capitalization, and with the associated audit risk. The specter of pro-viding managers with additional opportunities for earnings managementmust also weigh heavily on regulators” (p. 108). Our analysis indicates thatsuch concerns are indeed justified.

An increase in the uncertainty associated with the production of intan-gible investments, represented by σ 2

γ , has the opposite effect. This is be-cause such uncertainty decreases the information content of net cash flowsand leaves the information content of the earnings report unchanged.However, an important assumption underlying this result is that γ andω are uncorrelated; that is, the presence of random nonproductive ex-penditures in producing intangibles has no effect on errors in the mea-surement of earnings. Violation of this assumption may change the effectof σ 2

γ .An increase in ρ strengthens the case for measurement of intangible

investments because the greater the covariance between date 1 operatingprofits and date 2 operating profits, the greater is the information content ofthe earnings report that is provided in the intangibles measurement regime.


Consequently, the capital market attaches relatively more weight to the earn-ings report in pricing the firm, and this increases the firm’s incentives toinvest. All of these observations apply only to the intangibles measurementregime because, as shown in Proposition 2, equilibrium investments in theexpensing regime are completely independent of the noise in accountingmeasurements.

Because σ 2η does not appear in (25), it may appear that the noise due to

random classification errors between tangible and intangible investmentshas no effect on the relative desirability of measuring or expensing in-tangibles. Actually, the presence of such errors significantly damages thecase for measurement of intangibles. To see this, suppose σ 2

η = 0. Inthis case, the report on intangibles becomes IN = N + γ + ω, the reporton tangibles becomes IK = K , and reported earnings remain y = x1 + ω.Now, by reversing the measurement of intangibles, the capital marketwould calculate y − IN = x1 −N − γ . Thus, in the intangibles measurementregime the information available to the capital market would consist of{K , x1 − N − γ , x1 + ω}, whereas the expensing regime would provide theinformation {K , x1 −N − γ }. Thus, the intangibles measurement regimewould provide all of the information available in the expensing regime andmore, and would strictly dominate the expensing regime. This is essentiallythe argument made by proponents of capitalization; that is, the capitaliza-tion of intangibles could not possibly be harmful because such capitalizationcould be reversed and the information provided in the expensing regimecould be regained. It is argued that, this being the case, even crude esti-mates of intangibles could only enhance the information provided to themarket. Our analysis indicates there are two flaws in these arguments. First,crude (noisy) estimates of intangibles provide no information about the in-tangible investments. This is not an artifact of our model. It is genericallytrue that noisy information on endogenous actions provides no informationon the actions themselves. These crude estimates do change the structureand information content of the earnings report, but they also introduce anew source of noise, ω, that is absent in the expensing regime. Second, themeasurement of intangibles opens up the possibility of shifting cash flowsbetween tangibles and intangibles (represented by η), making it impossibleto regain the information in the expensing regime. It may be thought thatthese latter errors would be insignificant and could therefore be ignored.But we show that the magnitude of σ 2

η is irrelevant to the arguments favoringmeasurement or expensing of intangibles; only the presence of η is impor-tant. Even a small amount of noise in the classification of investments astangible or intangible fundamentally changes the information available tothe capital market.

To interpret the right-hand side of (25), note that β

α + βrepresents the

relative weight of intangibles in building the firm’s capital stock. We wishto examine how this relative weight of intangibles affects the desirability ofmeasuring intangible investments. To do this, hold α+β fixed at some valuer satisfying 0 < r < 1, and consider variations in β alone. In terms of r andβ, Proposition 5 can be restated as:


qc > q E iff(

1 + b2

1 + b1

)>

(1 + 1

1 − β

) r −β

r. (26)

Let f (β) denote the right-hand side of (26) and note that f (β) is a strictlydecreasing function of β. Because r is fixed, the range of β is [0, r ]. At β = 0,

f (β) = 2, and at β = r, f (β) = 1. Let T (σ 2ω , σ 2

γ , ρ) denote the left-handside of (26). Now, the lower bound on T is 1 because as σ 2

ω → ∞, T → 1.The upper bound on T is 2, which is attained when σ 2

ω = 0 and ρ = σ 2x . Thus,

T ∈ [1, 2] and f (β) ∈ [1, 2] and f (β) is strictly decreasing. This impliesthat for any fixed value of T there exists β∗(T ) such that β > β∗ ⇒ qc > q E .Conversely, for any fixed β there exists T∗(β) such that T > T∗ ⇒ qc > q E .We show that the following proposition holds.

PROPOSITION 6. Given any fixed level of noise in the measurement of intangibles,measurement is preferred to expensing if the relative weight of intangibles in buildingthe firm’s capital stock is large enough. Conversely, given the relative weight of intan-gibles, measurement is preferred to expensing if the noise associated with measuringintangibles is small enough. In all other cases, expensing of intangibles is preferred tomeasurement.

6.2 COMPARISON OF EXPECTED PAYOFFS TO CURRENT SHAREHOLDERS

The expected payoff to the firm’s current shareholders is equivalent to theexpected date 1 price in the capital market, where the expectation is takenfrom the perspective of date zero before the release of accounting reports.In both the expensing and the intangibles measurement regime, the date1 capital market price incorporates the market’s anticipation of the firm’schosen investments. In equilibrium, these anticipated investments coincidewith the firm’s actual investments. Thus, in all three regimes the expectedpayoff to current shareholders is V = 2µq (K , N)− K − N . We show that theequilibrium values of K and N are different in the three regimes, leadingto differences in the values of the firm’s capital stock q . However, becausethe mix of tangibles and intangibles used to form the firm’s capital stockvaries from one regime to another, it is not necessarily true that currentshareholders are better off when the firm’s capital stock is closer to firstbest. In the following, we explicitly calculate and compare the welfare of thefirm’s current shareholders in terms of the equilibrium expected payoffsthey earn in each of the three disclosure regimes. We show that resultssimilar to that in Proposition 6 continue to hold.

Let V ∗ denote the current shareholders’ equilibrium expected payoff inthe full-information regime, and let VE and Vc denote the correspondingpayoffs in the expensing and intangibles measurement regimes, respectively.

From Proposition 1, it follows that:

V ∗ = 2µ (2µα1−βββ)α

1−α−β (2µααβ1−α)β

1−α−β − (2µα1−βββ)1

1−α−β

− (2µααβ1−α)1

1−α−β .


Simplifying yields,

V ∗ = (2µααββ)1

1−α−β [1 − α − β]. (27)

Using the results in Proposition 2, similar calculations for the expensingregime yield:

VE =(

µ

(1 + 1

1 − β

)α

ααββ

) 11−α−β

[2 −

(1 + 1

1 − β

)α − β

].

For comparison purposes, it is convenient to express VE as:

VE = (2µααββ)1

1−α−β

[2 −

(1 + 1

1 − β

)α − β

]

×(

1 + 11 − β

) α1−α−β

(12

) 11−α−β

. (28)

Similar calculations for the intangibles measurement regime yield:

Vc = (2µααββ)1

1−α−β

[2T

− α − β

] [T2

] 11−α−β

. (29)

where T ≡ 1 + b21+b1

.

PROPOSITION 7. The equilibrium expected payoffs Vc and VE of the currentshareholders in the intangibles measurement and expensing regimes respectively arestrictly lower than the equilibrium payoff V ∗ of the current shareholders in the full-information regime. For any fixed value of T ∈ (1, 2) there exists β∗∗(T ) such thatβ > β∗∗ ⇒ Vc > VE . Conversely, for any fixed β ∈ (0, r ) there exists T ∗∗(β) suchthat T > T ∗∗ ⇒ Vc > VE .

We arrive at qualitatively similar conclusions regardless of whether disclo-sure regimes are evaluated in terms of their induced investments or in termsof the expected payoff to the firm’s current shareholders. Measurement ofintangibles is preferred if and only if the measurement noise associated withintangibles is sufficiently small and the relative weight of intangibles in thefirm’s capital stock is sufficiently large. In all other cases, it is better to leaveintangibles unmeasured and commingled with operating expenses.

We expect that the technology parameters α and β that fundamentallydetermine the relative mix of tangibles and intangibles in a firm’s capitalstock would vary considerably from one industry to another. The measure-ment noise associated with intangibles is also likely to vary across industries.Our analysis indicates that uniform accounting standards across all industriesmay be dysfunctional and investors may be better served by industry-specificaccounting standards.


7. Empirical Implications

Empirical studies document a positive association between estimated in-tangible investments and stock prices and returns even when the accountingsystem does not explicitly measure and report intangibles. This finding isconsistent with our theory. When intangibles are not reported, the marketdoes not naively price the firm as if its intangibles are zero (or $10 billion, orsome other equally arbitrary amount). In our theory, the market rationally(and correctly) anticipates the firm’s investment in intangibles and pricesthe firm accordingly. A simplistic regression of price against recorded bookvalues and recorded earnings, where the data are drawn from an expens-ing regime, assumes that the market prices the firm as if its intangibles arezero. Such regressions would be misspecified and would provide misleadingresults. It should not be surprising that when an estimate of intangibles isadded to the regression, significant coefficient values and improved R2 areobtained. These results do not necessarily imply that incorporating such esti-mates in formal accounting reports would actually provide new informationto the market, nor do they imply that an outside observer could use theseestimates to identify mispriced stocks and earn excess returns in the market.What they do imply is that the statistical estimates made by the researcherare a reasonably good proxy for market anticipations.

Our results also indicate that the value relevance of intangibles does not,by itself, imply that intangibles should be measured. In all three disclosureregimes analyzed in this paper, intangible investments are value relevant andare fully reflected in stock prices. How are these disclosure regimes to beranked on the basis of value relevance alone? But suppose we were to providethe value-relevance approach its best possible chance to evaluate accountingpolicy. Suppose we were to conduct a hypothetical experiment across two“island” economies, where intangibles are expensed in one economy andmeasured in the other economy. In each economy, an outside observerestimates a regression of stock price against earnings and book values. In theexpensing economy, reported book values and earnings are adjusted by anaccurate estimate of intangibles before the regression is estimated, whereasin the economy where intangibles are measured no adjustments are madeto accounting reports. Is it legitimate to compare coefficient values and R2sacross the two regimes to evaluate accounting policy? Again, the answer is inthe negative. The fundamental reason such comparisons are uninformativeis that the firm’s investments would be different in the two islands. Both thelevels of tangible and intangibles and the mix of tangibles and intangibleswould be different.

Propositions 5 and 6 indicate that the two critical factors that determinewhether intangibles should be measured or expensed are (1) the relativeweight on intangibles in the firm’s capital stock in the expensing regimeand (2) the relative weights assigned by the market to cash flows and earn-ings in the intangibles measurement regime. Measurement of intangibles ispreferred when the relative weight on intangibles in the expensing regime,


described by the technology parameter β

r , is large and the weight on cashflows relative to earnings that is implicit in market prices in the intangiblesmeasurement regime, described by 1

T ≡ 1 + b1b2

, is small. If β

r is interpretedas the relevance of intangibles and if 1

T is interpreted as the reliability orprecision with which intangibles can be measured, these results shed lighton the popular wisdom that there is a trade-off between relevance and reli-ability that must be taken into account in the determination of accountingstandards. We emphasize that this trade-off matters, not through its effecton correlations between accounting numbers and stock prices but throughits effect on the firm’s incentives to undertake investments in intangibles.

It can easily be verified that in all three disclosure regimes we analyze,the ratio of intangible investments to capital stock, N

q , is directly propor-tional to β, which suggests that this ratio can be used to estimate β. Aboodyand Lev [1998] use this ratio to provide evidence of a positive associationbetween software development intensity and the likelihood of a firm be-ing a capitalizer. They define software development intensity as the ratioof annual software development costs to sales. To the extent that softwaredevelopment intensity is a proxy for β, their evidence is consistent with thepredictions of our theory. Aboody and Lev do not, however, consider thesecond factor suggested by our theory, which would affect the likelihood ofa firm being a capitalizer. This second critical factor, T, is determined by thecoefficients b1 and b2 that represent the weights that capital market pricesassign to firms’ net cash flows and earnings, respectively. In principle, theseweights can be estimated and used in Aboody and Lev’s regression to yieldsharper insights.

Our theory suggests that requiring uniform application of generally ac-cepted accounting principles (GAAP) across all industries may be dysfunc-tional. The two critical factors β and T are likely to display considerablecross-sectional variation across industries. Therefore, it is conceivable thatmeasurement of intangibles is better for one industry whereas expensing isbetter for another industry. For the same reason, our theory questions thewisdom of requiring that R&D expenditures be measured and reported as aline item by firms in all industries. It is plausible that the relative importanceof R&D and the difficulty of separating it from operating expenses variesacross industries.

Our results may also be of independent interest to empirical researchersevaluating the quality of accounting regimes from a corporate governanceperspective. First, when the accounting regime is weak, we expect the qualityof earnings to be low, which in turn forces the capital market to rely moreheavily on a firm’s cash flows rather than on its earnings. Variations in thequality of accounting regimes would therefore map directly into the relativeweight that the capital market places on earnings and on cash flows. Second,the capital market’s reliance on cash flows deters firms from undertakingpositive net present value (NPV) investments. This disincentive to undertakepositive NPV investments is higher when the accounting regime is weaker.


8. Conclusion

We study the economic consequences of measuring intangibles eventhough most of the debate on the appropriate accounting treatment for in-tangibles centers around the issue of whether intangibles should be placedon the income statement or on the balance sheet. By addressing a moreprimitive question, we shed light on the relevance-reliability trade-off ofmeasuring intangibles. We show that intangibles should be measured onlywhen their relative importance in constituting the firm’s capital stock is highand when they can be measured with sufficiently high precision. In all othercases, attempts to separate intangible investments from operating expensesis counterproductive.4

There are other potential explanations for FASB’s reluctance to permitthe capitalization of intangibles. The value of tangible assets can actuallybe realized by creditors in times of financial distress because this value istransferable and observable in well-organized markets. However, most ofthe value of intangible assets is likely to be firm specific and nontradablein organized markets. This value cannot be seized by creditors in the eventof financial distress. Reporting such intangible assets on the balance sheetmay increase auditors’ exposure to litigation and legal liability in case offinancial distress. Our model does not address this issue.

Advocates of capitalization claim that the advantage of capitalization overexpensing stems primarily from the additional disclosures that must ac-company the classification of any expenditure as an asset. These enhanceddisclosures would include estimates of useful lives and magnitudes of im-pairment of intangible assets. This important issue cannot be addressed inthe kind of static model we analyze. Considerable additional insight couldbe obtained from a dynamic model where the useful lives of intangible as-sets changes stochastically over time and where there are opportunities foradditional investments over time.

An important limitation to our analysis concerns the assumption that thecapital market and the firm are symmetrically informed about the profitabil-ity of the firm’s capital stock. Given this assumption, noisy measurementsof endogenous investments cannot be used to make inferences about theinvestments themselves. However, if the firm’s investments are based on pri-vate information regarding the productivity or profitability of investment,noisy measurements of investments would have information content andwould lead to noisy signaling equilibria. The results in Kanodia, Singh, and

4 We assume that when alternative accounting measurement and disclosure regimes are fea-sible, only one of these alternatives must be chosen for reporting to the public. In principle,accountants could measure assets and income in multiple ways and disclose all of these mul-tiple statements to the public, letting each investor decide which disclosure to rely on. In thesetting we consider, the accountant could measure the firm’s investment under successivelyless conservative principles (the expensing regime being the most conservative) and discloseall of these different measurements. We rule out this possibility. Instead, we analyze the prosand cons of one measurement regime versus the other.


Spero [2002] suggest that in such settings some degree of measurementnoise may actually be desirable and therefore the trade-offs determiningthe desirability of measuring intangibles could change.

APPENDIX

Proof of Proposition 2. First, we calculate N ′(K ) from (12). Totally differ-entiating (12) with respect to K yields,

µβK α−1 Nβ−2[αN(K ) + (β − 1)K N ′(K )] = 0,

which implies,

N ′(K ) = αN(K )(1 − β)K

.

Using this, the first-order condition with respect to K described in (13)becomes,

2µαK α−1 Nβ(K ) + αN(K )(1 − β)K

= 1. (A1)

Now, inserting the expression for Nβ−1(K ) from (12) into (A1) yields,

N(K )[

2µαK α−1

µβK α+ α

(1 − β)K

]= 1,

which implies that the equilibrium relationship between K and N mustsatisfy,

β

α

(1 − β

2 − β

)K = N(K ). (A2)

Substituting for N(K ) from (A2) into (12), implies,(β

α

)β−1 (1 − β)2 − β)

)β−1

K β−1 = 1µβK α

,

which is equivalent to,

K 1−α−β =(

1 + 11 − β

)1−β

µα1−βββ. (A3)

The equilibrium value of N is obtained by evaluating N(K ) at the equilib-rium K . Equivalently, N(K ) can be calculated from the equilibrium rela-tionship (A2) rewritten as,

K 1−α−β

[β

α

(1 − β

2 − β

)]1−α−β

= N1−α−β.


Now, replacing K 1−α−β by the right-hand side of (A3) and simplifying yields,

N1−α−β =(

1 + 11 − β

)α

µααβ1−α,

completing the proof.

Proof of Proposition 3. For the specification, q (K , N) = K α Nβ , equations(21) and (22) reduce to:

µαK α−1 Nβ[1 + b1 + b2] = 1 + b1 (A4)

and

µβK α Nβ−1[1 + b1 + b2] = 1 + b1. (A5)

Dividing (A4) by (A5) yields KN = α

β. Substituting for K and N successively

in (A4) and (A5) yields the desired results.

Proof of Proposition 4. From Propositions 1 and 2 it is clear that K E < K ∗ iff(1 + 1

1−β)

1−β< 2, and NE < N∗ iff (1 + 1

1−β)α

< 2. From our assumptionthat α + β < 1, it follows that 1 − β > α; therefore, if K E < K ∗, it mustbe that NE < N∗. The result that K E < K ∗ follows from the algebraic factthat the function f (x) = (

1 + 1x

)xis strictly increasing and for 0 < x < 1,

1 < f (x) < 2. Turning to the intangibles measurement regime, it followsfrom Propositions 1 and 3 that both tangible and intangible investments arelower than first best if and only if b2

1+b1< 1. This inequality holds because

σ 2x ≥ ρ implies that b2 < 1 and clearly b1 > 0.

Proof of Proposition 7 . We first verify that Vc < V ∗ and VE < V ∗. The firstinequality follows if:[

2T

− α − β

] [T2

] 11−α−β

< 1 − α − β.

Now, 1 < T < 2, and over this interval the factor[ 2

T − α − β] [ T

2

] 11−α−β is

strictly increasing in T, attaining 1−α −β at T = 2, from which the desiredinequality follows. Additionally, VE < V ∗ if and only if,

[2 −

(1 + 1

1 − β

)α − β

] (1 + 1

1 − β

) α1−α−β

(12

) 11−α−β

< 1 − α − β

⇔[

2 − β −(

2 − β

1 − β

)α

] [2 − β

1 − β

] α1−α−β

< (1 − α − β)21

1−α−β

⇔(

2 − β

1 − β

)(1 − α − β)

[2 − β

1 − β

] α1−α−β

< (1 − α − β)21

1−α−β

⇔(

2 − β

1 − β

)1−β

< 2.


The left-hand side of the preceding inequality is strictly decreasing in β andattains the value 2 at β = 0. Therefore, VE < V ∗ for each β > 0.

We now compare the intangibles measurement regime with the expensingregime. From (28) and (29), it follows that Vc > VE if and only if:[

2T

− α − β

]T

11−α−β

>

[2 −

(1 + 1

1 − β

)α − β

] (1 + 1

1 − β

) α1−α−β

.

As shown in the preceding calculations, the right-hand side equals

(1 − α − β) [ 2−β

1−β]

1−β

1−α−β . Therefore, Vc > VE if and only if:(2T − α − β

1 − α − β

)1−α−β

T >

(2 − β

1 − β

)1−β

. (A6)

To assess (A6) for feasible values of α, β, and T, once again let α + β = r ,hold r ∈ (0, 1) fixed, and think of the left-hand side of (A6) as a functionof T and the right-hand side of (A6) as a function of β. Feasible values ofT are contained in the interval (1, 2) and feasible values of β are containedin the interval (0, r ). Now,

Vc > VE iff

(2T − r

1 − r

)1−r

T >

(2 − β

1 − β

)1−β

. (A7)

The left-hand side of (A7) does not depend on β and is strictly increasingin T over the interval (1, 2), attaining the value

( 2−r1−r

)1−rat T = 1 and

attaining the value 2 at T = 2. The right-hand side of (A7) does not dependon T and is strictly decreasing in β over the interval (0, r ), attaining thevalue 2 at β = 0 and attaining the value

( 2−r1−r

)1−rat β = r . Thus, as in

Proposition 6, for any fixed value of T ∈ (1, 2) there exists β∗∗(T ) such thatβ > β∗∗ ⇒ Vc > VE . Conversely, for any fixed β ∈ (0, r ) there exists T∗∗(β)such that T > T∗∗ ⇒ Vc > VE .

REFERENCES

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