Revenue Recognition in a Multiperiod Agency Setting *
Sunil Dutta
and
Xiao-Jun Zhang
Haas School of Business
University of California
Berkeley, CA 94720
forthcoming, Journal of Accounting Research
____________________________________________________________________________
* We are grateful to Chandra Kanodia, Arijit Mukherji, Jim Ohlson, Stefan Reichelstein, an
anonymous referee and seminar participants at University of Minnesota for their comments and
suggestions.
Revenue Recognition in a Multiperiod Agency Setting
Abstract
This paper examines how various revenue recognition rules affect the incentive
properties of accounting information in a stewardship setting. Our analysis demonstrates that if
revenues are recognized according to the realization principle, a single performance measure
based on aggregated accounting information can be used to provide desirable production and
effort incentives to the manager. In contrast, mark-to-market accounting does not provide
efficient aggregation of raw information to solve the stewardship problem. Mark-to-market
accounting, though sensible from a valuation perspective, fails to provide desirable incentives
because it relies on the anticipated, rather than the actual, performance of the manager. We also
consider a setting in which the manager can control the timing of the firm’s sales. It then
becomes desirable to modify the realization principle and apply the lower-of-cost-or-market
valuation rule. The desirable accounting thus exhibit a conservative bias.
Revenue Recognition in a Multiperiod Agency Setting
1. Introduction
Accrual accounting distinguishes revenues from cash inflows and expenses from cash
outflows, recognizing the differences between income and cash flows as liabilities or assets. The
principles which govern the recognition of revenues and expenses are the key determinants of
the properties of accrual accounting information. This paper studies the revenue recognition
question from a stewardship perspective. In particular, we examine how various revenue
recognition principles affect the incentive properties of performance measures based on
aggregated accounting data.
We consider a multiperiod agency setting in which a risk-averse agent manages a firm’s
operations. In each period, the manager receives information about the firm’s operating
environment and makes the firm’s production decision. In addition, the manager exerts
productive effort to improve the firm’s profitability in each period. The production process
spans over multiple reporting periods. Specifically, we assume that goods put in production in
the current period become available for sale in the next period. Depending on how revenues are
recognized, asset valuation rule ranges from historical cost to mark-to-market.
Our results show that when revenues are recognized according to the realization
principle, residual income provides optimal effort and production incentives (optimal within the
class of linear incentive schemes). Under the realization principle, products are carried at their
historical costs on the balance sheet. These costs are subsequently expensed when products are
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sold and revenues are realized.1 Income measurement under the realization principle, thus,
entails intertemporal matching of costs and revenues. Such matching ensures that the manager
makes the appropriate production decision in each period regardless of the relative magnitudes
of the bonus coefficients, which can be specifically chosen to solve the underlying hidden effort
problems.
In contrast, we demonstrate that mark-to-market accounting generally does not provide
efficient aggregation of raw information for the owner to solve the stewardship problems. Markto-market accounting, although sensible from an equity valuation perspective, fails to fulfil the
stewardship role for two reasons. First, given that the manager possesses private information
regarding the firm’s operating environment, mark-to-market accounting based on the public
information fails to properly align the intertemporal costs and benefits of managerial decisions,
and thus distorts the manager’s incentives to make such decisions. In particular, mark-to-market
accounting based on the anticipated performance of the manager does not induce the manager to
actually deliver such performance. Second, while mark-to-market accounting aggregates future
expected cash flows using the firm’s true cost of capital, it is generally necessary to use a
different rate for the optimal resolution of the agency problem.
The first part of the analysis is carried out under the assumption that the manager cannot
control the timing of sales. In such settings, we show that it is optimal to strictly adhere to the
realization principle. When the manager can also control the timing of realization, however, we
1
We define revenues as realized when the amount of associated cash inflows can be
measured in an objective and verifiable fashion without relying on the accountant’s beliefs
regarding the firm’s operating environment or various managerial decisions that led to such cash
flows.
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find that it becomes necessary to modify the realization criterion conservatively. Under pure
historical cost accounting, the manager would have incentives to hold obsolete products in
inventory if expost production costs exceed realizable revenues. From the owner’s perspective,
however, products with short life cycles should be promptly sold regardless of their historical
production costs, which are sunk. Our analysis shows that the lower-of-cost-or-market
valuation rule restores proper sales and production incentives. Under the lower-of-cost-ormarket rule, the manager is charged for all of the production costs regardless of his sales
decision. Consequently, he has no incentives to deviate from the efficient sales policy.
Our paper relates to the literature that recognizes multiple demands for accounting
information. Gjesdal [1981] formally demonstrates that valuation and stewardship needs are
likely to be best served by different information systems. 2 Antle and Demski [1989] examine
the specific issue of revenue recognition. Unlike our analysis, however, they consider a setting
in which shareholders rely on accounting information for their intertemporal consumption
decisions and show that the optimal recognition rule in a pure consumption setting is generally
not optimal in a stewardship setting.
This paper also contributes to the recent literature on managerial performance evaluation
based on accrual accounting information. The existing research in this area has abstracted away
from the issue of revenue recognition. For instance, Rogerson [1997], Reichelstein [2000] and
Dutta and Reichelstein [2000] take cash-based revenue recognition rule as given and examine
how costs should be matched against future revenues in order to create desirable managerial
2
Unlike our paper which focus on the desirability of a particular accounting choice from
stewardship perspective, Gjesdal [1981] considers an abstract information system choice
framework that does not address specific accounting choice questions.
-3-
incentives. Recent work by Baldenius and Reichelstein [2000] examines conditions under
which various inventory valuation rules can be used to provide desirable incentives to a riskneutral manager. Consistent with our findings, they show the desirability of historical cost
accounting in generating proper incentives. In contrast to their analysis, our paper examines the
choice of optimal revenue recognition rules in an incentive contracting setting with a risk- and
work-averse manager. Furthermore, our analysis focuses on comparing incentive properties of
historical cost accounting, which delays recognition of profits and losses until realization, with
incentive properties of mark-to-market accounting, which recognizes unrealized holding gains
and losses.
Finally, our paper contributes to the literature on accounting conservatism. Devine
[1963] discusses several economic and behavioral reasons for conservatism. Antle and Lambert
[1988] show how a principle-agent problem between client and auditor can induce a demand for
conservatism. In contrast, we focus on the agency conflict between owner and manager and
demonstrate that accounting conservatism may be desirable simply because the manager has
incentive to use his private information in an asymmetric fashion.
2. The Model
We model a firm whose operations involve purchasing of materials, conducting
production, and selling finished goods. Each operating cycle begins with the purchase of raw
materials and extends over more than one reporting period. Specifically, we assume that goods
put in production in period t become available for sale in period t+1. A manager is needed to
carry out the operation of the firm. In each period, the manager can exert effort et to reduce the
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production costs. Such effort may represent his input in the effective implementation of the
firm’s production activities. The total production cost incurred in period t depends on the
manager’s production decision qt+1, stochastic shocks
, and the manager’s effort et.
For simplicity, we assume that these costs are paid in cash so that the total cash outflow in
period t is given by
.
(1)
The parameter wt represents the productivity of the manager’s effort in period t. The random
shock
, which realizes at date t, is normally distributed with mean zero and variance
manager privately observes the realization of the stochastic shock
period t. The random variables {
. The
at the beginning of
} are assumed to be distributed with support over some
subset of positive reals.
The total cash inflow from selling products in period t+1 is given by:
,
(2)
The revenue parameters {pt} are commonly known at date 0. The random disturbance term
, which becomes realized at date t+1, is assumed to be normally distributed with mean zero
and variance
. For simplicity, all random variables are assumed to be independent of each
other.
In each period, the firm pays cash in the amount of c1t to start a new production cycle
and receives cash in the amount of c2t by selling products that become available for sale.
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Though each operating cycle lasts only two periods, the firm continues its operation by starting a
new cycle every period. Thus, the firm’s activities consist of overlapping operating cycles as
described above. Initially, we assume that all of the goods are sold in the same period in which
they are finished, and the manager has no control over the timing of sales. Therefore, the net
operating cash flow in period t is given by:
(3)
Later we also consider a setting in which the manager controls the timing of sales.
In addition to providing productive efforts each period, the manager is responsible for
the firm’s production planning (i.e., choosing qt+1) based on his assessment of the firm’s
operating environment in each period. Prior to making his production decision in period t, the
manager obtains information about the realized value of the stochastic shock
random disturbance term
. The additive
reflects residual cost uncertainty, which is resolved after the
manager has made his period t production decision.
While the firm continues indefinitely, we assume that the manager is hired for T periods.
The manager’s contract, which is drawn at date t=0, covers the entire T periods of the manager’s
planning horizon. Both the owner and the manager are assumed to be able to fully commit to
the contract. For contracting purposes, the available information at time t includes both the
current and the past cash inflows and outflows, i.e.,
It = It-1 c{c1t, c2t}.
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For tractibility, we restrict our analysis to compensation contracts that are linear functions of the
available information. Specifically, we assume that the manager’s compensation at time t is a
linear function of the whole history of cash inflows and outflows up to that point in time:
(4)
.3 Given our restriction to linear contracts, any reference to optimality will be
for
understood to mean optimality within the class of linear incentive schemes.
The risk-neutral owner seeks to maximize the present value of expected future cash flows
net of compensation payments to the manager. Let r denote the owner’s cost of capital and ( /
(1+r)-1 denote the corresponding discount factor. The owner’s objective is to maximize the
following expression:
,
(5)
where T denotes the manager’s planning horizon. We assume that the manager is risk-averse
and effort-averse. In particular, we assume that the manager’s preference over the future
compensation and effort streams can be represented by the following additively-separable
exponential utility function:
3
We assume that there are no sales in the first period (i.e., c22 = 0), and hence set
for all t $1. We also assume that there is no production in the last period (i.e., c1T =
0), and set
. These assumptions simplify the exposition. Our results readily extend to
a more realistic setting in which the manager begins his tenure with some unfinished goods
(which are then finished and sold in the first period) and ends his tenure with some unfinished
goods (which are finished and sold by the next manager).
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In the above expression, D is the manager’s degree of risk aversion, ht represents his
consumption in period t, and
is his personal cost of effort denoted in monetary terms. The
manager can smooth his consumption through access to credit market. In particular, we assume
that the manager can borrow and lend money at the interest rate r. If dt denotes the manager’s
savings at the end of period t, his consumption in period t is given by
.
Finally, without loss of generality, we normalize the manager’s initial wealth and external
market alternative to zero. Like in one-period models, this multiperiod linear contracting
framework leads to a mean-variance representation of the manager’s expected utility, thereby
allowing us to explicitly characterize optimal linear contracts.4
3. Optimal Contracts Based on Disaggregated Information
Before characterizing the optimal performance measures under asymmetric information,
we first examine the first-best case in which the manager and the owner have symmetric
information. Given the additively-separable structure between the manager’s effort and other
costs, it follows immediately that the first-best production decision is given by:
4
In a multiperiod model, the manager’s certainty equivalent expression reduces to a
mean-variance expression only if the manager has access to credit. (See Dutta and Reichelstein
[1999] for details.) The economic significance of the manager’s access to credit is that, in
designing optimal contracts, the principal does not need to concern herself with the manager’s
desire to smooth consumption. To eliminate consumption smoothing concerns, one could
alternatively assume a multiplicatively-separable CARA utility function for the manager. Our
setup allows for a convenient way to introduce discounting of future payoffs.
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(6)
After making the production decision, the manager chooses his effort et. In the first-best case,
the optimal effort level will satisfy the condition that the marginal cost of effort is equal to its
marginal product, i.e.,
.
In our setting with asymmetric information between the manager and the owner, the
manager makes the production decision after privately observing the period t decision-relevant
information
. Let us first consider the manager’s production choices if he were offered a
fixed salary contract. Since the planning decision by itself does not impose any personal cost to
the manager, we can safely assume that the manager will choose to maximize the owner’s
objective. Therefore, the production planning problem can be completely solved through a
simple fixed salary contract. However, a fixed salary contract would fail to induce any effort
form the manager. Therefore, the production planning problem imposes a cost to the owner only
because of the underlying hidden effort problem.
Solving for the manager’s optimal consumption and production planning problems by
backward induction yields the following expression for the certainty equivalent of the manager’s
date 0 expected utility from the linear contract (4):5
where
5
See Appendix A for derivation.
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and
.
The parameter β 1t (β 2t) can be interpreted as the effective bonus coefficient associated with cash
outflow c1t (cash inflow c2t) since it represents the date t present value of future bonus payments
for each dollar of cash outflow (cash inflow) in period t. The above certainty equivalent
expression makes clear that the manager is indifferent about the timing of compensation
payments. Since both the manager and owner care only about the effective bonus coefficients
β 1t and β 2t, the compensation contract in (4) is equivalent to the following contract:
.
(7)
Without loss of generality, therefore, we focus on contracts of the form in (7) in the remainder
of the analysis.
We show in Appendix A that the manager’s production decision in period t is given by:
.
(8)
A comparison with expression (6) reveals that the manager will produce at the first-best level if
the bonus coefficients of the linear compensation scheme are such that bt+1 = 1 for each t.
Substituting the optimal production decision from (8) into expressions (1) and (2), the
manager’s certainty equivalent can be written as follows:
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.
(9)
Expression (9) shows that the certainty equivalent of the manager’s expected utility is given by
the present value of the mean-variance expressions corresponding to the manager’s
compensation payment in each period. 6
We are now ready to derive the optimal contact with disaggregated information. Since
the manager’s market alternative is normalized to zero and the participation constraint will bind
in an optimal contract, it follows that CE0 = 0. Hence, expression (9) yields:
(10)
The manager’s incentive compatibility constraints with respect to his effort choices yield that
for each t. Substituting this and expression (10) into the owner’s objective function
lead to the following unconstrained optimization problem:
.
The first-order conditions give: 7 .
We note, however, that the effective coefficient of risk aversion, ρ@(1-γ), is less than the
nominal coefficient ρ because the agent can spread the effect of an income shock in any given
period over an infinite horizon.
6
7
To ensure that the second order condition holds, we assume that
.
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,
.
Equations (11) and (12) show that
(11)
(12)
. Hence, it follows from expression (8) that the
principal optimally induces under-production (relative to the first-best case). Ideally, it would
be desirable to shield the manager completely from the risk associated with c2t by setting bt+1 =
0. This would, however, induce the manager to severely under-produce. On the other hand, the
first-best production can be induced by setting bt+1 = 1, but at the expense of imposing
excessive risk on the risk-averse manager. In choosing the optimal bonus coefficients, the
principal trades off the opportunity cost of under-production with the cost of risk premium that
has to be paid to the manager.
4. Optimal Contracts based on Aggregated Accounting Information
Having characterized contracts that can depend on completely disaggregated data, we
now address the question whether there exist optimal contracts that rely on only aggregated
accounting information. Specifically, we are interested in accounting principles which enable
us to aggregate the vector of raw information It into a vector of lower dimension without losing
any incentive-relevant information.
In the following analysis, we use Inct to denote operating income before compensation
to the manager in period t. We use BVt to denote book value of the firm’s operating assets at
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date t. For simplicity, we assume that the owner is the direct recipient of the firm’s cash flows
in each period and the following clean surplus relation holds:
,
where
equals net income, and
use income before compensation,
represents net dividend. For incentive contracts, we
, rather than net income,
. Accounting measures
(i.e., income and book value) depend crucially on the underlying measurement rules, especially
how revenues and expenses are recognized. In the remainder of the analysis, we examine how
various revenue recognition principles affect the incentive properties of accounting
information.
In our setting, the most ‘natural’ revenue recognition rule is the one in which products
are carried at their historical costs until associated benefits become realized. Under such a
revenue recognition rule, book value at the end of period t simply equals c1t. Therefore, income
in period t is given by:
.
(13)
Recall that c1t-1 denotes the amount of ‘investment’ in period t-1, the period in which the t-th
operating cycle begins, while c2t represents the associated benefits that get realized in period t,
the period in which the t-th operating cycle ends. Income measurement in (13), therefore,
adheres to the realization principle which requires that revenues be recognized only after
benefits have become realized.
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Under a compensation contract of the form { st="t + β t@Inct} with β t $ 0, the manager
would make his period t-1 production decision to maximize
. This implies that
the manager would have incentives to over-produce relative to the second-best optimal quantity.
To see this, note that while the expression
represents the undiscounted value of
future cash flows, the owner seeks to maximize the discounted value of future cash flows, i.e,
. Moreover, in the second-best setting, the owner prefers to curtail production
even further because of the underlying agency costs. Intuitively, operating income induces the
manager to over-produce because it fails to make him internalize the owner’s cost of capital.
To provide desirable production incentives, operating income has to be appropriately
adjusted for the use of capital. Residual income, defined as operating income less an interest
charge on the beginning of the period book value, explicitly takes into account the owner’s cost
of capital. When revenues are recognized according to the realization principle, residual income
is given by:
,
where rt denotes the capital charge rate. We show in Appendix A that residual income based on
the hurdle rate:
>r
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would provide optimal production incentives.8 That is, any linear compensation contract which
is weakly increasing in residual income (i.e., any compensation contract { st="t + β t@RIt} with β t
$ 0 for each t) would induce the manager to make the optimal production decision in each
period.
In the following analysis, we say that a performance measure { πt } is optimal if there
exists coefficients { "t, β t} such that the compensation contract { st="t + β t@πt } achieves the
same expected profit for the owner as the optimal compensation scheme based on
disaggregated information.
PROPOSITION 1. Residual income based on the hurdle rate
is an optimal performance
measure provided that revenues are recognized according to the realization principle.
Proof. All proofs are in Appendix A.
Under the realization principle, the cash outflow in each period is capitalized as an asset
on the balance sheet. This asset is subsequently expensed when the associated finished goods
are sold and revenues are recognized. Therefore, income measurement under the realization
principle entails an intertemporal matching of costs and benefits. Such matching of costs and
benefits induces the manager to make the optimal production decision in each period regardless
8
That the optimal hurdle rate exceeds the firm’s cost of capital is consistent with the
findings in Dutta and Reichelstein [2000] and Christensen, Feltham, and Wu [2000]. These
papers show that the optimal capital charge rate may differ from the firm’s cost of capital due to
agency considerations.
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of the relative magnitudes of the bonus coefficients {β t} of his compensation contract. The
underlying hidden effort problems can then be addressed through the appropriate choice of the
bonus coefficients {β t}.
A key feature of the realization principle is that costs and benefits are matched by
delaying recognition of expenses to periods when the associated benefits become realized. An
alternative form of intertemporal matching would recognize expected future benefits as revenues
and the current expenditures as expenses in the current period. Such an accounting treatment
would resemble mark-to-market valuation in which assets would be carried at their expected net
realizable values of
. The question is whether such a revenue recognition
principle, which is rather sensible from a valuation perspective, can be used to aggregate
information for optimal contracting purposes.9 To address this question, suppose that the two
parties rely on an independent accountant for valuation purposes. Though the accountant does
not directly observe the manager’s decisions or the information on the basis of which such
decisions are made, his valuation would reflect rational inferences about the manager’s
decisions. Given a compensation contract, let
denote the accountant’s conjecture on the
manager’s production policy. The manager makes his production choice
taking the
accountant’s valuation as given. The accountant’s valuation is said to be rational if
for each
.
9
See Ohlson and Zhang [1998] for analysis of how accounting asset valuation rules
aggregate raw transactions and events for equity valuation.
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The next result shows that if the firm uses mark-to-market accounting, no performance
measure based on current accounting information can provide optimal incentives.10 To derive
this result, we consider accounting information based performance measures in the class
. This class includes cash, operating income, as well as residual
income.
COROLLARY 1.
If the firm uses mark-to-market accounting, no performance measure based
on current accounting information can achieve optimality.
At first glance it may seem surprising that mark-to-market accounting fails to provide
appropriate incentives even though, by definition, it values the expected net realizable benefits
in an unbiased and efficient manner. Though the accountant cannot directly observe the
manager’s decision or his decision-relevant information, he can rationally anticipate the
manager’s production policy in equilibrium given a compensation contract. Mark-to-market
accounting, therefore, relies on the anticipated benefits in equilibrium. However, this does not
necessarily induce the manager to undertake desirable production decisions. The manager’s
incentives come from the owner’s ability to detect and punish deviations of the delivered
benefits from the anticipated benefits. This is the reason that historical cost accounting which
10
We note an exception to this claim. If the parameters of the problem line up in such a
fashion that the optimal solution with disaggregated information entails
for each t, any
revenue recognition rule (e.g., mark-to-market or cash accounting) can be used to generate
optimal incentives. We rule out this special case by assuming that
for some t. In this
regard, we should point out that the condition
would hold if all of the periods were
identical.
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relies on the realized or delivered performance provides desired incentives, but mark-to-market
accounting fails to do so.
5. Endogenous Sales Decisions
The preceding analysis provides an agency-theoretic rationale for why it may be optimal
to carry assets at historical costs and delay revenue recognition until realization. In this section
we examine a more realistic setting in which the manager is responsible for both production and
selling decisions, and show why certain modifications of the realization principle may be
desirable from an incentive contracting perspective.
We have thus far presumed that all of the goods finished in a given period are sold in the
same period, and the manager has no control over the firm’s sales policy. Now we relax this
assumption and make the manager’s selling decisions endogenous. For simplicity, suppose that
the firm’s products become obsolete after one period, and hence it is efficient to sell them as
soon as they become ready for sale. Unlike the previous section, however, the manager will
adopt the efficient sales policy only if it is in his interests to do so. As before, the manager
makes his period t production decision after observing the realization of the decision-relevant
information
, but before observing the realization of the fixed cost shock
.
The question now becomes whether aggregated accounting information can be used to
provide desirable sales and production incentives. To examine this issue, as before, we focus on
linear compensation contracts that are based on current accounting information. First, we show
that any compensation contract that relies on accounting information based on the realization
principle will distort the manager’s sales/production incentives. To see this, let us consider the
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manager’s sales decision in the last period. When revenues are recognized according to the
realization principle, income in the last period is given by
where
denotes the fraction of period T-1 production that is sold in period T. Regardless of whether the
manager is compensated on the basis of operating income or residual income, he will choose
= 0 if the realized fixed cost shock
is such that
. This, in turn, will induce
him to distort his production decision in the previous period. Similar distortions would arise in
earlier periods.
The intuition for why pure historical cost accounting provides distorted sales incentives
is straightforward. Under historical cost accounting, assets are carried at their costs until sold.
If the fixed cost shock in a given period turns out to be sufficiently unfavorable, the manager
will find it optimal to defer recognition of the associated expenses by holding goods in inventory
until after he leaves. From the owner’s perspective, however, this is inefficient as stored goods
become obsolete and loose their value.
The next result shows that incentive schemes that are based on only aggregated
accounting information can still be used to induce optimal incentives provided that the revenue
recognition rule is appropriately modified.11 In particular, it shows that optimal
production/sales incentives can be generated if finished goods are carried at the lower-of-costor-market. Formally, an asset valuation rule is said to be lower-of-cost-or-market if:
11
Given our simplified setting which precludes any ‘legitimate’ reason for carrying
inventory, we note that the above incentive problem can be simply solved by imposing a large
penalty on the manager for carrying any inventory of finished goods. By construction,
however, such an incentive scheme cannot be implemented using only aggregated accounting
data.
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,
where HCJt (MVJt) denotes the historical cost (market value) of the period J production that
remains in the firm’s inventory stock at the end of period t.
PROPOSITION 2. If the manager has control over the timing of sales, it is optimal to use the
lower-of-cost-or-market asset valuation rule and compensate the manager on the basis of current
residual income.
This result shows that when the manager can control the timing of realization, it becomes
desirable to adopt a conservative accounting policy of valuing assets at the lower-of-cost-ormarket in order to generate proper selling incentives. In our model, the lower-of-cost-or-market
valuation rule ensures that the manager is charged for all of the production costs regardless of
his selling decision. Consequently, the manager has no incentives to deviate from the efficient
policy of selling goods as soon as they become ready for sale.
We conclude this section by commenting on the robustness of our main results. The
results have been derived in a stylized setting in which (i) the technology is linear-quadratic and
the manager’s decision-relevant information,
, is one-dimensional, and (ii) the compensation
contract is linear. We note that the first two assumptions regarding the production technology are
not crucial for the qualitative nature of our main results. On the other hand, it is admittedly
difficult to provide a sharp characterization of the optimal revenue recognition rules without a
restriction to linear contracts. It seems, however, that our main results should remain intact even
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if non-linear compensation functions are allowed provided that accounting aggregation rules are
restricted to be linear, which appears to be a reasonable assumption.
6. Conclusion
In this paper we examine how various revenue recognition principles affect the incentive
properties of performance measures based on accounting information. In addition to making the
firm’s production decisions, a manager contributes productive efforts in each period. Our results
show that if revenues are recognized according to the realization principle, residual income can
be used to generate optimal production and effort incentives. On the other hand, no performance
measure based on current accounting information can generate optimal incentives if the firm uses
mark-to-market accounting.
When the manager can control the timing of sales, our analysis shows that it becomes
necessary to modify the realization principle and use the lower-of-cost-or-market valuation rule in
order to provide the manager desirable selling incentives. This result demonstrates that
conservatism may be a desirable accounting ingredient for managerial performance evaluation
purposes. While rationales for accounting conservatism in prior research have typically relied on
asymmetric loss functions, our analysis shows that conservative accounting may be desirable
simply because the manager has incentives to use his private information in an asymmetric
fashion.
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APPENDIX A
Derivation of the Expression for the Manager’s Certainty Equivalent.
We illustrate the steps involved for the two period model. The arguments for the general case
are identical. When T = 2, the compensation contract in (4) reduces to {
,
}.
After the second period, the manager will optimally consume the interest on his wealth
at date 2 (i.e.,
for all t > 2) in order to generate a smooth consumption pattern. The
manager’s utility from future consumption therefore becomes
define
, where for brevity we
.
At the end of the second period, the manager chooses his savings to maximize:
.
The first-order condition for the optimal d2* yields
(14)
. Substituting this in
(14), we get
.
Thus, at the end of first period, the manager will choose his savings d1 to maximize:
(15)
Solving for the optimal d1* and substituting in (15) yield
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(16)
After observing θ2, the manager makes the first period production decision to maximize
the expected value of
. The first-order condition yields
,
where
(17)
,
. Substituting (17) into the expression for
c11 yield
(18)
The manager’s date 0 expected utility from future consumption is given by
.
Substituting (17) and (18) into (16) and completing the expectation show that the certainty
equivalent of the manager’s date 0 expected utility is given by:
.
Proof of Proposition 1. Under the realization principle or historical cost accounting, book value
at the end of each period equals production costs in that period, i.e.,
income measurement then yields
.
Residual income becomes:
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. Comprehensive
.
Thus, the compensation contract {
} is equivalent to the following contract based
on the disaggregated cash flow information:
.
Consequently, if the principal chooses the bonus coefficient
,
(19)
,
(20)
the hurdle rate
and the fixed salaries {αt} such that the manager’s participation constraint holds with equality,
then the contract {
Proof of Corollary 1.
} achieves the optimal performance.
To prove the result, we establish that it is impossible to generate optimal
production and effort incentives from a contract of the form {
}, where
is based on mark-to-market accounting . To the contrary, suppose the accountant conjectures
that the manager will make the optimal production decisions, i.e.,
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for each t # T-1.
Recall that
, where
and
(21)
denote the coefficient on period t cash outflow and
cash inflow, respectively, in the optimal linear incentive scheme based on disaggregated
information. Given the conjecture in (21), under mark-to-market accounting, the date t-1 book
value of the firm’s inventories is given by:
.
Therefore, book value at the end of each period is a known constant in the sense that it depends
neither on the agent’s choices nor on stochastic shocks. The period t performance measure can
be written as:
Consequently, the manager’s period t-1 production choice is given by
A comparison with (8) reveals that the manager will choose the optimal production only if
.
(22)
Optimal effort incentives in period t require that:
(23).
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Combining (22) and (23) yields that the manager’s period t production and effort decisions will
coincide with the optimal decisions only if
assumption that
. This, however, violates the maintained
for some t.
Proof of Proposition 2. In period t, MVJt = 0 for all J < t because of our assumption that goods
become obsolete after one period. Furthermore, HCtt = c1t. Under the lower-of-cost-or-market
valuation rule, therefore, book value at the end of period t simply equals c1t, and consequently
residual income becomes:
,
Suppose the principal chooses the bonus coefficients β t and the hurdle rates rt as in (19) and (20),
respectively. Under the contract {
}, the manager’s sales decision in a given
period affects his payoffs only in that period (through c2t). Since c2t is monotone increasing in the
fraction of the production sold, the manager will optimally choose to sell all of the production in
each period. Consequently, the manager will choose the optimal production decision in each
period. Therefore, the contract {
} induces optimal effort, production, and sales
incentives. If the owner chooses the fixed payments such that the manager’s participation
constraint holds with equality, {
} is optimal.
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