Revenue Recognition in a Multiperiod Agency Setting *

Transcription

1 Revenue Recognition in a Multiperiod Agency Setting * Sunil Dutta and Xiao-Jun Zhang Haas School of Business University of California Berkeley, CA 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.

2 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.

3 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 -1-

4 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. -2-

5 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-

6 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 e t to reduce the -4-

7 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 q t+1, stochastic shocks, and the manager s effort e t. 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 w t 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. The manager privately observes the realization of the stochastic shock at the beginning of period t. The random variables { } 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 {p t } 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 c 1t to start a new production cycle and receives cash in the amount of c 2t by selling products that become available for sale. -5-

8 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 q t+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. The additive random disturbance term 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., I t = I t-1 c{c 1t, c 2t }. -6-

9 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) for. 3 Given our restriction to linear contracts, any reference to optimality will be 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., c 22 = 0), and hence set for all t $1. We also assume that there is no production in the last period (i.e., c 1T = 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). -7-

10 In the above expression, D is the manager s degree of risk aversion, h t 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 d t 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 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. -8-

11 (6) After making the production decision, the manager chooses his effort e t. 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. -9-

12 and. The parameter β 1t (β 2t ) can be interpreted as the effective bonus coefficient associated with cash outflow c 1t (cash inflow c 2t ) 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 b t+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: -10-

13 . (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 CE 0 = 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. 6 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. 7 To ensure that the second order condition holds, we assume that. -11-

14 , (11). (12) Equations (11) and (12) show that. 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 c 2t by setting b t+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 b t+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 I t into a vector of lower dimension without losing any incentive-relevant information. In the following analysis, we use Inc t to denote operating income before compensation to the manager in period t. We use BV t to denote book value of the firm s operating assets at -12-

15 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 represents net dividend. For incentive contracts, we use income before compensation,, 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 c 1t. Therefore, income in period t is given by:. (13) Recall that c 1t-1 denotes the amount of investment in period t-1, the period in which the t-th operating cycle begins, while c 2t 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. -13-

16 Under a compensation contract of the form { s t =" t + β t } 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 r t denotes the capital charge rate. We show in Appendix A that residual income based on the hurdle rate: > r -14-

17 would provide optimal production incentives. 8 That is, any linear compensation contract which is weakly increasing in residual income (i.e., any compensation contract { s t =" t + β t } 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 { π t } is optimal if there exists coefficients {" t, β t } such that the compensation contract { s t =" t + β t } 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. -15-

18 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. -16-

19 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. -17-

20 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 -18-

21 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. -19-

22 , where HC J t (MV J t ) 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 -20-

23 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. -21-

24 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, where for brevity we define. At the end of the second period, the manager chooses his savings to maximize:. (14) The first-order condition for the optimal d 2 * yields. Substituting this in (14), we get. Thus, at the end of first period, the manager will choose his savings d 1 to maximize: (15) Solving for the optimal d 1 * and substituting in (15) yield -22-

25 (16) After observing θ 2, the manager makes the first period production decision to maximize the expected value of. The first-order condition yields, (17) where,. Substituting (17) into the expression for c 11 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.,. Comprehensive income measurement then yields. Residual income becomes: -23-

26 . 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) the hurdle rate, (20) and the fixed salaries {α t } such that the manager s participation constraint holds with equality, then the contract { } achieves the optimal performance. Proof of Corollary 1. 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., -24-

27 for each t # T-1. (21) Recall that, where and 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). -25-

28 Combining (22) and (23) yields that the manager s period t production and effort decisions will coincide with the optimal decisions only if. This, however, violates the maintained assumption that for some t. Proof of Proposition 2. In period t, MV t J = 0 for all J < t because of our assumption that goods become obsolete after one period. Furthermore, HC t t = c 1t. Under the lower-of-cost-or-market valuation rule, therefore, book value at the end of period t simply equals c 1t, and consequently residual income becomes:, Suppose the principal chooses the bonus coefficients β t and the hurdle rates r t 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 c 2t ). Since c 2t 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. -26-

29 REFERENCES Antle, R., and J. Demski. Revenue Recognition. Contemporary Accounting Research (Spring 1989): Antle, R., and R. Lambert. Accountants Loss Functions and Induced Preferences for Conservatism. In Economic Analysis of Information: Essays in Honor of John E. Butterworth, edited by G. Feltham; A. Amershi; and W. Ziemba, pp Boston: Kluwer Academic Publishers, Baldenius, T., and S. Reichelstein. Incentives for Efficient Inventory Management: The Role of Historical Cost. Working paper, University of California, Berkeley, Christensen, P.; G. Feltham; and M. Wu. Cost of Capital in Residual Income Measurement under Moral Hazard. Working paper, University of British Columbia, Devine, S. The Role of Conservatism Reexamined. Journal of Accounting Research, (Autumn 1963): Dutta, S., and S. Reichelstein. Asset Valuation and Performance Measurement in a Dynamic Agency Setting. Review of Accounting Studies (December 1999): Dutta, S., and S. Reichelstein. Controlling Investment Decisions: Depreciation- and Capital Charges. Working paper, University of California, Berkeley, Gjesdal, F. Accounting for Stewardship. Journal of Accounting Research (Spring 1981): Ohlson, J., and X. Zhang. Accrual Accounting and Equity Valuation. Journal of Accounting Research (Supplement 1998): Reichelstein, S. Providing Managerial Incentives: Cash Flows versus Accrual Accounting. Journal of Accounting Research (Autumn 2000): Rogerson, W. Inter-Temporal Cost Allocation and Managerial Investment Incentives. Journal of Political Economy (August 1997):