The Stewardship Role of Accounting

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1 The Stewardship Role of Accounting by Richard A. Young 1. Introduction One important role of accounting is in the valuation of an asset or firm. When markets are perfect one can value assets at their market value (mark-to-market accounting) and the change in the book value of owner's equity, or income, measures the change in firm value. When markets are not perfect, accounting can still be used to approximate the change in the value of the firm. Recommended references on the valuation role of accounting include Edwards and Bell (1961), Feltham and Ohlson (1995), Ijiri (1975), Ohlson (1995), Paton (1922), and Paton and Littleton (1940). Under the valuation perspective the emphasis is on how accounting measures firm value. An important additional role of accounting that arises when markets are not perfect is stewardship. Large firms entrust assets and decisions to managers. Managers have informational advantages with respect to whether they made appropriate use of the assets to which they were entrusted. This situation is one example of a market imperfection. Accounting data may be used to mitigate the negative effects of manager's private information and, in turn, enhance firm value. There is an array of literature in accounting and finance that examines this issue. Recommended references on the stewardship role of accounting include Demski (1982) and Gjesdal (1981). Other stewardship references include Harris and Raviv (1978) and Jensen and Meckling (1976). The stewardship issue is also of continuing practical interest. For example, in the early 1980 s the magnitude of CEO salaries came under close scrutiny, and in the 90 s there has been considerable attention given to using residual income and its variants such as EVA (Economic Value Added) to improve firm performance. Under the stewardship perspective, the emphasis is on how accounting affects firm value. To give insight into how accounting and other information can influence manager behavior and hence firm value, it is useful to think about a simple insurance setting. We may think of automobile drivers as demanding insurance because they are risk averse, and large insurance companies can profit because they are less risk averse. If insurance companies approach risk neutrality, the optimal insurance contract from a risk sharing perspective would remove all the risk from the risk averse driver. Yet automobile insurance contracts often are characterized by deductibles, which leave some of the risk on the driver. One explanation is that the driver is able to affect the probability of an accident. Further, the driver may get enjoyment from speeding. Thus, once completely insured (i.e., Copyright

2 no deductibles), the driver would have incentives to be less careful than if not insured. The driver's ability to buy insurance affects the probability that an accident occurs. This situation is called moral hazard. Deductibles are useful because they give the insured a stake in whether an accident occurs. For the insurance company to make a profit it is important that they choose a premium and deductible that gives the insured the appropriate incentives to drive carefully. That is, they trade off the benefits of lower accident probabilities against the benefits of improved risk sharing. 1 The insurance metaphor can be usefully applied to the role of accounting information in mitigating the stewardship problem and hence increasing firm value. Since we are developing intuition at this stage, we shall think of information in a generic way. But we should keep in mind that data collected by accountants has characteristics that make it especially useful in mitigating the stewardship problem. 2. A simple stewardship setting We proceed with a stylized example. Alice is the risk neutral owner of a retail firm. 2 Ralph is her only sales employee. We assume that Ralph's actions can affect sales. Expected sales will be higher if he tries every customer on the list, is careful to set up appointments convenient for the customer, and makes sure he is on time and prepared to discuss the specific customer's needs. The relationship between Ralph's actions, the state of nature (s 1 or s 2 ), and sales is described in the table below. Note that, even if Ralph is diligent ), he might get unlucky and obtain low sales (e.g., he might not meet up with receptive customers). However, if he is not diligent ), he has no chance at high sales. 3 P(s 1 ) = 1/2 P(s 2 ) = 1/2 s 1 s 2 a L = 0 $100,000 $100,000 a H = 1 0 $100,000 $200,000 In order to address a control or stewardship problem, there must be potential conflict between Ralph and Alice over actions. This is accomplished by assuming Ralph has preferences for both payments and action. In particular, we assume Ralph has a utility 1 The same sort of intuition applies to a setting where individuals have private information regarding their own health. The premium appropriate to charge a healthy individual would be too low for individuals of poor health. One way the insurance company can sort those applying for insurance is to offer different deductible/premium combinations. This problem is referred to as adverse selection. 2 Accounting information may be used to better share risk or to help with the stewardship problem. The assumption of risk neutrality allows us to focus on the latter and makes it easier to work out the numerical example. 3 All that is really important is that the probability of sales be affected by the action. Richard A. Young 2 Copyright

3 function defined over wealth (w) and action (a) as follows: U(w,a) = u(w) a. Ralph likes money and is either risk neutral or risk averse. That is, u > 0 and u 0. Further, we assume a L = 0 and a H = 10. Thus, for a given payment w, Ralph's utility (U) is lower under a H than under a L. This is a very simplistic way to capture conflict. We have simply assumed being diligent is costly to Ralph. For example, he may have to give up Monday night football or time with his family to take out a client. But be sure to understand the important thing is Ralph and Alice disagree about which action they should take. It is not important that we view choice of a L as being lazy. Nevertheless, for brevity we shall refer to Ralph s action as effort. The sequence of events is important. Alice first chooses a contract, and then offers it to Ralph. Then Ralph chooses either to accept the contract from Alice or to take an administrative position elsewhere. If he goes elsewhere, Ralph receives the certainty equivalent of $40,000 with no effort. If instead he decides to join Alice s firm, he then selects action a H or a L, according to his own self-interest. Ralph and Alice know that the contract is enforceable as long as it is based on things that are publicly observable or easily verifiable. 4 Thus, Alice can commit to any payment scheme that is based on observable performance measures. We will consider cases where Ralph s action is and is not observed by Alice. Throughout, we assume both Ralph and Alice observe the sales level. We emphasize that this is an extremely simple example of a stewardship problem, but that makes it a good place to start. 3. Finding an optimal contract general approach Alice's objective is to offer the best contract which induces Ralph to join her firm and take the action she desires, recognizing that Ralph acts in his own best interests. In order to determine which contract Alice should offer, we proceed in the following steps: (1) find the least-cost contract that induces Ralph to join the firm and to choose a L, (2) find the least-cost contract that induces Ralph to join the firm and to choose a H, (3) determine which of these two contracts maximizes Alice s expected utility. 4 One reason that accounting is especially useful in contracting is that it often uses "hard" data (see Ijiri, 1975). For example, accounting tends to rely less on expectations of the future (which are hard to verify) and more on the effects of historical transactions. Richard A. Young 3 Copyright

4 4. Risk neutral incentives In this section we show that potential incentive problems are easily resolve when Ralph is risk neutral (u(w) = w), despite Ralph s aversion to effort and Alice s potential uncertainty about effort. Step (1): Inducing a L If Alice were interested in finding the least-cost contract that induces a L, she must make sure of two things: Ralph will participate in the firm, and he will prefer a L to a H. This is formally stated in the linear programming problem below. Notice it allows for the general case where both effort and sales are observable. The subscript denotes sales in thousands and the argument in parenthesis is effort. Minimize w 100 ) Participation: w 100 ) 40,000 (P) Incentive compatibility: w 100 ).5 w 100 ) +.5 w 200 ) - 10 (IC) The objective function is Alice s expected cost if she writes an act- and salescontingent contract, assuming Ralph chooses a L. The (P) constraint ensures Ralph wishes to join Alice s firm if he chooses a L. The left-hand side of (P) reflects that if Ralph chooses a L, sales will definitely be 100,000 and his personal cost of effort is zero. The right-hand side of (P) is Ralph s expected utility if he does not join the firm which under our assumptions is: U(40,000,0) = 40,000 0 = 40,000. The (IC) constraint ensures Ralph prefers a L to a H. The right-hand side of (IC) reflects that if Ralph chooses a H, sales will be 100,000 with probability.5 and 200,000 with probability.5. One important thing to establish is that a L can be optimally induced with a simple, fixed-wage contract. A fixed-wage contract is one in which payment does not depend on sales. Thus, we substitute w 100 ) = w 100 ) = w 200 ) = w into the objective function and (P) and (IC) to obtain the following. Minimize w subject to: w 40,000 (P) w w 10 (IC) The solution is w = 40,000 and Alice s expected cost is 40,000. Observe that (P) is binding but (IC) is not binding. 5 The fact that (IC) is not binding tells us Alice would do no better if she could observe Ralph s action. 5 Not binding refers to a condition where the inequality is strict. Richard A. Young 4 Copyright

5 Step (2): Inducing a H If Alice were interested in finding the least-cost contract that induces a H, she must make sure Ralph will participate in the firm and will prefer a H to a L. Again, this program allows for the general case where both effort and sales are observable. Minimize.5 w 100 ) +.5 w 200 ) Participation:.5 w 100 ) +.5 w 200 ) 10 40,000 (P) Incentive compatibility:.5 w 100 ) +.5 w 200 ) - 10 w 100 ) (IC) The objective function is Alice s expected payment to Ralph, reflecting that when a H is chosen sales may be either 100,000 or 200,000. The left-hand side of (P) is now Ralph s expected utility if he chooses a H, and the right-hand side is his expected utility if he does not join the firm. The right-hand side of (IC) is Ralph s expected utility if he chooses a L. We see that the approach we tried earlier of paying Ralph the simple fixed-waged contract will not work, since IC would then appear as follows. w - 10 w (IC) This is, of course, impossible. There are two ways to resolve this problem. One is to observe Ralph s action. But this is in general costly to Alice. We shall see that because Ralph is assumed to be risk neutral (for now), Alice can costlessly motivate a H without observing Ralph s action. To see this, assume the payment to Ralph depends only on sales. That is, let w 100 ) = w 100 ) = w 100, and w 200 ) = w 200. Now the program to find the least-cost contract is as follows. Minimize.5 w w w w ,000 (P).5 w w w 100 (IC) Now the (IC) constraint can be satisfied if Alice pays a larger amount for sales of 200,000 than for sales of 100,000, i.e., if she offers a bonus for high sales. To see this, we can rewrite (IC) as follows..5 (w w 100 ) 10 (IC) w w Notice that this means the optimal contract that induces a H must place risk on Ralph. But so far Ralph is assumed risk neutral, so Alice does not need to pay a risk premium. One solution to this program is w 200 = 39,010 and w 100 = 41,010. Alice s expected cost is 40,010. Another solution is to set w 200 = 70,010 and w 100 = 10,010. In fact, Alice could simply sell the firm to Ralph and let him absorb all the sales risk. Notice again that (IC) is not binding, indicating there is no reason for Alice to observe Ralph s effort. Richard A. Young 5 Copyright

6 Step (3): Select the optimal contract Risk neutral case Now that we have found the least-cost way to motivate a L and a H, we determine which contract maximizes Alice's expected utility, defined as expected sales minus expected payment to Ralph. The least-cost contracts are written below. Since in this example Contract RN-2 gives Alice an expected utility level greater than Contract RN-1, Alice optimally offers Contract RN-2. Contract RN-1 Contract RN-2 w = 40,000 w 100 = 39,100 w 200 = 41,100 Ralph's optimal action a L a H Alice's expected utility 60, ,900 Ralph's expected utility 40,000 40,000 Finally, note that whichever level of effort is being motivated, no further improvement would be obtained by its observation. This implies that if Ralph were risk neutral, monitoring procedures such as internal auditing would not be valuable. Since we often observe monitoring of management behavior in practice, in order to understand it, we must expand the model. It turns out that by expanding the model to make Ralph risk averse, we will be able to derive a value to monitoring his effort. 5. Risk averse incentives In this section we will assume u(w) = w, which is a concave function and so captures risk aversion for Ralph. This assumption introduces a potential cost to Alice. If in order to induce incentives Alice must impose risk on Ralph, Alice will bear a cost due to the risk premium she must pay to induce Ralph to accept employment. Step (1): Inducing a L The mathematical program for the case where a L is to be induced is as follows. Again, the program allows for the general case where both effort and sales are observable. Minimize w 100 ) subject to: u(w 100 )) u(40,000) (P) u(w 100 )).5 u(w 100 )) +.5 u(w 200 )) - 10 (IC) In the risk neutral analysis conducted in section 4 we demonstrated that a L can be induced without placing risk on Ralph. That solution will work here, of course. And we know this is a good idea from a risk sharing perspective, since now Ralph is risk averse and Alice is risk neutral. We show that a L can be motivated without imposing risk on Ralph by setting w,w 100 ) = w,w 100 ) = w,w 100 ) = w, which transforms the program as follows. Richard A. Young 6 Copyright

7 Minimize w u(w) u(40,000) (P) u(w) u(w) - 10 (IC) Clearly, paying a fixed wage satisfies (IC) and is the least-cost way to satisfy (P) as well. The solution is w = 40,000, and Alice s expected cost is 40,000. Since (IC) is not binding, if a L is to be motivated there is no value to monitoring effort. Step (2): Inducing a H The program to find Alice s least-cost contract that induces a H when Ralph is risk averse is as follows. Minimize.5 w 100 ) +.5 w 200 ) subject to:.5 u(w 100 )) +.5 u(w 200 )) 10 u(40,000) (P).5 u(w 100 )) +.5 u(w 200 )) - 10 u(w 100 )) (IC) Case I: Act observable Unlike the case where Ralph is risk neutral, it will be important whether effort is observable. To see this, first consider the case where effort is observable. The goal is to see if (IC) and (P) can be satisfied without placing risk on the risk averse manager. This means that w 100 ) = w 200 ) = w H. Simplify the notation further by setting w 100 ) = w L. Then the program to induce a H becomes as follows. Minimize w H subject to: u(w H ) 10 u(40,000) (P) u(w H ) - 10 u(w L ) (IC) Clearly a contract which sets w H = 40,000 and w L sufficiently small (say, zero) will satisfy (IC) and place no risk on the risk averse manager. So here, with the act observable, Alice s cost is 40,000. Case II: Act unobservable: We now consider the case where Alice cannot directly observe whether Ralph is diligent. Alice may find it prohibitively costly to determine Ralph's effort. For example, she probably does not want to follow Ralph around. If that was a good idea, she would do the selling herself. Where the effort is not observable by Alice, Ralph s pay cannot depend on effort. So Alice must set w 100 ) = w 100 ) = w 100 and w 200 ) = w 200 ) = w 200. The program becomes as follows. Minimize.5 w w 200 subject to:.5 u(w 100 ) +.5 u(w 200 ) 10 u(40,000) (P).5 u(w 100 ) +.5 u(w 200 ) - 10 u(w 100 ) (IC) Richard A. Young 7 Copyright

8 Rewriting (IC), we obtain the following, which is similar to the risk neutral, act unobservable case..5 [ u(w 200 ) - u(w 100 ) ] 10 or u(w 200 ) - u(w 100 ) 20 (IC) Here we see risk must be place on Ralph, as in the risk neutral case. Since placing risk on Ralph is costly to Alice, (IC) will be binding. So now both (IC) and (P) are binding. Finding an optimal contract in this case involves solving two equations and two unknowns. The solution is u(w 100 ) = u(40,000), so w 100 = 40,000, and u(w 200 ) = u(w 100 ) Further, with u(w) = w, we obtain w 200 = (200+20) 2 = 48,400. Alice s expected cost is.5(40,000) +.5(48,400) = 44,200 Step (3): select the optimal contract Now that we have found the least-cost way to motivate a L and a H, we check to see which contract maximizes Alice's expected utility. We consider the observability assumptions separately. If Alice could observe Ralph s effort, Contract RA-2 is the least-cost contract that motivates a H. Since it provides Alice with an expected utility level greater than under Contract RA-1, Alice optimally offers Contract RA-2. Case I: Act observable Contract RA-1 Contract RA-2 w = 40,000 w H = 44,100, w L = 0 Ralph's optimal action a L a H Alice's expected utility 100,000 40,000 = 60, ,000 44,100 = 105,900 Ralph's expected utility If Alice were unable to observe Ralph s effort, Contract RA-3 is the least-cost contract that motivates a H. Since it provides Alice with an expected utility level greater than under Contract RA-1, Alice would optimally offer Contract RA-3. Case II: Act unobservable Contract RA-1 Contract RA-3 w = $ 40,000 w 100 = 40,000 w 200 = 48,400 Ralph's optimal action a L a H Alice's expected utility 100,000 40,000 = 60, ,000 44,200 = 105,800 Ralph's expected utility Summary There are several things to note. First, in the case where Ralph is risk neutral incentive compatibility is not binding. Whether Ralph s action is observable or not, Richard A. Young 8 Copyright

9 inducing a H has the same expected cost to Alice. This means that an IS that revealed Ralph s action would have no value. Further, complicated performance systems, those that use different performance measures, would not be necessary. Second, consider the case where Ralph is risk averse. Here, Alice s expected cost of inducing a H is higher if she cannot observe his action. Her expected utility when inducing a H decreases from 105,900 to 105,800. That is, her expected utility is lower under Contract RA-3 (the sales-contingent contract) than if she could offer Contract RA-2 (the act-contingent contract). The reason is when the act is unobservable, in order to motivate a H Alice must base Ralph's pay on the level of sales. Thus, Ralph faces risk, even if he chooses a H. Since Ralph is risk averse this is costly to Alice. In our example, when the act is observable Alice can place no risk on Ralph by offering him Contract RA-2, which pays $44,100 for sure under a H. However, under Contract RA-3 Alice pays an expected amount to Ralph of.5(40,000) +.5(48,400) = 44,200. The difference in expected pay to Ralph (44,200-44,100) is exactly the amount by which Alice's expected utility is lower in the act unobservable setting. The $100 is the risk premium that Alice must pay to induce Ralph to choose a H when the act is not observable. Third, we must check to see whether when the act is unobservable Alice still prefers that Ralph work hard. Why must we check? Remember that Alice's expected utility under Contract RA-3 would be lower than it was under Contract RA-2 (which was enforceable only when the act is observable). In fact, it is possible that when the act is observable Alice would prefer to motivate a H by offering Contract RA-2, but when the act is unobservable she would prefer to motivate a L and hence offer Contract RA-1. This dependence of the equilibrium action on whether it is observable may be a little counterintuitive, at least without careful thought. This phenomenon would occur if the risk premium Alice must provide to Ralph under Contract RA-3 exceeded Alice's incremental expected profit that would result in the act observable case between Contract RA-2 and Contract RA-1. Fourth, this analysis can be used to determine the maximum amount that Alice would pay for a perfect IS that revealed Ralph's effort. Alice would pay up to 105, ,800 = $100 for perfect auditing. The argument is as follows. If auditing costs more than $100, she would not hire the auditor and offer Ralph Contract RA-3 (the salescontingent contract). On the other hand, if auditing costs less than $100, she would hire the auditor and offer Contract RA-2 (the act-contingent contract). Richard A. Young 9 Copyright

10 Self-study exercise Assume an incentive problem of the type above, with a relationship between Ralph's action, the state of nature, and sales dollars as follows. P(s 1 ) = 1/2 P(s 2 ) = 1/2 s 1 s 2 a L = 0 $Y $Y a H = 10 $100,000 $X Ralph has utility function for wealth (w) and effort of w - v, and has the option of going to an administrative position where he receives $40,000 for sure, and which requires no effort. Write down the optimal contract for each of the following cases, considering both the act-observable and act-unobservable settings. Also, write down the maximum amount Alice would pay for perfect information about Ralph's action. CASE A: X = 200,000 Y = 101,000 CASE B: X = 108,300 Y = 100,000 CASE C: X = 108,000 Y = 100,000 Check Figures: Optimal Contract Act observable Act unobservable Value of information. A: w = 44,100 if a = a H w 100 = 44, , ,900 = 0 0 if a = a L w 200 = 44,100 w 101 =0 B: w = 44,100 if a = a H w = 40,000 60,050-60,000 = 50 0 if a = a L C: w = 40,000 w = 40,000 60,000-60,000 = 0 Richard A. Young 10 Copyright

11 References Demski, J., "Managerial Incentives," Information for Decision Making, A. Rappaport, ed., Prentice-Hall, Edwards, E. and P. Bell, The Theory and Measurement of Business Income, University of California Press, Feltham, G. and J. Ohlson, "Valuation and Clean Surplus Accounting for Operating and Financial Activities," Contemporary Accounting Research, forthcoming, Gjesdal, F., "Accounting for Stewardship," Journal of Accounting Research, Spring Harris, M. and A. Raviv, "Some Results on Incentive Contracts with Application to Education and Employment, Health Insurance and Law Enforcement," American Economic Review (March 1978). Ijiri, Y., Theory of Accounting Measurement, AAA, Jensen, M. and W. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure," Journal of Financial Economics, Vol. 3, Ohlson, J., "Earnings, Book Values, and Dividends in Equity Valuation," Contemporary Accounting Research, forthcoming, Paton, W., Accounting Theory, Accounting Studies Press, Ltd., and A. Littleton, An Introduction to Corporate Accounting Standards. AAA, Richard A. Young 11 Copyright

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