Residual Income, Depreciation, and Empire Building Anil Arya Ohio State University Tim Baldenius Columbia University Jonathan Glover Carnegie Mellon University December 1999 1. Introduction Residual income has received a great deal of recent attention in the practitioner and academic literatures on performance evaluation. In the practitioner literature, residual income often goes under the label of economic value added (Stewart, 1991). Assuming the charge for capital used to calculate residual income is equal to the discount rate, the discounted stream of residual income has the following properties. One, it does not depend on accounting choices.1 Two, it is equal to the net present value (NPV) of the project. However, local managers are often the source of project proposals, and these managers may discount at a rate different than firm owners. In this case, a goal incongruence may arise between managers and owners. The difference in discount rates also implies that accounting choices matter. This opens the door for accounting choices to be used to alleviate the goal incongruence. Consider a typical textbook problem on residual income (e.g., Anthony and Govindarajan, 1998, pp. 259-262). A project has an initial cash outflow followed by an annuity of cash inflows. If a standard depreciation schedule is used (straight-line or accelerated), the residual income of the project increases over time. This is because the capital charge decreases over time and the depreciation charge decreases or remains constant over time. The increasing residual income appears to indicate constantly improving profitability, whereas there has actually been no real change in profitability after the project has been undertaken. A solution to the problem is to use annuity depreciation, which produces a constant residual income in each year. In the constant cash inflow case, annuity depreciation is decelerated. The capital charge is decreasing over time and an offsetting depreciation charge increases over time. From an incentive perspective, annuity appreciation has the particularly appealing property that the present value of the residual income is positive if 1 By accounting choices, we mean those that affect the timing of income recognition but not the total amount of income recognized over the firm's life. 2 and only if the NPV of the project is positive, regardless of the manager's discount rate (Reichelstein 1997, Rogerson 1997). However, annuity depreciation is rarely used in practice (Reece and Cool, 1978). In this paper, we provide one possible explanation for the use of non-annuity and, in particular, non-decelerated depreciation. When used in conjunction with residual income, non-decelerated depreciation curbs the manager's tendency for empire-building. Agency costs have been used to explain many observed institutional practices. For example, a manager's desire to consume perquisites can make it optimal for a budget center to use a hurdle rate higher than the firm's cost of capital in evaluating projects (Antle and Eppen, 1985). Other traits of managers can lead to agency problems. For example, the manager may have a preference for large projects--he may want to build an empire (Berkovitch and Israel, 1998; Harris and Raviv, 1996; Jensen, 1986; Mueller, 1969; Stulz, 1990). Also, managers sometimes exhibit a short-term orientation/impatience (Reichelstein, 1997; Zimmerman, 1995). In our model, the manager prefers larger projects to smaller projects and has a higher discount rate than the firm's cost of capital. The former reflects the manager's tendency to empire-build; the latter reflects the manager's impatience. The reason for the manager's higher discount rate could be that, relative to firm owners, his access to capital markets is more constrained and/or he faces an exogenous probability of changing jobs each period (a horizon problem).2 Empire building introduces a force that has the manager accepting some negative NPV projects. The optimal depreciation schedule is chosen so as to introduce a counterbalancing force. Because of his impatience, the manager place a greater weight on the first-period (relative to the second-period) residual income than does the firm's owner. 2 Suppose the manager and the firm owner both discount future cash flows at the rate r, but the manager retains his job with probability p in each period. Then the manager effectively discounts future compensation (associated with retaining his job) at a rate of (1+r)/p - 1, which is greater than r. 3 By choosing a depreciation schedule that makes the first-period residual income less than the second-period residual income, the value of the residual income stream when discounted by the manager declines. The optimal depreciation schedule is chosen so that the decline in discounted residual income for the agent exactly offsets his benefit from empire-building. That is, one managerial trait (impatience) is used to keep another trait (empire building) in check. When the manager's desire to empire build is strong enough, the optimal depreciation schedule is non-decelerated. When projects are independent, this results in the manager undertaking a project if and only if its NPV is positive. In the case of mutually exclusive projects, the manager undertakes the project with the highest (positive) NPV. Our focus is on the use of an accounting instrument, depreciation. According to Davidson (1957), "[d]epreciation is probably the most discussed and most disputatious topic in all accounting." Depreciation is traditionally viewed as a way of matching expenses with revenues (Paton and Littleton, 1940). Other views include depreciation as a reserve for asset replacements, as matching physical deterioration, and as a statistic for an unknown long-run variable (Brief and Owen, 1970; Sunder 1997). In this paper, we develop a view of (non-decelerated) depreciation as a way of introducing a bias to counter managers' empire-building tendencies. The idea that accounting conventions can be used to offset undesirable managerial traits is not new. For example, conservatism is often discussed as a way of countering managers' tendency toward optimism. Non-accounting instruments can also be used to achieve goal congruence. We also study how depreciation can be used in conjunction with other instruments (capital charge and the scale of production) to achieve goal congruence in models of adverse selection. The remainder of the paper is organized into four sections. Section 2 presents the model. The main result is presented in Section 3. Section 4 studies an extension. Section 5 concludes the paper. 4 2. Model Consider a firm whose participants are a risk-neutral principal (owner) and a risk- neutral agent (manager). The firm faces a two-period investment opportunity with an initial investment of I and a cash inflow of c at the end of each period. There is uncertainty _ regarding c. It is common knowledge that c is drawn from the interval [c_,c], with a probability distribution function f(c). All cash in- and outflows are received (issued) directly by the principal. The agent's compensation is assumed to be proportional to residual income. Denote by d and (1-d) the depreciation rate in period one and period two, respectively, 0 ≤ d ≤ 1. In period one, residual income is RI = c - dI - r I; in period two, it is RI = c - (1-d)I - r (1-d)I. In 1 p 2 p the expression for residual income, the first term is the cash revenue, the second term is the depreciation expense, and the third term is the capital charge computed using the principal's discount rate r . Residual income is computed (and compensation is paid) at the end of p each period using the actual cash flows. The sequence of events is as follows. First, the agent privately observes c. Second, the agent decides whether or not to undertake the project.3 Third, if the agent decides to undertake the project, the principal provides funding of I. Finally, c is realized at the end of periods one and two. The principal would like the agent to undertake the project if and only if its net present value (NPV) is non-negative. That is, the agent should undertake the project if and only if -I + c(1+r )-1 + c(1+r )-2 ≥ 0. To make the problem interesting, we assume the p p _ NPV computed at c_ is negative and at c is positive. The agent's preferences over projects are given by RI (1+r )-1 + RI (1+r )-2 + eI. 1 a 2 a The first two terms are the present value of residual income computed using the agent's 3 We have assumed that the decision rights for project approval reside with the agent. Given the compensation arrangement and the fact that the agent can misstate the future cash flows associated with the project, this setting is equivalent to one in which the agent proposes projects and the principal makes project approval decisions. 5 discount rate, r . The last term reflects the fact that the agent derives utility from the size of a the project--the agent is an empire-builder. e is the agent's marginal rate of substitution of size for discounted residual income. A higher value of e implies that the agent is more of an empire-builder. The principal knows the agent's characteristics e and r . a There are two reasons the agent may choose to accept or reject projects differently than the principal would. First, because of taste for empire building, the agent is willing to accept some negative NPV projects. Second, the agent's discount rate r is greater than the a principal's discount rate r --the agent is impatient. The question we ask is: is it possible to p use the accounting instrument of depreciation to induce goal congruence between the principal and the agent? 3. Result Consider two benchmark cases. No empire building (e = 0) With e = 0, the only reason the principal and the agent value projects differently is because of their different discount rates. If r = r , the present value of residual income is a p equal to the NPV of the project and is free of the depreciation choice. If r ≠ r , goal a p incongruence can be eliminated by an appropriate choice of depreciation. The trick is to choose a depreciation schedule that produces a constant residual income, RI = RI . The 1 2 depreciation schedule that achieves this objective is called annuity depreciation (or relative benefit depreciation). Annuity depreciation ensures that the residual income in each period is positive if and only if the project has a positive NPV. Hence, the discount rate becomes irrelevant (Reichelstein, 1997; Rogerson, 1997). Observation 1. In the absence of empire building, goal congruence can be 1 achieved by setting d = . 2+r p 6 Two comments. First, in the case of constant cash inflows, the optimal depreciation schedule is decelerated (d < 1/2). Second, the depreciation schedule does not _ depend on r , c_, c, or f(c). a No managerial impatience (r = r ) a p With r = r , the only reason the principal and the agent value projects differently is a p because of the agent's tendency to empire-build. The present value of residual income is independent of depreciation choice. Hence, for all depreciation schedules, the agent's utility for a project is NPV + eI. Now, the agent will take on all projects with a NPV of -eI and above. Observation 2. In the case of identical discount rates, goal congruence cannot be achieved by the choice of depreciation method. Empire building and managerial impatience (e > 0 and r > r ) a p We now return to the case that the agent is both an empire-builder and impatient. Our result is that goal congruence can sometimes be achieved by using a depreciation schedule that is more accelerated than annuity depreciation. The idea is to curb the agent's empire-building tendency by designing a depreciation schedule that exploits his impatience. One undesirable trait of the agent is used to keep his other undesirable trait in check. _ Proposition. For all e, 0 ≤ e ≤ e, goal congruence can be achieved by setting 1 e(1+r )2 _ (r -r )(1+r ) d = d* = + a , where e = a p p . 2+r (r -r ) (1+r )2(2+r ) p a p a p Proof of the Proposition. Denote the value of c for which the project has a zero NPV by c*. c* is the solution to the equation -I + c(1+r )-1 + c(1+r )-2 = 0. Hence, p p c* = I(1+r )2(2+r )-1. p p 7 Goal congruence is achieved if the agent also uses c* as the cutoff in making investment decisions, i.e., the agent's utility is positive if c > c* and negative if c < c*. The optimal depreciation rate, d*, is chosen such that the agent's utility is 0 when c = c*. d* is the solution to the equation [c* - dI - r I](1+r )-1 + [c* - (1-d)I - r (1- p a p d)I](1+r )-2 + eI = 0. Substituting for c* and solving for d yields d*. As e increases, a so does d*. The upper bound on e is the value of e at which d* = 1. The optimal depreciation rate is made up of two parts. The first part is the annuity depreciation rate. The second part is an adjustment to curb the agent's empire building tendencies. This part is free of distributional assumptions but, unlike annuity depreciation, does depend on r (and e). a As the agent's desire to empire build increases, the depreciation schedule becomes more accelerated. The intuition for the result is as follows. Empire building introduces a force that has the agent accepting projects more often than the principal would. The depreciation schedule is chosen so as to introduce a counterbalancing force, one that has the agent rejecting projects more often than the principal would. Because of his impatience, the agent values the first-period residual income relative to the second-period residual income more than the principal does. By choosing a depreciation schedule that makes the first- period residual income less than the second-period residual income, the value of the residual income stream, when discounted by the agent, declines. The optimal depreciation schedule is chosen so that the decline in discounted residual income for the agent exactly offsets his benefit from empire-building. The upper bound on e reflects the requirement that depreciation be nonnegative in each period (0 ≤ d ≤ 1). If we allowed for depreciation greater than the initial investment in period one and negative depreciation in period two, goal congruence could always be achieved. 8 Not surprisingly, if the agent's tendency to empire-build is large enough, the optimal depreciation method is non-decelerated (d ≥ 1/2). (r -r )r (r -r )(1+r ) Corollary 1. For all e, a p p < e < a p p , the depreciation 2(1+r )2(2+r ) (1+r )2(2+r ) a p a p schedule that achieves goal congruence is non-decelerated. Proof of Corollary 1. The upper and lower bounds on e are found by equating the expression for d* to 1/2 and 1, respectively, and solving for e. Mutually exclusive projects So far we have considered the case of a single investment opportunity. Clearly, multiple projects that are independent can be dealt with in the same way. As it turns out, even if projects are mutually exclusive, the depreciation rate proposed in the proposition leads to goal congruence. That is, the agent undertakes the project with the highest (positive) NPV. _ Corollary 2. For all e, 0 ≤ e ≤ e, the agent's utility is linearly increasing in the NPV of the project if d = d*. Proof of Corollary 2. The agent's utility is [c - dI - r I](1+r )-1 + [c - (1- p a d)I - r (1-d)I](1+r )-2 + eI . Plugging d = d* into this expression yields: p a 2+r 1+r ( a) ( p)2 NPV. 2+r 1+r p a Varying depreciation and the capital charge So far in the paper, we studied the role of depreciation in achieving goal congruence. There are other instruments that can be used. For example, the capital charge can be varied. Ewert and Wagenhofer (pp. 528-532, 1997) curtail an agent's empire- building tendency by using a capital charge higher than the principal's discount rate. We 9 do not wish to single out any single instrument. In general, depreciation can be viewed as one in a portfolio of instruments that can be used to curb empire building. While in the previous setting, cost of capital could also be used to achieve goal congruence, there are settings in which having multiple instruments available is critical. We present an example in which both the capital charge and depreciation can be varied. For the particular setting studied, the unique optimal choice of these two instruments is to compute the capital charge at the principal's discount rate and to use the depreciation rate given in the proposition. Suppose there are two types of agents. A type 1 agent has the same preferences as the principal--he discounts at the same rate as the principal and is not an empire-builder. A type 2 agent is the same as in the previous section of the paper--he is impatient and an empire-builder. The principal does not know the agent's type. Here, we give the principal the flexibility of choosing both the capital charge, k, and the depreciation rate, d. The principal's objective is to maximize the expected NPV of the project subject to the constraints that the cutoffs c and c the principal intends a type 1 1 2 and type 2 agent to implement are incentive compatible. The only other constraints are that depreciation be a proper allocation scheme and that the cutoffs are within the set of possible cash inflows. _ Corollary 3. For all e, 0 ≤ e ≤ e, goal congruence can be achieved if and only if the principal sets k = r and d = d*. p Proof of Corollary 3. The best the principal can do is to implement c = c 1 2 = c*. Suppose the principal sets k = r and d = d*. Because a type 1 agent discounts at p r , the present value of residual income is invariant to depreciation and is equal to the p NPV of the project. Setting c = c* is incentive compatible for a type 1 agent. From 1 _ the Proposition, we know that as long as e < e, it is also incentive compatible for a type 2 agent to set c = c*. 2