Review of Accounting Studies, 7, 283–287, 2002©C 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.

Discussion of: “Controlling Investment Decisions:Depreciation and Capital Charges”

JONATHAN GLOVERCarnegie Mellon University, Graduate School of Industrial Administration, Pittsburgh, PA 15213-3890

1. Introduction

Residual income based performance evaluation has received a great deal of attention inboth the popular press and in academic research. To the best of my knowledge, Dutta andReichelstein (2002) is the first principal-agent model to provide a rationalization for the useof residual income in which the conflict of interest between the principal and agent overproject selection arises endogenously.

2. Example

Suppose an owner has an investment opportunity that requires a cash outflow of 109 todayand will produce equal cash inflows at the end of the next two years. The annual cashinflow is equally likely to be 72 or 108 per year. The owner’s discount rate is 20%. Eithertype of project has a positive NPV and, hence, should be accepted: −109 + 72/(1.2) +72/(1.2)2 = 1 and −109+108/(1.2)+108/(1.2)2 = 56. Now, suppose the decision rightsfor project acceptance resign with an (investment center) manager. There is no other agencyproblem. The owner’s objective is to compensate the manager in such a way that he hasstrict incentives to accept all positive NPV projects and strict incentives to reject all negativeNPV projects. This can be accomplished by basing the manager’s pay on residual income.For simplicity, suppose residual income for a period is simply the period cash inflow lessdepreciation less a capital charge (based on the beginning of period book value of the assetand the owner’s discount rate). Hence, if straight-line depreciation is used for the 72 inflowproject, the present value of residual income discounted using the owner’s discount rate is(72 − 54.5 − (0.2)(109))/(1.2) + (72 − 54.5 − (0.2)(54.5))/(1.2)2 = 1. That is, the NPVof the project and the present value of its residual income are equivalent when evaluated atthe owner’s discount rate. Moreover, this (well known) equivalence does not depend on thedepreciation method used.

The catch is that the manager may have a discount rate higher than the owner’s. Supposethe manager’s discount rate is 100%, yielding a present value of residual income for the72 inflow project of (72 − 54.5 − (0.2)(109))/(2) + (72 − 54.5 − (0.2)(54.5))/(4) = −0.5.The manager would not undertake the project. The solution proposed by Reichelstein (1997)and Rogerson (1997) is to use relative benefit depreciation, which makes the total charge(depreciation plus the capital charge) proportional to the relative contribution of each

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cash inflow. The total charge in each period is set equal to that period’s cash inflowdivided by the present value of all cash inflows. In our case, each period’s charge is(72/(72/1.2 + 72/1.22))(109) = 71.35. In the case of equal cash inflows, relative benefitdepreciation reduces to what is known as annuity depreciation. For an early discussion onannuity depreciation, see, for example, Dicksee (1903). Relative benefit depreciation en-sures that positive (negative) NPV projects will have a positive (negative) residual income ineach period. Hence, the manager will have the desired incentives, regardless of his discountrate.

A criticism of the Reichelstein/Rogerson explanation for residual income based perfor-mance evaluation and relative benefit depreciation is that there is no real agency conflict intheir model. If the manager is instead paid a salary, he is indifferent with respect to projectselection and can choose projects in the best interest of the firm’s owner. The main contri-bution of Dutta and Reichelstein is in providing a setting with a more compelling agencyconflict in which a similar result emerges. The basic idea is to make the manager’s weightson compensation arise from an underlying moral hazard problem instead of a discount ratedifferent than the owner’s.

Continue with the example, except the manager’s discount rate is now also 20%. Inaddition to the project’s cash flows, the manager can produce an operating cash inflow.If the manager exerts high effort in a given period, he produces an operating cash in-flow of 36 in that period. The personal cost to the manager of high effort is 36/2 inthe first period and 36/4 in the second period. The manager’s alternative is to exert loweffort at a personal cost of 0. The owner observes and the contract is based on only theaggregate cash inflow in each period. The manager’s payment in each period must be non-negative.

Suppose the manager’s pay is a salary plus a share of the cash inflow of that period. Ifthe owner were to observe and decide on projects herself, the following wage scheme isoptimal and achieves the first-best (efficient investment and no informational rents to theagent). For a 72 cash inflow project, pay the manger a salary of −36 plus a bonus of 1/2of the cash inflow in the first period and a salary of −18 plus a bonus of 1/4 of the cashinflow in the second period. For a 108 cash inflow project, the only change is that the salaryis −54 in the first period and −27 in the second period.

If instead the manager alone knows which type of project he has, the above salary andbonus scheme will not work. When the manager has a 108 cash inflow project, he willinstead claim to have a 72 cash inflow project and supply low effort, which will producethe same cash inflow as if the project had a cash inflow of 72 and the manager had suppliedhigh effort: 108 = 72 + 36. If we wish to have the manager undertake either type of projectand supply high effort to each, we need to offer him the same salary (−36 in the first periodand −18 in the second period) for both types of projects.

We could implement the same outcomes and payments using residual income as a perfor-mance measure and using the same bonus coefficients. Depreciation and the capital chargeare constants and do not affect the manger’s effort incentives. A one unit increase in the cashinflow translates into a one unit increase in residual income. The only adjustment neededis to the salary component.

The problem is that the change in bonus coefficients across periods (1/2 versus 1/4)changes the manager’s investment incentives. The difference in coefficients causes the same

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problem differences in discount rates caused in the Reichelstein/Rogerson setup. Relativebenefit depreciation will fix the problem in the same way it did before.

The combined effort-investment problem is separable in the following sense. We use bonuscoefficients to solve the moral hazard problem. When the bonus weights differ across peri-ods, the choice of depreciation can produce perverse investment incentives. We can providethe desired investment incentives by using relative benefit depreciation. The depreciationmethod does not disturb the effort incentives because it simply subtracts a constant.

It turns out to be optimal to curtail investment in order to limit the manager’s informationalrent (see also Antle and Eppen, 1985). In our example, we can reduce the manager’s salaryby 18 in the first period and 9 in the second period if we eliminate his incentive to undertakethe 72 inflow project (which has a NPV of only 1). This can be done in two ways. First, wecan use a higher capital charge to make marginally positive NPV projects unappealing to themanager. Second, we can use a different depreciation schedule. This could be a more accel-erated or a more decelerated schedule (both well defined for my two period example) thanrelative benefit depreciation, depending on the bonus coefficients. Hence, one might arguethat using a higher capital charge (as in Dutta and Reichelstein) is a more appealing solution.

3. Questions (Future Work)

I conclude my discussion with some questions related to the Dutta and Reichelstein paperwith the hope they will lead to future research.

(a) What if the manager alone knows the pattern of cash flows? A key assumption inthe Reichelstein/Rogerson and Dutta and Reichelstein models is that the owner knows thepattern of cash flows. The pattern, but not the level, is needed to calculate relative benefitdepreciation. A challenging extension of the paper would be to relax this assumption. Onesetting in which this relaxation may be more tractable is if the pattern of cash flows isdetermined by the manager’s effort. In this case, we could use the equilibrium effort level todetermine the depreciation schedule to be used. A complication is that perverse incentivesmay arise from using the “wrong” depreciation schedule when the manager supplies aneffort level other than the conjectured equilibrium effort level.

(b) When would we delegate the choice of depreciation to the manager? If the patternof cash flows is the private information (type) of the manager and other communication isblocked, it might be optimal to delegate the choice of depreciation method to the manager.In order to mitigate the manager’s incentive to choose a depreciation method that provideshim with more pay but the wrong investment incentives, something else will have to betraded off (for example, the level of investment).

(c) Why do we use bonus banks? In the popular press, bonus banks are sometimes advo-cated in conjunction with residual income based performance evaluation. The link betweenthese two practices would be interesting to explore in an agency model.

(d) Why do we compare residual income across time? Descriptions of residual incomebased bonus schemes often include residual income targets, which are based (at least in part)on past residual income. Again, I do not know of an agency model that explains this practice.

(e) Why do we use ratios? Many firms continue to use traditional return based measures ofperformance. The recent flurry of papers on residual income invariably reach the conclusion

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that residual income and not a ratio is optimal. Perhaps, the papers are too close to aneoclassical setting to have anything other than (modified) NPV arise as the optimal criteriafor evaluating projects. Because of the equivalence between NPV and discounted residualincome, residual income is always the answer for performance evaluation.

In practice, we use not only ratios but even cruder evaluation methods such as payback.One approach to understanding the use of such practices is to compare given performanceevaluation schemes rather than deriving an optimal scheme. This is a controversial butcommon approach when it comes to linear contracts—they are often simply assumed, asin Dutta and Reichelstein. (To be fair, Dutta and Reichelstein’s Appendix B studies a riskneutral setting in which such contracts are optimal.)

A contracting friction that may be useful in studying the payback method is a manager’stime horizon with the firm. For ratios, a manager who prefers large projects or empirebuilding (see Berkovitch and Israel, 1999) seems like a reasonable force to include. Ratioswith size in the denominator punish a manager for undertaking large projects. One way toview Reichelstein/Rogerson (and to some extent Dutta and Reichelstein) is that they provideuseful benchmark cases in which residual income based performance evaluation is optimal.We need to look for deviations from these benchmarks in order to explain other observedpractices.

(f) Do we use relative benefit depreciation in practice? Arguably, firms use more accel-erated depreciation methods in practice than relative benefit depreciation. Empire buildingtendencies can be used to explain more accelerated depreciation. We can make a managerwith a discount rate higher than the owner’s pay for large projects by using more accelerateddepreciation (see, Arya, Baldenius and Glover, 1999). Of course, other methods can be usedto provide the desired adjustment in incentives, such as increasing the capital charge (seeBaldenius, 2001; Ewert and Wagenhoffer, 1997; and Lambert, 2001).

A more fundamental problem is that we seem to observe much less fine tuning of dep-recation than relative benefit depreciation requires. This leads us to the broader issue ofdiscretion in accounting and why we limit it.

(g) What about interactions between accounting and non-accounting sources of informa-tion? One important limitation of the existing literature on residual income based perfor-mance evaluation is the lack of non-accounting information. As Liang (2000) and othershave observed, much of the value of accounting seems to derive from its disciplining roleon other softer (more manipulable) sources of information.

References

Antle, R. and G. Eppen. (1985). “Capital Rationing and Organizational Slack in Capital Budgeting.” ManagementScience 31, 163–174.

Arya, A., T. Baldenius and J. Glover. (1999). “Residual Income, Depreciation, and Empire Building.” WorkingPaper, Carnegie Mellon University.

Baldenius, T. (2001). “Delegated Investment Decisions and Private Benefits of Control.” Working Paper, ColumbiaUniversity.

Berkovitch, E. and R. Israel. (1999). “Why the NPV Criterion Does not Maximize NPV.” Working Paper, Universityof Michigan.

Dicksee, L. R. (1903). Depreciation, Reserves, and Reserve Funds. Gee, London.Dutta, S. and S. Reichelstein. (2002). “Controlling Investment Decisions: Depreciation and Capital Charges.”

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