# Delegated investment decisions and private benefits of control.

ABSTRACT: This paper studies the capital budgeting process in a
setting where a manager is privately informed about the profitability of
an investment project and enjoys nonpecuniary benefits of control
("empire benefits"). I characterize the optimal required rate
of return and show that a delegation scheme with residual income-based
compensation can replicate the benchmark performance achieved under
centralization. The main result of the paper is that the optimal capital
charge rate for computing residual income always exceeds the required
rate of return as a result of empire benefits. This highlights the
necessity for future empirical studies on capital budgeting to
distinguish between alternative forms of hurdle rates. Contrary to
conventional wisdom, I further show that if compensation contracts are
derived endogenously, then the shareholders will ultimately benefit from
the manager's empire benefits even under asymmetric information.

Keywords: capital budgeting; empire-building; residual income; hurdle rates.

I. INTRODUCTION

Capital budgeting ranks among the key managerial tasks in modern corporations and much of the attendant debate revolves around determining appropriate hurdle rates for accepting investment projects. Traditionally, the term "hurdle rate" has been used interchangeably with the required rate of return. Recently, however, a growing number of firms have adopted accounting-based performance measures known as residual income or "Economic Value Added" (EVA), which subtract a charge for the opportunity cost of capital from operating income. The capital charge rate employed is also often referred to as a hurdle rate. This dual nature of hurdle rates has remained largely unexplored in the academic literature. The present paper seeks to fill this gap by arguing that (and how) in practice the two hurdle rates should be expected to differ.

The practitioners' literature advocates using the firm's cost of capital as both the required rate of return and the capital charge rate (Brealey and Myers 2000; Young and O'Byrne 2001). On the other hand, Poterba and Summers (1995) have found that hurdle rates employed in practice significantly exceed the cost of capital. This clearly violates the net present value rule. Such underinvestment, or capital rationing, as a result of adverse selection is consistent with shareholders curtailing informational rents earned by their privately informed managers at the expense of reduced efficiency (e.g., Antle and Eppen 1985).

At the same time, managers are frequently accused of overinvesting in assets as a consequence of private benefits they derive from controlling "empires." (1) There are numerous reasons for such empire-building tendencies to arise. Apart from intrinsic motivation, division size often is positively associated with fringe benefits such as lavish office spaces or simply power within the organization. Moreover, managers of larger and/or more profitable divisions may be more likely to be promoted or become the future CEO. Somewhat surprisingly, empire benefits have so far been largely ignored in the accounting literature. (2)

As a means to align a division manager's objective with that of the shareholders, his compensation will generally be linked to realized investment returns. While this may mitigate excessive empire-building tendencies, the manager will still invest in projects that are marginally unprofitable (and hence will lower his compensation) provided the attendant empire benefits are sufficiently high. In fact, this may be equilibrium behavior as the manager's empire benefits allow shareholders to reduce his compensation and thereby to indirectly extract a share of these benefits. (3)

This paper characterizes the capital budgeting process in the presence of adverse selection and empire benefits. In particular, I compare the optimal required rate of return with the optimal capital charge rate and benchmark both these hurdle rates against the firm's cost of capital. I refer to a firm as centralized if the principal makes the investment decision based on a comprehensive "revelation" contract with the better informed manager. The required rate of return then is the relevant hurdle rate under centralization. In a decentralized firm, the investment decision is delegated to the manager who is compensated based on residual income. The capital charge rate used for computing residual income is the relevant hurdle rate under decentralization.

Beginning with centralized firms, I obtain a familiar capital rationing result: to economize on the manager's informational rents, the firm optimally forgoes some projects that would have received funding under symmetric information. Two countervailing forces are shown to determine the comparison of the optimal required rate of return with the firm's cost of capital. While the adverse selection problem calls for a restrictive budget (i.e., a high hurdle rate), the manager's empire benefits tend to have the opposite effect: by decreasing the hurdle rate, the principal can lower the manager's compensation and thereby extract a share of the empire benefits. Depending on the relative importance of the two control problems, the optimal required rate of return can be less or greater than the cost of capital.

I then show that the principal can replicate the second-best (centralized) solution by delegating the investment decision to the manager, compensating him based on residual income. This lends support to the increasing use of residual income in decentralized firms. (4) In contrast to the ambiguous results for the required rate of return, the optimal capital charge rate under delegation always exceeds the cost of capital. This holds, because the manager as the decision maker under decentralization compares both return streams (cash and empire returns) with the imputed capital charge, and he ignores any informational rents, which, from the viewpoint of the principal, should be netted against the investment returns. (5) The required rate of return, in contrast, only captures the cash returns from investing. As a consequence, the main result of this paper is that the capital charge rate always exceeds the required rate of return--that is, the hurdle rate is always higher under delegation than under centralization.

This divergence in the hurdle rates is in stark contrast to the practitioners' literature cited above. The findings in this paper indicate that lumping together required rates of return with capital charge rates, as is common in empirical studies on capital budgeting practices, adds noise. This may help explain the somewhat inconclusive cross-sectional findings on hurdle rates in Poterba and Summers (1995). Based on my results, a required rate of return of, say, 15 percent will result in lower levels of investment than an equally high capital charge rate in a decentralized, but otherwise identical, division or firm. This is further corroborated by additional results that predict qualitatively different comparative statics for the two hurdle rates.

The business press generally views empire-building tendencies as value-destructing because of the resulting investment distortions. As the preceding discussion suggests, this need not be true once compensation contracts are determined endogenously. Indeed, an immediate corollary of my results is that the firm owners can always extract a sizable share of the manager's empire benefits and, hence, will ultimately benefit from an exogenous increase in these benefits. It should be noted, however, that this result hinges on the assumption that empire benefits depend on the characteristics of the investment project in a deterministic and commonly known fashion. Put differently, for the negative connotation associated with empire benefits to be justified, it must therefore be the case that shareholders are imperfectly informed about bow these benefits are driven by the scale and profitability of the assets under a manager's control. (6)

This paper is related to several recent studies on capital budgeting. Christensen et al. (2002) and Dutta and Reichelstein (2002) examine optimal hurdle rates in the absence of empire benefits. (7) Closest to my model is Lambert (2001), who studies a capital budgeting model with asymmetric information and empire benefits. While Lambert (2001) does not allow for screening of the manager's private information, this paper derives suitable hurdle rates that implement the optimal revelation mechanism. All three earlier studies emphasize the role of project (or market) risk in that any deviations between required rates of return and capital charge rates are solely driven by differences in risk tolerance between shareholders and managers. (8) While corporate finance theory predicts that the required rate of return is, in general, increasing in a project's riskiness, Christensen et al. (2002) demonstrate that this need not hold for the capital charge rate under delegation. A risk-averse manager will internalize the project risk via the attendant increase in his compensation risk for a given capital charge rate. Raising the hurdle rate further would thus amount to "double-counting" of the risk premium. (9) In fact, Poterba and Summers (1995, 47) find that none of the traditional risk factors correlates with hurdle rates in their sample. By introducing empire benefits, the present paper takes the natural next step in this research agenda as it demonstrates systematic differences between the two hurdle rates even in a risk-neutral setting. (10)

The remainder of the paper is organized as follows. Section II describes the model. Section III characterizes the optimal centralized capital budgeting procedure and the corresponding required rate of return. Section IV addresses delegated investment decisions and capital charge rates. Section V analyzes the comparative statics. Section VI concludes.

II. MODEL

This section develops a single-period capital budgeting model of a firm consisting of a risk-neutral principal and a risk-neutral manager. The model entails private precontractual information (adverse selection), unobservable effort choices, and private benefits to the manager from controlling assets. At date 0, the firm can invest in a project, with I [member of] {0, 1} as an indicator variable that denotes whether the project is undertaken. If it is (I = 1), then the attendant expense equals b. At date 1, the return from the investment is realized. The gross cash return from investing equals k [member of] [[??], [bar]k] and is known only to the manager prior to accepting the contract. The manager exerts personally costly effort, denoted by a [member of] [0,[bar]a]. The (commonly known) marginal productivity of effort is normalized to 1, without loss of generality. Hence the date-1 cash flow equals c = kI + a. The principal maximizes the total date-0 value of the firm net of the manager's compensation, s:

[gamma][kI + a - s] - bI.

Here, [gamma] = [(1 + r).sup.-1] is the firm's discount factor and r is the cost of the capital, which in this risk-neutral setting equals the risk-free rate. The net present value of the investment alone hence is NPV(k|r) = [gamma]k - b.

In a key departure from traditional adverse selection models, I assume that the manager enjoys empire benefits or private benefits of control--from overseeing the project. As a consequence, the investment project has two return components: one accruing directly to the principal (the cash return) and one accruing directly to the manager (the empire return). The empire benefits, denoted by e(k,I), are nondecreasing in the profitability of the project and in the amount invested. The manager's utility, evaluated at date 1, comprises his compensation and empire benefits less his disutility of effort, v(a):

U = s + e(k,I) - v(a),

with v'(a) > 0, and v"(a) [greater than or equal to] 0. For ease of exposition (none of the results will depend on this), e(*) is assumed to be multiplicatively separable in that e(k,I) = e(k)I, where e'(k) [greater than to equal to] 0 and e"(k) [less than or equal to] 0. When the contract is signed, the principal, in contrast to the manager, knows only the distribution function F(k), with a corresponding density f(k), from which k is drawn. As is common in adverse selection models, the inverse hazard rate H(k) [equivalent to] [1 - F(k)]/f(k) is assumed to be decreasing.

As a benchmark, I begin by characterizing the first-best investment decision that would result if the principal could observe k and thereby could also infer the manager's effort choice a. (11) The effort and investment problems are then effectively separated. The principal reimburses the manager for his disutility of effort and invests according to: [??](k) [member of] arg [max.sub.I]{[gamma][kI + e(k)I] - bI}. The project would then be accepted if, and only if, k [greater than or equal to] [??], where:

(1) [gamma][[??] + e[??]] - b = 0.

Hence, under symmetric information the investment would be undertaken whenever the sum of the two return components (cash and empire benefits), in present value terms, exceeds the initial investment--that is, whenever NPV(k|r) + [gamma]e(k) [greater than or equal to] 0.

The practitioners' literature cited in the "Introduction" offers various explanations for empire benefits to arise, apart from intrinsic motivation. First, investments often entail hiring additional staff. Divisional managers may thereby gain more power or simply enjoy more lavish office spaces and other fringe benefits. Second, the manager's future career opportunities may improve if the projects under his control turn out to be profitable. (12) While in the first case, empire benefits will be largely independent of the project's profitability, this is not plausible in the second case. Here, empire benefits might well be negligible for low values of k, but increasing in k. To address these differences more formally, I shall invoke two specific linear functional forms for the manager's empire benefits for some of the results to follow. (13)

Definition 1 (alternative specifications of the e(k)-function):

(PO) "Plush Office" scenario: e(k) = [e.sub.0] + [e.sub.1]k, where k [member of] [0,[bar]k], [e.sub.0] > 0 and [e.sub.1] [right arrow] 0.

(REP) "Reputation" scenario: e(k) = [e.sub.0] + [e.sub.1]k, where k [member of] [0,k], [e.sub.0] [right arrow] 0 and [e.sub.1] > 0.

As shown below, these alternative specifications for empire benefits have qualitatively different implications for optimal capital budgeting procedures.

The following two sections analyze the optimal capital budgeting process for a centralized and a decentralized firm. Under centralization the investment decision rests with the principal, while under decentralization it is delegated to the manager, who is compensated based on some accounting-based performance measure. (14) Since the revelation principle applies, a decentralized firm can at best replicate the performance of a centralized firm. Delegation is nevertheless an important phenomenon to analyze, as it is pervasive in practice due to lower communication and commitment requirements.

III. CENTRALIZED INVESTMENT DECISIONS

In a centralized organization, the principal makes the investment decision based on some report submitted by the better informed manager. Under any message-contingent mechanism, the principal asks the manager to submit a report [??] on the gross investment return after committing to a scheme <I([??]), c(??), s([??])>, where c([??]) is the cash flow the manager has to deliver contingent on his report. It will be more convenient to suppress c(??) and instead to refer directly to the effort level that is induced by I([??]) and c([??]):

(2) a([??],k) [equivalent to]min{a|kI(??) + a [greater than or equal to] c(??)} = c([??]) - kI(??).

Let a(k) [equivalent to] a(k,k). The above mechanism can then be equivalently represented by the triplet <I([??],a([??],s([??])>. I assume throughout that the manager's marginal disutility of effort is small enough so that the principal always finds it worthwhile to elicit maximum effort, i.e., a(k) [equivalent to] [bar]a. This technical assumption allows me to ignore the issue of communication between principal and manager in connection with delegated investment decisions (below). The possibility that the manager chooses a suboptimal (out-of-equilibrium) effort level, however, creates scope for misreporting and hence for adverse selection. If the principal wanted to elicit interior effort levels, then the bonus coefficient under delegation in Section IV would need to depend on a profitability report; hence, a fully decentralized solution (one that requires no reporting) could not be optimal. (15) As demonstrated in Appendix B, however, the main results of the paper remain valid also for interior equilibrium effort choices, at the expense of increased complexity.

The manager's date-1 utility, if he reports[??] while actually being of type k, is:

(3) U([??],k) = s([??]) + e(k)I([??]) - v(a([??],k)).

Let U(k) [equivalent to] U(k,k). The revelation principle (e.g., Myerson 1979) applies and, hence, the search for optimal contracts can be confined to those that induce truthful reporting of k. Normalizing the manager's date-1 market alternative to zero, without loss of generality, the principal's problem becomes: (16)

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCTIBLE IN ASCII]

According to Program [P.sub.0], the principal maximizes the date-0 value of the firm, subject to an incentive compatibility constraint ensuring the manager reports truthfully and a participation constraint providing the manager with his reservation utility.

In contrast to the vast body of the adverse selection literature, the manager's private information parameter, k, enters his utility function in (3) twice, resulting in countervailing reporting incentives. Underreporting [??] < k results in a less demanding cash flow target, which the manager can achieve with less effort. On the other hand, overreporting [??] > k might trigger the investment decision, resulting in empire benefits. Unlike earlier studies on countervailing incentives (e.g., Lewis and Sappington 1989; Maggi and Rodriguez-Clare 1995), however, here the manager unambiguously benefits from a higher realization of the true profitability, k, because e'(k) [greater or equal to] 0 and a([??],k) is decreasing in k. That is, the manager consumes higher empire benefits and he can achieve a given cash flow target with less effort. As a consequence, standard techniques for solving adverse selection models suffice. (17)

For any feasible solution to [P.sub.0] satisfying individual rationality and "local" incentive compatibility, i.e., [delta]U/[delta][??] = 0, the manager's informational rent equals (see proof of Lemma 1 in Appendix A for details):

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Provided, as assumed above, it is always worthwhile to induce maximum managerial effort, by using (5) the isolated investment problem becomes:iS

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to: I(k) nondecreasing in k,

where v' [equivalent to] v'([bar]a), to simplify notation. The principal's problem thus amounts to maximizing the expected date-0 gross firm value cum empire benefits, less the manager's informational rents.

The solution to Program [P.sub.1] calls for the firm to invest in the project if, and only if, k [greater than or equal to] k*, where the optimal profitability cutoff k* is given by:

(7) [gamma][k* + e(k*) - (e'(k*) + v')H(k*)] - b = 0.

My first result is a variant of the standard capital rationing finding in the adverse selection literature (e.g., Antle and Eppen 1985).

Lemma 1: The second-best centralized contract solves Program [P.sub1] and is characterized by underinvestment: for k [member of] ([??],k*) the firm forgoes projects that would be undertaken if k were publicly observed.

Proof: All proofs are contained in Appendix A.

Capital rationing arises endogenously as a consequence of the principal's trade-off between maximizing the gross firm value cum empire benefits and minimizing the manager's informational rents. For any k < k*, the manager is compensated for his disutility of effort and just meets his reservation utility. If k exceeds the cutoff and the project is undertaken, then (as shown in Appendix A) the manager earns informational rents of:

(80) U(k > k*) = (k - k*)v' + e(k) - e(k*).

Note that Lemma 1 does not refer to the forgone projects as "profitable" in the classical corporate finance sense. They may well have a negative net present value as long as they are associated with offsetting private benefits of control. In the optimal centralized solution, the manager's compensation comprises his disutility of effort plus his informational rent, net of his empire benefits. Specifically, at the second-best cutoff, s(k*) = v([bar]a) - e(k*). (19)

Instead of determining cutoffs for absolute investment returns, k, firms in practice tend to set required rates of return. Empirical studies have shown that these relative profitability hurdle rates consistently exceed the firms' cost of capital (e.g., Poterba and Summers 1995). As noted above, this is consistent with shareholders curtailing managers' informational rents. The natural next step now is to ask whether this remains true once private benefits of control are accounted for.

Let the internal rate of return of an investment project with profitability k be denoted by R(k). Thus, NPV(k|R(k)) [equivalent to] 0 or, equivalently, R(k) [equivalent to] k/b - 1. Consistent with the traditional textbook notion of internal rates of return (Brealey and Myers 2000), R(k) captures only the cash returns from investing, ignoring any nonpecuniary empire benefits. Note that there is a one-to-one correspondence between k and R(k): instead of having the manager report k, an equivalent revelation mechanism exists where he is asked to report R(k). From (1), it follows that the first-best required rate of return in the absence of informational asymmetries is less than the firm's cost of capital, i.e., R([??]) [less than or equal to] r, since the principal can fully extract the manager's empire benefits. The second-best required rate of return that corresponds to k*--as given in (7)--equals:

(9) R* [equivalent to] R(k*) = k*/b - 1.

Recall that there are two control problems present: the manager enjoys private benefits of control, and he can reduce his effort input by underreporting the investment return (the agency problem). These two control problems have countervailing effects on the optimal required rate of return. Holding constant the manager's empire benefits, the importance of the agency problem is determined by v' and by the ex ante profitability of the project as parameterized by b. The lower b, the more profitable the project is in the expectation (all else equal) and, hence, the higher the probability that the investment is undertaken and that the manager earns informational rents.

The first main result compares the second-best required rate of return with the cost of capital for the plush office and reputation scenarios introduced in Definition 1.

Proposition 1: Suppose the principal makes the investment decision based on a required rate of return, R*.

1. If (PO) holds, then for any (b, v') there exists a unique cutoff [[??].sub.0] [greater than or equal to] 0, such that R* < r if [e.sub.0]>, while R* > r if [e.sub.0] < [[??].sub.0].

2. If (REP) holds, then for any (v', [e.sub.1] there exists an initial investment expense, [??], such that R* > r holds for all b < [??].

Empire benefits always result in a relaxation of the manager's participation constraint. In the plush office (PO) scenario, these benefits are independent of k and hence they cannot be used to screen different k-types. As a consequence, for high [e.sub.0] the principal invests in negative-NPV projects while reducing the manager's compensation. (20) On the other hand, as [e.sub.0] becomes small, the model converges to the standard adverse selection model and I recoup the classical capital rationing result that R* > r.

In the reputation (REP) scenario, the empire benefits are informative about k. Thus, they can be used to screen the manager's information more effectively. Technically speaking, empire benefits now also affect the manager's incentive constraint. If the project is very profitable in expectation (b is low) and the agency problem is severe (v' is high), then rent extraction weighs heavily in the principal's objective function for two reasons: the manager earns rents for many realizations of k, and these rents are increasing "steeply" in k. Therefore, the optimal capital budgeting policy tends to be more restrictive in that R* > r holds for any [e.sub.1]. (21) This is in contrast to the plush office scenario (Proposition 1, part 1) where R* < r always holds for sufficiently high empire benefits.

To make these trade-offs more transparent, I consider a specific example where k is uniformly distributed. This allows for closed-form solutions to be obtained.

Example: Suppose k ~ U[0, [??]] so that H(k) = [??] - k. Rewriting (7) for the case where e(k) = [e.sub.0] + [e.sub.1]k, as in (PO) and (REP), then gives:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The expression in (10) can in turn be rewritten to yield r = [k* + [delta](k*)]/b - 1, for [delta](k) [equivalent to] [e.sub.0] + (2k - [??]) [e.sub.1] - ([??]- k)v'. By comparison with (9),R* [equivalent to] k*/b - 1 > r, if [delta](k*) < 0, and vice versa. (22)

Consider the plush office (PO) scenario where e1 [right arrow] 0. Using (10), I find that [delta](k*) < 0 (and hence R* > r) if, and only if, [e.sub.0] < [[??].sub.0] = [k - (1 + r)b]v'. Note that [[??].sub.0] > 0 always holds. Thus, R* can indeed be less or greater than r for any (v',b), depending on [e.sub.0]. Now consider the reputation (REP) scenario where [e.sub.0] [right arrow] 0. Then, for b sufficiently small in that (1 + r)b < 1/2[bar]k, [delta](k*) < 0 holds if, and only if, [e.sub.1] < v'[[bar]k - (1 + r)b]/[2(1 + r)b - k] < 0. This contradicts the earlier assumption that [e.sub.1] [greater than or equal to] 0. Hence, if b < [??] = 1/2y[gamma][bar]k in the (REP) scenario with uniformly distributed types, then R* > r holds irrespective of the magnitude of empire benefits.

To summarize, the optimal required rate of return in connection with centralized investment decisions can be greater or less than the cost of capital, depending on the magnitude and the functional form of the manager's empire benefits. An unambiguous ranking is obtained only if empire benefits are driven by project scale and profitability--that is, in the reputation (REP) setting--and if the project is relatively profitable, ex ante. In this case, the hurdle rate always exceeds r.

IV. DELEGATED INVESTMENT DECISIONS

The capital budgeting model analyzed so far was characterized by a high degree of centralization. In practice, however, capital budgeting procedures tend to be more decentralized. I therefore now consider a regime where the manager makes the investment decision and is compensated based on residual income. First, residual income (or EVA) has been adopted by a large number of firms and, second, recent studies have shown that this metric has desirable features for delegating investment decisions (e.g., Rogerson 1997; Reichelstein 1997).

I consider linear contracts based on residual income (RI), which equals divisional income less a charge for the capital invested. In this one-period setting:

(11) RI(k,a,[rho]) = kI + a - (1 + [rho])bI,

with [rho] denoting the capital charge rate. The compensation contract is given by:

s(RI) = [alpha] + [beta] x RI,

where a denotes fixed salary and [beta] is the bonus coefficient. Residual income is said to be optimal, if such a linear compensation contract implements the second-best (centralized) effort and investment decisions and results in the second-best expected firm profit net of compensation. (23) It now becomes apparent that two alternative interpretations of "hurdle rates" are conceivable: as the required rate of return R(k) = k/b - 1, or as the capital charge rate, [rho], under delegation.

A manager compensated based on residual income will choose:

(12) max {[alpha] + [beta] x RI(k,a,p) - v(a) + e(k)I}.

Suppose the principal sets the bonus coefficient equal to the manager's marginal disutility of effort at the desired effort level, i.e., [beta] = v'. Then the manager will invest whenever:

(13) v'[k - (1 + [rho])b] + e(k) [greater than or equal to] 0.

The next result shows that a delegation scheme can replicate the benchmark performance of centralization and it characterizes the appropriate hurdle rate.

Proposition 2: Residual income constitutes an optimal performance measure. The optimal capital charge rate exceeds the firm's cost of capital; that is, [rho]* > r.

The proof of Proposition 2 proceeds by constructing contract parameters:

(14) [beta] = v' and [alpha] = v([bar]a) - v'[bar]a,

and an appropriate capital charge rate, for which the manager will take the desired actions and earn the second-best informational rent. As shown in Appendix A, the manager's informational rent under such a delegation scheme equals that under centralization, which is given in (8) above.

To see why the capital charge rate, [rho]* which together with the contract parameters in (14) achieves optimality, has to exceed the cost of capital, divide the condition that characterizes the second-best cutoff k*--Equation (7)--by the discount factor [gamma]. This yields (15) below. Then compare this with the condition that describes that manager's investment decision under delegation--Equation (13)--evaluated as an equality at k = k* and divided by the bonus coefficient [beta] = v'. This gives (16):

(15) k* + e(k*) - (e'(k*) + v')H(k*) - (1 + r)b = 0,

(16) k* + 1/v' e(k*) - (1 + [rho]*)b = 0.

At the margin, the manager trades off cash returns versus empire returns: he is willing to accept a decrease of $1 in the performance measure for an additional $(v') of nonpecuniary empire benefits. Comparing (15) with (16), it is apparent that [rho]* > r holds for two reasons: (i) the empire benefits are scaled by the bonus coefficient, and (ii) the manager does not subtract any informational rents when choosing the cutoff.

While Proposition 2 only lays out an optimal delegation scheme, this solution can indeed be shown to be unique within the class of residual income-type performance metrics. Note that the second-best investment and effort choices can also be implemented by a different delegation scheme with [beta] [member of] [v',1], [alpha] = v([bar]a) - [beta][bar]a and a hurdle rate, [rho]([beta]), chosen as a plug variable so that k* - [1 + [rho](beta)]b + e(k*)/[beta] = 0 holds. For this equality to hold for any [beta] [member of] [v',1], it must be that [rho](beta) < 0, yet [rho](1) > r. However, the manager's informational rent for any k > k* then equals (k - k*)beta + e(k) - e(k*), which exceeds that in (8) under centralization. Thus, setting [beta] > v' requires paying the manager excessive informational rents while setting beta < v' results in suboptimal effort input. Therefore, beta = v' characterizes the unique optimal solution. It is instructive to contrast these findings with Lambert (2001), who does not consider information-eliciting mechanisms: since the principal does not care about rent extraction in his model, the capital charge rate equals r and [beta] = 1 holds for a risk-neutral manager.

It is also important to note that the prediction of slope coefficients [beta] < 1 in my model is not an artifact of the assumed corner solution for effort choices. As shown in Appendix B, [beta](k) < 1 will hold for all k greater than the investment cutoff, even in the case of interior optimal effort choices (and thus type-dependent slope coefficients). A more steeply sloped contract (i.e., a higher value of [beta]) always implies higher informational rents for the manager. At the margin, the principal therefore is willing to accept suboptimal effort levels so as to economize on the manager's rents.

A comparison of Propositions 1 and 2 shows that the optimal hurdle rate under centralization, R*, can be either greater or less than the cost of capital, whereas the capital charge rate under delegation, p*, always exceeds r. This holds because the manager as the decision maker under delegation takes into account both cash and empire returns from investing. In contrast, the required rate of return, by definition, ignores the empire returns. Again rewriting (16) as:

(17) [rho]* = k*/b + 1/v' e(k*)/b - 1,

yields the following result by a direct comparison with the second-best required rate of return in (9). It is therefore stated without formal proof. (24)

Proposition 3: The hurdle rate under delegation always strictly exceeds that under centralization--that is, [rho]* > R*.

The results thus far demonstrate that the empirical findings reported in Poterba and Summers (1995) have to be viewed in the broader context of organizational design--in particular, the contracting environment. The above arguments imply that, for a given investment opportunity set, a required rate of return of, say, 15 percent would lead to a lower level of investment than a 15 percent capital charge rate under residual income-based compensation. Put differently, the two hurdle rates will differ in their economic consequences as a result of private benefits of control.

V. COMPARATIVE STATICS

This section addresses in more detail how empire benefits affect both kinds of hurdle rates. This discussion sheds light on two related questions. First, how does the optimal solution characterized above compare with the optimal capital budgeting mechanism in the absence of empire benefits? Second, do empire benefits invariably harm shareholders, as suggested by conventional wisdom?

To address these questions, I introduce a new and commonly known parameter, m [member of] [0,[bar]m], which captures the scale of the manager's empire benefits so that:

(18) e(k,I,m) =- me(k)L

For instance, Hennessy and Levy (2002) measure the propensity of managers to engage in empire-building by: (i) whether the manager is a member of the founding family; (ii) the percentage of insiders on the board of directors; and (iii) the manager's tenure. In their sample, managers who are members of the founding family are shown to consume higher empire benefits, while (ii) and (iii) are used as proxies for the likelihood that the manager's decision will be challenged by the board. Also, for the reputation setting (REP), one would expect m to be relatively high when the manager enjoys high external visibility (e.g., due to high analysts' following). The preceding analysis therefore has captured the special case of m = 1.

Upon substituting e(k, L m) for e(k, D, let k*(m) denote the solution to the centralized problem as in (7) for any m, and R*(m) =- R(k*(m)). Similarly, let p*(m) be the optimal capital charge rate under delegation when generalizing the solution characterized in (17). A first intuition suggests that k*(m) be decreasing in m as a consequence of the manager's compensation/empire benefits trade-off. While this intuition holds for the symmetric information case, it may fail under adverse selection, as the next result shows. (25)

Proposition 4: Suppose the manager's empire benefits are as given in (18).

1. If (PO) holds, then R*(m) is decreasing in m.

2. If (REP) holds, then R*(m) is increasing in m, for b sufficiently small.

3. In a decentralized firm with residual income-based compensation, the optimal capital charge rate, p*(m), is always increasing in m.

In the plush office scenario (PO) the intuition developed for the symmetric information case applies: an increase in m has the sole effect of relaxing the manager's participation constraint. The principal then lowers the required rate of return R* and at the same time reduces the manager's compensation. In the reputation setting (REP), an increase in m again also allows for improved screening of different k-types. If the project is sufficiently profitable in expectation (b is small), then this incentive constraint-effect dominates and the firm raises R* so as to reduce the rents earned by high-k managers. (26)

Under delegation, two effects are present. First, as m increases, the optimal profitability cutoff, k*(m), to be implemented via the capital charge rate, changes. As the preceding paragraph has shown, this effect can go either way. Second, the manager becomes more eager to invest irrespective of the project's profitability. As the proof demonstrates, this second, more direct, effect always dominates the first one so that p*(m) is always increasing. Note that the contract parameters ([alpha],[beta]) given in (14) are independent of the manager's empire benefits. Instead, the hurdle rate p*(m) is the sole instrument the principal uses to extract (a share of) these benefits.

Private benefits of control are commonly perceived as a "public bad" in the business press. The claim is that managers' inclination to overinvest relative to the NPV rule destroys firm value. As the previous analysis suggests, this need not be the case once compensation contracts are derived endogenously. In fact, the delegated investment condition in (13) reveals that shareholders in this model will ultimately benefit from their manager's empire benefits even in the presence of adverse selection. For any m > 0, the shareholders can always induce the manager to invest whenever k [greater than or equal to] k*(0) by simply raising p. Holding the contract parameters ([alpha],[beta]) fixed, this will transfer rents from the manager to the shareholders while ensuring all incentive and participation constraints remain intact. By revealed preference, the shareholders can do even better by choosing [rho]*(m) optimally. This discussion is summarized in the following corollary.

Corollary 1: Suppose the manager's empire benefits are as given in (18). Then the value of the firm, net of the manager's compensation, is increasing in m.

Rather than concluding that the conventional wisdom of empire benefits destroying firm value is false, it should be noted that Corollary 1 hinges on the assumption that a project's financial and nonpecuniary returns are related in a deterministic (and commonly known) fashion. In practice, this may not always be the case. Put differently, the corollary shows that a necessary condition for empire benefits to reduce firm value is that shareholders have only incomplete information about how these benefits depend on the size and profitability of investment projects (see also footnote 6). (27)

VI. CONCLUSION

This paper has studied optimal hurdle rates in a setting where investment decisions are subject to adverse selection and private benefits of control. The results have demonstrated systematic differences between the required rate of return and the capital charge rate, which are the two most common incarnations of hurdle rates. A key empirical implication of the model is that capital charge rates used for residual income/EVA-based bonus plans should on average be higher than required rates of return across comparable firms. Also, capital charge rates should be higher in high-empire-benefits environments (e.g., a manager has been with the firm for a long time; high percentage of insiders among the board members; high external visibility) as compared with low-empire-benefits environments. This need not be true for required rates of return.

The risk-neutral framework adopted in this paper was in part motivated by Poterba and Summers' (1995) finding of hurdle rates unrelated to measures of firm-specific risk. In light of Christensen et al. (2002) and Dutta and Reichelstein (2002), it would be desirable to reassess firms' choice of hurdle rates in a large-sample study, taking into account firm-specific and market-wide risk factors, as well as proxies for empire benefits.

The results in this paper have demonstrated that different assumptions regarding the specific nature of empire benefits have qualitatively different implications for the capital budgeting process. This has been ignored in previous studies. As shown here, the optimal hurdle rates depend on whether empire benefits are driven by project size and profitability, or by size only. From an empirical standpoint, this raises the question of how to distinguish between these two scenarios. One possible control variable that comes to mind is a manager's tenure. Near retirement, managers tend to put less emphasis on future career prospects and hence may prefer larger projects over smaller, but more profitable ones. (28) The opposite is likely to hold at an early stage in a manager's career where reputation effects play a more important role.

The present model can be generalized to analyze capital assets with a useful life of multiple periods, in which case accrual accounting issues arise. In the absence of empire benefits, this question of how to depreciate an asset so as to achieve intertemporal matching of investment costs with investment returns has been the subject of several recent studies? (29) These studies have argued that depreciation for projects with uniform cash flows over time should be decelerated--that is, increasing over time. This is clearly at odds with firm practice, as companies predominantly use straight-line (or even faster) depreciation. In the presence of empire benefits, intertemporal matching has to take both cash and nonpecuniary return streams into considerations. (30) In particular, it is plausible that empire benefits are particularly high in early periods--e.g., due to analysts' coverage. If this is the case, then, as shown in an earlier version of this study (Baldenius 2002), optimal depreciation tends to be more accelerated than previously suggested. Hence, empire benefits may help explain depreciation schedules observed in practice, and the recent call for more decelerated depreciation to overcome perceived underinvestment problems (Young and O'Byrne 2001) may thus be misguided.

APPENDIX A PROOFS

Proof of Lemma 1

I begin by stating a sufficient condition for the principal to induce the manager to exert maximum effort for any realization of k, i.e., for a(k) [equivalent to] [bar]a:

(19) 1 - v'(a) - v"(a)H([??]) [greater than or equal to] 0,

where H(k) [equivalent to] [1 - F(k)]/f(k). Here, [??] denotes the first-best profitability cutoff, i.e., the profitability parameter for which the project just breaks even, i.e., [gamma][[??] + e([??])] = b. I will show below that (19) is indeed sufficient for a(k) [equivalent to] [bra]a, for all k, in equilibrium.

The manager's date-1 utility if he reports [??] while actually being of type k equals U([??],k) = s([??]) + e(k)I([??]) - v(a([??],k)). An increase in the manager's true type, k, has a positive impact on his utility (i) due to higher empire benefits and (ii) because it will allow him to achieve a given cash flow objective with less effort, i.e., a([??],k) is decreasing in k since, by (2), a([??],k) = c(k) - kI(k). Hence, for any contract that satisfies the participation and (local) incentive compatibility constraints, the envelope theorem implies that U'(k) = [e'(k) + v'(a(k,k))]I(k) [greater than or equal to] 0. As a consequence, the manager's individual rationality constraint will be binding for k = [??] and his informational rent for any k equals:

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

In the optimal solution, the lowest type, [??], will earn zero rents. In expected terms, this implies [E.sub.k]{U(k)} = [[integral].sup.[??].sub.[??] [e'(k) + v'(a(k,k))]I(k)H(k)f(k)dk, after integration by parts. Hence:

[E.sub.k]{s(k)} = [[integral.sup.[??].sub.[??]] [v(a(k,k)) - e(k)l(k) + [e'(k) + v'(a(k,k))]l(k)H(k)]f(k)dk.

Recall from (2) that a(k,k) = c(k) - kI(k). Substituting the last two expressions into the principal's objective in [P.sub.0] yields:

(20) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

For any k [less than or equal to] [??], it follows that I(k) = 0. Now, if I(k) = 1, for some k > k, the principal will choose a so as to maximize a - v(a) - v'(a)H(k). Then condition (19), in conjunction with H(*) being decreasing, implies that the optimal solution in these cases entails maximum effort by the manager, i.e., a(k) [equivalent to] [bar]a. Hence the second-best cutoff, k*, is as given in (7). Moreover, since k* [greater than or equal to] [??], with the latter denoting the first-best cutoff, I find that the firm underinvests for all k [member of] (k,k*).

Given the discrete nature of the investment problem, the optimal decision rule, I([??]), is discontinuous at k* and insensitive to marginal changes in [??] elsewhere. Hence, for all types k [greater than or equal to] k*, there only is an incentive to underreport so as to reduce effort. For this to be ruled out, the manager must be paid the above informational rents. In equilibrium, the cutoff-type k* will just break even, i.e., s(k*) = v([bar]a) - e(k*) and c(k*) = k* + [bar]a. Hence, the required cash flow to be delivered at k = k* renders it unfeasible for a manager with type k < k* to mimic type k* so as to trigger the investment decision. (31)

Finally, I show that the optimal mechanism as characterized by (7) is indeed globally incentive compatible. Following Mirrlees (1986), a mechanism that is locally incentive compatible is also globally incentive compatible if [delta]/[delta]kU([??],k) is increasing in [??]. For the solution derived:

[delta]/[delta]-k U([??],k) = [e'(k) + v'(a[??]k))]l([??]).

The Mirrlees (1986) requirement is thus met, because v"(*) [greater than or equal to] 0, a([??],k) is increasing in [??] and the second-best investment policy, I(*), is upper-tailed.

Proof of Proposition 1

From (9) we know that the optimal required rate of return is given by:

R* [equivalent to] R(k*) = k*/b - 1.

To compare this term with the firm's cost of capital, I rewrite the first-order condition for the profitability cutoff k* in (7) as follows:

(31) Note that in a more general model with interior effort choices a([??],k) in equilibrium, it would be feasible for a manager of type k < k* to report [??] = k* and subsequently to increase his effort to deliver c(k*), but that would not be optimal, as it would result in negative utility since: 0 : U(k*) = s([??] = k*) + e(k*) - v(a([??]~*,k*)) > s([??] = k*) + e(k) - v(a([??] = k*,k)), for any k < k*.

(21) r = 1/b [k* + e(k*) - (e'(k*) + v')H(k*)] - 1.

Hence, a necessary and sufficient condition for R* > r is that:

[delta]](k) =- e(k) - (e'(k) + v')H(k) < 0,

for k = k*. For the two linear specifications of the e(*)-function in (PO) and (REP), we have:

[delta](k) = ([e.sub.o] + [e.sub.1]k) - ([e.sub.1] + v')H(k).

Part 1

Suppose (PO) holds, i.e., [e.sub.0]> 0 and [e.sub.1] [right arrow] 0. Then, [delta](k) [right arrow] [e.sub.0] - v'H(k), where v' is bounded above by 1 due to the assumed comer solution for a. It immediately follows that there is a unique value [[??].sub.0] > 0 such that [delta](k*) > 0 (and hence R* < r) for any [e.sub.0] > [[??].sub.0], and vice versa.

Part 2

Suppose (REP) holds, i.e., [e.sub.0] [right arrow] 0 and [e.sub.1] > 0. Hence, [delta](k) [right arrow] [e.sub.1][k - H(k)] - v'H(k). Since I have not restricted the initial investment expense b from below, for any v' and any type distribution function F(k) over the support [0,k], there exists a value b sufficiently low, such that k* [right arrow] [??] = 0. Hence, e(k*) [right arrow] e(k) [right arrow] 0. Since both [e.sub.1] and v' are assumed to be strictly positive, it follows that [delta](k*) < 0 and, hence, R* > r.

Proof of Proposition 2

Suppose the principal sets the contract parameters as follows:

(22) [beta] = v',

(23) [alpha] = v([bar]a) - v'[bar]a,

and the capital charge rate, p*, is chosen so that:

(24) v'[k* - (1 + [rho]*)b] + e(k*) = 0.

I now show that, given the contract parameters given in (22)-(24), the manager will (i) take the same actions and (ii) earn the same informational rent as in the centralized second-best benchmark solution. For comparison, the manager's informational rent under the centralized mechanism is:

(25) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

and zero otherwise.

Recall that the manager's objective is, for any ([alpha],[beta],[rho]) and any k, to choose a(*) and I(*) so as to maximize:

(26) [alpha] + [beta][kI + a - (1 + [rho])bI] - v(a) + e(k)I.

Hence, given the parameters in (22)-(24), the manager will indeed set a(k) [equivalent to] [bar]a and I(k) = 1 if, and only if, k [greater than or equal to] k*. Moreover, the manager's resulting date-1 informational rent for any k [greater than or equal to] k* under this delegated mechanism equals v'[k - (1 + [rho]*)b] + e(k) = v'[k - k*] + e(k) - e(k*), which coincides with that under centralization, given in (25).

Finally, to see that the optimal capital charge indeed exceeds the firm's cost of capital, r, rewrite (24) as:

[rho]* = k*/b + 1/v' e(k*)/b - 1.

By assumption, v' < 1. This completes the proof by a simple comparison with (21), since e(k) > [delta](k).

Proof of Proposition 4

First note that in the centralized contracting setting there is a one-to-one mapping from absolute profitability cutoffs, k*, to required rates of return, R*, with higher k* being equivalent to higher R*. Hence, this proof is confined to absolute profitability cutoffs, k*. Rewrite (7) for the case of e(k,I,m):

(27) k*(m) + me(k*(m)) - [me'(k*(m)) + v']H(k*(m)) - (1 + r)b = 0.

Applying the implicit function theorem to this necessary first-order condition gives (I henceforth suppress the dependence of k*(m) on m to save on notation):

(28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where I have used that, by Definition 1, e(k) = [e.sub.0] + [e.sub.1]k holds under both (PO) and (REP). Note that the denominator is always positive, hence sign{dk*/dm} = -sign{[e.sub.0] + [e.sub.1][k* - H(k*)] }.

Part 1

In the plush office (PO) scenario, [e.sub.0] > 0 and [e.sub.1] [right arrow] 0. Hence, dk*/dm < O.

Part 2

Consider next the reputation (REP) scenario, where [e.sub.0] [right arrow] 0 and e1 > 0. Then dk*/dm > 0 if k* < H(k*), and vice versa. Now, it follows from (27) that for any m, there exists a value b sufficiently small, so that k* [right arrow] k. By Definition 1, (REP) implies that [??] [right arrow] 0 so that k* [right arrow] 0, yet H(k*) > 0 for k* [right arrow] [??]. Hence, dk*/dm > 0 for b sufficiently small. Since H'(k) [less than or equal to] 0, the argument can be reversed to show that for high b, dk*/dm < 0 will hold.

Part 3

Finally, consider a decentralized firm with the manager making the investment decision while compensated based on residual income with p as the capital charge rate. Unlike in parts 1 and 2, e(k) is not restricted to be linear in k.

The manager, compensated based on residual income, will invest if and only if v'[k - (1 + [rho])b] + me(k) [greater than or equal to] 0. (Recall that the bonus coefficient must equal v' in the optimal solution, due to the arguments given in the main text.) For such a delegated contract to be optimal, this last weak inequality has to hold with equality for k = k*. Solving for the optimal capital charge rate as a function of m yields:

[[rho]*(m) = 1/b [k*(m) + 1/v' me(k*(m)) - 1.

Taking the first-order derivative with respect to m gives:

d[rho]*/dm = 1/v'b [k*(m) + 1/v' me(k*(m))] - 1.

Now, using (28) above, I can derive a lower bound on this previous expression by using the facts that v' < 1, e"(k) [less than or equal to] 0 and H'(k) < 0 for all k. Since v' are b both positive, the right-hand side of the last equation is proportional to (again suppressing the argument m in k*(m)):

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

This last inequality holds, because e"(k) [less than or equal to] 0 and H'(k) < 0 for all k imply that me"(k*)H(k*) + [v' + me'(k*)]H'(k*) < 0. As a consequence, the term in square brackets is positive and p*(m) is a monotonically increasing function. This completes the proof of Proposition 4.

APPENDIX B INTERIOR EFFORT CHOICES

In this appendix, I rephrase the model for the case that the condition in (19) does not hold, with the consequence that the principal may want to implement interior effort choices, a(k) [member of] (0,a). It is shown here that the preceding results--in particular, the key results in Propositions 1-3--can be generalized to this setting.

The first-best program (if the principal were to know k and could "force" the manager to choose a certain effort level) calls for the investment to be made whenever the present value of cash and empire returns exceeds b. At the same time, the first-best effort level just equates marginal effort costs with marginal effort returns. That is: [max.sub.I(k),a(k)]{([gamma],[k + e(k)] - b)I(k) + [gamma][a(k) - v(a(k))]}, so that:

(29) [gamma][[??]+ e([??])]- b = 0 and 1 - v'([??](k)) = 0.

Note that effort and investment choices are independent in the first-best solution.

In the second-best solution, the principal does not know k and has to elicit this information from the manager. Following similar steps as in the proof of Lemma 1 then yields the following optimization program:

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

Assuming unique interior solutions, the resulting first-order conditions are:

(30) [gamma][k* + e(k*) - [e'(k*) + v'(a(k*))]H(k*)] - b = 0,

(31) 1 - v'(a(k*)) - v"(a(k*))H(k*)I(k*) = 0.

Since I(k) = 1 if and only if k [greater than or equal to] k*, the investment and effort choices become intertwined for k [greater than or equal to] k*. In comparison with (29), the second-best solution in (30)-(31) is characterized by both underinvestment and underprovision of effort. The latter arises because higher effort levels can only be induced at the expense of higher informational rents. Note that a(k [greater than or equal to] k*) [less than or equal to] a(k < k*), and a(k) is monotonically increasing for all k [greater than or equal to] k* since H'(k) [less than or equal to] 0. It is easy to show now that Proposition 1 remains qualitatively unchanged once interior effort choices are allowed for.

Following similar steps as in the proof of Lemma l, the above mechanism can be shown to be globally incentive-compatible, and it results in date-1 informational rents for the manager of U(k > k*) = e(k) - e(k*) + v(a(k)) - v(a(k*)) and U(k [less than or equal to] k*) [equivalent to] 0.

Since the centralized solution now entails type-dependent effort choices, it is clear that a "pure" delegation mechanism, such as that described in Section IV, can no longer replicate this benchmark performance. Instead, I consider the following message-dependent delegation scheme. The manager reports [??] and thereby picks a compensation scheme from a menu of contracts all of which are linear in residual income: s(RI|[??]) = [alpha]([??]) + [beta]([??]) x RI. Then the manager makes the investment and effort decisions in a decentralized fashion.

Consider the following contract parameters:

(32) [beta](k) = v'(a(k)),

(33) [alpha](k) = v(a(k)) - v'(a(k))a(k) + A(k)I(k),

and a hurdle rate, p*, that is implicitly defined by:

(34) v'(a(k*))[k* - (1 + p*)b] + e(k*) = 0,

where the newly introduced function in (33) equals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

By (31) and (32), [beta](k) < 1 for all k [greater than or equivalent to] k*, even in the case of interior effort choices.

Using (32)-(34), it is a matter of straightforward algebra to show that, having truthfully reported [??] = k, the manager will indeed make the second-best investment and effort choices, (I(k), a(k)). The manager's resulting date-1 utility then equals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

which coincides with his date-1 informational rent under centralization.

By rewriting (34) and (30) in a fashion similar to (15) and (16), above, one finds that [rho]* > r, which mirrors Proposition 2. Moreover, since:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

the key result in Proposition 3 also generalizes to this more general setting.

I thank Moshe Bareket, Zhonglan Dai, Joel Demski, Volker Laux, Nahum Melumad, Madhav Rajan, Stefan Reichelstein, Amir Ziv, two anonymous reviewers, and workshop participants at the Carnegie Mellon Accounting Conference, the FEA Conference at Rutgers University, the Duke-UNC Fall Camp, the Burton Conference, and the Finance "Free Lunch" Workshop at Columbia University, the Arijit Mukherji Conference at the University of Minnesota, and Northwestern University for helpful comments, I am especially indebted to Anil Arya and Jon Glover for discussions on this subject.

Editor's note: This paper was accepted by Madhav V. Rajah, Editor.

(1) Empire benefits are discussed in anecdotal form in Donaldson (1984) and Jensen (1986). The Economist lists empire benefits as the main example for agency problems in its online "Economics A-Z" (http://www.economist.com/research/Economics/). Burrough and Helyar (1990) describe in detail how RJR-Nabisco management wasted corporate resources by using corporate jets for their dogs, etc. Hennessy and Levy (2002) find strong empirical evidence for empire benefits to affect investment decisions. They estimate that CEOs that are members of the founding family derive an annual benefit of $3.30 per $1,000 of installed capital. Their model includes more control variables than that tested in Aggarwal and Samwick (1999), who found no evidence of empire benefits. Throughout this paper, "empire benefits" is shorthand for any investment return components that accrue directly to the manager.

(2) Exceptions are Arya et al. (1999) and Lambert (2001). Dutta (2003) considers a setting where the manager can "walk away" with the project.

(3) Baiman and Verrecchia (1995) make a related observation, albeit in a very different setting. They argue that when a firm's manager can trade on his private information, the expected gains from insider trading allow the shareholders to lower his compensation.

(4) Note that in my model the compensation contract under delegation does not require any communication between manager and principal, while this is necessary for the centralized solution. Since I do not explicitly model any communication costs, however, the revelation principle implies that a decentralized firm can at best replicate the performance of a centralized firm.

(5) As shown below, under delegation the manager internalizes 100 percent of the empire returns, but only a fraction [beta] < 1 of the cash returns (and outlay) from investing. Here, [beta] is the bonus coefficient that is endogenously determined by the severity of the agency problem (i.e., by the marginal disutility of effort). The more severe the agency problem, the higher the bonus coefficient and, therefore, the less weight the manager assigns to the empire benefits relative to his utility from monetary compensation.

(6) Formally addressing this issue would require a two-dimensional adverse selection model where the manager privately observes k and a measure of his empire benefits, where the latter may or may not be correlated with k. However. the theory of such multidimensional screening problems is highly incomplete at this point; see Rochet and Stole (2001) for a survey of the current state of this literature.

(7) Baldenius and Ziv (2003) incorporate corporate income taxes into a capital budgeting setting. Their model, which builds on Rogerson (1997) and Reichelstein (1997), predicts that firms employing pre-tax residual income tend to set higher capital charge rates than comparable firms using after-tax metrics such as "Economic Value Added."

(8) Lambert (1986) analyzes the investment distortions that arise if a risk-averse manager has to be motivated to exert personally costly effort to become informed about a project's profitability.

(9) Christensen et al. (2002) distinguish between firm-specific and market risk. They argue against using the weighted-average cost of capital (WACC) as the capital charge rate and show that only firm-specific (diversifiable) risk affects the capital charge rate, whereas market risk does not. As a result of firm-specific risk, the hurdle rate can be less or greater than the risk-free rate depending on the information held by the manager at the time of investing.

(10) Bernardo et al. (2001) also study the role of compensation to control managers' empire-building tendencies, albeit only in a centralized decision-making setting. Their analysis is thus confined to required rates of return as hurdle rates, for which they derive results consistent with the earlier capital rationing literature, e.g., Harris et al. (1982), and Antle and Eppen (1985). In Harris and Raviv (1996, 1998), headquarters uses internal auditing procedures, instead of compensation, to mitigate its divisional managers' desire for empires.

(11) Since both the manager and the principal are risk-neutral, all results for the adverse selection model remain valid if the date-1 cash flow were subject to an additional random noise term: [??] = kl + a + [??] with E[??] = O. For the first-best benchmark setting this would require the principal to be able to directly observe a, as the latter could otherwise no longer be inferred from c.

(12) Note that the present model does not explicitly incorporate such dynamic features; see instead Holmstrom and Ricart i Costa (1986).

(13) Both these alternative sources of empire benefits have previously been studied separately. The reputation (REP) scenario underlies the models of Harris and Raviv (1996, 1998) and Bernardo et al. (2001). Here, it is conceivable that e(k) [less than or equal to] 0, i.e., the manager's reputation may suffer if the project is very unprofitable. The present model could easily be adapted to allow for this. The plush office (PO) scenario is closer in spirit to the way empire benefits are modelled in Hart and Moore (1995) and Lambert (2001). The terms "plush office" and "reputation" scenarios are purely chosen for expositional purposes.

(14) Note that this definition of decentralization differs from that in Bernardo et al. (2001), who refer to revelation mechanisms as decentralized schemes.

(15) A similar assumption is made in Dutta and Reichelstein (2002). The proof of Lemma 1 in Appendix A contains a technical condition that ensures such a corner solution.

(16) As pointed out by an anonymous reviewer, the empire benefits turn this adverse selection problem into one with type-dependent reservation utilities of U--e(k)I where U = 0; see also Jullien (2000).

(17) Note that this may not be the case in a model with continuous investments where, for some realizations of k, the over-and underreporting incentives may just offset each other.

(18) The monotonicity constraint in Program [P.sub.1] ensures that the solution found by observing only the "local" incentive constraints also satisfies "global" incentive compatibility, as required in Program [P.sub.0].

(19) Abstracting from empire benefits, the difference between the manager's compensation and his disutility of effort corresponds to the "organizational slack" in Antle and Eppen (1985).

(20) "High" empire benefits, [e.sub.0], here means high relative to the agency problem parameter, v'. Note that v' [greater than or equal to] 1 implicitly holds by the assumption that maximum effort is always desirable.

(21) Note that no explicit lower bound has been imposed on the initial investment expense, b. In fact, b can even be ("slightly") less than [gamma]k without making the investment problem under adverse selection trivial. Even then the principal may optimally forgo a project with a k-realization close to k so as to extract informational rents from the manager.

(22) Consistent with results in Section V, the following comparative statics hold for the optimal cutoff in (10): k* is decreasing in [e.sub.0], increasing in v' and b, while the sign of ak*l[delta][e.sub.1] is ambiguous.

(23) Note that the linear compensation schemes considered here do not require any communication between the principal and the manager. This would no longer be true if the optimal solution were to entail interior effort levels (see Appendix B).

(24) To avoid the trivial case where e(k*) = 0 and hence p* = R*, I assume that e(k) > 0 for small k.

(25) Note that, while parts 1 and 2 of Proposition 4 rely on linear specifications for the e(k)-function, this is not the case for part 3.

(26) Part 2 of Proposition 4 complements a comparative statics result derived in Bernardo et al. (2001). In their model, investments are continuous and effort and investment are complements. Their Proposition 4 part (i), shows that (pointwise) investment amounts are increasing in empire benefits for high types and decreasing for low types.

(27) In a similar vein, Corollary 1 is sensitive to the specifics of the manager's utility function. In my model, the manager views compensation and empire benefits as substitutes. Alternative specifications are conceivable--e.g., lexicographic preferences--for which this result may not hold.

(28) Gibbons and Murphy (1992) analyze investment levels as a function of managers' tenure and find investments in R&D to increase toward the end of managers' careers, which is inconsistent with maximizing earnings-based compensation. See also Hennessy and Levy (2002). However, neither of these studies tests for ex post profitability of investment projects.

(29) See Rogerson (1997), Reichelstein (1997), Bareket (2002), and Dutta and Reichelstein (2002).

(30) When addressing type-dependent empire benefits in form of a multiperiod "reputation" scenario, it is conceivable that the manager's reservation utility in future periods is endogenously determined by the realization of k. The principal would then have to take this into account when designing the optimal capital budgeting process, i.e., the optimal investment cutoff.

REFERENCES

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Reichelstein, S. 1997. Investment decisions and managerial performance evaluation. Review of Accounting Studies 2: 157-180.

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Young, D., and S. O'Byrne. 2001. EVA and Value-Based Management. Boston, MA: McGraw-Hill.

Tim Baldenius

Columbia University

Submitted May 2002

Accepted May 2003

Keywords: capital budgeting; empire-building; residual income; hurdle rates.

I. INTRODUCTION

Capital budgeting ranks among the key managerial tasks in modern corporations and much of the attendant debate revolves around determining appropriate hurdle rates for accepting investment projects. Traditionally, the term "hurdle rate" has been used interchangeably with the required rate of return. Recently, however, a growing number of firms have adopted accounting-based performance measures known as residual income or "Economic Value Added" (EVA), which subtract a charge for the opportunity cost of capital from operating income. The capital charge rate employed is also often referred to as a hurdle rate. This dual nature of hurdle rates has remained largely unexplored in the academic literature. The present paper seeks to fill this gap by arguing that (and how) in practice the two hurdle rates should be expected to differ.

The practitioners' literature advocates using the firm's cost of capital as both the required rate of return and the capital charge rate (Brealey and Myers 2000; Young and O'Byrne 2001). On the other hand, Poterba and Summers (1995) have found that hurdle rates employed in practice significantly exceed the cost of capital. This clearly violates the net present value rule. Such underinvestment, or capital rationing, as a result of adverse selection is consistent with shareholders curtailing informational rents earned by their privately informed managers at the expense of reduced efficiency (e.g., Antle and Eppen 1985).

At the same time, managers are frequently accused of overinvesting in assets as a consequence of private benefits they derive from controlling "empires." (1) There are numerous reasons for such empire-building tendencies to arise. Apart from intrinsic motivation, division size often is positively associated with fringe benefits such as lavish office spaces or simply power within the organization. Moreover, managers of larger and/or more profitable divisions may be more likely to be promoted or become the future CEO. Somewhat surprisingly, empire benefits have so far been largely ignored in the accounting literature. (2)

As a means to align a division manager's objective with that of the shareholders, his compensation will generally be linked to realized investment returns. While this may mitigate excessive empire-building tendencies, the manager will still invest in projects that are marginally unprofitable (and hence will lower his compensation) provided the attendant empire benefits are sufficiently high. In fact, this may be equilibrium behavior as the manager's empire benefits allow shareholders to reduce his compensation and thereby to indirectly extract a share of these benefits. (3)

This paper characterizes the capital budgeting process in the presence of adverse selection and empire benefits. In particular, I compare the optimal required rate of return with the optimal capital charge rate and benchmark both these hurdle rates against the firm's cost of capital. I refer to a firm as centralized if the principal makes the investment decision based on a comprehensive "revelation" contract with the better informed manager. The required rate of return then is the relevant hurdle rate under centralization. In a decentralized firm, the investment decision is delegated to the manager who is compensated based on residual income. The capital charge rate used for computing residual income is the relevant hurdle rate under decentralization.

Beginning with centralized firms, I obtain a familiar capital rationing result: to economize on the manager's informational rents, the firm optimally forgoes some projects that would have received funding under symmetric information. Two countervailing forces are shown to determine the comparison of the optimal required rate of return with the firm's cost of capital. While the adverse selection problem calls for a restrictive budget (i.e., a high hurdle rate), the manager's empire benefits tend to have the opposite effect: by decreasing the hurdle rate, the principal can lower the manager's compensation and thereby extract a share of the empire benefits. Depending on the relative importance of the two control problems, the optimal required rate of return can be less or greater than the cost of capital.

I then show that the principal can replicate the second-best (centralized) solution by delegating the investment decision to the manager, compensating him based on residual income. This lends support to the increasing use of residual income in decentralized firms. (4) In contrast to the ambiguous results for the required rate of return, the optimal capital charge rate under delegation always exceeds the cost of capital. This holds, because the manager as the decision maker under decentralization compares both return streams (cash and empire returns) with the imputed capital charge, and he ignores any informational rents, which, from the viewpoint of the principal, should be netted against the investment returns. (5) The required rate of return, in contrast, only captures the cash returns from investing. As a consequence, the main result of this paper is that the capital charge rate always exceeds the required rate of return--that is, the hurdle rate is always higher under delegation than under centralization.

This divergence in the hurdle rates is in stark contrast to the practitioners' literature cited above. The findings in this paper indicate that lumping together required rates of return with capital charge rates, as is common in empirical studies on capital budgeting practices, adds noise. This may help explain the somewhat inconclusive cross-sectional findings on hurdle rates in Poterba and Summers (1995). Based on my results, a required rate of return of, say, 15 percent will result in lower levels of investment than an equally high capital charge rate in a decentralized, but otherwise identical, division or firm. This is further corroborated by additional results that predict qualitatively different comparative statics for the two hurdle rates.

The business press generally views empire-building tendencies as value-destructing because of the resulting investment distortions. As the preceding discussion suggests, this need not be true once compensation contracts are determined endogenously. Indeed, an immediate corollary of my results is that the firm owners can always extract a sizable share of the manager's empire benefits and, hence, will ultimately benefit from an exogenous increase in these benefits. It should be noted, however, that this result hinges on the assumption that empire benefits depend on the characteristics of the investment project in a deterministic and commonly known fashion. Put differently, for the negative connotation associated with empire benefits to be justified, it must therefore be the case that shareholders are imperfectly informed about bow these benefits are driven by the scale and profitability of the assets under a manager's control. (6)

This paper is related to several recent studies on capital budgeting. Christensen et al. (2002) and Dutta and Reichelstein (2002) examine optimal hurdle rates in the absence of empire benefits. (7) Closest to my model is Lambert (2001), who studies a capital budgeting model with asymmetric information and empire benefits. While Lambert (2001) does not allow for screening of the manager's private information, this paper derives suitable hurdle rates that implement the optimal revelation mechanism. All three earlier studies emphasize the role of project (or market) risk in that any deviations between required rates of return and capital charge rates are solely driven by differences in risk tolerance between shareholders and managers. (8) While corporate finance theory predicts that the required rate of return is, in general, increasing in a project's riskiness, Christensen et al. (2002) demonstrate that this need not hold for the capital charge rate under delegation. A risk-averse manager will internalize the project risk via the attendant increase in his compensation risk for a given capital charge rate. Raising the hurdle rate further would thus amount to "double-counting" of the risk premium. (9) In fact, Poterba and Summers (1995, 47) find that none of the traditional risk factors correlates with hurdle rates in their sample. By introducing empire benefits, the present paper takes the natural next step in this research agenda as it demonstrates systematic differences between the two hurdle rates even in a risk-neutral setting. (10)

The remainder of the paper is organized as follows. Section II describes the model. Section III characterizes the optimal centralized capital budgeting procedure and the corresponding required rate of return. Section IV addresses delegated investment decisions and capital charge rates. Section V analyzes the comparative statics. Section VI concludes.

II. MODEL

This section develops a single-period capital budgeting model of a firm consisting of a risk-neutral principal and a risk-neutral manager. The model entails private precontractual information (adverse selection), unobservable effort choices, and private benefits to the manager from controlling assets. At date 0, the firm can invest in a project, with I [member of] {0, 1} as an indicator variable that denotes whether the project is undertaken. If it is (I = 1), then the attendant expense equals b. At date 1, the return from the investment is realized. The gross cash return from investing equals k [member of] [[??], [bar]k] and is known only to the manager prior to accepting the contract. The manager exerts personally costly effort, denoted by a [member of] [0,[bar]a]. The (commonly known) marginal productivity of effort is normalized to 1, without loss of generality. Hence the date-1 cash flow equals c = kI + a. The principal maximizes the total date-0 value of the firm net of the manager's compensation, s:

[gamma][kI + a - s] - bI.

Here, [gamma] = [(1 + r).sup.-1] is the firm's discount factor and r is the cost of the capital, which in this risk-neutral setting equals the risk-free rate. The net present value of the investment alone hence is NPV(k|r) = [gamma]k - b.

In a key departure from traditional adverse selection models, I assume that the manager enjoys empire benefits or private benefits of control--from overseeing the project. As a consequence, the investment project has two return components: one accruing directly to the principal (the cash return) and one accruing directly to the manager (the empire return). The empire benefits, denoted by e(k,I), are nondecreasing in the profitability of the project and in the amount invested. The manager's utility, evaluated at date 1, comprises his compensation and empire benefits less his disutility of effort, v(a):

U = s + e(k,I) - v(a),

with v'(a) > 0, and v"(a) [greater than or equal to] 0. For ease of exposition (none of the results will depend on this), e(*) is assumed to be multiplicatively separable in that e(k,I) = e(k)I, where e'(k) [greater than to equal to] 0 and e"(k) [less than or equal to] 0. When the contract is signed, the principal, in contrast to the manager, knows only the distribution function F(k), with a corresponding density f(k), from which k is drawn. As is common in adverse selection models, the inverse hazard rate H(k) [equivalent to] [1 - F(k)]/f(k) is assumed to be decreasing.

As a benchmark, I begin by characterizing the first-best investment decision that would result if the principal could observe k and thereby could also infer the manager's effort choice a. (11) The effort and investment problems are then effectively separated. The principal reimburses the manager for his disutility of effort and invests according to: [??](k) [member of] arg [max.sub.I]{[gamma][kI + e(k)I] - bI}. The project would then be accepted if, and only if, k [greater than or equal to] [??], where:

(1) [gamma][[??] + e[??]] - b = 0.

Hence, under symmetric information the investment would be undertaken whenever the sum of the two return components (cash and empire benefits), in present value terms, exceeds the initial investment--that is, whenever NPV(k|r) + [gamma]e(k) [greater than or equal to] 0.

The practitioners' literature cited in the "Introduction" offers various explanations for empire benefits to arise, apart from intrinsic motivation. First, investments often entail hiring additional staff. Divisional managers may thereby gain more power or simply enjoy more lavish office spaces and other fringe benefits. Second, the manager's future career opportunities may improve if the projects under his control turn out to be profitable. (12) While in the first case, empire benefits will be largely independent of the project's profitability, this is not plausible in the second case. Here, empire benefits might well be negligible for low values of k, but increasing in k. To address these differences more formally, I shall invoke two specific linear functional forms for the manager's empire benefits for some of the results to follow. (13)

Definition 1 (alternative specifications of the e(k)-function):

(PO) "Plush Office" scenario: e(k) = [e.sub.0] + [e.sub.1]k, where k [member of] [0,[bar]k], [e.sub.0] > 0 and [e.sub.1] [right arrow] 0.

(REP) "Reputation" scenario: e(k) = [e.sub.0] + [e.sub.1]k, where k [member of] [0,k], [e.sub.0] [right arrow] 0 and [e.sub.1] > 0.

As shown below, these alternative specifications for empire benefits have qualitatively different implications for optimal capital budgeting procedures.

The following two sections analyze the optimal capital budgeting process for a centralized and a decentralized firm. Under centralization the investment decision rests with the principal, while under decentralization it is delegated to the manager, who is compensated based on some accounting-based performance measure. (14) Since the revelation principle applies, a decentralized firm can at best replicate the performance of a centralized firm. Delegation is nevertheless an important phenomenon to analyze, as it is pervasive in practice due to lower communication and commitment requirements.

III. CENTRALIZED INVESTMENT DECISIONS

In a centralized organization, the principal makes the investment decision based on some report submitted by the better informed manager. Under any message-contingent mechanism, the principal asks the manager to submit a report [??] on the gross investment return after committing to a scheme <I([??]), c(??), s([??])>, where c([??]) is the cash flow the manager has to deliver contingent on his report. It will be more convenient to suppress c(??) and instead to refer directly to the effort level that is induced by I([??]) and c([??]):

(2) a([??],k) [equivalent to]min{a|kI(??) + a [greater than or equal to] c(??)} = c([??]) - kI(??).

Let a(k) [equivalent to] a(k,k). The above mechanism can then be equivalently represented by the triplet <I([??],a([??],s([??])>. I assume throughout that the manager's marginal disutility of effort is small enough so that the principal always finds it worthwhile to elicit maximum effort, i.e., a(k) [equivalent to] [bar]a. This technical assumption allows me to ignore the issue of communication between principal and manager in connection with delegated investment decisions (below). The possibility that the manager chooses a suboptimal (out-of-equilibrium) effort level, however, creates scope for misreporting and hence for adverse selection. If the principal wanted to elicit interior effort levels, then the bonus coefficient under delegation in Section IV would need to depend on a profitability report; hence, a fully decentralized solution (one that requires no reporting) could not be optimal. (15) As demonstrated in Appendix B, however, the main results of the paper remain valid also for interior equilibrium effort choices, at the expense of increased complexity.

The manager's date-1 utility, if he reports[??] while actually being of type k, is:

(3) U([??],k) = s([??]) + e(k)I([??]) - v(a([??],k)).

Let U(k) [equivalent to] U(k,k). The revelation principle (e.g., Myerson 1979) applies and, hence, the search for optimal contracts can be confined to those that induce truthful reporting of k. Normalizing the manager's date-1 market alternative to zero, without loss of generality, the principal's problem becomes: (16)

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCTIBLE IN ASCII]

According to Program [P.sub.0], the principal maximizes the date-0 value of the firm, subject to an incentive compatibility constraint ensuring the manager reports truthfully and a participation constraint providing the manager with his reservation utility.

In contrast to the vast body of the adverse selection literature, the manager's private information parameter, k, enters his utility function in (3) twice, resulting in countervailing reporting incentives. Underreporting [??] < k results in a less demanding cash flow target, which the manager can achieve with less effort. On the other hand, overreporting [??] > k might trigger the investment decision, resulting in empire benefits. Unlike earlier studies on countervailing incentives (e.g., Lewis and Sappington 1989; Maggi and Rodriguez-Clare 1995), however, here the manager unambiguously benefits from a higher realization of the true profitability, k, because e'(k) [greater or equal to] 0 and a([??],k) is decreasing in k. That is, the manager consumes higher empire benefits and he can achieve a given cash flow target with less effort. As a consequence, standard techniques for solving adverse selection models suffice. (17)

For any feasible solution to [P.sub.0] satisfying individual rationality and "local" incentive compatibility, i.e., [delta]U/[delta][??] = 0, the manager's informational rent equals (see proof of Lemma 1 in Appendix A for details):

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Provided, as assumed above, it is always worthwhile to induce maximum managerial effort, by using (5) the isolated investment problem becomes:iS

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

subject to: I(k) nondecreasing in k,

where v' [equivalent to] v'([bar]a), to simplify notation. The principal's problem thus amounts to maximizing the expected date-0 gross firm value cum empire benefits, less the manager's informational rents.

The solution to Program [P.sub.1] calls for the firm to invest in the project if, and only if, k [greater than or equal to] k*, where the optimal profitability cutoff k* is given by:

(7) [gamma][k* + e(k*) - (e'(k*) + v')H(k*)] - b = 0.

My first result is a variant of the standard capital rationing finding in the adverse selection literature (e.g., Antle and Eppen 1985).

Lemma 1: The second-best centralized contract solves Program [P.sub1] and is characterized by underinvestment: for k [member of] ([??],k*) the firm forgoes projects that would be undertaken if k were publicly observed.

Proof: All proofs are contained in Appendix A.

Capital rationing arises endogenously as a consequence of the principal's trade-off between maximizing the gross firm value cum empire benefits and minimizing the manager's informational rents. For any k < k*, the manager is compensated for his disutility of effort and just meets his reservation utility. If k exceeds the cutoff and the project is undertaken, then (as shown in Appendix A) the manager earns informational rents of:

(80) U(k > k*) = (k - k*)v' + e(k) - e(k*).

Note that Lemma 1 does not refer to the forgone projects as "profitable" in the classical corporate finance sense. They may well have a negative net present value as long as they are associated with offsetting private benefits of control. In the optimal centralized solution, the manager's compensation comprises his disutility of effort plus his informational rent, net of his empire benefits. Specifically, at the second-best cutoff, s(k*) = v([bar]a) - e(k*). (19)

Instead of determining cutoffs for absolute investment returns, k, firms in practice tend to set required rates of return. Empirical studies have shown that these relative profitability hurdle rates consistently exceed the firms' cost of capital (e.g., Poterba and Summers 1995). As noted above, this is consistent with shareholders curtailing managers' informational rents. The natural next step now is to ask whether this remains true once private benefits of control are accounted for.

Let the internal rate of return of an investment project with profitability k be denoted by R(k). Thus, NPV(k|R(k)) [equivalent to] 0 or, equivalently, R(k) [equivalent to] k/b - 1. Consistent with the traditional textbook notion of internal rates of return (Brealey and Myers 2000), R(k) captures only the cash returns from investing, ignoring any nonpecuniary empire benefits. Note that there is a one-to-one correspondence between k and R(k): instead of having the manager report k, an equivalent revelation mechanism exists where he is asked to report R(k). From (1), it follows that the first-best required rate of return in the absence of informational asymmetries is less than the firm's cost of capital, i.e., R([??]) [less than or equal to] r, since the principal can fully extract the manager's empire benefits. The second-best required rate of return that corresponds to k*--as given in (7)--equals:

(9) R* [equivalent to] R(k*) = k*/b - 1.

Recall that there are two control problems present: the manager enjoys private benefits of control, and he can reduce his effort input by underreporting the investment return (the agency problem). These two control problems have countervailing effects on the optimal required rate of return. Holding constant the manager's empire benefits, the importance of the agency problem is determined by v' and by the ex ante profitability of the project as parameterized by b. The lower b, the more profitable the project is in the expectation (all else equal) and, hence, the higher the probability that the investment is undertaken and that the manager earns informational rents.

The first main result compares the second-best required rate of return with the cost of capital for the plush office and reputation scenarios introduced in Definition 1.

Proposition 1: Suppose the principal makes the investment decision based on a required rate of return, R*.

1. If (PO) holds, then for any (b, v') there exists a unique cutoff [[??].sub.0] [greater than or equal to] 0, such that R* < r if [e.sub.0]>, while R* > r if [e.sub.0] < [[??].sub.0].

2. If (REP) holds, then for any (v', [e.sub.1] there exists an initial investment expense, [??], such that R* > r holds for all b < [??].

Empire benefits always result in a relaxation of the manager's participation constraint. In the plush office (PO) scenario, these benefits are independent of k and hence they cannot be used to screen different k-types. As a consequence, for high [e.sub.0] the principal invests in negative-NPV projects while reducing the manager's compensation. (20) On the other hand, as [e.sub.0] becomes small, the model converges to the standard adverse selection model and I recoup the classical capital rationing result that R* > r.

In the reputation (REP) scenario, the empire benefits are informative about k. Thus, they can be used to screen the manager's information more effectively. Technically speaking, empire benefits now also affect the manager's incentive constraint. If the project is very profitable in expectation (b is low) and the agency problem is severe (v' is high), then rent extraction weighs heavily in the principal's objective function for two reasons: the manager earns rents for many realizations of k, and these rents are increasing "steeply" in k. Therefore, the optimal capital budgeting policy tends to be more restrictive in that R* > r holds for any [e.sub.1]. (21) This is in contrast to the plush office scenario (Proposition 1, part 1) where R* < r always holds for sufficiently high empire benefits.

To make these trade-offs more transparent, I consider a specific example where k is uniformly distributed. This allows for closed-form solutions to be obtained.

Example: Suppose k ~ U[0, [??]] so that H(k) = [??] - k. Rewriting (7) for the case where e(k) = [e.sub.0] + [e.sub.1]k, as in (PO) and (REP), then gives:

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The expression in (10) can in turn be rewritten to yield r = [k* + [delta](k*)]/b - 1, for [delta](k) [equivalent to] [e.sub.0] + (2k - [??]) [e.sub.1] - ([??]- k)v'. By comparison with (9),R* [equivalent to] k*/b - 1 > r, if [delta](k*) < 0, and vice versa. (22)

Consider the plush office (PO) scenario where e1 [right arrow] 0. Using (10), I find that [delta](k*) < 0 (and hence R* > r) if, and only if, [e.sub.0] < [[??].sub.0] = [k - (1 + r)b]v'. Note that [[??].sub.0] > 0 always holds. Thus, R* can indeed be less or greater than r for any (v',b), depending on [e.sub.0]. Now consider the reputation (REP) scenario where [e.sub.0] [right arrow] 0. Then, for b sufficiently small in that (1 + r)b < 1/2[bar]k, [delta](k*) < 0 holds if, and only if, [e.sub.1] < v'[[bar]k - (1 + r)b]/[2(1 + r)b - k] < 0. This contradicts the earlier assumption that [e.sub.1] [greater than or equal to] 0. Hence, if b < [??] = 1/2y[gamma][bar]k in the (REP) scenario with uniformly distributed types, then R* > r holds irrespective of the magnitude of empire benefits.

To summarize, the optimal required rate of return in connection with centralized investment decisions can be greater or less than the cost of capital, depending on the magnitude and the functional form of the manager's empire benefits. An unambiguous ranking is obtained only if empire benefits are driven by project scale and profitability--that is, in the reputation (REP) setting--and if the project is relatively profitable, ex ante. In this case, the hurdle rate always exceeds r.

IV. DELEGATED INVESTMENT DECISIONS

The capital budgeting model analyzed so far was characterized by a high degree of centralization. In practice, however, capital budgeting procedures tend to be more decentralized. I therefore now consider a regime where the manager makes the investment decision and is compensated based on residual income. First, residual income (or EVA) has been adopted by a large number of firms and, second, recent studies have shown that this metric has desirable features for delegating investment decisions (e.g., Rogerson 1997; Reichelstein 1997).

I consider linear contracts based on residual income (RI), which equals divisional income less a charge for the capital invested. In this one-period setting:

(11) RI(k,a,[rho]) = kI + a - (1 + [rho])bI,

with [rho] denoting the capital charge rate. The compensation contract is given by:

s(RI) = [alpha] + [beta] x RI,

where a denotes fixed salary and [beta] is the bonus coefficient. Residual income is said to be optimal, if such a linear compensation contract implements the second-best (centralized) effort and investment decisions and results in the second-best expected firm profit net of compensation. (23) It now becomes apparent that two alternative interpretations of "hurdle rates" are conceivable: as the required rate of return R(k) = k/b - 1, or as the capital charge rate, [rho], under delegation.

A manager compensated based on residual income will choose:

(12) max {[alpha] + [beta] x RI(k,a,p) - v(a) + e(k)I}.

Suppose the principal sets the bonus coefficient equal to the manager's marginal disutility of effort at the desired effort level, i.e., [beta] = v'. Then the manager will invest whenever:

(13) v'[k - (1 + [rho])b] + e(k) [greater than or equal to] 0.

The next result shows that a delegation scheme can replicate the benchmark performance of centralization and it characterizes the appropriate hurdle rate.

Proposition 2: Residual income constitutes an optimal performance measure. The optimal capital charge rate exceeds the firm's cost of capital; that is, [rho]* > r.

The proof of Proposition 2 proceeds by constructing contract parameters:

(14) [beta] = v' and [alpha] = v([bar]a) - v'[bar]a,

and an appropriate capital charge rate, for which the manager will take the desired actions and earn the second-best informational rent. As shown in Appendix A, the manager's informational rent under such a delegation scheme equals that under centralization, which is given in (8) above.

To see why the capital charge rate, [rho]* which together with the contract parameters in (14) achieves optimality, has to exceed the cost of capital, divide the condition that characterizes the second-best cutoff k*--Equation (7)--by the discount factor [gamma]. This yields (15) below. Then compare this with the condition that describes that manager's investment decision under delegation--Equation (13)--evaluated as an equality at k = k* and divided by the bonus coefficient [beta] = v'. This gives (16):

(15) k* + e(k*) - (e'(k*) + v')H(k*) - (1 + r)b = 0,

(16) k* + 1/v' e(k*) - (1 + [rho]*)b = 0.

At the margin, the manager trades off cash returns versus empire returns: he is willing to accept a decrease of $1 in the performance measure for an additional $(v') of nonpecuniary empire benefits. Comparing (15) with (16), it is apparent that [rho]* > r holds for two reasons: (i) the empire benefits are scaled by the bonus coefficient, and (ii) the manager does not subtract any informational rents when choosing the cutoff.

While Proposition 2 only lays out an optimal delegation scheme, this solution can indeed be shown to be unique within the class of residual income-type performance metrics. Note that the second-best investment and effort choices can also be implemented by a different delegation scheme with [beta] [member of] [v',1], [alpha] = v([bar]a) - [beta][bar]a and a hurdle rate, [rho]([beta]), chosen as a plug variable so that k* - [1 + [rho](beta)]b + e(k*)/[beta] = 0 holds. For this equality to hold for any [beta] [member of] [v',1], it must be that [rho](beta) < 0, yet [rho](1) > r. However, the manager's informational rent for any k > k* then equals (k - k*)beta + e(k) - e(k*), which exceeds that in (8) under centralization. Thus, setting [beta] > v' requires paying the manager excessive informational rents while setting beta < v' results in suboptimal effort input. Therefore, beta = v' characterizes the unique optimal solution. It is instructive to contrast these findings with Lambert (2001), who does not consider information-eliciting mechanisms: since the principal does not care about rent extraction in his model, the capital charge rate equals r and [beta] = 1 holds for a risk-neutral manager.

It is also important to note that the prediction of slope coefficients [beta] < 1 in my model is not an artifact of the assumed corner solution for effort choices. As shown in Appendix B, [beta](k) < 1 will hold for all k greater than the investment cutoff, even in the case of interior optimal effort choices (and thus type-dependent slope coefficients). A more steeply sloped contract (i.e., a higher value of [beta]) always implies higher informational rents for the manager. At the margin, the principal therefore is willing to accept suboptimal effort levels so as to economize on the manager's rents.

A comparison of Propositions 1 and 2 shows that the optimal hurdle rate under centralization, R*, can be either greater or less than the cost of capital, whereas the capital charge rate under delegation, p*, always exceeds r. This holds because the manager as the decision maker under delegation takes into account both cash and empire returns from investing. In contrast, the required rate of return, by definition, ignores the empire returns. Again rewriting (16) as:

(17) [rho]* = k*/b + 1/v' e(k*)/b - 1,

yields the following result by a direct comparison with the second-best required rate of return in (9). It is therefore stated without formal proof. (24)

Proposition 3: The hurdle rate under delegation always strictly exceeds that under centralization--that is, [rho]* > R*.

The results thus far demonstrate that the empirical findings reported in Poterba and Summers (1995) have to be viewed in the broader context of organizational design--in particular, the contracting environment. The above arguments imply that, for a given investment opportunity set, a required rate of return of, say, 15 percent would lead to a lower level of investment than a 15 percent capital charge rate under residual income-based compensation. Put differently, the two hurdle rates will differ in their economic consequences as a result of private benefits of control.

V. COMPARATIVE STATICS

This section addresses in more detail how empire benefits affect both kinds of hurdle rates. This discussion sheds light on two related questions. First, how does the optimal solution characterized above compare with the optimal capital budgeting mechanism in the absence of empire benefits? Second, do empire benefits invariably harm shareholders, as suggested by conventional wisdom?

To address these questions, I introduce a new and commonly known parameter, m [member of] [0,[bar]m], which captures the scale of the manager's empire benefits so that:

(18) e(k,I,m) =- me(k)L

For instance, Hennessy and Levy (2002) measure the propensity of managers to engage in empire-building by: (i) whether the manager is a member of the founding family; (ii) the percentage of insiders on the board of directors; and (iii) the manager's tenure. In their sample, managers who are members of the founding family are shown to consume higher empire benefits, while (ii) and (iii) are used as proxies for the likelihood that the manager's decision will be challenged by the board. Also, for the reputation setting (REP), one would expect m to be relatively high when the manager enjoys high external visibility (e.g., due to high analysts' following). The preceding analysis therefore has captured the special case of m = 1.

Upon substituting e(k, L m) for e(k, D, let k*(m) denote the solution to the centralized problem as in (7) for any m, and R*(m) =- R(k*(m)). Similarly, let p*(m) be the optimal capital charge rate under delegation when generalizing the solution characterized in (17). A first intuition suggests that k*(m) be decreasing in m as a consequence of the manager's compensation/empire benefits trade-off. While this intuition holds for the symmetric information case, it may fail under adverse selection, as the next result shows. (25)

Proposition 4: Suppose the manager's empire benefits are as given in (18).

1. If (PO) holds, then R*(m) is decreasing in m.

2. If (REP) holds, then R*(m) is increasing in m, for b sufficiently small.

3. In a decentralized firm with residual income-based compensation, the optimal capital charge rate, p*(m), is always increasing in m.

In the plush office scenario (PO) the intuition developed for the symmetric information case applies: an increase in m has the sole effect of relaxing the manager's participation constraint. The principal then lowers the required rate of return R* and at the same time reduces the manager's compensation. In the reputation setting (REP), an increase in m again also allows for improved screening of different k-types. If the project is sufficiently profitable in expectation (b is small), then this incentive constraint-effect dominates and the firm raises R* so as to reduce the rents earned by high-k managers. (26)

Under delegation, two effects are present. First, as m increases, the optimal profitability cutoff, k*(m), to be implemented via the capital charge rate, changes. As the preceding paragraph has shown, this effect can go either way. Second, the manager becomes more eager to invest irrespective of the project's profitability. As the proof demonstrates, this second, more direct, effect always dominates the first one so that p*(m) is always increasing. Note that the contract parameters ([alpha],[beta]) given in (14) are independent of the manager's empire benefits. Instead, the hurdle rate p*(m) is the sole instrument the principal uses to extract (a share of) these benefits.

Private benefits of control are commonly perceived as a "public bad" in the business press. The claim is that managers' inclination to overinvest relative to the NPV rule destroys firm value. As the previous analysis suggests, this need not be the case once compensation contracts are derived endogenously. In fact, the delegated investment condition in (13) reveals that shareholders in this model will ultimately benefit from their manager's empire benefits even in the presence of adverse selection. For any m > 0, the shareholders can always induce the manager to invest whenever k [greater than or equal to] k*(0) by simply raising p. Holding the contract parameters ([alpha],[beta]) fixed, this will transfer rents from the manager to the shareholders while ensuring all incentive and participation constraints remain intact. By revealed preference, the shareholders can do even better by choosing [rho]*(m) optimally. This discussion is summarized in the following corollary.

Corollary 1: Suppose the manager's empire benefits are as given in (18). Then the value of the firm, net of the manager's compensation, is increasing in m.

Rather than concluding that the conventional wisdom of empire benefits destroying firm value is false, it should be noted that Corollary 1 hinges on the assumption that a project's financial and nonpecuniary returns are related in a deterministic (and commonly known) fashion. In practice, this may not always be the case. Put differently, the corollary shows that a necessary condition for empire benefits to reduce firm value is that shareholders have only incomplete information about how these benefits depend on the size and profitability of investment projects (see also footnote 6). (27)

VI. CONCLUSION

This paper has studied optimal hurdle rates in a setting where investment decisions are subject to adverse selection and private benefits of control. The results have demonstrated systematic differences between the required rate of return and the capital charge rate, which are the two most common incarnations of hurdle rates. A key empirical implication of the model is that capital charge rates used for residual income/EVA-based bonus plans should on average be higher than required rates of return across comparable firms. Also, capital charge rates should be higher in high-empire-benefits environments (e.g., a manager has been with the firm for a long time; high percentage of insiders among the board members; high external visibility) as compared with low-empire-benefits environments. This need not be true for required rates of return.

The risk-neutral framework adopted in this paper was in part motivated by Poterba and Summers' (1995) finding of hurdle rates unrelated to measures of firm-specific risk. In light of Christensen et al. (2002) and Dutta and Reichelstein (2002), it would be desirable to reassess firms' choice of hurdle rates in a large-sample study, taking into account firm-specific and market-wide risk factors, as well as proxies for empire benefits.

The results in this paper have demonstrated that different assumptions regarding the specific nature of empire benefits have qualitatively different implications for the capital budgeting process. This has been ignored in previous studies. As shown here, the optimal hurdle rates depend on whether empire benefits are driven by project size and profitability, or by size only. From an empirical standpoint, this raises the question of how to distinguish between these two scenarios. One possible control variable that comes to mind is a manager's tenure. Near retirement, managers tend to put less emphasis on future career prospects and hence may prefer larger projects over smaller, but more profitable ones. (28) The opposite is likely to hold at an early stage in a manager's career where reputation effects play a more important role.

The present model can be generalized to analyze capital assets with a useful life of multiple periods, in which case accrual accounting issues arise. In the absence of empire benefits, this question of how to depreciate an asset so as to achieve intertemporal matching of investment costs with investment returns has been the subject of several recent studies? (29) These studies have argued that depreciation for projects with uniform cash flows over time should be decelerated--that is, increasing over time. This is clearly at odds with firm practice, as companies predominantly use straight-line (or even faster) depreciation. In the presence of empire benefits, intertemporal matching has to take both cash and nonpecuniary return streams into considerations. (30) In particular, it is plausible that empire benefits are particularly high in early periods--e.g., due to analysts' coverage. If this is the case, then, as shown in an earlier version of this study (Baldenius 2002), optimal depreciation tends to be more accelerated than previously suggested. Hence, empire benefits may help explain depreciation schedules observed in practice, and the recent call for more decelerated depreciation to overcome perceived underinvestment problems (Young and O'Byrne 2001) may thus be misguided.

APPENDIX A PROOFS

Proof of Lemma 1

I begin by stating a sufficient condition for the principal to induce the manager to exert maximum effort for any realization of k, i.e., for a(k) [equivalent to] [bar]a:

(19) 1 - v'(a) - v"(a)H([??]) [greater than or equal to] 0,

where H(k) [equivalent to] [1 - F(k)]/f(k). Here, [??] denotes the first-best profitability cutoff, i.e., the profitability parameter for which the project just breaks even, i.e., [gamma][[??] + e([??])] = b. I will show below that (19) is indeed sufficient for a(k) [equivalent to] [bra]a, for all k, in equilibrium.

The manager's date-1 utility if he reports [??] while actually being of type k equals U([??],k) = s([??]) + e(k)I([??]) - v(a([??],k)). An increase in the manager's true type, k, has a positive impact on his utility (i) due to higher empire benefits and (ii) because it will allow him to achieve a given cash flow objective with less effort, i.e., a([??],k) is decreasing in k since, by (2), a([??],k) = c(k) - kI(k). Hence, for any contract that satisfies the participation and (local) incentive compatibility constraints, the envelope theorem implies that U'(k) = [e'(k) + v'(a(k,k))]I(k) [greater than or equal to] 0. As a consequence, the manager's individual rationality constraint will be binding for k = [??] and his informational rent for any k equals:

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

In the optimal solution, the lowest type, [??], will earn zero rents. In expected terms, this implies [E.sub.k]{U(k)} = [[integral].sup.[??].sub.[??] [e'(k) + v'(a(k,k))]I(k)H(k)f(k)dk, after integration by parts. Hence:

[E.sub.k]{s(k)} = [[integral.sup.[??].sub.[??]] [v(a(k,k)) - e(k)l(k) + [e'(k) + v'(a(k,k))]l(k)H(k)]f(k)dk.

Recall from (2) that a(k,k) = c(k) - kI(k). Substituting the last two expressions into the principal's objective in [P.sub.0] yields:

(20) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

For any k [less than or equal to] [??], it follows that I(k) = 0. Now, if I(k) = 1, for some k > k, the principal will choose a so as to maximize a - v(a) - v'(a)H(k). Then condition (19), in conjunction with H(*) being decreasing, implies that the optimal solution in these cases entails maximum effort by the manager, i.e., a(k) [equivalent to] [bar]a. Hence the second-best cutoff, k*, is as given in (7). Moreover, since k* [greater than or equal to] [??], with the latter denoting the first-best cutoff, I find that the firm underinvests for all k [member of] (k,k*).

Given the discrete nature of the investment problem, the optimal decision rule, I([??]), is discontinuous at k* and insensitive to marginal changes in [??] elsewhere. Hence, for all types k [greater than or equal to] k*, there only is an incentive to underreport so as to reduce effort. For this to be ruled out, the manager must be paid the above informational rents. In equilibrium, the cutoff-type k* will just break even, i.e., s(k*) = v([bar]a) - e(k*) and c(k*) = k* + [bar]a. Hence, the required cash flow to be delivered at k = k* renders it unfeasible for a manager with type k < k* to mimic type k* so as to trigger the investment decision. (31)

Finally, I show that the optimal mechanism as characterized by (7) is indeed globally incentive compatible. Following Mirrlees (1986), a mechanism that is locally incentive compatible is also globally incentive compatible if [delta]/[delta]kU([??],k) is increasing in [??]. For the solution derived:

[delta]/[delta]-k U([??],k) = [e'(k) + v'(a[??]k))]l([??]).

The Mirrlees (1986) requirement is thus met, because v"(*) [greater than or equal to] 0, a([??],k) is increasing in [??] and the second-best investment policy, I(*), is upper-tailed.

Proof of Proposition 1

From (9) we know that the optimal required rate of return is given by:

R* [equivalent to] R(k*) = k*/b - 1.

To compare this term with the firm's cost of capital, I rewrite the first-order condition for the profitability cutoff k* in (7) as follows:

(31) Note that in a more general model with interior effort choices a([??],k) in equilibrium, it would be feasible for a manager of type k < k* to report [??] = k* and subsequently to increase his effort to deliver c(k*), but that would not be optimal, as it would result in negative utility since: 0 : U(k*) = s([??] = k*) + e(k*) - v(a([??]~*,k*)) > s([??] = k*) + e(k) - v(a([??] = k*,k)), for any k < k*.

(21) r = 1/b [k* + e(k*) - (e'(k*) + v')H(k*)] - 1.

Hence, a necessary and sufficient condition for R* > r is that:

[delta]](k) =- e(k) - (e'(k) + v')H(k) < 0,

for k = k*. For the two linear specifications of the e(*)-function in (PO) and (REP), we have:

[delta](k) = ([e.sub.o] + [e.sub.1]k) - ([e.sub.1] + v')H(k).

Part 1

Suppose (PO) holds, i.e., [e.sub.0]> 0 and [e.sub.1] [right arrow] 0. Then, [delta](k) [right arrow] [e.sub.0] - v'H(k), where v' is bounded above by 1 due to the assumed comer solution for a. It immediately follows that there is a unique value [[??].sub.0] > 0 such that [delta](k*) > 0 (and hence R* < r) for any [e.sub.0] > [[??].sub.0], and vice versa.

Part 2

Suppose (REP) holds, i.e., [e.sub.0] [right arrow] 0 and [e.sub.1] > 0. Hence, [delta](k) [right arrow] [e.sub.1][k - H(k)] - v'H(k). Since I have not restricted the initial investment expense b from below, for any v' and any type distribution function F(k) over the support [0,k], there exists a value b sufficiently low, such that k* [right arrow] [??] = 0. Hence, e(k*) [right arrow] e(k) [right arrow] 0. Since both [e.sub.1] and v' are assumed to be strictly positive, it follows that [delta](k*) < 0 and, hence, R* > r.

Proof of Proposition 2

Suppose the principal sets the contract parameters as follows:

(22) [beta] = v',

(23) [alpha] = v([bar]a) - v'[bar]a,

and the capital charge rate, p*, is chosen so that:

(24) v'[k* - (1 + [rho]*)b] + e(k*) = 0.

I now show that, given the contract parameters given in (22)-(24), the manager will (i) take the same actions and (ii) earn the same informational rent as in the centralized second-best benchmark solution. For comparison, the manager's informational rent under the centralized mechanism is:

(25) [MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

and zero otherwise.

Recall that the manager's objective is, for any ([alpha],[beta],[rho]) and any k, to choose a(*) and I(*) so as to maximize:

(26) [alpha] + [beta][kI + a - (1 + [rho])bI] - v(a) + e(k)I.

Hence, given the parameters in (22)-(24), the manager will indeed set a(k) [equivalent to] [bar]a and I(k) = 1 if, and only if, k [greater than or equal to] k*. Moreover, the manager's resulting date-1 informational rent for any k [greater than or equal to] k* under this delegated mechanism equals v'[k - (1 + [rho]*)b] + e(k) = v'[k - k*] + e(k) - e(k*), which coincides with that under centralization, given in (25).

Finally, to see that the optimal capital charge indeed exceeds the firm's cost of capital, r, rewrite (24) as:

[rho]* = k*/b + 1/v' e(k*)/b - 1.

By assumption, v' < 1. This completes the proof by a simple comparison with (21), since e(k) > [delta](k).

Proof of Proposition 4

First note that in the centralized contracting setting there is a one-to-one mapping from absolute profitability cutoffs, k*, to required rates of return, R*, with higher k* being equivalent to higher R*. Hence, this proof is confined to absolute profitability cutoffs, k*. Rewrite (7) for the case of e(k,I,m):

(27) k*(m) + me(k*(m)) - [me'(k*(m)) + v']H(k*(m)) - (1 + r)b = 0.

Applying the implicit function theorem to this necessary first-order condition gives (I henceforth suppress the dependence of k*(m) on m to save on notation):

(28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where I have used that, by Definition 1, e(k) = [e.sub.0] + [e.sub.1]k holds under both (PO) and (REP). Note that the denominator is always positive, hence sign{dk*/dm} = -sign{[e.sub.0] + [e.sub.1][k* - H(k*)] }.

Part 1

In the plush office (PO) scenario, [e.sub.0] > 0 and [e.sub.1] [right arrow] 0. Hence, dk*/dm < O.

Part 2

Consider next the reputation (REP) scenario, where [e.sub.0] [right arrow] 0 and e1 > 0. Then dk*/dm > 0 if k* < H(k*), and vice versa. Now, it follows from (27) that for any m, there exists a value b sufficiently small, so that k* [right arrow] k. By Definition 1, (REP) implies that [??] [right arrow] 0 so that k* [right arrow] 0, yet H(k*) > 0 for k* [right arrow] [??]. Hence, dk*/dm > 0 for b sufficiently small. Since H'(k) [less than or equal to] 0, the argument can be reversed to show that for high b, dk*/dm < 0 will hold.

Part 3

Finally, consider a decentralized firm with the manager making the investment decision while compensated based on residual income with p as the capital charge rate. Unlike in parts 1 and 2, e(k) is not restricted to be linear in k.

The manager, compensated based on residual income, will invest if and only if v'[k - (1 + [rho])b] + me(k) [greater than or equal to] 0. (Recall that the bonus coefficient must equal v' in the optimal solution, due to the arguments given in the main text.) For such a delegated contract to be optimal, this last weak inequality has to hold with equality for k = k*. Solving for the optimal capital charge rate as a function of m yields:

[[rho]*(m) = 1/b [k*(m) + 1/v' me(k*(m)) - 1.

Taking the first-order derivative with respect to m gives:

d[rho]*/dm = 1/v'b [k*(m) + 1/v' me(k*(m))] - 1.

Now, using (28) above, I can derive a lower bound on this previous expression by using the facts that v' < 1, e"(k) [less than or equal to] 0 and H'(k) < 0 for all k. Since v' are b both positive, the right-hand side of the last equation is proportional to (again suppressing the argument m in k*(m)):

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

This last inequality holds, because e"(k) [less than or equal to] 0 and H'(k) < 0 for all k imply that me"(k*)H(k*) + [v' + me'(k*)]H'(k*) < 0. As a consequence, the term in square brackets is positive and p*(m) is a monotonically increasing function. This completes the proof of Proposition 4.

APPENDIX B INTERIOR EFFORT CHOICES

In this appendix, I rephrase the model for the case that the condition in (19) does not hold, with the consequence that the principal may want to implement interior effort choices, a(k) [member of] (0,a). It is shown here that the preceding results--in particular, the key results in Propositions 1-3--can be generalized to this setting.

The first-best program (if the principal were to know k and could "force" the manager to choose a certain effort level) calls for the investment to be made whenever the present value of cash and empire returns exceeds b. At the same time, the first-best effort level just equates marginal effort costs with marginal effort returns. That is: [max.sub.I(k),a(k)]{([gamma],[k + e(k)] - b)I(k) + [gamma][a(k) - v(a(k))]}, so that:

(29) [gamma][[??]+ e([??])]- b = 0 and 1 - v'([??](k)) = 0.

Note that effort and investment choices are independent in the first-best solution.

In the second-best solution, the principal does not know k and has to elicit this information from the manager. Following similar steps as in the proof of Lemma 1 then yields the following optimization program:

[MATHEMATICAL EXPRESSION IS NOT REPRODUCIBLE IN ASCII]

Assuming unique interior solutions, the resulting first-order conditions are:

(30) [gamma][k* + e(k*) - [e'(k*) + v'(a(k*))]H(k*)] - b = 0,

(31) 1 - v'(a(k*)) - v"(a(k*))H(k*)I(k*) = 0.

Since I(k) = 1 if and only if k [greater than or equal to] k*, the investment and effort choices become intertwined for k [greater than or equal to] k*. In comparison with (29), the second-best solution in (30)-(31) is characterized by both underinvestment and underprovision of effort. The latter arises because higher effort levels can only be induced at the expense of higher informational rents. Note that a(k [greater than or equal to] k*) [less than or equal to] a(k < k*), and a(k) is monotonically increasing for all k [greater than or equal to] k* since H'(k) [less than or equal to] 0. It is easy to show now that Proposition 1 remains qualitatively unchanged once interior effort choices are allowed for.

Following similar steps as in the proof of Lemma l, the above mechanism can be shown to be globally incentive-compatible, and it results in date-1 informational rents for the manager of U(k > k*) = e(k) - e(k*) + v(a(k)) - v(a(k*)) and U(k [less than or equal to] k*) [equivalent to] 0.

Since the centralized solution now entails type-dependent effort choices, it is clear that a "pure" delegation mechanism, such as that described in Section IV, can no longer replicate this benchmark performance. Instead, I consider the following message-dependent delegation scheme. The manager reports [??] and thereby picks a compensation scheme from a menu of contracts all of which are linear in residual income: s(RI|[??]) = [alpha]([??]) + [beta]([??]) x RI. Then the manager makes the investment and effort decisions in a decentralized fashion.

Consider the following contract parameters:

(32) [beta](k) = v'(a(k)),

(33) [alpha](k) = v(a(k)) - v'(a(k))a(k) + A(k)I(k),

and a hurdle rate, p*, that is implicitly defined by:

(34) v'(a(k*))[k* - (1 + p*)b] + e(k*) = 0,

where the newly introduced function in (33) equals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

By (31) and (32), [beta](k) < 1 for all k [greater than or equivalent to] k*, even in the case of interior effort choices.

Using (32)-(34), it is a matter of straightforward algebra to show that, having truthfully reported [??] = k, the manager will indeed make the second-best investment and effort choices, (I(k), a(k)). The manager's resulting date-1 utility then equals:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

which coincides with his date-1 informational rent under centralization.

By rewriting (34) and (30) in a fashion similar to (15) and (16), above, one finds that [rho]* > r, which mirrors Proposition 2. Moreover, since:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

the key result in Proposition 3 also generalizes to this more general setting.

I thank Moshe Bareket, Zhonglan Dai, Joel Demski, Volker Laux, Nahum Melumad, Madhav Rajan, Stefan Reichelstein, Amir Ziv, two anonymous reviewers, and workshop participants at the Carnegie Mellon Accounting Conference, the FEA Conference at Rutgers University, the Duke-UNC Fall Camp, the Burton Conference, and the Finance "Free Lunch" Workshop at Columbia University, the Arijit Mukherji Conference at the University of Minnesota, and Northwestern University for helpful comments, I am especially indebted to Anil Arya and Jon Glover for discussions on this subject.

Editor's note: This paper was accepted by Madhav V. Rajah, Editor.

(1) Empire benefits are discussed in anecdotal form in Donaldson (1984) and Jensen (1986). The Economist lists empire benefits as the main example for agency problems in its online "Economics A-Z" (http://www.economist.com/research/Economics/). Burrough and Helyar (1990) describe in detail how RJR-Nabisco management wasted corporate resources by using corporate jets for their dogs, etc. Hennessy and Levy (2002) find strong empirical evidence for empire benefits to affect investment decisions. They estimate that CEOs that are members of the founding family derive an annual benefit of $3.30 per $1,000 of installed capital. Their model includes more control variables than that tested in Aggarwal and Samwick (1999), who found no evidence of empire benefits. Throughout this paper, "empire benefits" is shorthand for any investment return components that accrue directly to the manager.

(2) Exceptions are Arya et al. (1999) and Lambert (2001). Dutta (2003) considers a setting where the manager can "walk away" with the project.

(3) Baiman and Verrecchia (1995) make a related observation, albeit in a very different setting. They argue that when a firm's manager can trade on his private information, the expected gains from insider trading allow the shareholders to lower his compensation.

(4) Note that in my model the compensation contract under delegation does not require any communication between manager and principal, while this is necessary for the centralized solution. Since I do not explicitly model any communication costs, however, the revelation principle implies that a decentralized firm can at best replicate the performance of a centralized firm.

(5) As shown below, under delegation the manager internalizes 100 percent of the empire returns, but only a fraction [beta] < 1 of the cash returns (and outlay) from investing. Here, [beta] is the bonus coefficient that is endogenously determined by the severity of the agency problem (i.e., by the marginal disutility of effort). The more severe the agency problem, the higher the bonus coefficient and, therefore, the less weight the manager assigns to the empire benefits relative to his utility from monetary compensation.

(6) Formally addressing this issue would require a two-dimensional adverse selection model where the manager privately observes k and a measure of his empire benefits, where the latter may or may not be correlated with k. However. the theory of such multidimensional screening problems is highly incomplete at this point; see Rochet and Stole (2001) for a survey of the current state of this literature.

(7) Baldenius and Ziv (2003) incorporate corporate income taxes into a capital budgeting setting. Their model, which builds on Rogerson (1997) and Reichelstein (1997), predicts that firms employing pre-tax residual income tend to set higher capital charge rates than comparable firms using after-tax metrics such as "Economic Value Added."

(8) Lambert (1986) analyzes the investment distortions that arise if a risk-averse manager has to be motivated to exert personally costly effort to become informed about a project's profitability.

(9) Christensen et al. (2002) distinguish between firm-specific and market risk. They argue against using the weighted-average cost of capital (WACC) as the capital charge rate and show that only firm-specific (diversifiable) risk affects the capital charge rate, whereas market risk does not. As a result of firm-specific risk, the hurdle rate can be less or greater than the risk-free rate depending on the information held by the manager at the time of investing.

(10) Bernardo et al. (2001) also study the role of compensation to control managers' empire-building tendencies, albeit only in a centralized decision-making setting. Their analysis is thus confined to required rates of return as hurdle rates, for which they derive results consistent with the earlier capital rationing literature, e.g., Harris et al. (1982), and Antle and Eppen (1985). In Harris and Raviv (1996, 1998), headquarters uses internal auditing procedures, instead of compensation, to mitigate its divisional managers' desire for empires.

(11) Since both the manager and the principal are risk-neutral, all results for the adverse selection model remain valid if the date-1 cash flow were subject to an additional random noise term: [??] = kl + a + [??] with E[??] = O. For the first-best benchmark setting this would require the principal to be able to directly observe a, as the latter could otherwise no longer be inferred from c.

(12) Note that the present model does not explicitly incorporate such dynamic features; see instead Holmstrom and Ricart i Costa (1986).

(13) Both these alternative sources of empire benefits have previously been studied separately. The reputation (REP) scenario underlies the models of Harris and Raviv (1996, 1998) and Bernardo et al. (2001). Here, it is conceivable that e(k) [less than or equal to] 0, i.e., the manager's reputation may suffer if the project is very unprofitable. The present model could easily be adapted to allow for this. The plush office (PO) scenario is closer in spirit to the way empire benefits are modelled in Hart and Moore (1995) and Lambert (2001). The terms "plush office" and "reputation" scenarios are purely chosen for expositional purposes.

(14) Note that this definition of decentralization differs from that in Bernardo et al. (2001), who refer to revelation mechanisms as decentralized schemes.

(15) A similar assumption is made in Dutta and Reichelstein (2002). The proof of Lemma 1 in Appendix A contains a technical condition that ensures such a corner solution.

(16) As pointed out by an anonymous reviewer, the empire benefits turn this adverse selection problem into one with type-dependent reservation utilities of U--e(k)I where U = 0; see also Jullien (2000).

(17) Note that this may not be the case in a model with continuous investments where, for some realizations of k, the over-and underreporting incentives may just offset each other.

(18) The monotonicity constraint in Program [P.sub.1] ensures that the solution found by observing only the "local" incentive constraints also satisfies "global" incentive compatibility, as required in Program [P.sub.0].

(19) Abstracting from empire benefits, the difference between the manager's compensation and his disutility of effort corresponds to the "organizational slack" in Antle and Eppen (1985).

(20) "High" empire benefits, [e.sub.0], here means high relative to the agency problem parameter, v'. Note that v' [greater than or equal to] 1 implicitly holds by the assumption that maximum effort is always desirable.

(21) Note that no explicit lower bound has been imposed on the initial investment expense, b. In fact, b can even be ("slightly") less than [gamma]k without making the investment problem under adverse selection trivial. Even then the principal may optimally forgo a project with a k-realization close to k so as to extract informational rents from the manager.

(22) Consistent with results in Section V, the following comparative statics hold for the optimal cutoff in (10): k* is decreasing in [e.sub.0], increasing in v' and b, while the sign of ak*l[delta][e.sub.1] is ambiguous.

(23) Note that the linear compensation schemes considered here do not require any communication between the principal and the manager. This would no longer be true if the optimal solution were to entail interior effort levels (see Appendix B).

(24) To avoid the trivial case where e(k*) = 0 and hence p* = R*, I assume that e(k) > 0 for small k.

(25) Note that, while parts 1 and 2 of Proposition 4 rely on linear specifications for the e(k)-function, this is not the case for part 3.

(26) Part 2 of Proposition 4 complements a comparative statics result derived in Bernardo et al. (2001). In their model, investments are continuous and effort and investment are complements. Their Proposition 4 part (i), shows that (pointwise) investment amounts are increasing in empire benefits for high types and decreasing for low types.

(27) In a similar vein, Corollary 1 is sensitive to the specifics of the manager's utility function. In my model, the manager views compensation and empire benefits as substitutes. Alternative specifications are conceivable--e.g., lexicographic preferences--for which this result may not hold.

(28) Gibbons and Murphy (1992) analyze investment levels as a function of managers' tenure and find investments in R&D to increase toward the end of managers' careers, which is inconsistent with maximizing earnings-based compensation. See also Hennessy and Levy (2002). However, neither of these studies tests for ex post profitability of investment projects.

(29) See Rogerson (1997), Reichelstein (1997), Bareket (2002), and Dutta and Reichelstein (2002).

(30) When addressing type-dependent empire benefits in form of a multiperiod "reputation" scenario, it is conceivable that the manager's reservation utility in future periods is endogenously determined by the realization of k. The principal would then have to take this into account when designing the optimal capital budgeting process, i.e., the optimal investment cutoff.

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Tim Baldenius

Columbia University

Submitted May 2002

Accepted May 2003

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Publication: | Accounting Review |

Date: | Oct 1, 2003 |

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