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Capital budgeting and the value of information
Management Accounting Research, 1990, 1, 2 1-35
Capital budgeting and the value of information L. A. Gordon,* M. P. Loeb* and A. W. Starkt Conventional wisdom related to capital budgeting suggests that providing a project sponsor with an improved cash flow forecasting system should lead to higher firm value. Recent agency theoretic work related to the value of an information system makes such wisdom suspect. However, such work has implicitly assumed that, where communication between the subordinate and superior is allowed, it is used by the superior for control purposes only. We show that the value of providing a subordinate (e.g. project sponsor) with a new information and communication system is unclear even in a case where a superior (e.g. central management) uses communication for planning as well as control purposes. We also identify necessary and sufficient circumstances under which it is not beneficial to the superior to provide the subordinate with a new information and communication system under previous agency theoretic work, but is beneficial under our expanded analysis. Key words: capital budgeting; cash flow forecasting; information economics; agency
theory.
Introduction The importance of cash flow forecasts to the capital budgeting process is well documented in the literature [l-41. The problems associated with acquiring accurate and reliable cash flow forecasts are well stated by Clark et al. [5] in the following: The entire capital budgeting process hinges on the accuracy of the forecasts of the cash outflows and inflows surrounding a project. Thus, it is important for the analyst to obtain accurate forecasts and have some measure of the reliability of these forecasts. . . (p. 124).
Furthermore, in a recent survey by Howell et al. [6], p. 30, 48% of the survey's respondents considered preparing more accurate forecasts as an important factor in improving investment decisions. The survey's results also suggested that this factor is considered the single most important in improving investment decision-making. Most of the conventional capital budgeting discussions concerning the cash flow forecasting process assume that providing an improved forecasting system to a project sponsor (e.g. a divisional manager) will be beneficial to those responsible for allocating organizational resources (e.g. central management) and, ultimately, the organization's *College of Business and Management, University of Maryland at College Park, MD, U.S.A. t Faculty of Business and Management, University of Ulster, Shore Road, Jordanstown, County Antrim, Northern Ireland BT37 OQB, U.K. Author to whom correspondence should be addressed. Received 18 December 1989; accepted 26 January 1990. @ 1990 Academic Press Limited
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shareholders. Hence, in such a scenario, an improved information system that can be used for forecasting cash flows associated with an investment should lead to better investment decision-making and, in turn, to a higher value of the firm. More recently, the general question of the value of information has been studied using agency theory, with explicit recognition given to divergence of preferences and asymmetric information. One group of agency papers that has particular relevance in this regard deals with the question of whether or not it is in the interest of a superior (e.g. central management) to provide a subordinate (e.g. divisional manager) with a costless predecision information system that enables the subordinate to become better informed than the superior. In these papers, the information system is provided after the superior and subordinate have contracted, but before the subordinate takes some unobservable action. Christensen [7] gives examples to demonstrate that provision of such an information system may or may not be beneficial to the superior. In one of his examples, the welfare of the superior is improved by the provision of such an information system and in another example the superior's welfare is reduced. Baiman and Evans [8] provide a sufficient condition which identifies circumstances whereby the introduction of a costless predecision information system will not decrease the welfare of the superior. Penno [9] extends the result of Baiman and Evans by providing a sufficient condition which identifies circumstances in which the introduction of the information system will result in a strict increase in the welfare of the superior. In the above noted papers, capital is always made available to the subordinate. Where communication between subordinate and superior is allowed (and communication only makes sense if the subordinate is better informed about the outcome possibilities than the superior), it is used by the superior for control purposes only (e.g. by allowing the subordinate to choose from a menu of contracts). These environments are characteristic of what might be called the standard agency model. This paper builds upon the standard agency model in a capital budgeting setting. In such a setting, the assumption that capital is always made available to the subordinate (e.g. a project sponsor) is, of course, unrealistic. Hence, the primary purpose of this paper is to consider the value of providing a subordinate with a private information system, where communication based on the information system is used by the superior for planning (i.e. the superior uses the messages received to decide whether or not to make capital available to the subordinate) as well as for control purposes. That is, we consider an accept/reject decision by the superior, in terms of allocating funds to the subordinate for investment purposes, in addition to the motivation issues that arise if the project is accepted. In the model employed, a single capital project is considered with a defined technology (i.e. a defined stochastic relationship between inputs and outputs) and a non-negative cost of acquisition. Our analysis shows that where providing a subordinate with a new information and communication system is valuable in the standard agency analysis (i.e. one where the superior uses communication for control purposes only), it is also valuable in our expanded agency analysis (i.e. one where the superior uses communication for planning as well as control purposes). Further, and more important, we identify necessary and sufficient conditions for which a new information and related communication system is not valuable in the standard analysis but is valuable in our expanded analysis. In other words, we define circumstances in which providing a costless private predecision information system to the subordinate is not valuable to the superior from a control standpoint, but is valuable to the superior from a combined
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23
planning and control standpoint. Therefore, our results show that the likelihood of the information and communication system being of value to the agency increases if the superior uses the combined system for planning in addition to control. The remainder of the paper is organized as follows. In the next section, the model of the firm employed in the analysis is presented. The third section contains an analysis of the value of introducing a costless information system which enables the subordinate to evaluate the cash flow outcomes associated with the project more accurately than the superior. Results are presented that identify circumstances in which the provision of the information system increases/decreases the welfare of the superior. The fourth, and final, section provides a brief summary of the main points made in the paper.
Model Consider the problem faced by a risk-neutral superior in determining whether or not to invest in a single-period project and how to contract with an effort-averse subordinate. The subordinate's role is to manage an accepted project and, under certain circumstances, provide information to the superior about the projected cash flows associated with the project. The project's cash inflows, gross of any payments to the subordinate, will depend stochastically upon an exogenously determined factor referred to as the productivity state1 and the subordinate's effort level (which is unobservable to the superior). If it is assumed that both the superior and the subordinate share identical beliefs about the likelihood of each possible productivity state being realized, there is no further information which the subordinate can give to the superior relevant to the decision concerning acceptance of the project. In contrast, assume the superior provides the agent with access to an information system that enables himlher to perfectly and privately ascertain the productivity state.2 The subordinate now has better information relative to the superior and, hence, it is clearly worthwhile to consider the possibility of communication of the subordinate's private information to the superior. This can be thought of as analogous to the subordinate submitting a specific capital budgeting proposal. By comparing the superior's welfare under different assumptions related to the distribution of information between superior and subordinate, we evaluate whether the superior will benefit by providing the subordinate with the information system. The situations described above are modelled as follows. The superior determines whether or not to invest in a single period capital project that will yield a cash flow, gross of any payments to the agent, of Cj E {C1, C2, . . ,C,) at the end of the period, where 0 < C, < C, < . - . < C,. If the project is not accepted, cash flows, denoted C,, equal zero. There are n productivity states denoted 8,, where 8i E {8,, 8 2 , . . . ,8,). In the absence of an information system, both the superior and the subordinate believe that the probability of productivity state i occurring is strictly positive and given by p(8,). In the presence of an information system, the subordinate observes the true
'
Although it is referred to as a productivity state, it can also be thought of in other terms (e.g. an indicator of general economic prospects). The use of the term productivity state is consistent with the interpretation placed on this variable in the agency literature. Later in the paper it will be possible to think of these states as ordering the profitability of the project under consideration. Implicit in this analysis is the assumption that the subordinate can use the new information system, but the superior cannot. This situation may be the result of (1) the system not being formalized, and/or (2) the subordinate having special skills that the superior cannot duplicate.
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productivity state. If the project is accepted, the subordinate has to manage the project and chooses one of a finite number of different effort levels drawn from the set A = {a,, a,, . . . ak). The subordinate selects the level of effort without knowledge of the productivity state when no information system is provided and with knowledge of the productivity state when the information system is provided. The subordinate's choice of effort interacts with the productivity state and the decision choice to determine a probability distribution over the possible cash flows via the function B,(a, Oi) which describes the probability of cash flow outcome j (j= 1 to q) occurring when the subordinate has chosen effort level a, the productivity state is Oi, and the superior's decision is to accept. These q B,(., .) functions, together with the probabilities p(O,), i = 1 to n, and the cash flow outcomes C,, j = 1 to q, we define as a technology. The acceptlreject decision is modelled via the use of a decision variable, d, which can take one of two values, i.e. d = 0, if the project is rejected, and d = 1, if the project is accepted. Depending on the circumstances, the decision variable can be modelled as a function of a message sent by the subordinate to the superior. The acquisition cost of the project is K and the superior faces a constant cost of capital of r per dollar of capital. It is assumed that the superior either knows, or can costlessly observe, the cost of acquiring the project. Thus, issues of adverse selection do not arise with respect to identifying the acquisition cost. Also, although the cash flow outcome of the project will eventually be revealed to both the superior and the subordinate, the realization of the productivity state will never be directly revealed to the superior (nor can the superior infer the productivity state). Therefore, the superior cannot include the productivity state in the contract offered to the subordinate. The subordinate's utility function, which is known to the superior, is separable in money and effort and can be denoted by U(s) - V(a), where s is monetary reward, V(al) < V(a2)< . . . < V(ak), U1(s)> 0 and U"(s) 5 0. For convenience, it is assumed that U(0) = 0. If the project is rejected, the subordinate does not have to work any more in connection with the project and, hence, no disutility of effort is associated with project rejection. The reservation utility associated with managing or proposing an additional project is assumed to equal 0.' Programme 1 considers the case when the subordinate has no better information about the project outcomes relative to the superior (i.e. no better information about the productivity state). The subordinate is offered a contract, or compensation function, s(C), C E {CO,C1, C2, . . . ,Cq), in connection with the project. All payments are made at the end of the period, after the cash flow has been realized. For this case, the superior has to solve the following programme: Programme 1 (P1)
subject to
'
If a posirive reservation utility level were allowed, the subordinate's utility could always be increased simply by proposing a new project.
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25
and
a* E argmax a d
xx
[,:1,:1
p(Bi)Bj(a,B,)u(s(c,))] - V ( a ) , if d = 1 .
Expression ( 1 ) represents the expected value of the superior's wealth summed over the two decision branches. Inequalities (2) and (3) are minimum utility constraints on the subordinate's utility for each of the two decision branches. Notice that constraint (3) limits the liability of the subordinate in the event of the technology not proving suitable for purchase. The implications of, and justification for, making this assumption are discussed below. Constraint (4) ensures that the action, a*, implemented if the project is accepted, has the self-selection property. It is not difficult to solve this programme. The superior calculates the optimal contract as if the project is to be accepted. If the project is rejected, the subordinate is paid nothing. The superior then calculates the present value of investing in the project and determines whether that amount is in excess of the amount invested, K. Attention is now shifted to the situation where the subordinate alone is provided with an information system which enables himlher to perfectly and privately observe the productivity state after contracting but before taking any effort.' The subordinate then sends a message, m E (81, 0 2 , . . . ,On), to the superior. It is assumed that there is no cost associated with sending the message. This message now can be an argument of the subordinate's compensation function. The message, in combination with the contract offered and the true productivity state, will induce an action strategy a(m, 8,). The superior must now determine a decision strategy, d(m), to be made known to the subordinate, and a compensation function s(m, C ) . The decision strategy, d(m), partitions the index set of the productivity states into two complementary subsets. These are defined as I = { i 1 d(8,)= 1 ) and NI = { i I d(&)= 0 ) . The compensation function is defined either for cash flow outcome C , , if i E NZ, or for cash flow outcomes C,, j = 1 to q, if i E I . Without loss of generality, the superior can restrict hislher attention to decision strategies and compensation functions which ensure truth-telling [ l o ] .The superior, then, has to solve the following programme:
Programme 2 (P2)
subject to:
[ ABj(a(8i,8i), 8t)u(s(8i,Cj))
- V(a(81,8i))] 2 0,
j= 1
U(s(8,,Co))r 0 , V i E N I ,
'
V i E 1,
(6)
(7)
The assumption that the information system enables the subordinate to forecast the productivity state with perfect accuracy simplifies the analysis. However, the formulation could be interpreted equally as well in terms of whatever signals the information system is expected to produce.
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and
Expression (5) represents the superior's welfare, constraints (6) and (7) represent minimum utility constraints dependent upon the investment decision taken as a result of the message sent, constraint (8) represents the subordinate's optimal action choice, given a message m (inducing investment) and a true productivity state 8,, and constraint (9) ensures that truth-telling is the optimal strategy for the subordinate. Note that the formulation of constraint (6) implies that the superior cannot force the subordinate to manage the project for less than the minimum utility in any of the states in which investment occurs. Also, constraints (6) and (7) [as with constraints (2) and (3) in Programme 11, taken together, limit the liability of the subordinate with respect to the realization of the productivity state. The driving force behind the subordinate's limited liability in Programme 2 is, however, constraint (7). In fact, constraint (7), combined with constraints (8) and (9), implies constraint (6). This is not the only way in which the minimum utility constraint(s) can be modelled. The formulation used here, in particular with regard to constraint (7) [and constraint (3) in Programme 11, is justifiable as a result of casual empiricism that suggests that subordinates are rarely penalized for submitting projects that subsequently are not undertaken on the grounds that they are unprofitable ex ante.
The value of information As noted in the introduction, various authors have considered the effect of private information on the welfare of the superior in a situation where the superior uses the information system, and any communication system used in combination with it, for control (incentive) purposes only [7-91. The programmes formulated in the previous section can be used to explicitly consider the value of providing the subordinate with a cash flow forecasting system in a capital budgeting setting, where the superior uses messages sent (based on the output of the information system) for planning as well as control purposes.1 In other words, in our analysis, the superior is in a position to accept or reject a project (i.e. allocate funds to the subordinate) based on the message received from the subordinate. Even in this expanded analysis, it will be seen that the value of information to the superior is ambiguous. However, circumstances are identified which determine when the information system is or is not beneficial to the superior. These circumstances are identified by comparing the superior's welfare when the subordinate and the superior are equally well informed as to the prospects of the
'
The work of Melumad and Reichelstein [ll] also points out that a subordinate's message can be used by the superior for both planning and control purposes. Their paper, however, assumes the existence of private information in the possession of the subordinate prior to contracting and, hence, does not address the issue considered in this paper (that is, the creation of private information in the hands of the subordinate subsequent to contracting). Furthermore, their approach is concerned with asking whether it is in the interest of the superior to delegate the investment decision to the subordinate in the presence of private information. Other papers have considered investment decision-making in an agency framework, e.g. [12-141. All of these papers assume the existence of private information in the possession of the subordinate prior to contracting.
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proposed project with the latter's welfare when the subordinate is better informed (due to the private information system) than the superior. Given the presence of investment decision-making by the superior in our analysis, an additional advantage of providing an information system to the subordinate in a capital budgeting setting is to avoid the cost of investing in some states of nature. For given C,'S, p(Oi)'s, Bj(a, Oi)'~,r, U(.) and v(.), circumstances are identified in which the information system is either strictly valuable or never valuable. Attention is confined to technologies for which, in Programme 1, it is optimal to invest when K = 0, and, in Programme 2, it is optimal to invest in all productivity states when K = 0. Further, in this latter case, only technologies where, as K increases, investment progressively ceases in the low indexed productivity states are considered (in other words, the sequence of decision strategies as K increases is given by d(0,) = 1, V i = 1 to n, then d(0,) = 1, V i = 2 to n, 0 otherwise, then d(0,) = 1, V i = 3 to n, 0 otherwise, etc.).' Let T(P1, K) represent the value of Programme 1 for a given cost of investing, K . A similar meaning is attached to T(P2, K). Recall that U(0) = 0 and the reservation utility level associated with managing an additional project is assumed to be zero. Therefore, the superior can use the decision rule 'always reject the project' [withlwithout state information in Programme 2/11, and always give the subordinate a zero payment. Since this decision rule is always feasible for Programmes 1 and 2, T(P1, K), T(P2, K) r 0, V K. Define the value of (private) information (with communication) by I(K) represents the value to the superior of providing the costless information system to the subordinate (for the specified technology). When K = 0, investment occurs in Programme 1 and in all states in Programme 2 (by assumption). Thus, I(0) represents the value of information (with communication) in a standard agency setting, where information has value to the superior for control purposes, but not for decision-malung (planning purposes). Now define PV(i), i = 1 to n, as the present value to the superior (i.e. calculated net of payments to the subordinate) of adopting a decision strategy of d(0,) = 1, V j = i to n, 0 otherwise (e.g. T(P2,O) = PV(1)). Further, defines the inmemental present value of investing in the ith productivity state, denoted IPV,, by
Thus, T(P2,O) can be represented by
In other words, the value of the project when the subordinate is provided with an information (and associated communication) system, and the cost of acquiring the
'
As long as the sequence of decision strategies, as K increases, is invest in all states, followed by, invest in all but one state, etc., the states of nature can be reordered such that 8, is the first state in which investment ceases to take place, 8, is the second etc. The key restriction on the analysis is, therefore, the specification of the allowable sequences of decision strategies. Although specific formulae might be different, relaxing this restriction would produce essentially the same qualitative conclusions.
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project is zero, is the probability weighted average of the incremental present values for each productivity state. In addition, if the sequence of optimal decision strategies is as described above, the following must hold: I P V , < IPV, < . . . < IPV,.
(14)
In such circumstances, the productivity states also can be thought of as profitability states. IPV, is referred to as the incremental present value of investing in productivity state i because, by assumption, the only projects being analysed are those for which, as K increases, it is optimal to progressively cease to invest in the low indexed states. Notice that the incremental value of investing in any state i only can be defined with respect to a sequence of optimal decision strategies. Furthermore, it is straightforward to derive that at K = ZPV, it is optimal to change from a decision strategy of d(8,) = 1, V j = i to n, 0 otherwise, to one of d(8,) = 1, V j = i 1 to n, 0 otherwise, V i = 1 to n - 1. In addition, the point at which investment ceases is K = IPV,. Thus, although our method of defining the incremental present value associated with a given productivity state might seem overly complex (in particular, the appearance of the probability term in the definition), it lends itself to the natural interpretation that investment will take place in a state as long as the incremental present value associated with the state exceeds the cost of investing. A series of propositions representing the main results of the analysis now can be presented for a given technology. Our first proposition demonstrates that information is strictly valuable in the standard agency setting if and only if information (with communication) is strictly valuable in our expanded setting for all levels of acquisition cost for which investment would be strictly valuable in Programme 2 in the highest profitability state.
+
Proposition 1. I(0) > 0 if and only if, V K E [0, IPV,), (i.e. V K such that d(8,) = l), I(K) > 0. Proof See Appendix. Comments. This proposition states that if provision of the information system (with communication) is strictly valuable to the superior in the absence of any need for investment decision-making (i.e. the standard agency setting), the provision of the information system (with communication) will also be strictly valuable when a need for investment decision-making is introduced. Our next two propositions are concerned with the case where the provision of the information system is not strictly valuable in the standard agency setting. Proposition 2 gives a necessary and sufficient condition for the provision of the information system to the subordinate to have strictly negative value to the superior for all values of K for which investment would be strictly valuable in Programme 2 in the highest profitability state. Proposition 2. I(K) < 0, V K E [0, IPV,), if and only if T(P 1,0) r ZPV,. Proof See Appendix. Comments This proposition states that, if the project under consideration is such that its present value in the absence of the information system is in excess of the highest incremental present value associated with the project when the information (and
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associated communication) system is introduced, the value of information (and communication) for investment decision-making purposes is not sufficient to outweigh the control losses resulting from the introduction of the system. From Proposition 1, we know that if information is not valuable in the standard agency setting, then, for some positive K < IPV,, information is not valuable in our expanded capital budgeting setting. From Proposition 2, we know that, if IPV, > r(P1, O), then, for some positive K < IPV,, information is strictly valuable in our expanded capital budgeting setting. Thus, even if providing the subordinate with an information system does not increase the superior's welfare when the superior uses the communication for control purposes only, the welfare of the superior may be improved when the information is used to avoid investing in low profitability states. That is, the provision of information may be valuable in our expanded capital budgeting setting, even though the information is not valuable in the standard agency setting. Proposition 3 formally states this result and also provides the greatest lower bound on the values of the acquisition cost of the project for which the information system is valuable. Proposition 3 Suppose I(0) 5 0 and IPV, > T(P 1,O), then 3 K E (0, IPV,) such that I(K) > 0. Furthermore, I(K) > 0 if and only if K* < K < IPV,, where:
and j is defined such that T(P2, IPV,) T(P1, IPV,+I).
IT(P 1, IPV,)
and T(P2, IPV,+ ,) >
Proof See Appendix. For the special case where the superior is indifferent as to whether or not to provide the subordinate with the information system in the standard agency setting, Proposition 3 may be simplified to: Corollary 1 If I(0) = 0, then I(K) > 0 if and only if I P V , < K < IPV,. Proof See Appendix. Comments Proposition 3 and the corollary state that, in spite of the fact that the information (and associated communication) system is not valuable when there is no requirement for investment decision-making, if the present value of the project in the absence of the information system is less than the highest incremental present value associated with the project when the information system is provided to the subordinate, there are some values for the cost of acquiring the project such that the value of the information for investment decision-making purposes exceeds the control losses from the introduction of the system. The second part of Proposition 3, however, suggests that the acquisition values of the technology for which the information system is strictly valuable when a capital budgeting context is added to the standard agency setting depend heavily on the characteristics of the technology under consideration.' Limitations that are common to most agency theoretic papers are not avoided in this paper. For example, one limitation of the above analysis is that it views a single project
'
If Programme 2 were formulated with no limited liability, this would not alter the Propositions. Even without limited liability, virtually no results exist defining circumstances in which the type of information system described in this paper is valuable in the standard agency setting. An exception is Proposition 3 of Baiman and Evans [8].
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as if it were the only one to be considered and, if accepted, subsequently managed by the subordinate. In such an environment, identifying the cash flow outcomes of the project for contracting purposes is, essentially, non-problematic. In an environment where the project under consideration is to join, if accepted, many other projects already under the control of the subordinate, issues of disaggregation of cash flow outcomes can arise. If it is optimal to contract with the subordinate for each project separately (as opposed to contracting on the aggregate cash flow outcome of all the projects), identification of individual project outcomes becomes necessary. In this situation, it may be desirable to conduct postaudits which concentrate on realized cash flow outcomes from individual projects. Although identifying those circumstances under which it is optimal to contract on individual project cash flow outcomes, as opposed to the aggregate cash flow outcome, is beyond the scope of this paper, such an exercise would be of interest to those studying the design of organizational control mechanisms in the context of investment decision-making. Another limitation of our analysis is that we do not consider whether it might be advantageous to restrict the allowable message space in any fashion (as in, for example [9]). Further, multi-period aspects of the problem are not modelled and interactions between different projects are not considered. Also, we do not consider information asymmetries in the absence of the information system. In this regard, the introduction of an information system might add to already existing information asymmetries. Finally, this paper also ignores the issue raised in Lambert [15] and Demslu and Sappington [16] of motivating the agent to work to generate information. Despite these limitations, we believe that our analysis captures enough of the capital budgeting environment to lend insight into the problems of evaluating whether to provide subordinates with better information systems in the pursuit of better cash flow forecasts.
Summary The accounting and finance literature addressing the subject of capital budgeting is abundant. Conventional wisdom derived from this literature suggests that providing a project sponsor (e.g. a divisional manager) with an improved cash flow forecasting system should lead to higher firm value. Recent agency theoretic work related to the value of an information system makes such wisdom suspect. However, such work has implicitly assumed that capital is always made available to a project sponsor. By applying and extending previous agency theoretic work to a capital budgeting setting, it is possible to show that conventional wisdom concerning the value of a cash flow forecasting system is not always dependable even in the case where a superior (i.e. person responsible for allocating resources to a project), is permitted to make an acceptlreject decision on a project after the introduction of the new information system. However, we are able to identify necessary and sufficient circumstances under which it is not beneficial to the superior to provide the subordinate with a private information system under the standard agency analysis (i.e. one where the superior uses communication for control purposes only) but it is beneficial in our extended
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analysis (i.e. one where the superior uses communication for planning as well as control purposes).
'
Acknowledgements: The authors would like to thank Joel Demski, Emmett Griner, George Monahan, George Pinches, Robert Fildes and Martin Walker for helpful comments on earlier drafts of this paper.
References 1. Sundem, G. L. Evaluating simplified capital budgeting models using a time-state preference metric, The Accounting Review, April, 306-320, 1974. 2. Gordon, L. A., Larcker, D. F. and Tuggle, F. D. Informational impediments to the use of capital budgeting models, Omega, 67-74, 1979. 3. Larcker, D. F. Perceived importance of selected information characteristics to the use of capital budgeting models, The Accounting Review, July, 519-538, 1981. 4. Horngren, C. and Foster, G. Cost Accounting: A Managerial Emphasis, Englewood Cliffs, NJ, Prentice-Hall, 1987. 5. Clark, J. L., Hindelang, T. and Pritchard, R. Capital Budgeting: Planning and Control of Capital Expenditures, Englewood Cliffs, NJ, Prentice-Hall, 1984. 6. Howell, R. A., Brown, J. D., Soucy, S. R. and Seed 111, A. H. Management Accounting in the New Manufacturing Environment, Montvale, NJ, National Association of Accountants, 1987. 7. Christensen, J. Communication in agencies, Bell Journal of Economics, Autumn, 661-674, 1981. 8. Baiman, S. and Evans, H. Pre-decision information and participative management control systems, J o u m l of Accounting Research, Autumn, 371-395, 1983. 9. Penno, M. Asymmetry of pre-decision information and management, Journal of Accounting Research, Spring, 177-191, 1984. 10. ~ ~ e r s o nR.; ~icentivecompatibility and the bargaining problem, Econometrics, January, 61-74. 1979. 11. ~ e l u m a d ,N. and Reichelstein, S. Centralization versus delegation and the value of communication, Journal of Accounting Research, Supplement, 1-18, 1987. 12. Antle, R. and Eppen, G. Capital rationing and organizational slack in capital budgeting, Management Science, February, 163-174, 1985. 13. Holmstrom, B. and Weiss, L. Managerial incentives, investment and aggregate implications: scale effects, Review of Economic Studies, 403-425, 1985. 14. Rees, R. Incentive compatible discount rates for public investment, Journal of Public Economics, 249-257, 1984. 15. Lambert, R. Executive effort and the selection of risky projects, Rand Journal of Economics, Spring, 77-88, 1986. 16. Demski, J. S. and Sappington, D. E. M. Delegated expertise, Journal of Accounting Research, Spring, 68-89, 1987.
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It might be argued that an addition to the planning and control structure modelled in this paper would be an internal audit of some sort. A postaudit concentrating on realized project cash outflows and inflows, which is one specific form of internal auditing, was suggested by the respondents to the Howell et al. [6] study to be the second most useful method of improving investment decisions. Further Antle and Eppen [12] view such a postaudit as an alternative means of ameliorating organizational problems related to the unobservability of expenditures on productive resources by the subordinate. In the environment modelled in this paper, such a postaudit would be of no value since realized cash inflows and outflows are perfectly revealed to the superior. In our model, an internal audit would only be of use if it provided information about the productivity state or the subordinate's effort level.
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Appendix I The proof of our propositions and corollary follow from the geometric arguments given below and illustrated (for the case of three productivity states) in Figures A1-A4. First, consider the curve of the NPV of Programme 1, T(P1, K), against K. The curve consists of two straight line segments, since T(P1, K) = max (r(P1,O) - K, 0). Now, consider the curve of the NPV of Programme 2, T(P2, K), against K. This latter curve consists of a sequence of straight line segments whose slope changes as the decision strategy changes. The manner in which the gradient of the curve changes is that if IPVi 5 K 5 IPVi+l, the gradient is -(p(Oi+]) + + . . +p(On)), for i = 1 to n - 1. Note that the gradient of the NPV curve for Programme 2 becomes more and more shallow. For K < T(P1, O), the gradient of the T(P2, K ) curve is greater than or equal to -1 (the slope of the T(P1, K) curve) and, for K r IPV,, the value of the curve is zero. Proof of Proposition 1: (see Figure A 1) Necessity Assume Z(0) > 0, i.e. T(P2,O) > T(P1,O). As K increases, the curve for Programme 2 bends further away from the curve for Programme 1. Therefore, if I(0) > 0, the information system will be strictly valuable for all non-negative values of K for which investment is strictly valuable in some realization of the productivity state, i.e. I(K) > 0 V non-negative K < ZPVn. Sufficiency Suppose I(K) > 0 V non-negative K < IPV, . Then, clearly, I(K) > 0 for K=0. NPV
-
IPV,
T(P1.0)
IPV*
..
I PV3
Figure Al. NPV for information and no information, Case I: I(0) > 0 (for n = 3).
Capital Budgeting
1PVl
1PV2
33
IPV. T(P1.0)
Figure A2. NPV for information and no information, Case 11: I(0) < 0, T(P1,O) 2 IPV, (for n = 3).
NPV
IPV,
I P V ~K'
~ ( P I , o )I P V ~
Figure A3. NPV for information and no information, Case 111: I(0) < 0, IPV, > T ( P l , 0) (for n = 3).
34
L. A. Gordon et al.
Figure A4. NPV for information and no information, Case IV: (Pl, 0) = T(P2,O)(for n = 3).
Proof of Proposition 2: (see Figure A2) Necessity Assume I ( K )< 0, V 0 IK < IPV,. Then at K E < IPV,) we have: ,
= IPV,
- E , (for any positive
r(m,IPV, - E ) > r ( p 2 , IPV, - E). As T(P2, K ) is non-increasing in K , it follows that
r(P1, IPV,
- E ) >r
( ~ 2IPV,). ,
By the definition of IPV,, T(P2, IPV,) = 0. Thus
r ( P 1, IPV, - E ) > 0, for all positive follows that
E
< IPV,. Since, T(P1, IPV, - E ) = Max{r(P1 , O ) r(Pi,o)-IPv,
- IPV,
+ E, 0 ) , it
+ E>O,
for all positive E < IPV, . Therefore,
T(P1,O) r IPV,. Sufficiency Suppose T(P1,0) r IPV, . Since r ( P 1, IPV,) = max {T(P1 , O ) - IPV,, 0 ), it follows that r ( P 1, IPV,)
= r(P1,o) - IPV,,
and, hence,
r ( P 1 , IPV,)
2 0.
Capital Budgeting
35
Since T(P2, IPV,) = 0, we have
As (1) the gradient of the curve of T(P2, K ) against K 2 - 1, and - 1 is the gradient of the curve of T(P 1, K) against K, V K < T(P 1, O), and (2) IPV, IT(P 1,O) by assumption, the gradient of the curve of I(K) against K is greater or equal to 0, V K T(P 1, 0), then there must exist a K * > 0 such that for all K* < K < IPV,, the curve of T(P2, K) against K lies above the curve of T(P1, K ) against K, and for all K such that 0 < K < K*, the curve of T(P2, K ) against K lies below, or is coincident with, the curve of T(P 1, K ) against K. To identify K*, note that, for any i, the curve of T(P2, K) against K is a straight line between IPVi and IPV,,,. Therefore, defining j as in the Proposition gives the interval (IPV,, IPV,,,) which contains the point of intersection. In the interval under consideration, the curve of T(P2, K ) against K takes the form given below:
Further, the curve of T(P1, K ) against K can be described by the equation below, in the interval under consideration: Equating the expressions for T(P1, K ) and T(P2, K), defining the point of intersection as K*, and a rearrangement of terms, gives the result (remembering the definition of I(0)). Proof of Corollary : (see Figure A4) The proof follows immediately from Proposition 3 by substituting 0 for I(0) and 1 for j into equation (IS), and then using equation (1 1).
Capital budgeting and the value of information L. A. Gordon,* M. P. Loeb* and A. W. Starkt Conventional wisdom related to capital budgeting suggests that providing a project sponsor with an improved cash flow forecasting system should lead to higher firm value. Recent agency theoretic work related to the value of an information system makes such wisdom suspect. However, such work has implicitly assumed that, where communication between the subordinate and superior is allowed, it is used by the superior for control purposes only. We show that the value of providing a subordinate (e.g. project sponsor) with a new information and communication system is unclear even in a case where a superior (e.g. central management) uses communication for planning as well as control purposes. We also identify necessary and sufficient circumstances under which it is not beneficial to the superior to provide the subordinate with a new information and communication system under previous agency theoretic work, but is beneficial under our expanded analysis. Key words: capital budgeting; cash flow forecasting; information economics; agency
theory.
Introduction The importance of cash flow forecasts to the capital budgeting process is well documented in the literature [l-41. The problems associated with acquiring accurate and reliable cash flow forecasts are well stated by Clark et al. [5] in the following: The entire capital budgeting process hinges on the accuracy of the forecasts of the cash outflows and inflows surrounding a project. Thus, it is important for the analyst to obtain accurate forecasts and have some measure of the reliability of these forecasts. . . (p. 124).
Furthermore, in a recent survey by Howell et al. [6], p. 30, 48% of the survey's respondents considered preparing more accurate forecasts as an important factor in improving investment decisions. The survey's results also suggested that this factor is considered the single most important in improving investment decision-making. Most of the conventional capital budgeting discussions concerning the cash flow forecasting process assume that providing an improved forecasting system to a project sponsor (e.g. a divisional manager) will be beneficial to those responsible for allocating organizational resources (e.g. central management) and, ultimately, the organization's *College of Business and Management, University of Maryland at College Park, MD, U.S.A. t Faculty of Business and Management, University of Ulster, Shore Road, Jordanstown, County Antrim, Northern Ireland BT37 OQB, U.K. Author to whom correspondence should be addressed. Received 18 December 1989; accepted 26 January 1990. @ 1990 Academic Press Limited
22
L. A. Gordon et al.
shareholders. Hence, in such a scenario, an improved information system that can be used for forecasting cash flows associated with an investment should lead to better investment decision-making and, in turn, to a higher value of the firm. More recently, the general question of the value of information has been studied using agency theory, with explicit recognition given to divergence of preferences and asymmetric information. One group of agency papers that has particular relevance in this regard deals with the question of whether or not it is in the interest of a superior (e.g. central management) to provide a subordinate (e.g. divisional manager) with a costless predecision information system that enables the subordinate to become better informed than the superior. In these papers, the information system is provided after the superior and subordinate have contracted, but before the subordinate takes some unobservable action. Christensen [7] gives examples to demonstrate that provision of such an information system may or may not be beneficial to the superior. In one of his examples, the welfare of the superior is improved by the provision of such an information system and in another example the superior's welfare is reduced. Baiman and Evans [8] provide a sufficient condition which identifies circumstances whereby the introduction of a costless predecision information system will not decrease the welfare of the superior. Penno [9] extends the result of Baiman and Evans by providing a sufficient condition which identifies circumstances in which the introduction of the information system will result in a strict increase in the welfare of the superior. In the above noted papers, capital is always made available to the subordinate. Where communication between subordinate and superior is allowed (and communication only makes sense if the subordinate is better informed about the outcome possibilities than the superior), it is used by the superior for control purposes only (e.g. by allowing the subordinate to choose from a menu of contracts). These environments are characteristic of what might be called the standard agency model. This paper builds upon the standard agency model in a capital budgeting setting. In such a setting, the assumption that capital is always made available to the subordinate (e.g. a project sponsor) is, of course, unrealistic. Hence, the primary purpose of this paper is to consider the value of providing a subordinate with a private information system, where communication based on the information system is used by the superior for planning (i.e. the superior uses the messages received to decide whether or not to make capital available to the subordinate) as well as for control purposes. That is, we consider an accept/reject decision by the superior, in terms of allocating funds to the subordinate for investment purposes, in addition to the motivation issues that arise if the project is accepted. In the model employed, a single capital project is considered with a defined technology (i.e. a defined stochastic relationship between inputs and outputs) and a non-negative cost of acquisition. Our analysis shows that where providing a subordinate with a new information and communication system is valuable in the standard agency analysis (i.e. one where the superior uses communication for control purposes only), it is also valuable in our expanded agency analysis (i.e. one where the superior uses communication for planning as well as control purposes). Further, and more important, we identify necessary and sufficient conditions for which a new information and related communication system is not valuable in the standard analysis but is valuable in our expanded analysis. In other words, we define circumstances in which providing a costless private predecision information system to the subordinate is not valuable to the superior from a control standpoint, but is valuable to the superior from a combined
Capital Budgeting
23
planning and control standpoint. Therefore, our results show that the likelihood of the information and communication system being of value to the agency increases if the superior uses the combined system for planning in addition to control. The remainder of the paper is organized as follows. In the next section, the model of the firm employed in the analysis is presented. The third section contains an analysis of the value of introducing a costless information system which enables the subordinate to evaluate the cash flow outcomes associated with the project more accurately than the superior. Results are presented that identify circumstances in which the provision of the information system increases/decreases the welfare of the superior. The fourth, and final, section provides a brief summary of the main points made in the paper.
Model Consider the problem faced by a risk-neutral superior in determining whether or not to invest in a single-period project and how to contract with an effort-averse subordinate. The subordinate's role is to manage an accepted project and, under certain circumstances, provide information to the superior about the projected cash flows associated with the project. The project's cash inflows, gross of any payments to the subordinate, will depend stochastically upon an exogenously determined factor referred to as the productivity state1 and the subordinate's effort level (which is unobservable to the superior). If it is assumed that both the superior and the subordinate share identical beliefs about the likelihood of each possible productivity state being realized, there is no further information which the subordinate can give to the superior relevant to the decision concerning acceptance of the project. In contrast, assume the superior provides the agent with access to an information system that enables himlher to perfectly and privately ascertain the productivity state.2 The subordinate now has better information relative to the superior and, hence, it is clearly worthwhile to consider the possibility of communication of the subordinate's private information to the superior. This can be thought of as analogous to the subordinate submitting a specific capital budgeting proposal. By comparing the superior's welfare under different assumptions related to the distribution of information between superior and subordinate, we evaluate whether the superior will benefit by providing the subordinate with the information system. The situations described above are modelled as follows. The superior determines whether or not to invest in a single period capital project that will yield a cash flow, gross of any payments to the agent, of Cj E {C1, C2, . . ,C,) at the end of the period, where 0 < C, < C, < . - . < C,. If the project is not accepted, cash flows, denoted C,, equal zero. There are n productivity states denoted 8,, where 8i E {8,, 8 2 , . . . ,8,). In the absence of an information system, both the superior and the subordinate believe that the probability of productivity state i occurring is strictly positive and given by p(8,). In the presence of an information system, the subordinate observes the true
'
Although it is referred to as a productivity state, it can also be thought of in other terms (e.g. an indicator of general economic prospects). The use of the term productivity state is consistent with the interpretation placed on this variable in the agency literature. Later in the paper it will be possible to think of these states as ordering the profitability of the project under consideration. Implicit in this analysis is the assumption that the subordinate can use the new information system, but the superior cannot. This situation may be the result of (1) the system not being formalized, and/or (2) the subordinate having special skills that the superior cannot duplicate.
24
L. A. Gordon et al.
productivity state. If the project is accepted, the subordinate has to manage the project and chooses one of a finite number of different effort levels drawn from the set A = {a,, a,, . . . ak). The subordinate selects the level of effort without knowledge of the productivity state when no information system is provided and with knowledge of the productivity state when the information system is provided. The subordinate's choice of effort interacts with the productivity state and the decision choice to determine a probability distribution over the possible cash flows via the function B,(a, Oi) which describes the probability of cash flow outcome j (j= 1 to q) occurring when the subordinate has chosen effort level a, the productivity state is Oi, and the superior's decision is to accept. These q B,(., .) functions, together with the probabilities p(O,), i = 1 to n, and the cash flow outcomes C,, j = 1 to q, we define as a technology. The acceptlreject decision is modelled via the use of a decision variable, d, which can take one of two values, i.e. d = 0, if the project is rejected, and d = 1, if the project is accepted. Depending on the circumstances, the decision variable can be modelled as a function of a message sent by the subordinate to the superior. The acquisition cost of the project is K and the superior faces a constant cost of capital of r per dollar of capital. It is assumed that the superior either knows, or can costlessly observe, the cost of acquiring the project. Thus, issues of adverse selection do not arise with respect to identifying the acquisition cost. Also, although the cash flow outcome of the project will eventually be revealed to both the superior and the subordinate, the realization of the productivity state will never be directly revealed to the superior (nor can the superior infer the productivity state). Therefore, the superior cannot include the productivity state in the contract offered to the subordinate. The subordinate's utility function, which is known to the superior, is separable in money and effort and can be denoted by U(s) - V(a), where s is monetary reward, V(al) < V(a2)< . . . < V(ak), U1(s)> 0 and U"(s) 5 0. For convenience, it is assumed that U(0) = 0. If the project is rejected, the subordinate does not have to work any more in connection with the project and, hence, no disutility of effort is associated with project rejection. The reservation utility associated with managing or proposing an additional project is assumed to equal 0.' Programme 1 considers the case when the subordinate has no better information about the project outcomes relative to the superior (i.e. no better information about the productivity state). The subordinate is offered a contract, or compensation function, s(C), C E {CO,C1, C2, . . . ,Cq), in connection with the project. All payments are made at the end of the period, after the cash flow has been realized. For this case, the superior has to solve the following programme: Programme 1 (P1)
subject to
'
If a posirive reservation utility level were allowed, the subordinate's utility could always be increased simply by proposing a new project.
Capital Budgeting
25
and
a* E argmax a d
xx
[,:1,:1
p(Bi)Bj(a,B,)u(s(c,))] - V ( a ) , if d = 1 .
Expression ( 1 ) represents the expected value of the superior's wealth summed over the two decision branches. Inequalities (2) and (3) are minimum utility constraints on the subordinate's utility for each of the two decision branches. Notice that constraint (3) limits the liability of the subordinate in the event of the technology not proving suitable for purchase. The implications of, and justification for, making this assumption are discussed below. Constraint (4) ensures that the action, a*, implemented if the project is accepted, has the self-selection property. It is not difficult to solve this programme. The superior calculates the optimal contract as if the project is to be accepted. If the project is rejected, the subordinate is paid nothing. The superior then calculates the present value of investing in the project and determines whether that amount is in excess of the amount invested, K. Attention is now shifted to the situation where the subordinate alone is provided with an information system which enables himlher to perfectly and privately observe the productivity state after contracting but before taking any effort.' The subordinate then sends a message, m E (81, 0 2 , . . . ,On), to the superior. It is assumed that there is no cost associated with sending the message. This message now can be an argument of the subordinate's compensation function. The message, in combination with the contract offered and the true productivity state, will induce an action strategy a(m, 8,). The superior must now determine a decision strategy, d(m), to be made known to the subordinate, and a compensation function s(m, C ) . The decision strategy, d(m), partitions the index set of the productivity states into two complementary subsets. These are defined as I = { i 1 d(8,)= 1 ) and NI = { i I d(&)= 0 ) . The compensation function is defined either for cash flow outcome C , , if i E NZ, or for cash flow outcomes C,, j = 1 to q, if i E I . Without loss of generality, the superior can restrict hislher attention to decision strategies and compensation functions which ensure truth-telling [ l o ] .The superior, then, has to solve the following programme:
Programme 2 (P2)
subject to:
[ ABj(a(8i,8i), 8t)u(s(8i,Cj))
- V(a(81,8i))] 2 0,
j= 1
U(s(8,,Co))r 0 , V i E N I ,
'
V i E 1,
(6)
(7)
The assumption that the information system enables the subordinate to forecast the productivity state with perfect accuracy simplifies the analysis. However, the formulation could be interpreted equally as well in terms of whatever signals the information system is expected to produce.
26
L. A. Gordon et al.
and
Expression (5) represents the superior's welfare, constraints (6) and (7) represent minimum utility constraints dependent upon the investment decision taken as a result of the message sent, constraint (8) represents the subordinate's optimal action choice, given a message m (inducing investment) and a true productivity state 8,, and constraint (9) ensures that truth-telling is the optimal strategy for the subordinate. Note that the formulation of constraint (6) implies that the superior cannot force the subordinate to manage the project for less than the minimum utility in any of the states in which investment occurs. Also, constraints (6) and (7) [as with constraints (2) and (3) in Programme 11, taken together, limit the liability of the subordinate with respect to the realization of the productivity state. The driving force behind the subordinate's limited liability in Programme 2 is, however, constraint (7). In fact, constraint (7), combined with constraints (8) and (9), implies constraint (6). This is not the only way in which the minimum utility constraint(s) can be modelled. The formulation used here, in particular with regard to constraint (7) [and constraint (3) in Programme 11, is justifiable as a result of casual empiricism that suggests that subordinates are rarely penalized for submitting projects that subsequently are not undertaken on the grounds that they are unprofitable ex ante.
The value of information As noted in the introduction, various authors have considered the effect of private information on the welfare of the superior in a situation where the superior uses the information system, and any communication system used in combination with it, for control (incentive) purposes only [7-91. The programmes formulated in the previous section can be used to explicitly consider the value of providing the subordinate with a cash flow forecasting system in a capital budgeting setting, where the superior uses messages sent (based on the output of the information system) for planning as well as control purposes.1 In other words, in our analysis, the superior is in a position to accept or reject a project (i.e. allocate funds to the subordinate) based on the message received from the subordinate. Even in this expanded analysis, it will be seen that the value of information to the superior is ambiguous. However, circumstances are identified which determine when the information system is or is not beneficial to the superior. These circumstances are identified by comparing the superior's welfare when the subordinate and the superior are equally well informed as to the prospects of the
'
The work of Melumad and Reichelstein [ll] also points out that a subordinate's message can be used by the superior for both planning and control purposes. Their paper, however, assumes the existence of private information in the possession of the subordinate prior to contracting and, hence, does not address the issue considered in this paper (that is, the creation of private information in the hands of the subordinate subsequent to contracting). Furthermore, their approach is concerned with asking whether it is in the interest of the superior to delegate the investment decision to the subordinate in the presence of private information. Other papers have considered investment decision-making in an agency framework, e.g. [12-141. All of these papers assume the existence of private information in the possession of the subordinate prior to contracting.
Capital Budgeting
27
proposed project with the latter's welfare when the subordinate is better informed (due to the private information system) than the superior. Given the presence of investment decision-making by the superior in our analysis, an additional advantage of providing an information system to the subordinate in a capital budgeting setting is to avoid the cost of investing in some states of nature. For given C,'S, p(Oi)'s, Bj(a, Oi)'~,r, U(.) and v(.), circumstances are identified in which the information system is either strictly valuable or never valuable. Attention is confined to technologies for which, in Programme 1, it is optimal to invest when K = 0, and, in Programme 2, it is optimal to invest in all productivity states when K = 0. Further, in this latter case, only technologies where, as K increases, investment progressively ceases in the low indexed productivity states are considered (in other words, the sequence of decision strategies as K increases is given by d(0,) = 1, V i = 1 to n, then d(0,) = 1, V i = 2 to n, 0 otherwise, then d(0,) = 1, V i = 3 to n, 0 otherwise, etc.).' Let T(P1, K) represent the value of Programme 1 for a given cost of investing, K . A similar meaning is attached to T(P2, K). Recall that U(0) = 0 and the reservation utility level associated with managing an additional project is assumed to be zero. Therefore, the superior can use the decision rule 'always reject the project' [withlwithout state information in Programme 2/11, and always give the subordinate a zero payment. Since this decision rule is always feasible for Programmes 1 and 2, T(P1, K), T(P2, K) r 0, V K. Define the value of (private) information (with communication) by I(K) represents the value to the superior of providing the costless information system to the subordinate (for the specified technology). When K = 0, investment occurs in Programme 1 and in all states in Programme 2 (by assumption). Thus, I(0) represents the value of information (with communication) in a standard agency setting, where information has value to the superior for control purposes, but not for decision-malung (planning purposes). Now define PV(i), i = 1 to n, as the present value to the superior (i.e. calculated net of payments to the subordinate) of adopting a decision strategy of d(0,) = 1, V j = i to n, 0 otherwise (e.g. T(P2,O) = PV(1)). Further, defines the inmemental present value of investing in the ith productivity state, denoted IPV,, by
Thus, T(P2,O) can be represented by
In other words, the value of the project when the subordinate is provided with an information (and associated communication) system, and the cost of acquiring the
'
As long as the sequence of decision strategies, as K increases, is invest in all states, followed by, invest in all but one state, etc., the states of nature can be reordered such that 8, is the first state in which investment ceases to take place, 8, is the second etc. The key restriction on the analysis is, therefore, the specification of the allowable sequences of decision strategies. Although specific formulae might be different, relaxing this restriction would produce essentially the same qualitative conclusions.
28
L. A. Gordon et al.
project is zero, is the probability weighted average of the incremental present values for each productivity state. In addition, if the sequence of optimal decision strategies is as described above, the following must hold: I P V , < IPV, < . . . < IPV,.
(14)
In such circumstances, the productivity states also can be thought of as profitability states. IPV, is referred to as the incremental present value of investing in productivity state i because, by assumption, the only projects being analysed are those for which, as K increases, it is optimal to progressively cease to invest in the low indexed states. Notice that the incremental value of investing in any state i only can be defined with respect to a sequence of optimal decision strategies. Furthermore, it is straightforward to derive that at K = ZPV, it is optimal to change from a decision strategy of d(8,) = 1, V j = i to n, 0 otherwise, to one of d(8,) = 1, V j = i 1 to n, 0 otherwise, V i = 1 to n - 1. In addition, the point at which investment ceases is K = IPV,. Thus, although our method of defining the incremental present value associated with a given productivity state might seem overly complex (in particular, the appearance of the probability term in the definition), it lends itself to the natural interpretation that investment will take place in a state as long as the incremental present value associated with the state exceeds the cost of investing. A series of propositions representing the main results of the analysis now can be presented for a given technology. Our first proposition demonstrates that information is strictly valuable in the standard agency setting if and only if information (with communication) is strictly valuable in our expanded setting for all levels of acquisition cost for which investment would be strictly valuable in Programme 2 in the highest profitability state.
+
Proposition 1. I(0) > 0 if and only if, V K E [0, IPV,), (i.e. V K such that d(8,) = l), I(K) > 0. Proof See Appendix. Comments. This proposition states that if provision of the information system (with communication) is strictly valuable to the superior in the absence of any need for investment decision-making (i.e. the standard agency setting), the provision of the information system (with communication) will also be strictly valuable when a need for investment decision-making is introduced. Our next two propositions are concerned with the case where the provision of the information system is not strictly valuable in the standard agency setting. Proposition 2 gives a necessary and sufficient condition for the provision of the information system to the subordinate to have strictly negative value to the superior for all values of K for which investment would be strictly valuable in Programme 2 in the highest profitability state. Proposition 2. I(K) < 0, V K E [0, IPV,), if and only if T(P 1,0) r ZPV,. Proof See Appendix. Comments This proposition states that, if the project under consideration is such that its present value in the absence of the information system is in excess of the highest incremental present value associated with the project when the information (and
Capital Budgeting
29
associated communication) system is introduced, the value of information (and communication) for investment decision-making purposes is not sufficient to outweigh the control losses resulting from the introduction of the system. From Proposition 1, we know that if information is not valuable in the standard agency setting, then, for some positive K < IPV,, information is not valuable in our expanded capital budgeting setting. From Proposition 2, we know that, if IPV, > r(P1, O), then, for some positive K < IPV,, information is strictly valuable in our expanded capital budgeting setting. Thus, even if providing the subordinate with an information system does not increase the superior's welfare when the superior uses the communication for control purposes only, the welfare of the superior may be improved when the information is used to avoid investing in low profitability states. That is, the provision of information may be valuable in our expanded capital budgeting setting, even though the information is not valuable in the standard agency setting. Proposition 3 formally states this result and also provides the greatest lower bound on the values of the acquisition cost of the project for which the information system is valuable. Proposition 3 Suppose I(0) 5 0 and IPV, > T(P 1,O), then 3 K E (0, IPV,) such that I(K) > 0. Furthermore, I(K) > 0 if and only if K* < K < IPV,, where:
and j is defined such that T(P2, IPV,) T(P1, IPV,+I).
IT(P 1, IPV,)
and T(P2, IPV,+ ,) >
Proof See Appendix. For the special case where the superior is indifferent as to whether or not to provide the subordinate with the information system in the standard agency setting, Proposition 3 may be simplified to: Corollary 1 If I(0) = 0, then I(K) > 0 if and only if I P V , < K < IPV,. Proof See Appendix. Comments Proposition 3 and the corollary state that, in spite of the fact that the information (and associated communication) system is not valuable when there is no requirement for investment decision-making, if the present value of the project in the absence of the information system is less than the highest incremental present value associated with the project when the information system is provided to the subordinate, there are some values for the cost of acquiring the project such that the value of the information for investment decision-making purposes exceeds the control losses from the introduction of the system. The second part of Proposition 3, however, suggests that the acquisition values of the technology for which the information system is strictly valuable when a capital budgeting context is added to the standard agency setting depend heavily on the characteristics of the technology under consideration.' Limitations that are common to most agency theoretic papers are not avoided in this paper. For example, one limitation of the above analysis is that it views a single project
'
If Programme 2 were formulated with no limited liability, this would not alter the Propositions. Even without limited liability, virtually no results exist defining circumstances in which the type of information system described in this paper is valuable in the standard agency setting. An exception is Proposition 3 of Baiman and Evans [8].
30
L. A. Gordon et 41.
as if it were the only one to be considered and, if accepted, subsequently managed by the subordinate. In such an environment, identifying the cash flow outcomes of the project for contracting purposes is, essentially, non-problematic. In an environment where the project under consideration is to join, if accepted, many other projects already under the control of the subordinate, issues of disaggregation of cash flow outcomes can arise. If it is optimal to contract with the subordinate for each project separately (as opposed to contracting on the aggregate cash flow outcome of all the projects), identification of individual project outcomes becomes necessary. In this situation, it may be desirable to conduct postaudits which concentrate on realized cash flow outcomes from individual projects. Although identifying those circumstances under which it is optimal to contract on individual project cash flow outcomes, as opposed to the aggregate cash flow outcome, is beyond the scope of this paper, such an exercise would be of interest to those studying the design of organizational control mechanisms in the context of investment decision-making. Another limitation of our analysis is that we do not consider whether it might be advantageous to restrict the allowable message space in any fashion (as in, for example [9]). Further, multi-period aspects of the problem are not modelled and interactions between different projects are not considered. Also, we do not consider information asymmetries in the absence of the information system. In this regard, the introduction of an information system might add to already existing information asymmetries. Finally, this paper also ignores the issue raised in Lambert [15] and Demslu and Sappington [16] of motivating the agent to work to generate information. Despite these limitations, we believe that our analysis captures enough of the capital budgeting environment to lend insight into the problems of evaluating whether to provide subordinates with better information systems in the pursuit of better cash flow forecasts.
Summary The accounting and finance literature addressing the subject of capital budgeting is abundant. Conventional wisdom derived from this literature suggests that providing a project sponsor (e.g. a divisional manager) with an improved cash flow forecasting system should lead to higher firm value. Recent agency theoretic work related to the value of an information system makes such wisdom suspect. However, such work has implicitly assumed that capital is always made available to a project sponsor. By applying and extending previous agency theoretic work to a capital budgeting setting, it is possible to show that conventional wisdom concerning the value of a cash flow forecasting system is not always dependable even in the case where a superior (i.e. person responsible for allocating resources to a project), is permitted to make an acceptlreject decision on a project after the introduction of the new information system. However, we are able to identify necessary and sufficient circumstances under which it is not beneficial to the superior to provide the subordinate with a private information system under the standard agency analysis (i.e. one where the superior uses communication for control purposes only) but it is beneficial in our extended
Capital Budgeting
31
analysis (i.e. one where the superior uses communication for planning as well as control purposes).
'
Acknowledgements: The authors would like to thank Joel Demski, Emmett Griner, George Monahan, George Pinches, Robert Fildes and Martin Walker for helpful comments on earlier drafts of this paper.
References 1. Sundem, G. L. Evaluating simplified capital budgeting models using a time-state preference metric, The Accounting Review, April, 306-320, 1974. 2. Gordon, L. A., Larcker, D. F. and Tuggle, F. D. Informational impediments to the use of capital budgeting models, Omega, 67-74, 1979. 3. Larcker, D. F. Perceived importance of selected information characteristics to the use of capital budgeting models, The Accounting Review, July, 519-538, 1981. 4. Horngren, C. and Foster, G. Cost Accounting: A Managerial Emphasis, Englewood Cliffs, NJ, Prentice-Hall, 1987. 5. Clark, J. L., Hindelang, T. and Pritchard, R. Capital Budgeting: Planning and Control of Capital Expenditures, Englewood Cliffs, NJ, Prentice-Hall, 1984. 6. Howell, R. A., Brown, J. D., Soucy, S. R. and Seed 111, A. H. Management Accounting in the New Manufacturing Environment, Montvale, NJ, National Association of Accountants, 1987. 7. Christensen, J. Communication in agencies, Bell Journal of Economics, Autumn, 661-674, 1981. 8. Baiman, S. and Evans, H. Pre-decision information and participative management control systems, J o u m l of Accounting Research, Autumn, 371-395, 1983. 9. Penno, M. Asymmetry of pre-decision information and management, Journal of Accounting Research, Spring, 177-191, 1984. 10. ~ ~ e r s o nR.; ~icentivecompatibility and the bargaining problem, Econometrics, January, 61-74. 1979. 11. ~ e l u m a d ,N. and Reichelstein, S. Centralization versus delegation and the value of communication, Journal of Accounting Research, Supplement, 1-18, 1987. 12. Antle, R. and Eppen, G. Capital rationing and organizational slack in capital budgeting, Management Science, February, 163-174, 1985. 13. Holmstrom, B. and Weiss, L. Managerial incentives, investment and aggregate implications: scale effects, Review of Economic Studies, 403-425, 1985. 14. Rees, R. Incentive compatible discount rates for public investment, Journal of Public Economics, 249-257, 1984. 15. Lambert, R. Executive effort and the selection of risky projects, Rand Journal of Economics, Spring, 77-88, 1986. 16. Demski, J. S. and Sappington, D. E. M. Delegated expertise, Journal of Accounting Research, Spring, 68-89, 1987.
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It might be argued that an addition to the planning and control structure modelled in this paper would be an internal audit of some sort. A postaudit concentrating on realized project cash outflows and inflows, which is one specific form of internal auditing, was suggested by the respondents to the Howell et al. [6] study to be the second most useful method of improving investment decisions. Further Antle and Eppen [12] view such a postaudit as an alternative means of ameliorating organizational problems related to the unobservability of expenditures on productive resources by the subordinate. In the environment modelled in this paper, such a postaudit would be of no value since realized cash inflows and outflows are perfectly revealed to the superior. In our model, an internal audit would only be of use if it provided information about the productivity state or the subordinate's effort level.
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L. A. Gordon et al.
Appendix I The proof of our propositions and corollary follow from the geometric arguments given below and illustrated (for the case of three productivity states) in Figures A1-A4. First, consider the curve of the NPV of Programme 1, T(P1, K), against K. The curve consists of two straight line segments, since T(P1, K) = max (r(P1,O) - K, 0). Now, consider the curve of the NPV of Programme 2, T(P2, K), against K. This latter curve consists of a sequence of straight line segments whose slope changes as the decision strategy changes. The manner in which the gradient of the curve changes is that if IPVi 5 K 5 IPVi+l, the gradient is -(p(Oi+]) + + . . +p(On)), for i = 1 to n - 1. Note that the gradient of the NPV curve for Programme 2 becomes more and more shallow. For K < T(P1, O), the gradient of the T(P2, K ) curve is greater than or equal to -1 (the slope of the T(P1, K) curve) and, for K r IPV,, the value of the curve is zero. Proof of Proposition 1: (see Figure A 1) Necessity Assume Z(0) > 0, i.e. T(P2,O) > T(P1,O). As K increases, the curve for Programme 2 bends further away from the curve for Programme 1. Therefore, if I(0) > 0, the information system will be strictly valuable for all non-negative values of K for which investment is strictly valuable in some realization of the productivity state, i.e. I(K) > 0 V non-negative K < ZPVn. Sufficiency Suppose I(K) > 0 V non-negative K < IPV, . Then, clearly, I(K) > 0 for K=0. NPV
-
IPV,
T(P1.0)
IPV*
..
I PV3
Figure Al. NPV for information and no information, Case I: I(0) > 0 (for n = 3).
Capital Budgeting
1PVl
1PV2
33
IPV. T(P1.0)
Figure A2. NPV for information and no information, Case 11: I(0) < 0, T(P1,O) 2 IPV, (for n = 3).
NPV
IPV,
I P V ~K'
~ ( P I , o )I P V ~
Figure A3. NPV for information and no information, Case 111: I(0) < 0, IPV, > T ( P l , 0) (for n = 3).
34
L. A. Gordon et al.
Figure A4. NPV for information and no information, Case IV: (Pl, 0) = T(P2,O)(for n = 3).
Proof of Proposition 2: (see Figure A2) Necessity Assume I ( K )< 0, V 0 IK < IPV,. Then at K E < IPV,) we have: ,
= IPV,
- E , (for any positive
r(m,IPV, - E ) > r ( p 2 , IPV, - E). As T(P2, K ) is non-increasing in K , it follows that
r(P1, IPV,
- E ) >r
( ~ 2IPV,). ,
By the definition of IPV,, T(P2, IPV,) = 0. Thus
r ( P 1, IPV, - E ) > 0, for all positive follows that
E
< IPV,. Since, T(P1, IPV, - E ) = Max{r(P1 , O ) r(Pi,o)-IPv,
- IPV,
+ E, 0 ) , it
+ E>O,
for all positive E < IPV, . Therefore,
T(P1,O) r IPV,. Sufficiency Suppose T(P1,0) r IPV, . Since r ( P 1, IPV,) = max {T(P1 , O ) - IPV,, 0 ), it follows that r ( P 1, IPV,)
= r(P1,o) - IPV,,
and, hence,
r ( P 1 , IPV,)
2 0.
Capital Budgeting
35
Since T(P2, IPV,) = 0, we have
As (1) the gradient of the curve of T(P2, K ) against K 2 - 1, and - 1 is the gradient of the curve of T(P 1, K) against K, V K < T(P 1, O), and (2) IPV, IT(P 1,O) by assumption, the gradient of the curve of I(K) against K is greater or equal to 0, V K
Further, the curve of T(P1, K ) against K can be described by the equation below, in the interval under consideration: Equating the expressions for T(P1, K ) and T(P2, K), defining the point of intersection as K*, and a rearrangement of terms, gives the result (remembering the definition of I(0)). Proof of Corollary : (see Figure A4) The proof follows immediately from Proposition 3 by substituting 0 for I(0) and 1 for j into equation (IS), and then using equation (1 1).