Fin- ct 9

Journal of Banking & Finance 36 (2012) 2543–2551

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Journal of Banking & Finance

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / j b f

Intertemporal capital budgeting

Andrew H. Roper a, Martin E. Ruckes b,⇑ a Cornerstone Research, 1000 El Camino Real, Menlo Park, CA 94025, United States b Karlsruhe Institute of Technology (KIT), Kaiserstrasse 12, 76131 Karlsruhe, Germany

a r t i c l e i n f o

Article history: Received 3 February 2011 Accepted 27 May 2012 Available online 6 June 2012

JEL classification: G31 D82

Keywords: Capital budgeting Investment policy Incentives

0378-4266/$ - see front matter � 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.jbankfin.2012.05.012

⇑ Corresponding author. Tel.: +49 721 608 43427; f E-mail addresses: [email protected] (A.H. R

(M.E. Ruckes).

a b s t r a c t

This paper analyzes the optimal capital budgeting mechanism when divisional managers are privately informed about the arrival of future investment projects. Consistent with field study evidence, an optimal allocation mechanism can include a stipulation that a capital request for discretionary investment will be declined with positive probability in the period after a significant investment was made even though this is ex post suboptimal. The model derives a number of empirical predictions regarding capital budgeting and the investment of financially constrained firms.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction Informed division managers are not likely to credibly communi-

In determining the allocation of a firm’s scarce capital budget, headquarters weighs investment alternatives identified by in- formed division managers. In some cases, the best alternative is a competing project that occurs contemporaneously. However, the best alternative use of the firm’s capital is often an investment opportunity that arrives with uncertainty in the future. Therefore, even if headquarters can costlessly monitor the quality of all pro- jects proposed by division managers, division managers may still possess an information advantage with respect to the likelihood that profitable opportunities are on the horizon. Division managers may, for example, know more than headquarters about subtle changes in customer demand. Those changes do not necessarily warrant an immediate response entailing capital investment, but, if they turn out to be permanent or become more pronounced, do so in the future. Division managers are also likely to be better informed than headquarters about the probability of market entry or exit, quality or pricing adjustments of existing competitors, or new production technologies in development. Any of these changes in market structure may involve capital investment in the future. Without this information, headquarters cannot effi- ciently allocate its scarce capital today. This paper is concerned with identifying the optimal capital budgeting strategies of head- quarters in such settings.

ll rights reserved.

ax: +49 721 359 200. oper), [email protected]

cate the likelihood of future profitable investment opportunities. Even though division managers may benefit from profitable pro- jects, their investment incentives are often not perfectly aligned with those of headquarters. For example, a division manager ob- tains utility not only when the project is profitable but also derive private benefits that increase with the amount of resources under their control. This agency problem creates an incentive for a divi- sion manager to understate the probability of profitable future pro- jects in financially constrained firms: smaller future investment needs increase the capital allocated to current projects as capital conservation concerns are diminished. In such circumstances, the capital allocation mechanism serves not only the purpose of allo- cating capital efficiently but may also be designed to elicit informa- tion about the probability of new projects in the future from a privately informed division manager.

We show that in these circumstances headquarters frequently finds it optimal to grant a capital request for a discretionary project under the condition that the division accepts that positive net pres- ent value discretionary projects will be rejected in the second per- iod with some pre-announced probability. Such an intertemporal capital allocation mechanism restricts the level of overall invest- ment in the division and therefore limits the need to raise costly external capital. In addition, this policy enables headquarters to in- duce the truthful revelation of the division manager’s assessment of the division’s investment outlook.

Under such a rule, a division manager who expects a profitable project in the coming period has the incentive to pass up the cur- rent marginal discretionary project, because accepting it implies

2544 A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551

foregoing a high level of expected utility from investing next peri- od. A manager who associates a low probability to having a profit- able project next period prefers to accept the capital allocation in the current period. This truthful revelation allows headquarters to reduce the hurdle rate in the current period as the division man- ager accepts a grant when he predicts a low probability of invest- ment. The cost of such an intertemporal capital allocation mechanism is that headquarters may deny funding to second-per- iod projects that are value enhancing when judged as stand-alone projects.

We show that dynamic capital allocation mechanisms are ex- pected to be frequently found in firms facing financial constraints. Ross (1986) describes how the degree of financial constraints af- fects the type of capital budgeting mechanism employed within the firm. He finds that more financially constrained firms tend to not allocate capital according to posted hurdle rates but through a process in which projects compete for allocation from a fixed budget. If a division wants to fund projects beyond its typical allo- cation, the division uses up ‘‘credit’’ with headquarters. The latter indicates that it is impossible for a division to receive additional funds every period, but rather that there is a limit to how often an additional budget will be available. Thus, such a policy is an example of a capital allocation mechanism that makes it harder to receive capital after a period of large investment as described in this paper.

While it is not surprising that capital preservation consider- ations are more important in firms with tighter financial con- straints, our results are consistent with the empirical result that when a significant investment is observed in a division, it takes on average longer to observe another large investment when, cete- ris paribus, financial constraints are more severe (Whited, 2006). In our model, since the dynamic capital allocation mechanism re- duces the expected size of next period’s budget whenever a signif- icant investment is made in the current period, a larger fraction of overall investment in a division (or plant) is concentrated in one period. Thus, the model demonstrates how a dynamic capital allo- cation mechanism can lead to ‘‘lumpy’’ intertemporal investment flows (Doms and Dunne, 1998; Cooper et al., 1999).

When the firm’s financial constraint becomes binding because of profitable investment opportunities in other divisions, the opti- mal dynamic capital budgeting process implies that headquarters moves resources away from divisions plagued by asymmetric information and towards other divisions. Thus, it is relatively likely that after investing in a significant project in one division, the next large investment will be in a different one.

A growing literature examines capital allocation mechanisms in internal capital markets. Our paper is most closely related to the literature that analyzes capital allocation rules of headquarters subject to agency problems or asymmetric information. This liter- ature typically describes capital allocation mechanisms when divi- sional managers have a preference for capital and private information about the quality of current investment opportunities. Harris et al. (1982) and Antle and Eppen (1985) focus on transfer prices to allocate capital across divisions, Harris and Raviv (1996, 1998) and Malenko (2012) study the possibility of costly monitor- ing and Zhang (1997) and Bernardo et al. (2001) analyze situations in which managers are also expected to exert value-enhancing ef- fort. Stoughton and Zechner (2007) study capital allocation in financial firms where capital is related to risk. Different from these papers, Berkovitch and Israel (2004) assume that headquarters can costlessly observe the quality of all projects presented to it. In their model, a manager can, however, hide projects that are more prof- itable to the firm’s owners and less valuable to themselves. The authors show that in this context the net present value criterion maybe inefficient in determining capital budgets and alternative criteria are preferred. We introduce asymmetric information about

the probability of future project arrival. This renders our setting inherently dynamic and leads to a dynamic capital allocation mechanism.

Harris and Raviv (1998) also discuss a dynamic capital alloca- tion mechanism. They argue that when monitoring project quality is costly for headquarters, it may be optimal to allow divisions to ‘‘roll over’’ capital budgets to future periods. This rollover of un- used funds reduces a division manager’s incentive to invest imme- diately as the funds are certain to be available in the future. Malenko (2012) shows that with costly auditing the optimal arrangement may be to provide the manager with a discretionary spending account that he can use to finance investment projects. In our setting, headquarters will never delegate the investment decision to the division manager because headquarters is fully in- formed about project quality at the time of the investment deci- sion. In addition, our model examines the relation between the degree of financing constraints and the extent to which a dynamic capital allocation mechanism is optimal.

A strand of literature analyzes the extent to which delegation of capital budgeting decisions within the firm can lead to increased investment efficiency (see Harris and Raviv, 1998, 2005; Marino and Matsusaka, 2005; Ozbas, 2005). In our setup it is never optimal to delegate investment authority as informational problems can be addressed more efficiently by introducing dynamic capital alloca- tion mechanisms.

The remainder of the paper is organized as follows: Section 2 out- lines the model and Section 3 describes the optimal capital alloca- tion in the benchmark case of symmetric information about the probability of the arrival of a profitable future project. Section 4.1 shows how capital is optimally allocated when the division manager is better informed about the project arrival rate and headquarters lacks the power to commit to restricting its action space in the fu- ture. Section 4.2 allows for such commitment and derives predic- tions regarding the capital budgeting of firms. Section 5 describes empirical predictions for corporate investment. Section 6 concludes.

2. Model

2.1. Players

We model a firm with a headquarters and one division operat- ing over two periods. Headquarters has access to capital but pos- sesses relatively coarse information about second-period investment opportunities. The division is headed by a manager who has private information regarding the arrival rate of invest- ment projects but has no access to capital on his own. Headquar- ters would like to use the manager’s private information to allocate capital across the two periods, but the manager has pref- erences that prevent him from revealing his information truthfully unless provided with incentives to do so. Our objective is to char- acterize the capital budgeting mechanism that maximizes ex- pected profits to shareholders.

2.2. Investment opportunities

At the beginning of each of two periods, t = 0, 1, the division manager identifies an investment project. Each project requires a capital outlay of one unit and yields a positive gross cash flow at the end of the second period, t = 2. The cash flow of the first-period project is labeled b1 > 0. We also assume that the first-period pro- ject has to be initiated at t = 0 to yield b1. If delayed, its cash flow is non-positive. At t = 1 a profitable project may be available. Its cash flow is denoted by b2 and the project is available either with prob- ability 1 (which we will refer to as favorable investment outlook) or with probability p 2 (0, 1) (unfavorable investment outlook).

A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551 2545

2.3. Capital budget

Headquarters is endowed with one unit of capital and has ac- cess to an additional unit of capital at a cost c > 0, i.e., headquarters faces a ‘‘soft capital constraint’’. The additional cost may result from informational asymmetries associated with accessing exter- nal finance.1 Since we are interested in the internal allocation of cap- ital within the firm, we assume the manager can only obtain capital from headquarters.

2.4. Preferences

Both headquarters and the division manager are risk neutral. We assume headquarters maximizes the net present value of investment. Headquarters’ utility UH is defined as

UH ¼ ðb1 � 1Þ when headquarters funds first-period investment ðb2 � 1Þ when headquarters funds second-period investment ðb1 � 1Þþðb2 � 1 � cÞ when headquarters funds first- and second-period investment

8 >< >:

Whenever headquarters chooses to fund only one investment pro- ject, either first- or second-period investment but not both, the cost of investment is 1. However, when headquarters chooses to fund both first- and second-period investment projects, headquar- ters must raise additional capital at cost c. Hence, the cost of capital is path-dependent and varies across headquarters’ time horizon.

To introduce a preference for capital allocation in a simple way, the division manager is assumed to ignore the cost of investment and to obtain a private, non-contractible benefit proportional to gross project cash flow. 2 Division manager utility UM is defined as

UM ¼ qb1 when headquarters funds first-period investment qb2 when headquarters funds second-period investment qðb1 þ b2Þ when headquarters funds first- and second-period investment

8 >< >:

where q is a positive constant. Because the manager ignores the cost of investment, he prefers to submit all projects for approval to head- quarters regardless of their economic value.

2.5. Information

In order to focus on the role of financial constraints on cap- ital budgeting, we abstract from costly monitoring and assume that headquarters can observe project cash flows at no cost during the process of a capital request by the division manager. There remains, however, one informational advantage of the manager at t = 0. At t = 1 a profitable project is observed either with probability 1 or with probability p. While the manager knows perfectly whether the investment opportunity arises with probability 1 or with probability p, headquarters ex-ante assigns a probability of 0.5 to each of the two investment outlooks.

1 Alternatively, the additional cost can be interpreted as the net present value lost in reallocating capital within the firm. We discuss the implications of such an interpretation in Section 5.2.

2 This assumption is standard in the internal capital markets literature. See, for example, Stein (1997).

2.6. Sequence of actions

Fig. 1 provides a time line for the model. At the beginning of the first period, t = 0, the division manager learns the cash flow of the first period project to be received at t = 2. As monitoring by head- quarters is perfect and without cost, we assume that headquarters observes the level of project cash flows as well. Based on this infor- mation, headquarters announces a rule according to which capital is allocated. In the analysis we distinguish whether this rule can credibly govern also the capital allocation at t = 1 or not. This rule may or may not distinguish between investment outlooks. As the investment outlook is private information to the divisional man- ager, the capital allocation can only be based on the outlook re- ported by the manager. Afterwards, money is potentially transferred to the division and if so, investment takes place.

At t = 1, the division manager and headquarters learn whether a profitable project is available. The realization of the cash flow is governed by the random variable characterizing a favorable or an unfavorable investment outlook. Then, headquarters possibly allo- cates capital to the division and investment takes place.

At t = 2, the cash flows from the projects are realized. In our analysis, we impose the parametric assumption that

b2 > 1 + c. If this restriction is violated, it is never optimal to invest in both periods. Such a ‘‘hard capital constraint’’ is straightforward to ana- lyze and does not permit interesting capital allocation mechanisms.

In the model, headquarters must decide whether or not to fund proposed projects using its existing unit of capital and its ability to raise additional capital at cost c. In formulating its decision, head- quarters’ strategy space includes the determination of hurdle rates for investment projects in both periods.3 These hurdle rates may potentially be large, i.e., headquarters may decide to deny a project funding regardless of the level of its payoff.

In defining headquarters’ capital allocation mechanism, we examine mechanisms that foster separation and those that do not. Capital budgeting mechanisms that lead to separation impose certain costs on the division manager. Mechanisms that do not fos- ter separation impose no costs on the division manager, but can imply costs associated with asymmetric information on behalf of headquarters. We are interested in when headquarters finds it optimal to employ a separating mechanism at date 0 that restrict its flexibility to accept or reject funding proposals at date 1.

All proofs of formal results are in the appendix.

3 Because we assume there is no cost associated with monitoring project cash flows, headquarters capital allocation schemes will always employ monitoring with probability one. Thus, auditing constitutes a trivial part of headquarters strategy space. In Harris and Raviv (1996, 1998), auditing is costly. Hence, headquarters’ strategy space includes the monitoring probability, the amount of capital allocated with no monitoring, and the amount of capital allocated with monitoring.

Fig. 1. Timing of decisions.

2546 A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551

3. Benchmark case: symmetric information

Before analyzing headquarters’ capital allocation problem un- der asymmetric information, we consider the allocation of capital when headquarters knows as of t = 0 the investment outlook for investment in the second period as a benchmark. Headquarters faces two choices as of t = 0: reserve the unit of endowed capital and focus on the potentially higher returns whenever the sec- ond-period project is available or use the unit of endowed capital to fund b1 and raise additional capital in the event of a second-per- iod investment opportunity.

Suppose the investment outlook is favorable. In this case, head- quarters will accept the proposal for period one investment pro- vided that the following condition holds

ðb1 � 1Þþðb2 � 1 � cÞ P ðb2 � 1Þ: ð1Þ

The left hand side of Eq. (1) is the net present value of accepting the manager’s first-period proposal of b1 and accepting the second-per- iod project proposal resulting in b2. Since headquarters uses its unit of endowed capital to fund the first-period project, it must obtain additional capital at cost c to fund the second-period project. The second-period project is profitable, because of the parametric assumption b2 > 1 + c. The right hand side of Eq. (1) is the net pres- ent value from rejecting the manager’s first-period capital proposal and using the unit of endowed capital to fund the second-period project that returns b2.

By rearranging (1), we can identify the hurdle level for first-per- iod project cash flows when the investment outlook is favorable, bG, as bG = 1 + c. For all b1 2 [bG,1), headquarters provides funding for the first-period project. Similarly, when the economic outlook is unfavorable, the hurdle rate for first-period projects is bB = 1 + pc. Note that the thresholds bG and bB depend only indirectly on the level of the second-period revenue, b2, via the restriction b2 > 1 + c.

Due to headquarters’ capital conservation considerations the hurdle level is higher than the myopic level of 1 in both environ- ments. The hurdle rate for first-period projects is higher whenever the investment outlook is favorable. Knowing the investment out- look is favorable, headquarters realizes it is more likely to need capital for investment in the second period.

This implies that for b1 2 (bB, bG), the expected investment level of a firm facing a favorable investment outlook is lower than that of one with an unfavorable outlook. This is a consequence of the firm’s dynamic capital preservation motive; such a behavior would not be optimal in a static setting.4 This result implies that in the presence of capital preservation concerns firms with higher book-

4 To the contrary, in a repeated static setting without capital preservation concerns and constant investment opportunities, a high level in the current period indicates a high investment in the future.

to-market ratios due to better future investment opportunities may not display higher investment levels on average.

4. Asymmetric information about investment prospects

Consider a situation in which b1 2 (bB, bG) and headquarters ap- plies the capital budgeting rule as specified in the section above. When the manager is privately informed about the investment outlook for the second period, he will not truthfully disclose a favorable investment outlook. This follows from a comparison of the manager’s expected utility from truthful reporting, qb2, and from misrepresenting the investment outlook, q(b1 + b2). The latter is strictly larger as the manager prefers more investment to less and reporting an unfavorable outlook lowers the hurdle rate for first-period investment. Thus, in contrast to static models of capital allocation where headquarters devises mechanisms to overcome managers’ overly optimistic portrayals of current investment opportunities (for example, Harris and Raviv, 1996) and/or fight suboptimally low managerial effort (for example, Bernardo et al., 2001), in a dynamic context headquarters has to guard against managers’ understatement regarding future investment needs.

In the following, we first analyze headquarters’ optimal policy when it is unable to commit to a second-period policy as a function of first-period capital allocation. Afterwards we allow headquarters to commit to such a policy.

4.1. Capital allocation under asymmetric information without commitment

Headquarters understands the incentive to understate the investment outlook and assigns equal probability to both invest- ment outlooks, favorable and unfavorable, whenever managers are privately informed and headquarters does not provide manag- ers with sufficient incentives to truthfully disclose the state of the world. Whenever headquarters lacks the possibility to commit to an intertemporal capital allocation schedule, in the second period it will always decide to allocate capital whenever a profitable pro- ject is available, because b2 > 1 + c. Then, its only instrument to take into account the informational asymmetry is to adjust the hurdle level for b1. It is straightforward to verify that in this case for b1 2 (bB, bG) truthful reporting by both parties cannot be achieved except for the case in which the investment policy for both reported states is identical. Thus, both possible types of man- agers are effectively pooled together. As a consequence, under asymmetric information, the hurdle rate for first-period invest- ment is determined by the following condition:

ðb1 � 1Þþ 1 2 ð1 þ pÞðb2 � 1 � cÞ P

1 2 ð1 þ pÞðb2 � 1Þ: ð2Þ

A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551 2547

Eqs. (2) and (1) are similar. The only difference being, in the present case, headquarters does not know with certainty the investment outlook and assigns equal probability to both favorable and unfa- vorable outlooks.

By rearranging (1), we identify the hurdle rate for first-period investment projects when managers are privately informed, i.e., bNC ¼ 1 þ 12ð1 þ pÞc. This hurdle rate can be used to implement a capital allocation mechanism when division types are pooled. Headquarters provides funding for all first-period projects with returns b1 P b

NC. For b1 < b NC, headquarters denies funding for

first-period projects. Whenever headquarters is uninformed about the future invest-

ment outlook, the hurdle rate for first-period projects lies between the hurdle rates under symmetric information described previously. This new hurdle rate has implications for the utility of both parties and the amount of investment observed in equilibrium. For a given b1, the manager’s expected utility as well as the expected investment level may be below or above those in the first-best case.

4.2. Capital allocation under asymmetric information with commitment

The capital allocation process described in the previous section does not allow headquarters to commit to a decision rule for allo- cating capital in the second period.

In this section, we analyze whether there exists a capital alloca- tion mechanism that allows headquarters to improve the efficiency of capital allocation when managers are privately informed. In or- der to improve investment efficiency, headquarters must devise a capital allocation mechanism that leads to truthful revelation of the future investment outlook by managers despite possibly implying no first-period funding in case of a favorable outlook. Such a mechanism requires the ability for headquarters to commit to tie the second-period capital allocation to the capital allocation in the first period. Because the resulting capital allocation in the second period is optimal ex ante but not ex post, any intertemporal- ly committing mechanism is only feasible when there exists a credible commitment device or in which similar decisions occur repeatedly and a reputation can be established.5

To improve upon the capital allocation by funding a first-period project only when the investment outlook is unfavorable, head- quarters must design a mechanism which discourages misrepre- sentation of investment prospects by managers with favorable investment outlooks. In line with a significant fraction of the inter- nal capital markets literature we focus on non-monetary incentive mechanisms and abstract from financial incentive contracts.

To achieve truthful reporting, headquarters can use the follow- ing two instruments: (1) For a given level of first-period cash flow, b1, headquarters determines the probability of allowing the man- ager to invest in the first period. (2) Headquarters declines to pro- vide funding in the second period with a certain probability even if a profitable project is available. Each instrument can be applied dif- ferently for the two reported investment outlooks. Define aG 2 [0, 1] and aB 2 [0, 1] as the probabilities that headquarters funds a first-period project with given cash flow b1 when the man- ager reports a favorable and an unfavorable outlook, respectively, and dG 2 [0, 1] and dB 2 [0, 1] as the probabilities that headquarters declines funding to a profitable second-period project when the manager reports a favorable and an unfavorable investment out- look, respectively. 6

5 Other papers that assume the possibility of commitment are Harris and Raviv (1996, 1998).

6 Note that we ignore that dG and dB could possibly be made contingent on the realization of aG and aB. If this is possible the analysis is more tedious without yielding any additional insight.

Headquarters uses these acceptance and denial probabilities in order to achieve truthful revelation of the investment outlook. The maximization problem of headquarters can be written as

max aG;dG;aB;dB

1 2 ½aGðb1 � 1Þþð1 � dGÞðb2 � 1Þ� aGð1 � dGÞc�

þ 1 2 ½aBðb1 � 1Þþ pð1 � dBÞðb2 � 1Þ� paBð1 � dBÞc� ð3Þ

s:t: qðaGb1 þð1 � dGÞb2Þ P qðaB b1 þð1 � dBÞb2Þ ð4Þ qðaGb1 þ pð1 � dGÞb2Þ6 qðaB b1 þ pð1 � dBÞb2Þ ð5Þ 0 6 aG; aB 6 1 ð6Þ 0 6 dG; dB 6 1 ð7Þ

The incentive compatibility constraint in Eq. (4) ensures that man- agers with favorable investment opportunities do not misrepresent their true investment opportunities. By truthfully reporting their investment opportunity and foregoing investment today with prob- ability (1 � aG), managers with favorable investment opportunities receive funding in the second period for b2 with probability (1 � dG). The incentive compatibility constraint in Eq. (5) ensures the managers with unfavorable investment opportunities do not overstate their investment outlook.

The possible optimal capital allocation rules derived in Section 4.1 when commitment is impossible are given by ((aG, dG), (aB, dB)) = ((0, 0), (0, 0)) for b1 < b

NC and ((aG, dG), (aB, dB)) = ((1, 0), (1, 0)) for b1 P b

NC. Note that both of these rules fulfill the incentive compatibility constraint of the manager for both investment out- looks. A benefit of commitment can only be achieved when invest- ment policies are different for the different outlooks. In the remainder of this paper we refer to a policy rule that creates truth- ful reporting while establishing different investment policies for the two investment outlooks as intertemporal separation. Establishing such a rule may provide a benefit to headquarters only for the parameter range in which the first best policy includes differential investment, b1 2 (bB, bG). Thus we restrict our analysis to that set of parameters.

The resulting equilibrium is characterized in the following proposition.

Proposition 1. For b2 > pð2þð1þpÞcÞð1þcÞ

pð2þð1þpÞcÞ�ð1�pÞc � b̂2, headquarters’ alloca- tion policy when commitment is possible is identical to the policy when commitment is impossible.

For b2 6 b̂2, headquarters’ allocation policy when commitment is possible is

ððaG;dGÞ;ðaB;dBÞÞ¼

ðð0;0Þ;ð0;0ÞÞ for b1 2 1þpc; 1þpc 1�p 1�1þc

b2

� � 0 @

1 A

ð0;0Þ; 1;b1b2 � �� �

for b1 2 1þpc 1�p 1�1þc

b2

� �; 1þc 1þp 1�1þc

b2

� � 2 4

3 5

ðð1;0Þ;ð1;0ÞÞ for b1 2 1þc 1þp 1�1þc

b2

� �;1þc 0 @

1 A

8 >>>>>>>>>>>>>>< >>>>>>>>>>>>>>:

If b2 6 b̂2 , intertemporal separation may be optimal. It is achieved by declining to fund a second-period project with probability b1/b2 in case of an unfavorable investment outlook. Doing so allows headquarters to decline first-period funding if the investment out- look is favorable by maintaining the manager’s incentive to report truthfully. Thus, the model is able to rationalize a capital budgeting process where upon a significant capital allocation to a division headquarters will unlikely provide a large capital allocation in the period thereafter. This is consistent with Ross (1986) who provides

Fig. 2. The figure depicts headquarters’ optimal policy choices under symmetric

information, aSG; d S G

� � and aSB; d

S B

� � , and under asymmetric information with

commitment and intertemporal separation, a�G; d � G

� � and a�B; d

� B

� � . The figure also

shows the indifference curves relevant to the division manager with favorable (solid line) and unfavorable investment prospects (dashed line), respectively, under headquarters’ policy of intertemporal separation; arrows indicate the direction of higher managerial utility. Parameters used: p = 0.5, c = 0.2, b1 = 1.125, b2 = 1.25.

2548 A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551

field study evidence that firms with financial constraints do not set hurdle rates for project approval but rather provide limited budgets to divisions. These budgets are only initially fixed: ‘‘If division man- agement wanted to, they could increase capital allocation by mak- ing a good case for it. But this would require a major effort and would use up some of the division’s ‘‘credit’’ with corporate head- quarters (Ross, 1986)’’. The latter statement indicates that albeit increasing current capital allocation is possible, it comes with a cost to the division. As credit with headquarters is not unlimited, a cur- rent increase in the division’s capital budget makes it harder to ob- tain capital in the future. This dynamic component of the capital budgeting process may well serve as the instrument to distinguish between those divisions that have a high likelihood of profitable fu- ture projects and those that do not.

It is never optimal to complement declining second-period funding in case of an unfavorable outlook by accepting a first-per- iod project with positive probability if the investment outlook is favorable. In order to avoid underreporting of investment pros- pects, headquarters restricts access to second-period capital for a manager with an unfavorable outlook rather than allowing a man- ager with a favorable outlook to invest some of the time. The rea- son is that whereas a change in dB affects the incentive constraint of both manager types differentially, this is not the case for a change in aG (see constraints (4) and (5)). This implies that a policy of intertemporal separation leads to underinvestment relative to the level under symmetric information.

Fig. 2 illustrates headquarters’ considerations by depicting first- period project acceptance probabilities and second-period project rejection probabilities for the two types of divisional managers.

Points aSG; d S G

� � and aSB; d

S B

� � characterize headquarters’ optimal

policies under symmetric information for a division with favorable and with unfavorable investment prospects, respectively. As divi- sion manager types’ indifference curves show, this policy cannot be implemented under asymmetric information, because both

types receive a higher utility at aSB; d S B

� � . With a slope of b2/b1,

the indifference curve of the manager with a favorable investment outlook is the steeper of the indifference curves. Thus, that man- ager’s incentive compatibility constraint (4) is the binding one in an equilibrium allocation with intertemporal separation. For the parameter values of b1 satisfying the restrictions in the middle seg- ment of the equation in the proposition, the firm’s maximum ex- pected profit is reached by maintaining the optimal policy for the

manager with favorable prospects, a�G; d � G

� � ¼ aSG; d

S G

� � , and adjust-

ing the policy for the manager with unfavorable prospects, a�B; d

� B

� � , such that (4) is satisfied with equality. If b1 exceeds

ð1 þ cÞ= 1 þ p 1 � 1þcb2 � �� �

, the firm’s expected profit increases as

the policy combination moves along the indifference curve of the manager with favorable prospects towards the left upper corner. Because expected profits vary linearly with changes in the policy combination, headquarters’ optimal policy is to offer an identical policy for both manager types investing with probability one in the first period and in the second period whenever a project is available, ((aG, dG), (aB, dB)) = ((1, 0), (1, 0)). If b1 is small,

b1 < ð1 þ pcÞ=1 � p 1 � 1þcb2 � �

, the inefficiency generated by imple-

menting a policy with a significant probability of declining a sec- ond-period project for the manager with an unfavorable investment outlook, a�B; d

� B

� � , is too large such that headquarters de-

clines to invest in the first period and accepts second-period pro- ject proposals of both manager types ((aG, dG), (aB, dB)) = ((1, 0), (1, 0)).

If b2 exceeds the threshold b̂2 , intertemporal separation is not desirable from headquarters’ point of view as the alternative allocation policies are more profitable. This implies that headquar- ters does not apply a ‘‘policy of dynamic rationing’’ in divisions or units whose (unplanned) investment opportunities are typically large in profitability. One example for this are the production units of firms, in which unscheduled investment opportunities typically arise if machines break down and it is very costly for the firm to not replace the machine. Then, even if unit management is pri- vately informed about the probability of machine breakdowns, headquarters refrains from eliciting unit management’s informa- tion by creating intertemporal separation. In contrast, headquar- ters tends to apply a policy of dynamic rationing in divisions with predominantly discretionary investment opportunities. The result that b2 cannot be too large for a policy of dynamic rationing to be optimal implies also that such policies tend to be applied in firms of at least a certain degree of maturity rather than in young firms with strong growth, where investment opportunities are highly profitable.

5. Implications for corporate investment

Besides providing predictions regarding the use of intertempo- ral budgeting processes, the model has a number of implications for the investment of financially constrained firms.

5.1. Investment and financial constraints

Relative to exclusively setting hurdle rates, intertemporal sepa- ration tends to concentrate investment in one of the two periods as it reduces the probability of investment in the period after a

7 If, however, an investment of moderate profitability provides negative informa- tion to the market about the quality of future investments, headquarters may ration capital in case of poor prospects. Then, first-period investment may indicate an increased probability of second-period investment.

A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551 2549

substantial capital allocation. Empirical studies document that at the plant level a large percentage of investments occurs in very few years. For example, Doms and Dunne (1998) report that from 25% to 40% of an average plant’s cumulative investment over 17 years is concentrated in a single year. Our results suggest that internal capital allocation procedures may affect the level of the ‘‘lumpiness’’ of investment as such rules tie the probability of fu- ture investment to the current capital allocation. Macroeconomic models generate this lumpiness of investment by assuming a linear or convex cost of adjusting the capital stock (see, for example, Coo- per et al., 1999). This model suggests that capital budgeting pro- cesses that combat problems of asymmetric information may contribute to the existence of adjustment costs.

Using an intertemporal capital budgeting process is more attractive for firms facing more severe capital constraints. This af- fects investment as described in the following result:

Corollary 1. Consider two levels of severity of financial constraints, 0 6 c� < c+ 6 b2 � 1.

For a given set of remaining parameters, suppose an investment takes place in the first period for both c� and c+. Then, the probability of an investment in the second period for c� is larger or equal to that for c+, with a strict inequality for a non-empty set of remaining parameters.

The corollary states that more severe financial restrictions tend to reduce the probability of a second-period investment if a significant first-period investment takes place. This result implies that on average an increase in the severity of financial constraints increases the expected time between significant investments. Whited (2006) empirically distinguishes between firms with more and less severe financial restrictions by examining whether a business has recently paid dividends, is smaller or operates on a stand-alone basis (rather than being a division of a conglomerate). She indeed documents that firms with more severe financial con- straints display larger time intervals between large investments. Note that in our setting the result follows purely from an optimal decision by headquarters to switch to a capital allocation process with dynamic rejection. In other words, this result does not hold under symmetric information or under asymmetric information without commitment.

The choice of capital budgeting process influences the expected relative investment volumes for the two different investment outlooks.

Corollary 2. When headquarters chooses to not implement a policy of intertemporal separation, the expected investment volume is higher for the favorable investment outlook than for the unfavorable outlook. The opposite holds when an intertemporal separation policy is implemented.

This result implies that among firms that do not apply budget- ing policies of dynamic rationing, such as firms with strong growth, the empirical relationships between the quality of invest- ment opportunities and the actual investment levels is stronger than among firms that tend to use intertemporal separation pol- icies, such as somewhat mature firms. If for such firms markets form opinions about investment prospects from current invest- ment, a significant investment in a moderately profitable project indicates a low arrival rate of a more profitable project in the fu- ture. Headquarters of a firm with a high probability of a more profitable investment opportunity finds it optimal to not invest. Thus, an investment may negatively affect valuation. This bears some resemblance to Carlson et al. (2004) who show that an investment as a result of exercising a timing option tends to pro- vide negative information about firm value and where a firm’s refraining from making an investment tends to be perceived pos- itively. The implication is typically different, however, from a set-

ting without capital preservation concerns. Then, the firm invests in each profitable project available. If, as in our model, having a moderately profitable investment is uninformative about future opportunities, the investment in such a project itself is not a neg- ative signal.7

5.2. Implications for investment in multi-division firms

Alternatively to representing the cost of raising a unit of exter- nal funds, the cost of capital of a second unit of investment, c, can be understood as the profitability of an investment opportunity in the second period of a second division with an investment amount of one and a return of 1 + c. The firm is assumed to have two units of capital and no access to external finance. Thus, the second divi- sion’s project will have to be passed up if the first division imple- ments two projects.

Implicit in the present formulation is that c is common knowl- edge and the second division is not affected by a problem of asym- metric information as the first division is. This model structure is obviously quite specific, but it allows us to capture in a simple way that divisions are associated with different degrees of prob- lems of asymmetric information. The first division is one where headquarters faces its share of surprises and where division man- agement that receives information relatively early on enjoys a material information advantage. In the second division investment opportunities can be predicted accurately. Thus, it may be a divi- sion that operates in a mature industry.

Consider first the investment amounts of the two divisions under symmetric information. In case of a favorable investment outlook no investment is made in the first period and each division invests one unit in the second period. If the investment outlook is unfavorable, the first division invests one unit in the first period and one unit in the second with probability p, i.e. if a project is available. The second division invests one unit in the second period with the complementary probability (1 � p).

Under asymmetric information and a policy of intertemporal separation, investment is identical to that under symmetric infor- mation if the investment outlook is positive. If investment pros- pects are unfavorable, the first division still invests one unit in the first period, but one unit in the second period only with prob-

ability 1 � b1b2 � �

p < p. Again, the second division’s second-period

investment is one unit with the complementary probability

1 � 1 � b1b2 � �

p > ð1 � pÞ. The following corollary summarizes this investment behavior:

Corollary 3. Suppose parameters are such that headquarters imple- ments a policy of intertemporal separation in the first division. If the first division invests in the first period, the firm is more likely to invest in the second division in the second period than under symmetric information.

This implies investment distortions in financially constrained multi-division firms take the form that after a significant capital investment in one division, the firms tends to invest available cap- ital in a different division next (relative to its allocation under sym- metric information). Doing so keeps a division from requesting in the present capital when it is likely that it can be used even more effectively in the future.

2550 A.H. Roper, M.E. Ruckes / Journal of Banking & Finance 36 (2012) 2543–2551

6. Concluding remarks

This paper demonstrates that, consistent with field study evidence, firms facing capital restrictions can find it optimal to stipulate that after a division accepts a significant capital alloca- tion it will likely have to wait some time until it receives another significant allocation (a policy of dynamic rationing). This result is based on the notion that in the agency relationship between headquarters and divisional managers headquarters has to guard against the understatement of tomorrow’s investment prospects. The described policy leads the division manager to disclose his information about the extent of future investment opportunities.

The budgeting policy of dynamic rationing is consistent with empirical evidence that investment at the plant level is concen- trated in few periods, that firms facing ceteris paribus more severe financial constraints display more periods of idleness after signifi- cant investments and that firms bias investment towards divisions with weaker investment opportunities.

The paper’s results are derived under the assumption that the divisional manager’s compensation cannot be made contingent on the manager’s report regarding the division’s investment out- look. Allowing compensation to depend on this report would pro- vide headquarters with an additional instrument to elicit truthful reporting. Even though the manager’s limited liability may render contingent compensation relatively costly in certain circum- stances, an optimally chosen compensation contract is likely to diminish investment distortions.

Implementing a policy of dynamic rationing may provide bene- fits to the firm beyond those captured in the model. While inter- temporal separation requires that the divisional manager know his type, this is not the case under the alternative policies. Thus, a policy of dynamic rationing incentives for managers to identify their investment outlook. In the case of a positive investment out- look this leads to a perfect forecast of second-period investment. One advantage of this may be that communication with capital markets becomes more effective and may provide long-term ben- efits for the firm.

In this paper we consider the existence of a second division only in a specific way. A generalization of the setting would potentially prove economically interesting. For example, the existence of mul- tiple divisions may affect the possibility for headquarters to com- mit to a policy of dynamic rationing. With multiple divisions, several budgets have to be allocated in each period, which may in- crease headquarters’ possibility to acquire a reputation for inter- temporal separation. However, with multiple divisions, the budgeting process becomes more complex and transparency may be reduced for divisional managers. This would make it harder for headquarters to commit to applying a policy of dynamic ration- ing. As there is uncertainty about the other divisions’ investment outlooks, the existence of multiple divisions also creates a timing incentive for divisional managers. This may lead to a coordination problem. For example, there may be a tendency to compete for a positive capital budget early when the other divisions are assumed to do so as well. A policy of dynamic rationing may provide an effective way to mitigate this problem and improve the investment policy of a firm.

Acknowledgements

We are grateful to Andrey Malenko, Antonio Mello, Min Shi, Masako Ueda, Toni Whited and participants of the Minnesota- Wisconsin Finance Conference for helpful comments. We thank Margarita Sevostiyanova for excellent research assistance.

Appendix A. Proof of Proposition 1

Proof. All functions of the optimization problem are continuously differentiable. Thus, the problem describes a closed set and a maximum exists. The Hessian of the objective function is positive definite, which implies that the maximum is on the boundary of the problem’s domain.

Inequality (4) can be written as aG � aB P b2b1 ðdG � dBÞ and inequality (5) as aG � aB 6 p b2b1 ðdG � dBÞ. As p 2 (0, 1), this implies

dG � dB 6 0 and aG � aB 2 b2b1 ðdG � dBÞ; p b2 b1 ðdG � dBÞ

h i . Invoking

these restrictions, the boundaries of the problem’s domain can now be analyzed and the result described in the proposition obtains. h

Appendix B. Proof of Corollary 1

Proof. A first-period investment may occur for b1 2

1þpc

1�p 1�1þc b2

� � ; 1 þ c 2 4

1 A. Suppose a first-period investment does indeed

take place. In the parameter range where no intertemporal

separation is induced, b1 2 1þc 1þp 1�1þc

b2

� � ; 1 þ c 0 @

1 A, the probability of

second-period investment after a first period investment is 1 2ð1 þ pÞ. In the parameter range where an intertemporal process

is employed, b1 2 1þpc 1�p 1�1þc

b2

� � ; 1þc 1þp 1�1þc

b2

� � 2 4

3 5, this probability is

1 � b1b2 � �

p, which is strictly smaller than 12ð1 þ pÞ. The condition for the separation of the regimes reveals that an increase in c may mean that headquarters moves from the former to the latter but

not the other way around, d 1þc 1þp 1�1þc

b2

� �=dc ¼ b22 1þpðb2ð1þpÞ�pð1þcÞÞ2 > 0

which establishes the result. h

Appendix C. Proof of Corollary 2

Proof. In case of no intertemporal separation, headquarters does not discriminate between investment outlooks in the first period and grants an investment budget whenever a profitable project is available in the second period. Because a favorable investment outlook is characterized by a higher probability of a second-period project, investment is more likely in this state. In case of intertemporal separation, a favorable investment outlook results in an expected level of investment of 1 and an unfavorable outlook in an expected investment of 1 þ 1 � b1b2

� � > 1. h

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