# Financing multiple investment projects.

This paper investigates how a multiproject firm's choice of
organization structure affects its value. We develop a framework in
which agency and corporate tax considerations simultaneously influence
investment incentives, then evaluate how an entrepreneur would optimally
organize the operation of two positive-NPV, risky investment projects
which share no scope economies. In order to finance these projects at
their optimal levels, the entrepreneur must sell "outside"
debt or equity claims. The entrepreneur must also choose between two
alternative forms of corporate organization: separate incorporation(1)
or the joint incorporation of both projects within a single firm. Under
separate incorporation (SI), each project is operated by a distinct
firm, whose shareholders and bondholders have claims only on one
project's cash flows. In addition, each firm pays corporate taxes
according to the returns on its own investment project. By contrast,
when both projects are jointly incorporated (JI) into a single firm,
security holders receive payoffs from the sum of the projects' cash
flows, and corporate taxes are based on the sum of the projects'
profits.

In choosing the type of outside claim to issue, debt has obvious tax advantages because its interest payments are made from pre-tax corporate earnings. However, when the entrepreneur's investment decisions are not contractible, debt also imposes agency costs in the form of underinvestment (Myers |21~) and/or asset substitution (Jensen and Meckling |14~, Galai and Masulis |6~, Green |9~) incentives. In efficient security markets, outside claimants will rationally price these deadweight costs, which therefore fall entirely on the firm's organizers. A prominent view of corporate capital structure is that the firm balances the agency costs of debt against its tax advantages.

This paper's principal intended contribution is to demonstrate that the agency costs of debt financing are also importantly influenced by the firm's method of incorporation. Consequently, the firm must simultaneously select a capital structure and organizational form on the basis of agency cost and tax considerations. By combining the projects into a single entity, the firm reaps coinsurance benefits: less risky cash flows mitigate the underinvestment problem. At the same time, joint incorporation creates an asset substitution problem which does not exist when projects are incorporated separately. The potential asset substitution tends to make the debt riskier and exacerbate the underinvestment problem, ceteris paribus. Another benefit of separate project incorporation is that, when project risks differ, each firm can adjust its leverage to trade off the underinvestment costs of debt against its tax benefits more precisely than when both projects are merged into a single firm.(2) Finally, Green and Talmor |10~, |11~ demonstrate that the asymmetric nature of corporate taxes also influences a firm's investment choice. Because corporate tax payments are analogous to a call option on the firm's earnings, firm owners will sometimes choose less risky investments than they would under symmetric taxation.

Our model simultaneously considers these tax effects with the effect of organizational form on the agency costs of debt, in order to determine the optimal corporate form and the optimal capital structure for a given set of investment projects. For a given set of tax and production parameters, we evaluate the maximum attainable value of equity under separate incorporation, and then compare it to the maximum attainable value under joint operation of the two projects. Our computations take full account of underinvestment, asset substitution, and taxes, and primarily investigate the impact of variations in the two projects' relative variances and the correlation between their returns.

Our analysis has several straightforward applications concerning the corporate organization of multifaceted firms. First, our results suggest how a diversified holding company should structure its public debt. For example, our model explains why manufacturers' financing subsidiaries frequently issue their own debt, rather than having the parent obtain the required financing. Second, we can evaluate the effects of mergers on the agency costs of risky debt in order to determine the types of projects that are best combined and those that are best financed separately. This enables us to interpret not only the factors influencing a firm's initial choice of organizational structure, but why a firm may choose to change its organizational structure over time through mergers or spin-offs. In other words, our analysis carries implications about the financial "life cycle" of a conglomerate firm.

The paper proceeds as follows. Section I reviews the existing literature on the financial aspects of corporate organization. Section II describes our model of the optimal means of financing risky investment opportunities under separate versus joint incorporation of two separable projects. Because of the maximization problem's complexity, we employ numerical techniques to solve it. Section III reports our numerical results, which illustrate the factors that make merged operation more valuable than separate incorporation (or vice versa). The final section summarizes and briefly discusses the implications of our analysis for financial corporate structure.

I. Prior Literature

The diversification value of mergers has been discussed frequently in the economics and finance literature. Much of the early work in this area sought to explain conglomerate mergers. For example, Lewellen |20~ argued that combining imperfectly correlated firms could increase the merged entity's debt capacity, and hence its market value.(3)

These early papers do not consider the debt-related effects of underinvestment and asset substitution on firm investment policies. Yet combining two projects into a single conglomerate with centralized borrowing generates a complex set of influences on firm investment incentives. Myers |21~ offers a "preliminary analysis" of the impact of diversification on one of these agency costs -- underinvestment -- and predicts |21, p. 167~ that "there should be no consistent relationship between 'diversification' and 'debt capacity'." John |15~ and John and John |16~ explicitly evaluate the optimal way to organize a multiproject firm. John |15~ examines the effect of corporate structure on a levered firm's investment incentives. Following Myers |21~, she shows that a levered firm with a single investment option might forego a positive-NPV project because its implementation would transfer too much value to the firm's debtholders. Combining two (perfectly correlated) investment options into a conglomerate firm, however, can improve the firm's investment decisions, and hence enhance the combined firms' market value. John and John |16~ evaluate a similar model in the presence of corporate taxes. Their firm chooses its optimal leverage by trading off the tax benefits of debt against its agency (underinvestment) costs. Once again, this model treats two available investment options, whose returns are perfectly positively correlated. The projects can be owned by two separate firms or by a conglomerate. The authors conclude that SI is always optimal, because it permits each project to be operated with a different debt-equity ratio, which provides shareholders a more efficient set of ex post investment incentives. Whether the unambiguous results from these two papers would continue to hold under a less extreme assumption about project return correlation constitutes an important focus of our present paper.

Kahn's |17~ analysis of a multiproject firm's corporate structure problem yields an insight very similar to ours: that corporate structure affects firm value by influencing owners' (noncontractible) investment incentives. However, his analytical framework cannot fully evaluate the effects of project return correlation, and (perhaps more importantly) omits any treatment of corporate taxes. Yet the corporate tax code's asymmetric treatment of profits and losses will also influence a firm's optimal leverage and investment incentives. Green and Talmor |10~, |11~ describe situations in which the tax structure may either aggravate or mitigate asset substitution and underinvestment incentives. Their analysis fully incorporates tax and agency considerations, and while their model has important implications for determining organizational structure, they do not formally address the impact of organizational structure on investment incentives.

Numerous other papers address related finance issues.(4) Shah and Thakor |23~ derive the conditions under which a special form of "project financing" constitutes the best way for a firm to add an additional project to its existing portfolio. Campbell and Kracaw |4~ describe conditions under which a firm may choose to hedge away its observable risk in order to reduce its ex post incentive to asset substitute. Unfortunately, their model permits unambiguous analytical conclusions about the firm's optimal risk exposure only when the observable and unobservable risks are perfectly positively correlated.(5) Gavish and Kalay |7~ report that the shareholders' incentive to substitute riskier assets for safe assets does not increase monotonically with firm leverage. Finally, Chemmanur and John |5~ examine optimal firm organization in the context of corporate control rights. Their entrepreneur initially controls two projects, from which he derives important control rights (perquisites). The entrepreneur chooses between SI and JI in order to strategically allocate his own equity investment across the two projects, in an effort to protect his control rights from outside takeover threats.

To summarize, a number of papers have recognized that agency or tax considerations are important determinants of a firm's investment policy. With the notable exception of the work by Green and Talmor |10~, few of these papers have integrated tax and agency effects in a single model. At the same time, a more recent literature recognizes that the firm's choice of organizational structure may also affect its investment incentives. Most of these papers, however, have employed restrictive assumptions about the investment projects' stochastic returns in order to determine the firm's optimal organizational form. Our analysis considers a more general framework, in which taxes and agency costs simultaneously determine capital and organizational structures. In our model, JI provides tax benefits as well as coinsurance benefits which reduce underinvestment. The cost of JI is that it reduces capital structure flexibility and creates an asset substitution problem.

II. A Model of Debt, Taxes, and Investment Incentives

Consider an entrepreneur with access to two nontransferable projects which may be implemented at a variety of alternative scale levels. Both projects offer positive NPV, but their cash flow distributions may differ. Financial contracts may be written on the final cash flows, which are freely observable to outside claimants. The entrepreneur seeks to maximize the initial market value of firm equity, which (under rational pricing of the outside securities) is equivalent to maximizing the magnitude of the economic rents resulting from his access to the investment projects. Corporate taxation encourages the issue of debt to fund investment needs, but debt also entails potentially severe agency costs since bondholders cannot force the firm to implement a particular investment strategy after the debt has been sold. Investors must therefore conjecture about the entrepreneur's subsequent investment choices, which will be characterized by incentives to underinvest and (with JI) to favor the riskier asset over the safer one.

Each project lasts for a single period, and provides an end-of-period cash flow |Mathematical Expression Omitted~ characterized by decreasing stochastic returns to scale:

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~ = a random variable describing the stochastic returns to investment in project i;

|I.sub.i~ = the number of dollars invested in project i (|I.sub.i~ |is greater than~ 0); and

||Alpha~.sub.i~ = project i's returns to scale parameter (0 |is less than~ ||Alpha.sub.i~ |is less than~ 1).

The model's other assumptions are as follows:

A1. The entrepreneur cannot sell or defer the investment projects.

A2. The entrepreneur's objective is to maximize the rents attainable from his access to two investment projects. In order to finance part of his investment, the entrepreneur may issue "outside" bonds (whose interest is tax-deductible) or "outside" equity.(6)

A3. There are no bankruptcy costs. Realized cash flows (|C.sub.i~) are freely observed by all firm claimants.

A4. The entrepreneur and all investors are risk-neutral.

A5. The riskless market interest rate is zero.

A6. The two projects share no scope economies of any kind.

A7. The random variables |Mathematical Expression Omitted~ have marginal cumulative density functions |Mathematical Expression Omitted~, and joint density |Mathematical Expression Omitted~. Also,

||Mu~.sub.i~ = the mean value of |Mathematical Expression Omitted~.

||Sigma~.sub.i~ = the standard deviation of |Mathematical Expression Omitted~.

A8. Bondholders cannot perfectly observe the entrepreneur's actual investment behavior, so they cannot force the entrepreneur to pursue any preannounced investment plan.

A9. In pricing the firm's debt, bondholders rationally anticipate the entrepreneur's ex post investment incentives.

A10. The corporate tax rate is |T.sub.c~. Taxes are paid on all income net of interest payments and depreciation, i.e., on the amount |Mathematical Expression Omitted~, where

|B.sub.i~ = the (endogenously chosen) volume of bonds issued by firm i;

|r.sub.i~ = is the market's (rational) required interest rate on these bonds; and

|Lambda~ = the tax code's depreciation allowance.

Under these assumptions, the entrepreneur may organize his debt issues in either of the following ways:

(i) Two separate firms, each of which sells debt secured only by its own project's cash flows, or

(ii) One (conglomerate) firm which borrows from the capital market and allocates investable resources between the two investment projects in an unobservable manner.

Assumption A8 means that bondholders cannot write effective covenants to constrain the entrepreneur's ex post investment behavior. Indeed, the entrepreneur will confront incentives to underinvest and/or to substitute more of the riskier project after his debt has been issued. The deadweight costs of these investment distortions accrue to the entrepreneur when outside claims are rationally priced, giving him the incentive to minimize these debt agency costs. Corporate organizational form can importantly influence the amount of these agency costs. When projects are organized into separate firms, the entrepreneur can credibly convince bondholders that their funds will be invested only in a single project.(7) By contrast, with JI the entrepreneur will sell debt on less advantageous terms because investors will be concerned about his ability to substitute more of the risky project for the safer one. The entrepreneur will choose between SI and JI as part of his effort to maximize his personal wealth (A2).

We analyze our model of debt finance and risky investment in three stages. First, we evaluate optimal investment policy in the absence of moral hazard and distortionary taxes. This provides a benchmark for the effects of agency costs and asymmetric taxes. We then compare the projects' maximized value under each organizational form, for various values of the projects' joint return parameters.

A. Optimal Investment in the Absence of Moral Hazard and Taxes(8)

In the absence of taxes and moral hazard, investment is determined where the marginal expected return in each project equals the marginal cost of investment. Under risk-neutrality, the optimal value of |I.sub.i~ maximizes

|Mathematical Expression Omitted~

Differentiating Equation (2) with respect to |I.sub.i~ yields an expression for the optimal scale of project i:

|Mathematical Expression Omitted~

A project with greater mean return (||Mu~.sub.i~) and smaller stochastic scale diseconomies (larger ||Alpha~.sub.i~) will be more extensively implemented. Naturally, the project's variance does not influence |I*.sub.i~ in a risk-neutral capital market.

An all-equity firm would optimally choose |I.sub.i~ to maximize Equation (2) for each available project. However, the tax advantage of debt generally leads the entrepreneur to include some debt in his capital structure. The debt creates agency costs (in the form of suboptimal investment incentives), which must be traded off against its tax benefits to determine an optimal capital structure. Because the corporate form influences the extent of these agency costs in a multiproject firm, the entrepreneur must simultaneously determine an optimal capital structure and corporate organizational form.

B. Projects' Market Values Under SI

Consider first the maximized value of a firm operating only one project. The equityholders receive the project cash flows net of corporate tax obligations and promised debt payments. As shown by Green and Talmor |10~, the effect of asymmetric taxes on investments and firm value will depend on whether or not the tax shields exceed the promised payments to the bondholder. For our case -- with a single-period investment -- the payoff to equity is shown in Exhibit 1. If project cash flows fall below C1 (= B|1+r~), the firm earns less than the promised payment on outstanding bonds. In this region, bankruptcy occurs and equity receives no payment. The firm's tax deductions amount to C2 (=rB + |Lambda~I). For realized cash flows between C1 and C2, shareholders receive 100% of the project's additional cash flows, while to the right of C2 the firm's owners share additional cash flows with the tax collector. We assume that the payoffs in our model are consistent with the case depicted in Exhibit 1, which then requires that(9)

|B.sub.i~(1 + |r.sub.i~) |is less than~ |r.sub.i~|B.sub.i~ + |Lambda~|I.sub.i~

or

|B.sub.i~ |is less than~ |Lambda~|I.sub.i~. (4)

Under these conditions, the after-tax payoff to equity becomes

|Mathematical Expression Omitted~

Equity receives the project's total cash flows |Mathematical Expression Omitted~, less payments to bondholders and to the government. Since the firm pays taxes only when cash flows exceed the tax shields, the (asymmetric) tax liability in Equation (5) is analogous to a call option on the firm's profits (Green and Talmor |10~).

For a given financing package (|B.sub.i~, |r.sub.i~), the entrepreneur chooses his preferred investment level by solving

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

is the realization of ||Theta~.sub.i~ below which the firm defaults to its bondholders. This corresponds to C1 in Exhibit 1. Similarly,

|Mathematical Expression Omitted~

is the realization of ||Theta~.sub.i~ below which the firm pays no taxes. This corresponds to the point C2 in Exhibit 1.

Differentiating Equation (6) with respect to |I.sub.i~ yields the first-order condition (FOC)

|Mathematical Expression Omitted~

The left-hand side of Equation (9) represents the net marginal benefit to equity (after taxes and depreciation) of an additional dollar invested; the right-hand side measures the marginal cost of additional investment. The underinvestment effects of risky debt can be illustrated most readily for the case of zero corporate taxes. When |T.sub.c~ = 0, Equation (9) indicates that shareholders only consider the marginal benefit of additional investment to themselves, ignoring cash flows that occur in the "bankruptcy states." As a consequence, the levered firm will forego some valuable investment -- the familiar underinvestment problem.(10) With a nonzero corporate tax rate, the firm would also take into account its tax obligation and depreciation when determining its preferred investment level. All else equal, higher corporate tax rates discourage investment, while a more generous depreciation allowance encourages investment.

The implicit solution to Equation (9) is a function |I.sub.i~(|B.sub.i~, |r.sub.i~) that represents the owners' incentive-compatible investment policy. In a competitive capital market, investors will only purchase bonds which are fairly priced, given this ex post investment policy. The rational pricing constraint for debt is(11)

|Mathematical Expression Omitted~

The optimal investment level (|I.sub.i~) and financing package (|B.sub.i~, |r.sub.i~) for an SI firm must satisfy both the incentive compatibility condition (9) and the rational pricing condition (10). The problem's complexity makes analytical solutions impractical. Accordingly, we undertake our further analysis in terms of numerical computations, computing the maximum firm market value for various combinations of problem parameters.

Some properties of the maximized SI firm are illustrated in Exhibits 2 and 4. Exhibit 2 demonstrates that project variance prominently influences the amount of "outside" debt which the entrepreneur chooses to sell. Higher-variance projects make outstanding debt riskier (ceteris paribus), which exacerbates the incentive to underinvest. Accordingly, an increase in project variance reduces the optimal level of outside debt issued. The effect of this decision on the optimized project's value is shown in Exhibit 3: as project variance rises, the lower use of tax-advantaged debt financing results in a lower project value.

C. Projects' Market Value Under JI

Instead of operating two separately financed firms, the entrepreneur can form a conglomerate, whose bondholders are paid from the two projects' combined cash flows. The conglomerate firm's maximization problem closely resembles that for the single-project firm. The conglomerate's owner will jointly select his most preferred scale for each project, taking full account of the tax structure and the (rational) terms on which external bond and equity investors will provide financing. In particular, the entrepreneur now maximizes

|Mathematical Expression Omitted~

Assuming that B |is less than~ |Lambda~(|I.sub.1~ + |I.sub.2~) (that is, that the firm's depreciation allowance exceeds its bond repayment obligations, as we also assumed for the SI case above), Equation (11) can be simplified to

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

In Equation (12), the first integral represents the expected cash flow to equity before taxes. The second integral represents the firm's expected tax liability. Maximizing Equation (12) with respect to |I.sub.1~ and |I.sub.2~ for an arbitrary financing plan (B, r) yields two first-order conditions:

|Mathematical Expression Omitted~

which are similar to Equation (9) above. Note that the optimal investment level from Equation (15) depends on the assumed financing plan (B and r).

Consider the special case where the two technologies have the same scale parameter, i.e., ||Alpha~.sub.1~ = ||Alpha~.sub.2~, and the distribution of ||Theta~.sub.2~ is a mean preserving spread of ||Theta~.sub.1~ (with ||Sigma~.sub.2~ |is greater than~ ||Sigma~.sub.1~). We can rearrange the first-order conditions to get

|Mathematical Expression Omitted~

The right-hand side of Equation (16) indicates the extent to which investment incentives are influenced by the default and tax options. In both the numerator and the denominator, the first term represents the extent to which the existence of risky debt distorts investments. The second term captures the additional effect of asymmetric taxes. Consider the case when the tax rate (|T.sub.c~) is zero. The right-hand side then always exceeds one, since the first term in the numerator is greater than the corresponding first term in the denominator. This implies that |I.sub.1~ |is less than~ |I.sub.2~, which is the standard asset substitution problem examined in the literature. With positive tax rates, however, the additional term creates an offsetting effect. The second term in the numerator is larger in absolute value than the corresponding second term in the denominator. Consequently, at "sufficiently high" tax rates, the right-hand side of Equation (16) could actually become less than one, implying that |I.sub.1~ |is greater than~ |I.sub.2~. Thus, taxes may actually encourage the firm to invest in the less risky project. This incentive effect of the tax code has been analyzed carefully by Green and Talmor |10~.

The rational pricing constraint for bonds is now

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~ is the complement of ||Theta~.sub.d~. The firm's optimal investment and financing decisions emerge by maximizing Equation (12) through the choice of the amount of debt (B) raised ex ante, where Equations (17) and (15), respectively, determine the required coupon rate (r) and the incentive compatible investment policy. The primary addition to this maximization problem from the SI case (6) is that the firm can now choose the riskiness of its investment portfolio in addition to its investment levels.

Exhibit 4 illustrates the effect of project return correlation on the optimal investment allocation under SI and JI. For the sake of concreteness, we consider the case where |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~. From Equation (16), a risk-neutral, all-equity firm would invest equal amounts in each available project. This is indicated by the lower horizontal line in Exhibit 4, at the level where |I.sub.1~/|I.sub.2~ = 1. When the two projects are operated in separate firms, their return correlation will not affect investment allocations, but Exhibit 4 shows that the entrepreneur would optimally invest almost 30% more in the safer project (that is, |I.sub.1~/|I.sub.2~ |is greater than~ 1). Because the underinvestment cost of debt is greater for the firm investing in the riskier project, this firm optimally issues less debt. This decision to forego the tax advantages of debt makes the firm's optimal scale smaller when its technology has higher variance. Finally, the downward-sloping line in Exhibit 4 indicates the impact of the projects' return correlation on the relative investment level chosen by a JI firm. For low |Rho~, the firm optimally invests more in the safer project, though never to the extent it would under SI. As the coinsurance benefits diminish with higher project correlation, the asset substitution effect of JI takes over. For |Rho~ |is greater than~ 0.74, the JI firm invests more in the riskier project.

III. Optimal Corporate Form With Two Risky Investment Projects

To summarize the discussion thus far, JI offers the benefit of coinsurance: total cash flows will be stabilized (relative to the average SI firm) whenever the project returns are less than perfectly correlated. This influence makes the JI firm's debt safer, which mitigates the underinvestment effects of debt, making it optimal for the firm to exploit debt's tax advantage more fully. By contrast, with SI the bondholders encounter no asset substitution problem, and the entrepreneur retains more flexibility in his leverage decisions. In addition to these agency considerations, corporate taxes also affect the relative values of SI versus JI. We have already discussed how asymmetric taxes tend to mitigate the JI firm's asset substitution problem. But taxes also influence the choice of corporate form in a more direct fashion. Green and Talmor |10~ show that the tax liability is analogous to a call option on the firm's profits. Because a portfolio of options is worth more to the government tax collector than an option on a portfolio, corporations should tend to merge their independent projects into a single entity, at least for tax purposes. We now compare the attainable market value of two projects under alternative organizational forms, for various values of the tax parameters and of the projects' cash flow distributions. Exhibits 5, 6 and 7 illustrate the net effect of these influences on a firm's optimal corporate form.

The value of the option to allocate different leverage levels to the two projects is shown in Exhibit 5. In the example, |Mathematical Expression Omitted~, |Mathematical Expression Omitted~, and |Rho~ = 1. The separately incorporated TABULAR DATA OMITTED firms are exogenously constrained to issue $50 of combined debt, which approximates the optimal debt that two SI firms would issue. This debt is exogenously allocated across the two projects in a variety of combinations (|B.sub.1~ and |B.sub.2~). Note that the investment levels (|I.sub.i~, i = 1, 2) and (consequently) project values (|V.sub.i~, i = 1, 2) vary with the way debt is allocated across the two firms. In most cases, the SI firms are worth less than $27.66, which is the value of a JI firm with the same ($50) debt level. For the middle debt allocation (|B.sub.1~ = 30, |B.sub.2~ = 20), however, the separately incorporated firms produce a greater combined value than JI can produce. Because Exhibit 5 is based on exogenously imposed debt levels, we cannot conclude anything about optimal corporate structure. It does, however, clearly indicate that the option to leverage projects differently constitutes a potentially important benefit of separate incorporation.(12)

In Exhibit 6, we plot the maximized, combined value of the entrepreneur's two projects under each alternative form of incorporation over a range of project correlations. The exhibit plots two set of firm values, for two different pairs of project return variances. In both cases, JI dominates SI for a broad range of correlation values. When project correlation is low, expected taxes are lower under JI and coinsurance mitigates the underinvestment problem for both projects. Only when |Rho~ is very high (above 0.80) do the costs of asset substitution outweigh these benefits. Exhibit 6 also indicates that relative project variance influences optimal corporate form. When the two projects' volatilities are more similar to one another (the upper pair of lines), the asset substitution problem is less severe and JI is chosen over a broad range of values for |Rho~ -- specifically, for |Rho~ |is less than~ 0.90. By contrast, with disparate project variances, JI dominates SI only for a narrower range of correlation values: |Rho~ |is less than~ 0.82.

To examine the effect of taxes, Exhibit 7 repeats the previous exercise at a lower tax rate (|T.sub.c~ = 5%). As in Exhibit 6, JI is more likely to be selected the lower the correlation between the two projects. Reducing the corporate tax rate, however, weakens the tax incentive to merge the two projects: comparing the intersection points in Exhibits 6 and 7 indicates that as the corporate tax rate goes down, JI is selected for a narrower range of correlations.(13)

IV. Summary and Implications

We have evaluated the effects of debt's agency costs and tax benefits on a firm's optimal organizational structure. Our analysis abstracts from issues such as bankruptcy costs, managerial incentive plans (effort), and scope economies, to focus exclusively on agency and tax explanations for the choice of organizational form. In deciding whether to operate separately or as a merged entity, the entrepreneur trades off JI's benefits (coinsurance and tax savings) against its costs (asset substitution and the merged firm's inability to allocate equity differentially across the two projects). When the coinsurance and tax benefits dominate, the entrepreneur chooses to merge the two projects into a single firm; when the asset substitution and equity allocation options are relatively more important, he chooses to separate incorporation of each project.

Our numerical results demonstrate how the optimal organizational form is influenced by changes in the project returns' correlation, changes in the projects' relative variances, and changes in the corporate tax rate. SI becomes more attractive the greater the correlation between the two projects' returns because, all else being equal, the benefits of coinsurance decline with the projects' correlation coefficient. SI is also more likely to occur when the projects have sufficiently different variances, because the cost of asset substitution (and thus the cost of merger) rises with the variance differential. A higher corporate tax rate also tends to discourage SI, by raising the tax savings associated with consolidating the projects' profits.

Our analysis has several applications. In particular, the results indicate how a diversified holding company might optimally structure its debt. SI is equivalent to having subsidiaries issue their own debt rather than relying on the parent company for financing. Our analysis predicts that debt financing on a subsidiary level is more likely to occur if the subsidiary's cash flows are highly correlated with the cash flows from the remaining portion of the holding company, and if the variance of the subsidiary's cash flows are significantly different from the cash flow variance of the remaining portion of the holding company. In such instances, issuing debt at the subsidiary level reduces a significant asset substitution problem, while, at the same time, issuing debt at the parent level would do little to reduce the cost of the holding company's debt, since the coinsurance benefits would be negligible.

While the majority of holding companies issue their debt exclusively at the holding company level, a notable exception appears to be the financing subsidiaries of manufacturing corporations. Our analysis suggests that combining manufacturing and financing activities within the same holding company creates significant asset substitution problems. In the context of our model, asset substitution occurs when the firm overinvests in risky projects. However, the notion of asset substitution can be more broadly defined to include the ability of managers to transfer assets across activities within the same subsidiary. For example, bondholders may fear that funds generated from financing activities may be diverted to manufacturing projects. These concerns may be mitigated through the establishment of a separate financing subsidiary.

Our analysis also provides a rationale for conglomerate mergers that is similar to that raised by Lewellen |20~. Conglomerate mergers are unlikely to generate large synergies or cost savings since they involve the combining of diverse activities within a single firm. However, combining diverse activities whose cash flows are not highly correlated does provide benefits. By combining diverse activities, the firm is able to reduce the riskiness of its debt, which, in turn, improves its investment incentives. This effect is strongest when the diverse activities have similar levels of risk, thereby limiting problems of asset substitution.

While we focus on the ex ante choice of organizational structure, our analysis also applies to subsequent incentives to merge or spin-off particular subsidiaries as their stochastic characteristics change over time. For example, if the relative variance of two projects rises over time, the entrepreneur may choose to spin-off one of the subsidiaries to reduce the asset substitution problem which has become increasingly important. Alternatively, if the correlation between the project returns falls over time, the entrepreneur may choose to merge the two firms in order to take advantage of the increased coinsurance benefits. We have also determined that, at least under certain circumstances, a higher corporate tax rate encourages mergers among formerly separate firms or holding company subsidiaries.

In this paper, we assume that the interests of managers and shareholders are aligned. This enables us to focus on the extent to which stockholder-bondholder conflicts and tax considerations influence organizational structure. Recent work by Ramakrishnan and Thakor |22~ and by Aron |1~ suggests, however, that organizational structure may also influence managerial incentives, which, in turn, influence firm investment policies. A more complete analysis of organizational structure would incorporate both of these factors. For example, incorporating management incentives into our analysis may suggest a greater use of SI. It can be argued that managers are less willing to invest in risky projects than are shareholders, since managers may bear significant costs if risky investments do not succeed, and depending on the structure of their compensation, managers may not realize the same gains from risk-taking as do shareholders. In such instances, JI may lead managers to underinvest in risky projects. Indeed, many argue that the bust-ups or spin-offs of conglomerate mergers during the 1980s were instituted to better align the incentives of firm managers and to ultimately improve the firm's investment policies (Bhagat, Shleifer, and Vishny |2~).

The interaction among organizational structure, capital structure, and investment incentives is rather complex. In order to keep the analytics tractable, we have restricted the entrepreneur to organizing his projects into either a jointly incorporated firm or two separately incorporated firms. A more complete analysis would evaluate a richer set of organizational structures, including the issuance of secured debt or "project financing" (in the sense of Shah and Thakor |23~ or Kensinger and Martin |18~) within a JI firm. At the same time, we could also allow the firm to include securities other than debt and equity in its capital structure. Indeed, many authors have noted the agency cost benefits of issuing contingent claims such as callable debt, convertible debt, and loan commitments (Bodie and Taggart |3~, Green |9~, and Houston and Venkataraman |13~). These represent issues for future investigation.

We are grateful to an anonymous referee and to the editor (Anjan Thakor) for substantial comments and suggestions on the prior draft of this paper. The usual disclaimer applies.

1 This terminology is consistent with the terms used in Chemmanur and John |5~.

2 John and John |16~ describe a similar benefit in discussing corporate spin-offs.

3 A number of subsequent papers critiqued or extended Lewellen's analysis. See, for example, Higgins and Schall |12~, Kim and McConnell |19~, and Stapleton |24~.

4 While this paper and many others are primarily concerned with the agency problem between debtholders and equityholders, another perspective investigates the effect of corporate form and diversification on managerial incentives. See, for example, Aron |1~ or Ramakrishnan and Thakor |22~.

5 When observable and unobservable risks are perfectly positively correlated, Campbell and Kracaw |4~ prove that hedging observable risk always raises firm value by reducing the incentive to asset substitute. When the risks are less than perfectly correlated, their analysis permits a less precise conclusion:

|M~anager-equityholders should benefit from hedging when observable and unobservable risks are sufficiently positively correlated. |4, p. 1685~

6 Other authors, including Green |9~, Bodie and Taggart |3~, and Houston and Venkataraman |13~, have evaluated the impact of convertible or optionlike securities on a firm's agency costs and investment incentives. We assume here that the firm can issue only debt or equity claims against its future cash flows.

7 This assumption resembles Glassman's |8~ description of corporate spin-offs as a form of "securitization":

By selling an ownership interest in a narrowly focused business instead of offering a stake in the larger, more diverse parent, management reduces uncertainty for investors. |8, p. 87~

8 Green and Talmor |10~ employ an alternative benchmark: the level of privately optimal investment given symmetric (nondistorting) corporate taxation. Since our primary concern is with the optimal corporate form, our ensuing analysis combines the investment distorting effects of asymmetric taxes and of risky debt.

9 In the case of a single-period investment, a depreciation rate (|Lambda~) near unity seems natural, thereby assuring that condition (4) holds unless the firm is extremely highly leveraged.

10 Inspecting the left-hand side of Equation (9) clearly indicates that a mean-preserving spread of ||Theta~.sub.i~ will cause shareholders to ignore a larger proportion of the investment's total cash flows. That is, the underinvestment problem is worse for riskier projects, ceteris paribus.

11 Note that debt is restricted to sell at par. Otherwise, the firm would issue extremely high coupon debt at a premium (since the principal component is negligible) in order to maximize the amount of its cash flows which are deductible for corporate taxes.

12 John and John |16~ similarly conclude that

The flexibility of being able to allocate debt individually against the separate projects will be shown to lead to a reduction in the total agency costs resulting in value gains. |16, p. 62~

13 The computations underlying Exhibits 6 and 7 assume that the projects' profits cannot be consolidated for tax purposes unless they are also operated in the same legal corporation. In other words, we have assumed that a firm wishing to minimize its tax payments must necessarily suffer the asset substitution costs associated with JI. In reality, however, a holding company may choose to file a consolidated tax return even if its subsidiaries issue their own separate debt. Hence, the implied restrictions on return correlations required to make SI optimal are probably too severe. We should therefore observe a number of conglomerate firms issuing subsidiary debt, even if their projects' return correlations are not extremely high.

References

1. D.J. Aron, "Ability, Moral Hazard, Firm Size, and Diversification," Rand Journal of Economics (Spring 1988), pp. 72-87.

2. S. Bhagat, A. Shleifer, and R. Vishny, "Hostile Takeovers in the 1980s: The Return to Corporate Specialization," Brookings Papers: Microeconomics 1990, Washington Brookings Institute, pp. 1-73.

3. Z. Bodie and R.A. Taggart, "Future Investment Opportunities and the Value of the Call Provision on a Bond," Journal of Finance (September 1978), pp. 1187-1200.

4. T.S. Campbell and W.A. Kracaw, "Corporate Risk Management and the Incentive Effects of Debt," Journal of Finance (March 1990), pp. 1673-1686.

5. T.J. Chemmanur and K. John, "Optimal Incorporation, Structure of Debt Contracts, and Limited-Recourse Project Financing," New York University Working Paper No. FD-91-26, August 1991.

6. D. Galai and R.W. Masulis, "The Option Pricing Model and the Risk Factor of Stock," Journal of Financial Economics (January/March 1976), pp. 53-81.

7. B. Gavish and A. Kalay, "On the Asset Substitution Problem," Journal of Financial and Quantitative Analysis (March 1983), pp. 21-30.

8. D.M. Glassman, "Spin-offs and Spin-outs: Using 'Securitization' to Beat the Bureaucracy," Journal of Applied Corporate Finance (Fall 1988), pp. 82-89.

9. R.C. Green, "Investment Incentives, Debt, and Warrants," Journal of Financial Economics (March 1984), pp. 115-136.

10. R.C. Green and E. Talmor, "The Structure and Incentive Effects of Corporate Tax Liabilities," Journal of Finance (September 1985), pp. 1095-1114.

11. R.C. Green and E. Talmor, "Effects of Asymmetric Taxation on the Scale of Corporate Investment," in Recent Developments in Corporate Finance, J. Edwards, J. Franks, C. Mayer, and S. Schaefer (eds.), Cambridge University Press, 1986, pp. 83-97.

12. R.C. Higgins and L.D. Schall, "Corporate Bankruptcy and Conglomerate Merger," Journal of Finance (March 1975), pp. 93-114.

13. J.F. Houston and S. Venkataraman, "Liquidation Under Moral Hazard: The Incentive Effects of Commitments to Lend," University of Florida Working Paper, 1990.

14. M.C. Jensen and W.H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure," Journal of Financial Economics (October 1976), pp. 305-360.

15. T.A. John, "Mergers and Investment Incentives," Journal of Financial and Quantitative Analysis (December 1986), pp. 393-413.

16. T.A. John and K. John, "Optimality of Project Financing: Theory and Empirical Implications in Finance and Accounting," Review of Quantitative Finance and Accounting (Vol. 1, 1991), pp. 51-74.

17. C.M. Kahn, "Project Choice, Moral Hazard, and Optimal Subsidiary Structure for Intermediaries," University of Illinois Working Paper, July 1992.

18. J.W. Kensinger and J.D. Martin, "Project Finance: Raising Money the Old-Fashioned Way," Journal of Applied Corporate Finance (Fall 1988), pp. 69-81.

19. H.E. Kim and J.J. McConnell, "Corporate Mergers and the Coinsurance of Corporate Debt," Journal of Finance (May 1977), pp. 349-353.

20. W.G. Lewellen, "A Pure Financial Rationale for the Conglomerate Merger," Journal of Finance (May 1971), pp. 521-537.

21. S.C. Myers, "Determinants of Corporate Borrowing," Journal of Financial Economics (November 1977), pp. 147-175.

22. R.T.S. Ramakrishnan and A.V. Thakor, "Cooperation versus Competition in Agency," Journal of Law, Economics, & Organization (Fall 1991), pp. 248-283.

23. S. Shah and A.V. Thakor, "Optimal Capital Structure and Project Financing," Journal of Economic Theory (August 1987), pp. 209-243.

24. R.C. Stapleton, "Mergers, Debt Capacity, and the Valuation of Corporate Loans," in Mergers and Acquisitions, M. Keenan and L.J. White (eds.), Lexington, MA, Lexington Books, 1982, pp. 9-28.

Mark J. Flannery is Barnett Banks Professor of Finance, and Joel F. Houston and Subramanyam Venkataraman are Professors of Finance, all at the Graduate School of Business Administration, University of Florida, Gainesville, Florida.

In choosing the type of outside claim to issue, debt has obvious tax advantages because its interest payments are made from pre-tax corporate earnings. However, when the entrepreneur's investment decisions are not contractible, debt also imposes agency costs in the form of underinvestment (Myers |21~) and/or asset substitution (Jensen and Meckling |14~, Galai and Masulis |6~, Green |9~) incentives. In efficient security markets, outside claimants will rationally price these deadweight costs, which therefore fall entirely on the firm's organizers. A prominent view of corporate capital structure is that the firm balances the agency costs of debt against its tax advantages.

This paper's principal intended contribution is to demonstrate that the agency costs of debt financing are also importantly influenced by the firm's method of incorporation. Consequently, the firm must simultaneously select a capital structure and organizational form on the basis of agency cost and tax considerations. By combining the projects into a single entity, the firm reaps coinsurance benefits: less risky cash flows mitigate the underinvestment problem. At the same time, joint incorporation creates an asset substitution problem which does not exist when projects are incorporated separately. The potential asset substitution tends to make the debt riskier and exacerbate the underinvestment problem, ceteris paribus. Another benefit of separate project incorporation is that, when project risks differ, each firm can adjust its leverage to trade off the underinvestment costs of debt against its tax benefits more precisely than when both projects are merged into a single firm.(2) Finally, Green and Talmor |10~, |11~ demonstrate that the asymmetric nature of corporate taxes also influences a firm's investment choice. Because corporate tax payments are analogous to a call option on the firm's earnings, firm owners will sometimes choose less risky investments than they would under symmetric taxation.

Our model simultaneously considers these tax effects with the effect of organizational form on the agency costs of debt, in order to determine the optimal corporate form and the optimal capital structure for a given set of investment projects. For a given set of tax and production parameters, we evaluate the maximum attainable value of equity under separate incorporation, and then compare it to the maximum attainable value under joint operation of the two projects. Our computations take full account of underinvestment, asset substitution, and taxes, and primarily investigate the impact of variations in the two projects' relative variances and the correlation between their returns.

Our analysis has several straightforward applications concerning the corporate organization of multifaceted firms. First, our results suggest how a diversified holding company should structure its public debt. For example, our model explains why manufacturers' financing subsidiaries frequently issue their own debt, rather than having the parent obtain the required financing. Second, we can evaluate the effects of mergers on the agency costs of risky debt in order to determine the types of projects that are best combined and those that are best financed separately. This enables us to interpret not only the factors influencing a firm's initial choice of organizational structure, but why a firm may choose to change its organizational structure over time through mergers or spin-offs. In other words, our analysis carries implications about the financial "life cycle" of a conglomerate firm.

The paper proceeds as follows. Section I reviews the existing literature on the financial aspects of corporate organization. Section II describes our model of the optimal means of financing risky investment opportunities under separate versus joint incorporation of two separable projects. Because of the maximization problem's complexity, we employ numerical techniques to solve it. Section III reports our numerical results, which illustrate the factors that make merged operation more valuable than separate incorporation (or vice versa). The final section summarizes and briefly discusses the implications of our analysis for financial corporate structure.

I. Prior Literature

The diversification value of mergers has been discussed frequently in the economics and finance literature. Much of the early work in this area sought to explain conglomerate mergers. For example, Lewellen |20~ argued that combining imperfectly correlated firms could increase the merged entity's debt capacity, and hence its market value.(3)

These early papers do not consider the debt-related effects of underinvestment and asset substitution on firm investment policies. Yet combining two projects into a single conglomerate with centralized borrowing generates a complex set of influences on firm investment incentives. Myers |21~ offers a "preliminary analysis" of the impact of diversification on one of these agency costs -- underinvestment -- and predicts |21, p. 167~ that "there should be no consistent relationship between 'diversification' and 'debt capacity'." John |15~ and John and John |16~ explicitly evaluate the optimal way to organize a multiproject firm. John |15~ examines the effect of corporate structure on a levered firm's investment incentives. Following Myers |21~, she shows that a levered firm with a single investment option might forego a positive-NPV project because its implementation would transfer too much value to the firm's debtholders. Combining two (perfectly correlated) investment options into a conglomerate firm, however, can improve the firm's investment decisions, and hence enhance the combined firms' market value. John and John |16~ evaluate a similar model in the presence of corporate taxes. Their firm chooses its optimal leverage by trading off the tax benefits of debt against its agency (underinvestment) costs. Once again, this model treats two available investment options, whose returns are perfectly positively correlated. The projects can be owned by two separate firms or by a conglomerate. The authors conclude that SI is always optimal, because it permits each project to be operated with a different debt-equity ratio, which provides shareholders a more efficient set of ex post investment incentives. Whether the unambiguous results from these two papers would continue to hold under a less extreme assumption about project return correlation constitutes an important focus of our present paper.

Kahn's |17~ analysis of a multiproject firm's corporate structure problem yields an insight very similar to ours: that corporate structure affects firm value by influencing owners' (noncontractible) investment incentives. However, his analytical framework cannot fully evaluate the effects of project return correlation, and (perhaps more importantly) omits any treatment of corporate taxes. Yet the corporate tax code's asymmetric treatment of profits and losses will also influence a firm's optimal leverage and investment incentives. Green and Talmor |10~, |11~ describe situations in which the tax structure may either aggravate or mitigate asset substitution and underinvestment incentives. Their analysis fully incorporates tax and agency considerations, and while their model has important implications for determining organizational structure, they do not formally address the impact of organizational structure on investment incentives.

Numerous other papers address related finance issues.(4) Shah and Thakor |23~ derive the conditions under which a special form of "project financing" constitutes the best way for a firm to add an additional project to its existing portfolio. Campbell and Kracaw |4~ describe conditions under which a firm may choose to hedge away its observable risk in order to reduce its ex post incentive to asset substitute. Unfortunately, their model permits unambiguous analytical conclusions about the firm's optimal risk exposure only when the observable and unobservable risks are perfectly positively correlated.(5) Gavish and Kalay |7~ report that the shareholders' incentive to substitute riskier assets for safe assets does not increase monotonically with firm leverage. Finally, Chemmanur and John |5~ examine optimal firm organization in the context of corporate control rights. Their entrepreneur initially controls two projects, from which he derives important control rights (perquisites). The entrepreneur chooses between SI and JI in order to strategically allocate his own equity investment across the two projects, in an effort to protect his control rights from outside takeover threats.

To summarize, a number of papers have recognized that agency or tax considerations are important determinants of a firm's investment policy. With the notable exception of the work by Green and Talmor |10~, few of these papers have integrated tax and agency effects in a single model. At the same time, a more recent literature recognizes that the firm's choice of organizational structure may also affect its investment incentives. Most of these papers, however, have employed restrictive assumptions about the investment projects' stochastic returns in order to determine the firm's optimal organizational form. Our analysis considers a more general framework, in which taxes and agency costs simultaneously determine capital and organizational structures. In our model, JI provides tax benefits as well as coinsurance benefits which reduce underinvestment. The cost of JI is that it reduces capital structure flexibility and creates an asset substitution problem.

II. A Model of Debt, Taxes, and Investment Incentives

Consider an entrepreneur with access to two nontransferable projects which may be implemented at a variety of alternative scale levels. Both projects offer positive NPV, but their cash flow distributions may differ. Financial contracts may be written on the final cash flows, which are freely observable to outside claimants. The entrepreneur seeks to maximize the initial market value of firm equity, which (under rational pricing of the outside securities) is equivalent to maximizing the magnitude of the economic rents resulting from his access to the investment projects. Corporate taxation encourages the issue of debt to fund investment needs, but debt also entails potentially severe agency costs since bondholders cannot force the firm to implement a particular investment strategy after the debt has been sold. Investors must therefore conjecture about the entrepreneur's subsequent investment choices, which will be characterized by incentives to underinvest and (with JI) to favor the riskier asset over the safer one.

Each project lasts for a single period, and provides an end-of-period cash flow |Mathematical Expression Omitted~ characterized by decreasing stochastic returns to scale:

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~ = a random variable describing the stochastic returns to investment in project i;

|I.sub.i~ = the number of dollars invested in project i (|I.sub.i~ |is greater than~ 0); and

||Alpha~.sub.i~ = project i's returns to scale parameter (0 |is less than~ ||Alpha.sub.i~ |is less than~ 1).

The model's other assumptions are as follows:

A1. The entrepreneur cannot sell or defer the investment projects.

A2. The entrepreneur's objective is to maximize the rents attainable from his access to two investment projects. In order to finance part of his investment, the entrepreneur may issue "outside" bonds (whose interest is tax-deductible) or "outside" equity.(6)

A3. There are no bankruptcy costs. Realized cash flows (|C.sub.i~) are freely observed by all firm claimants.

A4. The entrepreneur and all investors are risk-neutral.

A5. The riskless market interest rate is zero.

A6. The two projects share no scope economies of any kind.

A7. The random variables |Mathematical Expression Omitted~ have marginal cumulative density functions |Mathematical Expression Omitted~, and joint density |Mathematical Expression Omitted~. Also,

||Mu~.sub.i~ = the mean value of |Mathematical Expression Omitted~.

||Sigma~.sub.i~ = the standard deviation of |Mathematical Expression Omitted~.

A8. Bondholders cannot perfectly observe the entrepreneur's actual investment behavior, so they cannot force the entrepreneur to pursue any preannounced investment plan.

A9. In pricing the firm's debt, bondholders rationally anticipate the entrepreneur's ex post investment incentives.

A10. The corporate tax rate is |T.sub.c~. Taxes are paid on all income net of interest payments and depreciation, i.e., on the amount |Mathematical Expression Omitted~, where

|B.sub.i~ = the (endogenously chosen) volume of bonds issued by firm i;

|r.sub.i~ = is the market's (rational) required interest rate on these bonds; and

|Lambda~ = the tax code's depreciation allowance.

Under these assumptions, the entrepreneur may organize his debt issues in either of the following ways:

(i) Two separate firms, each of which sells debt secured only by its own project's cash flows, or

(ii) One (conglomerate) firm which borrows from the capital market and allocates investable resources between the two investment projects in an unobservable manner.

Assumption A8 means that bondholders cannot write effective covenants to constrain the entrepreneur's ex post investment behavior. Indeed, the entrepreneur will confront incentives to underinvest and/or to substitute more of the riskier project after his debt has been issued. The deadweight costs of these investment distortions accrue to the entrepreneur when outside claims are rationally priced, giving him the incentive to minimize these debt agency costs. Corporate organizational form can importantly influence the amount of these agency costs. When projects are organized into separate firms, the entrepreneur can credibly convince bondholders that their funds will be invested only in a single project.(7) By contrast, with JI the entrepreneur will sell debt on less advantageous terms because investors will be concerned about his ability to substitute more of the risky project for the safer one. The entrepreneur will choose between SI and JI as part of his effort to maximize his personal wealth (A2).

We analyze our model of debt finance and risky investment in three stages. First, we evaluate optimal investment policy in the absence of moral hazard and distortionary taxes. This provides a benchmark for the effects of agency costs and asymmetric taxes. We then compare the projects' maximized value under each organizational form, for various values of the projects' joint return parameters.

A. Optimal Investment in the Absence of Moral Hazard and Taxes(8)

In the absence of taxes and moral hazard, investment is determined where the marginal expected return in each project equals the marginal cost of investment. Under risk-neutrality, the optimal value of |I.sub.i~ maximizes

|Mathematical Expression Omitted~

Differentiating Equation (2) with respect to |I.sub.i~ yields an expression for the optimal scale of project i:

|Mathematical Expression Omitted~

A project with greater mean return (||Mu~.sub.i~) and smaller stochastic scale diseconomies (larger ||Alpha~.sub.i~) will be more extensively implemented. Naturally, the project's variance does not influence |I*.sub.i~ in a risk-neutral capital market.

An all-equity firm would optimally choose |I.sub.i~ to maximize Equation (2) for each available project. However, the tax advantage of debt generally leads the entrepreneur to include some debt in his capital structure. The debt creates agency costs (in the form of suboptimal investment incentives), which must be traded off against its tax benefits to determine an optimal capital structure. Because the corporate form influences the extent of these agency costs in a multiproject firm, the entrepreneur must simultaneously determine an optimal capital structure and corporate organizational form.

B. Projects' Market Values Under SI

Consider first the maximized value of a firm operating only one project. The equityholders receive the project cash flows net of corporate tax obligations and promised debt payments. As shown by Green and Talmor |10~, the effect of asymmetric taxes on investments and firm value will depend on whether or not the tax shields exceed the promised payments to the bondholder. For our case -- with a single-period investment -- the payoff to equity is shown in Exhibit 1. If project cash flows fall below C1 (= B|1+r~), the firm earns less than the promised payment on outstanding bonds. In this region, bankruptcy occurs and equity receives no payment. The firm's tax deductions amount to C2 (=rB + |Lambda~I). For realized cash flows between C1 and C2, shareholders receive 100% of the project's additional cash flows, while to the right of C2 the firm's owners share additional cash flows with the tax collector. We assume that the payoffs in our model are consistent with the case depicted in Exhibit 1, which then requires that(9)

|B.sub.i~(1 + |r.sub.i~) |is less than~ |r.sub.i~|B.sub.i~ + |Lambda~|I.sub.i~

or

|B.sub.i~ |is less than~ |Lambda~|I.sub.i~. (4)

Under these conditions, the after-tax payoff to equity becomes

|Mathematical Expression Omitted~

Equity receives the project's total cash flows |Mathematical Expression Omitted~, less payments to bondholders and to the government. Since the firm pays taxes only when cash flows exceed the tax shields, the (asymmetric) tax liability in Equation (5) is analogous to a call option on the firm's profits (Green and Talmor |10~).

For a given financing package (|B.sub.i~, |r.sub.i~), the entrepreneur chooses his preferred investment level by solving

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

is the realization of ||Theta~.sub.i~ below which the firm defaults to its bondholders. This corresponds to C1 in Exhibit 1. Similarly,

|Mathematical Expression Omitted~

is the realization of ||Theta~.sub.i~ below which the firm pays no taxes. This corresponds to the point C2 in Exhibit 1.

Differentiating Equation (6) with respect to |I.sub.i~ yields the first-order condition (FOC)

|Mathematical Expression Omitted~

The left-hand side of Equation (9) represents the net marginal benefit to equity (after taxes and depreciation) of an additional dollar invested; the right-hand side measures the marginal cost of additional investment. The underinvestment effects of risky debt can be illustrated most readily for the case of zero corporate taxes. When |T.sub.c~ = 0, Equation (9) indicates that shareholders only consider the marginal benefit of additional investment to themselves, ignoring cash flows that occur in the "bankruptcy states." As a consequence, the levered firm will forego some valuable investment -- the familiar underinvestment problem.(10) With a nonzero corporate tax rate, the firm would also take into account its tax obligation and depreciation when determining its preferred investment level. All else equal, higher corporate tax rates discourage investment, while a more generous depreciation allowance encourages investment.

The implicit solution to Equation (9) is a function |I.sub.i~(|B.sub.i~, |r.sub.i~) that represents the owners' incentive-compatible investment policy. In a competitive capital market, investors will only purchase bonds which are fairly priced, given this ex post investment policy. The rational pricing constraint for debt is(11)

|Mathematical Expression Omitted~

The optimal investment level (|I.sub.i~) and financing package (|B.sub.i~, |r.sub.i~) for an SI firm must satisfy both the incentive compatibility condition (9) and the rational pricing condition (10). The problem's complexity makes analytical solutions impractical. Accordingly, we undertake our further analysis in terms of numerical computations, computing the maximum firm market value for various combinations of problem parameters.

Some properties of the maximized SI firm are illustrated in Exhibits 2 and 4. Exhibit 2 demonstrates that project variance prominently influences the amount of "outside" debt which the entrepreneur chooses to sell. Higher-variance projects make outstanding debt riskier (ceteris paribus), which exacerbates the incentive to underinvest. Accordingly, an increase in project variance reduces the optimal level of outside debt issued. The effect of this decision on the optimized project's value is shown in Exhibit 3: as project variance rises, the lower use of tax-advantaged debt financing results in a lower project value.

C. Projects' Market Value Under JI

Instead of operating two separately financed firms, the entrepreneur can form a conglomerate, whose bondholders are paid from the two projects' combined cash flows. The conglomerate firm's maximization problem closely resembles that for the single-project firm. The conglomerate's owner will jointly select his most preferred scale for each project, taking full account of the tax structure and the (rational) terms on which external bond and equity investors will provide financing. In particular, the entrepreneur now maximizes

|Mathematical Expression Omitted~

Assuming that B |is less than~ |Lambda~(|I.sub.1~ + |I.sub.2~) (that is, that the firm's depreciation allowance exceeds its bond repayment obligations, as we also assumed for the SI case above), Equation (11) can be simplified to

|Mathematical Expression Omitted~

where

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

In Equation (12), the first integral represents the expected cash flow to equity before taxes. The second integral represents the firm's expected tax liability. Maximizing Equation (12) with respect to |I.sub.1~ and |I.sub.2~ for an arbitrary financing plan (B, r) yields two first-order conditions:

|Mathematical Expression Omitted~

which are similar to Equation (9) above. Note that the optimal investment level from Equation (15) depends on the assumed financing plan (B and r).

Consider the special case where the two technologies have the same scale parameter, i.e., ||Alpha~.sub.1~ = ||Alpha~.sub.2~, and the distribution of ||Theta~.sub.2~ is a mean preserving spread of ||Theta~.sub.1~ (with ||Sigma~.sub.2~ |is greater than~ ||Sigma~.sub.1~). We can rearrange the first-order conditions to get

|Mathematical Expression Omitted~

The right-hand side of Equation (16) indicates the extent to which investment incentives are influenced by the default and tax options. In both the numerator and the denominator, the first term represents the extent to which the existence of risky debt distorts investments. The second term captures the additional effect of asymmetric taxes. Consider the case when the tax rate (|T.sub.c~) is zero. The right-hand side then always exceeds one, since the first term in the numerator is greater than the corresponding first term in the denominator. This implies that |I.sub.1~ |is less than~ |I.sub.2~, which is the standard asset substitution problem examined in the literature. With positive tax rates, however, the additional term creates an offsetting effect. The second term in the numerator is larger in absolute value than the corresponding second term in the denominator. Consequently, at "sufficiently high" tax rates, the right-hand side of Equation (16) could actually become less than one, implying that |I.sub.1~ |is greater than~ |I.sub.2~. Thus, taxes may actually encourage the firm to invest in the less risky project. This incentive effect of the tax code has been analyzed carefully by Green and Talmor |10~.

The rational pricing constraint for bonds is now

|Mathematical Expression Omitted~

where |Mathematical Expression Omitted~ is the complement of ||Theta~.sub.d~. The firm's optimal investment and financing decisions emerge by maximizing Equation (12) through the choice of the amount of debt (B) raised ex ante, where Equations (17) and (15), respectively, determine the required coupon rate (r) and the incentive compatible investment policy. The primary addition to this maximization problem from the SI case (6) is that the firm can now choose the riskiness of its investment portfolio in addition to its investment levels.

Exhibit 4 illustrates the effect of project return correlation on the optimal investment allocation under SI and JI. For the sake of concreteness, we consider the case where |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~. From Equation (16), a risk-neutral, all-equity firm would invest equal amounts in each available project. This is indicated by the lower horizontal line in Exhibit 4, at the level where |I.sub.1~/|I.sub.2~ = 1. When the two projects are operated in separate firms, their return correlation will not affect investment allocations, but Exhibit 4 shows that the entrepreneur would optimally invest almost 30% more in the safer project (that is, |I.sub.1~/|I.sub.2~ |is greater than~ 1). Because the underinvestment cost of debt is greater for the firm investing in the riskier project, this firm optimally issues less debt. This decision to forego the tax advantages of debt makes the firm's optimal scale smaller when its technology has higher variance. Finally, the downward-sloping line in Exhibit 4 indicates the impact of the projects' return correlation on the relative investment level chosen by a JI firm. For low |Rho~, the firm optimally invests more in the safer project, though never to the extent it would under SI. As the coinsurance benefits diminish with higher project correlation, the asset substitution effect of JI takes over. For |Rho~ |is greater than~ 0.74, the JI firm invests more in the riskier project.

III. Optimal Corporate Form With Two Risky Investment Projects

To summarize the discussion thus far, JI offers the benefit of coinsurance: total cash flows will be stabilized (relative to the average SI firm) whenever the project returns are less than perfectly correlated. This influence makes the JI firm's debt safer, which mitigates the underinvestment effects of debt, making it optimal for the firm to exploit debt's tax advantage more fully. By contrast, with SI the bondholders encounter no asset substitution problem, and the entrepreneur retains more flexibility in his leverage decisions. In addition to these agency considerations, corporate taxes also affect the relative values of SI versus JI. We have already discussed how asymmetric taxes tend to mitigate the JI firm's asset substitution problem. But taxes also influence the choice of corporate form in a more direct fashion. Green and Talmor |10~ show that the tax liability is analogous to a call option on the firm's profits. Because a portfolio of options is worth more to the government tax collector than an option on a portfolio, corporations should tend to merge their independent projects into a single entity, at least for tax purposes. We now compare the attainable market value of two projects under alternative organizational forms, for various values of the tax parameters and of the projects' cash flow distributions. Exhibits 5, 6 and 7 illustrate the net effect of these influences on a firm's optimal corporate form.

The value of the option to allocate different leverage levels to the two projects is shown in Exhibit 5. In the example, |Mathematical Expression Omitted~, |Mathematical Expression Omitted~, and |Rho~ = 1. The separately incorporated TABULAR DATA OMITTED firms are exogenously constrained to issue $50 of combined debt, which approximates the optimal debt that two SI firms would issue. This debt is exogenously allocated across the two projects in a variety of combinations (|B.sub.1~ and |B.sub.2~). Note that the investment levels (|I.sub.i~, i = 1, 2) and (consequently) project values (|V.sub.i~, i = 1, 2) vary with the way debt is allocated across the two firms. In most cases, the SI firms are worth less than $27.66, which is the value of a JI firm with the same ($50) debt level. For the middle debt allocation (|B.sub.1~ = 30, |B.sub.2~ = 20), however, the separately incorporated firms produce a greater combined value than JI can produce. Because Exhibit 5 is based on exogenously imposed debt levels, we cannot conclude anything about optimal corporate structure. It does, however, clearly indicate that the option to leverage projects differently constitutes a potentially important benefit of separate incorporation.(12)

In Exhibit 6, we plot the maximized, combined value of the entrepreneur's two projects under each alternative form of incorporation over a range of project correlations. The exhibit plots two set of firm values, for two different pairs of project return variances. In both cases, JI dominates SI for a broad range of correlation values. When project correlation is low, expected taxes are lower under JI and coinsurance mitigates the underinvestment problem for both projects. Only when |Rho~ is very high (above 0.80) do the costs of asset substitution outweigh these benefits. Exhibit 6 also indicates that relative project variance influences optimal corporate form. When the two projects' volatilities are more similar to one another (the upper pair of lines), the asset substitution problem is less severe and JI is chosen over a broad range of values for |Rho~ -- specifically, for |Rho~ |is less than~ 0.90. By contrast, with disparate project variances, JI dominates SI only for a narrower range of correlation values: |Rho~ |is less than~ 0.82.

To examine the effect of taxes, Exhibit 7 repeats the previous exercise at a lower tax rate (|T.sub.c~ = 5%). As in Exhibit 6, JI is more likely to be selected the lower the correlation between the two projects. Reducing the corporate tax rate, however, weakens the tax incentive to merge the two projects: comparing the intersection points in Exhibits 6 and 7 indicates that as the corporate tax rate goes down, JI is selected for a narrower range of correlations.(13)

IV. Summary and Implications

We have evaluated the effects of debt's agency costs and tax benefits on a firm's optimal organizational structure. Our analysis abstracts from issues such as bankruptcy costs, managerial incentive plans (effort), and scope economies, to focus exclusively on agency and tax explanations for the choice of organizational form. In deciding whether to operate separately or as a merged entity, the entrepreneur trades off JI's benefits (coinsurance and tax savings) against its costs (asset substitution and the merged firm's inability to allocate equity differentially across the two projects). When the coinsurance and tax benefits dominate, the entrepreneur chooses to merge the two projects into a single firm; when the asset substitution and equity allocation options are relatively more important, he chooses to separate incorporation of each project.

Our numerical results demonstrate how the optimal organizational form is influenced by changes in the project returns' correlation, changes in the projects' relative variances, and changes in the corporate tax rate. SI becomes more attractive the greater the correlation between the two projects' returns because, all else being equal, the benefits of coinsurance decline with the projects' correlation coefficient. SI is also more likely to occur when the projects have sufficiently different variances, because the cost of asset substitution (and thus the cost of merger) rises with the variance differential. A higher corporate tax rate also tends to discourage SI, by raising the tax savings associated with consolidating the projects' profits.

Our analysis has several applications. In particular, the results indicate how a diversified holding company might optimally structure its debt. SI is equivalent to having subsidiaries issue their own debt rather than relying on the parent company for financing. Our analysis predicts that debt financing on a subsidiary level is more likely to occur if the subsidiary's cash flows are highly correlated with the cash flows from the remaining portion of the holding company, and if the variance of the subsidiary's cash flows are significantly different from the cash flow variance of the remaining portion of the holding company. In such instances, issuing debt at the subsidiary level reduces a significant asset substitution problem, while, at the same time, issuing debt at the parent level would do little to reduce the cost of the holding company's debt, since the coinsurance benefits would be negligible.

While the majority of holding companies issue their debt exclusively at the holding company level, a notable exception appears to be the financing subsidiaries of manufacturing corporations. Our analysis suggests that combining manufacturing and financing activities within the same holding company creates significant asset substitution problems. In the context of our model, asset substitution occurs when the firm overinvests in risky projects. However, the notion of asset substitution can be more broadly defined to include the ability of managers to transfer assets across activities within the same subsidiary. For example, bondholders may fear that funds generated from financing activities may be diverted to manufacturing projects. These concerns may be mitigated through the establishment of a separate financing subsidiary.

Our analysis also provides a rationale for conglomerate mergers that is similar to that raised by Lewellen |20~. Conglomerate mergers are unlikely to generate large synergies or cost savings since they involve the combining of diverse activities within a single firm. However, combining diverse activities whose cash flows are not highly correlated does provide benefits. By combining diverse activities, the firm is able to reduce the riskiness of its debt, which, in turn, improves its investment incentives. This effect is strongest when the diverse activities have similar levels of risk, thereby limiting problems of asset substitution.

While we focus on the ex ante choice of organizational structure, our analysis also applies to subsequent incentives to merge or spin-off particular subsidiaries as their stochastic characteristics change over time. For example, if the relative variance of two projects rises over time, the entrepreneur may choose to spin-off one of the subsidiaries to reduce the asset substitution problem which has become increasingly important. Alternatively, if the correlation between the project returns falls over time, the entrepreneur may choose to merge the two firms in order to take advantage of the increased coinsurance benefits. We have also determined that, at least under certain circumstances, a higher corporate tax rate encourages mergers among formerly separate firms or holding company subsidiaries.

In this paper, we assume that the interests of managers and shareholders are aligned. This enables us to focus on the extent to which stockholder-bondholder conflicts and tax considerations influence organizational structure. Recent work by Ramakrishnan and Thakor |22~ and by Aron |1~ suggests, however, that organizational structure may also influence managerial incentives, which, in turn, influence firm investment policies. A more complete analysis of organizational structure would incorporate both of these factors. For example, incorporating management incentives into our analysis may suggest a greater use of SI. It can be argued that managers are less willing to invest in risky projects than are shareholders, since managers may bear significant costs if risky investments do not succeed, and depending on the structure of their compensation, managers may not realize the same gains from risk-taking as do shareholders. In such instances, JI may lead managers to underinvest in risky projects. Indeed, many argue that the bust-ups or spin-offs of conglomerate mergers during the 1980s were instituted to better align the incentives of firm managers and to ultimately improve the firm's investment policies (Bhagat, Shleifer, and Vishny |2~).

The interaction among organizational structure, capital structure, and investment incentives is rather complex. In order to keep the analytics tractable, we have restricted the entrepreneur to organizing his projects into either a jointly incorporated firm or two separately incorporated firms. A more complete analysis would evaluate a richer set of organizational structures, including the issuance of secured debt or "project financing" (in the sense of Shah and Thakor |23~ or Kensinger and Martin |18~) within a JI firm. At the same time, we could also allow the firm to include securities other than debt and equity in its capital structure. Indeed, many authors have noted the agency cost benefits of issuing contingent claims such as callable debt, convertible debt, and loan commitments (Bodie and Taggart |3~, Green |9~, and Houston and Venkataraman |13~). These represent issues for future investigation.

We are grateful to an anonymous referee and to the editor (Anjan Thakor) for substantial comments and suggestions on the prior draft of this paper. The usual disclaimer applies.

1 This terminology is consistent with the terms used in Chemmanur and John |5~.

2 John and John |16~ describe a similar benefit in discussing corporate spin-offs.

3 A number of subsequent papers critiqued or extended Lewellen's analysis. See, for example, Higgins and Schall |12~, Kim and McConnell |19~, and Stapleton |24~.

4 While this paper and many others are primarily concerned with the agency problem between debtholders and equityholders, another perspective investigates the effect of corporate form and diversification on managerial incentives. See, for example, Aron |1~ or Ramakrishnan and Thakor |22~.

5 When observable and unobservable risks are perfectly positively correlated, Campbell and Kracaw |4~ prove that hedging observable risk always raises firm value by reducing the incentive to asset substitute. When the risks are less than perfectly correlated, their analysis permits a less precise conclusion:

|M~anager-equityholders should benefit from hedging when observable and unobservable risks are sufficiently positively correlated. |4, p. 1685~

6 Other authors, including Green |9~, Bodie and Taggart |3~, and Houston and Venkataraman |13~, have evaluated the impact of convertible or optionlike securities on a firm's agency costs and investment incentives. We assume here that the firm can issue only debt or equity claims against its future cash flows.

7 This assumption resembles Glassman's |8~ description of corporate spin-offs as a form of "securitization":

By selling an ownership interest in a narrowly focused business instead of offering a stake in the larger, more diverse parent, management reduces uncertainty for investors. |8, p. 87~

8 Green and Talmor |10~ employ an alternative benchmark: the level of privately optimal investment given symmetric (nondistorting) corporate taxation. Since our primary concern is with the optimal corporate form, our ensuing analysis combines the investment distorting effects of asymmetric taxes and of risky debt.

9 In the case of a single-period investment, a depreciation rate (|Lambda~) near unity seems natural, thereby assuring that condition (4) holds unless the firm is extremely highly leveraged.

10 Inspecting the left-hand side of Equation (9) clearly indicates that a mean-preserving spread of ||Theta~.sub.i~ will cause shareholders to ignore a larger proportion of the investment's total cash flows. That is, the underinvestment problem is worse for riskier projects, ceteris paribus.

11 Note that debt is restricted to sell at par. Otherwise, the firm would issue extremely high coupon debt at a premium (since the principal component is negligible) in order to maximize the amount of its cash flows which are deductible for corporate taxes.

12 John and John |16~ similarly conclude that

The flexibility of being able to allocate debt individually against the separate projects will be shown to lead to a reduction in the total agency costs resulting in value gains. |16, p. 62~

13 The computations underlying Exhibits 6 and 7 assume that the projects' profits cannot be consolidated for tax purposes unless they are also operated in the same legal corporation. In other words, we have assumed that a firm wishing to minimize its tax payments must necessarily suffer the asset substitution costs associated with JI. In reality, however, a holding company may choose to file a consolidated tax return even if its subsidiaries issue their own separate debt. Hence, the implied restrictions on return correlations required to make SI optimal are probably too severe. We should therefore observe a number of conglomerate firms issuing subsidiary debt, even if their projects' return correlations are not extremely high.

References

1. D.J. Aron, "Ability, Moral Hazard, Firm Size, and Diversification," Rand Journal of Economics (Spring 1988), pp. 72-87.

2. S. Bhagat, A. Shleifer, and R. Vishny, "Hostile Takeovers in the 1980s: The Return to Corporate Specialization," Brookings Papers: Microeconomics 1990, Washington Brookings Institute, pp. 1-73.

3. Z. Bodie and R.A. Taggart, "Future Investment Opportunities and the Value of the Call Provision on a Bond," Journal of Finance (September 1978), pp. 1187-1200.

4. T.S. Campbell and W.A. Kracaw, "Corporate Risk Management and the Incentive Effects of Debt," Journal of Finance (March 1990), pp. 1673-1686.

5. T.J. Chemmanur and K. John, "Optimal Incorporation, Structure of Debt Contracts, and Limited-Recourse Project Financing," New York University Working Paper No. FD-91-26, August 1991.

6. D. Galai and R.W. Masulis, "The Option Pricing Model and the Risk Factor of Stock," Journal of Financial Economics (January/March 1976), pp. 53-81.

7. B. Gavish and A. Kalay, "On the Asset Substitution Problem," Journal of Financial and Quantitative Analysis (March 1983), pp. 21-30.

8. D.M. Glassman, "Spin-offs and Spin-outs: Using 'Securitization' to Beat the Bureaucracy," Journal of Applied Corporate Finance (Fall 1988), pp. 82-89.

9. R.C. Green, "Investment Incentives, Debt, and Warrants," Journal of Financial Economics (March 1984), pp. 115-136.

10. R.C. Green and E. Talmor, "The Structure and Incentive Effects of Corporate Tax Liabilities," Journal of Finance (September 1985), pp. 1095-1114.

11. R.C. Green and E. Talmor, "Effects of Asymmetric Taxation on the Scale of Corporate Investment," in Recent Developments in Corporate Finance, J. Edwards, J. Franks, C. Mayer, and S. Schaefer (eds.), Cambridge University Press, 1986, pp. 83-97.

12. R.C. Higgins and L.D. Schall, "Corporate Bankruptcy and Conglomerate Merger," Journal of Finance (March 1975), pp. 93-114.

13. J.F. Houston and S. Venkataraman, "Liquidation Under Moral Hazard: The Incentive Effects of Commitments to Lend," University of Florida Working Paper, 1990.

14. M.C. Jensen and W.H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure," Journal of Financial Economics (October 1976), pp. 305-360.

15. T.A. John, "Mergers and Investment Incentives," Journal of Financial and Quantitative Analysis (December 1986), pp. 393-413.

16. T.A. John and K. John, "Optimality of Project Financing: Theory and Empirical Implications in Finance and Accounting," Review of Quantitative Finance and Accounting (Vol. 1, 1991), pp. 51-74.

17. C.M. Kahn, "Project Choice, Moral Hazard, and Optimal Subsidiary Structure for Intermediaries," University of Illinois Working Paper, July 1992.

18. J.W. Kensinger and J.D. Martin, "Project Finance: Raising Money the Old-Fashioned Way," Journal of Applied Corporate Finance (Fall 1988), pp. 69-81.

19. H.E. Kim and J.J. McConnell, "Corporate Mergers and the Coinsurance of Corporate Debt," Journal of Finance (May 1977), pp. 349-353.

20. W.G. Lewellen, "A Pure Financial Rationale for the Conglomerate Merger," Journal of Finance (May 1971), pp. 521-537.

21. S.C. Myers, "Determinants of Corporate Borrowing," Journal of Financial Economics (November 1977), pp. 147-175.

22. R.T.S. Ramakrishnan and A.V. Thakor, "Cooperation versus Competition in Agency," Journal of Law, Economics, & Organization (Fall 1991), pp. 248-283.

23. S. Shah and A.V. Thakor, "Optimal Capital Structure and Project Financing," Journal of Economic Theory (August 1987), pp. 209-243.

24. R.C. Stapleton, "Mergers, Debt Capacity, and the Valuation of Corporate Loans," in Mergers and Acquisitions, M. Keenan and L.J. White (eds.), Lexington, MA, Lexington Books, 1982, pp. 9-28.

Mark J. Flannery is Barnett Banks Professor of Finance, and Joel F. Houston and Subramanyam Venkataraman are Professors of Finance, all at the Graduate School of Business Administration, University of Florida, Gainesville, Florida.

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Title Annotation: | Corporate Investments Special Issue |
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Author: | Flannery, Mark J.; Houston, Joel F.; Venkataraman, Subramanyam |

Publication: | Financial Management |

Date: | Jun 22, 1993 |

Words: | 7010 |

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