Capital Structure, Compensation Contracts and Managerial Incentives by Alan V. S. Douglas JEL classification codes: G3, D82. Keywords: Capital structure, Optimal Compensation, Manager-Owner and Shareholder- Bondholder Incentive Conflicts, Information Asymmetries, Corporate Efficiency Corresponding author: Alan V. S. Douglas Finance Centre 289 Hagey Hall, University of Waterloo Waterloo, Ont., Canada N2L 3G1 Office: (519) 888-4567 e-mail: adouglas@uwaterloo.ca
Capital Structure, Compensation Contracts and Managerial Incentives Abstract This paper models the influence of capital structure on managerial incentives in the presence of explicit compensation contracts. Capital structure can mitigate a managerial incentive to substitute into riskier first period investments that increase his second period information advantage. In particular, if such asset substitution makes second period debt risky, the shareholders offer a compensation contract that focuses excessively on the manager s information rents (as they accrue only in high states). The optimal capital structure therefore balances shareholder-bondholder and manager-owner incentive conflicts. An interesting feature of this balance is that the shareholder-bondholder conflict dominates when the firm performs poorly, and manager-owner conflict dominates when the firm is doing well. In addition, the shareholder-bondholder conflict can be effectively controlled via short-term debt obligations and the manager-owner conflict can be effectively controlled via short-term dividend payments. Optimal capital structure and debt maturity are therefore related to both contracting costs and dividend policy, in a manner that is consistent with existing evidence and suggests some interesting directions for future investigations. 1
Capital Structure, Compensation Contracts and Managerial Incentives The literature studying corporate incentive conflicts provides invaluable insight into the determinants of corporate capital structure. In their seminal studies, Fama and Miller (1972) and Jensen and Meckling (1976) illustrate that the shareholders have an incentive to expropriate bondholder wealth by substituting into riskier investments, and Myers (1977) illustrates that the shareholders have an incentive to under-invest when part of the return accrues to bondholders. Other studies distinguish between managers and shareholders, and examine the effects of capital structure on managerial incentives. For example, Jensen (1986) and Zwiebel (1996) argue that debt can focus managers on value maximization rather than personal objectives, and Stulz (1990) illustrates that debt can force the disbursement of cash flows to deter over-investment. A potential criticism of this literature is that it does not explain why managerial decisions are influenced by capital structure rather than explicit managerial compensation contracts. Indeed, studies that focus on the explicit design of managerial incentive contracts have questioned the insights above. For example, Dybvig and Zender (1991) illustrate that if the owners can implement a long-term compensation contract at the outset, managerial decisions are in fact independent of capital structure (effectively resurrecting the Modigliani-Miller irrelevancy results). In response, Persons (1994) illustrates that such a long-term contract is dynamically inconsistent: the shareholders can profitably renegotiate the contract when the opportunity to expropriate bondholder wealth arises. While the implication is that capital structure is indeed relevant, Persons stops short of illustrating the capital structure that is optimal in the presence of dynamically consistent compensation contracts. In this paper, we formally investigate the interaction between capital structure and dynamically consistent compensation contracts, and illustrate the value-maximizing (optimal) capital structure. The interaction between capital structure and compensation stems from managerial discretion over an initial investment choice that affects his subsequent (second period) information advantages. These second period information advantages include both hidden actions and hidden knowledge regarding the success of the investments in place. The valuemaximizing second period compensation contract trades off managerial rents in the high state with inefficient actions in the low state, such that the resulting level of rents increases with the manager s information advantage. The manager can therefore increase his rents by choosing first period investments that generate greater second period information advantages. Such 2
investments, however, increase risk (produce a mean preserving spread in project outcomes) and reduce firm value (i.e. reduce the cash flow available for the firm s owners). The manager s incentive to choose such investments therefore represents an adverse asset substitution incentive in the first period. Long-term debt can deter this asset substitution because the second period incentive contract that maximizes shareholder wealth also depends on the amount of debt outstanding. In particular, risky debt distorts the shareholders incentive to choose an incentive contract that efficiently trades off managerial rents in the high state with inefficient actions in the low state i.e. if the debt level is risky, the bondholders bear the cost of inefficient actions in the low state, inducing the shareholders to choose a compensation contract that minimizes the manager s rents (debt overhang leads to under-investment in the low state, similar to Myers (1977)). This implies that a long-term debt level that becomes risky with asset substitution, but not otherwise, can induce efficient investment in the first period. Moreover, with efficient first period investment, the longterm does not become risky and the shareholders optimally choose the value-maximizing second period compensation contract. The interaction between long-term debt and compensation also creates a role for short-term debt and dividend payments. This role arises because the incentives associated with long-term debt also depend on the firm s short-term performance (represented by the realization of first period cash flows): particularly low cash flow realizations can make the second period debt payment risky even without asset substitution (causing under-investment), while particularly high cash flow realizations can ensure the second period payment despite asset substitution. To control for the effects of first period cash flows, the firm optimally issues short-term debt. Shortterm debt can deter asset substitution by forcing the manager to disburse excess cash when the realization is particularly high, and can deter under-investment by providing the debt holders with additional power when the realization is particularly low (so that the firm defaults). In addition, when default costs are substantial, the firm can substitute (performancecontingent) dividends for short-term debt, in order to deter asset substitution following high cash flows but avoid default costs. Since the manager is reluctant to disburse a self-disciplining dividend, however, the optimal combination of short-term debt and dividends reflects the relative cost of inducing such a dividend, which is positively related to the cost of managerial replacement. The resulting capital structure therefore combines short and long term debt 3
payments in a manner that reflects the firm s ability to control managerial investment incentives via dividend policy. Dewatripont and Tirole (1994) also present a theoretical analysis in which capital structure combines with an explicit managerial compensation contract to induce an efficient first period action (effort choice) by the manager. In their model, however, the manager s effort choice depends on a non-contractible second period asset substitution choice made by the controlling investor specifically, the controlling party, shareholders or bondholders, can stop existing investments, which reduces risk (Berkovitch, Israel and Speigel (2000) provide a similar analysis, except that stopping the current investments (framed as replacement) leads to an increase rather than a decrease in risk). The second period asset substitution choice affects effort because the optimal compensation scheme provides higher compensation for higher outcomes, so that the incentive to provide effort reflects the probability of high outcomes. In the end, therefore, the firm s debt level affects asset substitution because default transfers decision rights, and the shareholders and bondholders have different asset substitution preferences. Our analysis differs from Dewatripont and Tirole (and Berkovitch, Israel and Speigel (2000)) in a number of ways. First, building on the work of Dybvig and Zender (1991) and Persons (1994), we focus on the implications of capital structure when shareholders and bondholders have conflicting incentives with respect to the actions induced by managerial incentive contracts (in Dewatripont and Tirole, and Berkovitch, Israel and Speigel, both shareholders and bondholders prefer a compensation contract that induces high managerial effort). Additionally, long-term debt in our analysis can support efficient first period behavior without sacrificing ex-post efficiency. 1 Most importantly, however, we focus on the case where the manager s first period action is designed to affect the subsequent contracting environment. Dow and Raposo (2002) also examine a manager s incentive to pursue initial strategies that affect subsequent compensation contracts. While Dow and Raposo focus on the links between the firm s environment (the scope for opportunistic strategies) and the features of optimal compensation schemes (e.g. ex-ante versus ex-post contracting), our analysis focuses on the links between incentives and optimal capital structure. 2 Finally, our analysis has a number of interesting empirical implications. In particular, capital structure and dividend policy are jointly determined, with optimal debt and dividend payments decreasing in equilibrium contracting costs. These implications are consistent with the 4
findings of Titman and Wessels (1988), Jensen, Solberg and Zorn (1992), Barclay Smith and Watts (1995), Rajan and Zingales (1995), and Fama and French (2002). In addition, the maturity structure is consistent with the original finding of Barclay and Smith (1995) that debt maturity (measured by the proportion of debt with a maturity of at least three years) decreases with contracting costs (measured by market to book), and can reconcile this finding with the mixed relationship between maturity and contracting costs found by Stohs and Mauer (1996), since optimal maturity also depends on contracting costs that are avoided in our model. Specifically, our analysis predicts that the potential for asset substitution is reflected in the firm s debt to dividend ratio, such that negative relationship between maturity and contracting costs is stronger for firms with a higher debt to dividend ratio. Additionally, since the cost of inducing dividends is positively related to the cost of managerial replacement, our model predicts that both dividends and debt maturity are negatively related to managerial entrenchment. Our analysis also implies that the corporate agency conflict of greatest concern is related to the firm s performance. Specifically, the shareholder-bondholder conflict (i.e. the underinvestment incentive) is the major concern when performance is low, whereas the manager-owner conflict (i.e. manager s asset substitution incentive) is the major concern when performance is high. Although it is intuitive that managers are less inclined to pursue self-serving projects in bad times, and shareholders are less inclined to induce managerial actions that expropriate bondholder wealth in good times, to the best of our knowledge, this prediction has yet to be directly tested. The analysis is organized as follows. Section I presents the basic model. The dynamically consistent second period compensation contracts are characterized in section I.1, and the asset substitution and under-investment problems are presented in sections I.2 and I.3 respectively. Section II illustrates the role of short-term debt and dividend payments, and presents the optimal capital structure. Section III discusses empirical implications and extensions, and section IV concludes. I. Model. This section develops an agency model in which non-contractible decisions significantly affect corporate value. We begin with a general outline of the time line and the sequence of events, as given in figure 1: 5
Figure 1: Time Line and Sequence of Events. t = 0 t = 1 t = 2 Capital structure (short and longterm debt levels, F 1 and F 2 ) chosen Cash flow c 1 realized, Debt and dividend payments, F 1 and d 1, made (if possible) Manager s asset substitution choice ( y) 2 nd period compensation contract designed Investment success (ε i ) learned by manager, Managerial action (a) chosen Final value distributed At t = 0, the firm chooses its capital structure, defined as the combination of first and second period debt payments F 1 and F 2. During the first period, cash flow c (, C) is realized 1 0 first period debt and dividends payments F 1 and d 1 are made (if c 1 < F 1, the firm defaults as below), and the manager makes a non-contractible asset substitution choice. Similar to Jensen and Meckling (1976) and Gorton and Kahn (2000), the asset substitution choice determines the risk (dispersion) in second period outcomes, denoted by ε ε H ε L. Specifically, the manager can maintain the existing dispersion, in which case ε = x, or add a mean preserving spread y, such that ε = x + y (where x x H x L and y y H y L ). In contrast to standard asset substitution analyses, this decision reflects the impact on the manager s future (second period) compensation. To ensure dynamic consistency, the manager s second period compensation contract is designed at t = 1. 3 In particular, compensation is designed to maximize t = 1 shareholder wealth, subject to the manager s second period information advantages. These information advantages include the manager s hidden second period action, represented by a, and her hidden knowledge of investment success, represented by ε. As above, there are two equally likely realizations of the L H second period uncertainty term, ε { ε, ε } with ε H L > ε 0. Since the manager s asset substitution choice determines ε ε H ε L as above, it influences the manager s second period information advantage. 6
The total cash flow (value) available at the end of the second period (t = 2) is given by v = c1 F1 d1 + ε + a. This value is divided between the shareholders, debt holders and the manager according to the contracts outstanding. The investors receive total value less the payment to the manager specified in the compensation contract. Of this, the debt holders receive up to the face value F 2 in the debt contract, and shareholders receive the residual. The investors care only about expected returns, while the manager has utility given by uwa (, ) = w Aa ( ) where w is monetary compensation, and A(a) is the manager s disutility of her action a (e.g. effort or foregone perquisites). The action is defined on the set a [ a, a], and to simplify, the disutility function is given by 4 ={ 2 ka / 2 if a 0 Aa ( ) 0 if a < 0. Finally, the manager's reservation utility, denoted u, is normalized to zero, as is the manager s outside wealth. The remainder of this section analyses the decisions made after the capital structure is chosen at t = 0. Section I.1 presents the t = 1 compensation design problem when the outstanding debt level is risk free. Section I.2 illustrates the manager s asset substitution incentive associated with this compensation scheme, and section I.3 illustrates the effects of risky debt on the shareholders compensation design problem (i.e. the shareholders under-investment incentive). Section II presents the capital structure and dividend policy that maximize the initial (t = 0) value of the firm. I.1 Second Period incentive contracts To simplify, we begin with the t = 1 compensation design problem in the case without first period debt or dividends (F 1 = d 1 = 0) and where the second period debt level F 2 0 is riskfree. Three factors in our model determine whether F 2 is risk-free at t = 1: the level of F 2, the realization of c 1 and the choice of ε. The analysis here represents any combination of these factors such that F 2 is risk-free, so that there are no shareholder-bondholder agency conflicts and the incentive contract addresses only manager-owner agency conflicts. We present the case of risky debt (due to a higher F 2, lower c 1, or higher ε) in section I.3, and introduce first period debt and dividends in section II. 7
Risk Free Debt c At t = 1, both the assets in place, ε { x, x + y}, and the existing cash flow, (, C), are observed by the shareholders (though neither variable is contractible, as noted 1 0 above). The dynamically consistent compensation contract therefore focuses on the manager s second period information advantages, which include the realization of ε and the choice of a as above. Specifically, the shareholders observe only the combined outcome ε + a (or equivalently, total value v = c1 + ε + a), knowing that each realization ε i was equally likely. Thus, they design the incentive contract to maximize their t = 1 expected payoff H H H L L L.( 5 c + ε + a w ) +.( 5 c + ε + a w ) F, 1 1 2 where a i denotes the incentive compatible action for each realization of ε i. The incentive contract i i must satisfy the manager's reservation utility constraint for each possibility (w A( a ) u) to ensure the manager s participation both when there is good news and when there is bad news. It must also satisfy the manager's incentive compatibility constraints for each possibility, given by L L H H H H L L w A( a ) w A( a + ε ) and w A( a ) w A( a ε ). These incentive compatibility constraints ensure that the manager in fact chooses the intended levels of a i, given his ability to claim that either value of ε i was realized. 5 Some important features of the optimal contract follow immediately from the constraints. In particular, the incentive compatibility constraint for the high state enables the manager to L L obtain rents, as seen by substituting w = u+ A( a ) into the constraint, yielding H H L L w Aa ( ) u+ Aa ( ) Aa ( ε ). Thus, the simultaneous information advantages provide the manager with an information rent L L equal to Aa ( ) Aa ( ε ) in the high state and the reservation utility constraint for i = H does not bind. Additionally, the two incentive compatibility constraints cannot simultaneously bind, as seen by rewriting them as H L H L H L H L w w Aa ( + ε) Aa ( ) and w w Aa ( ) Aa ( ε ). H L H L Since Aʹ > 0 and Aʺ > 0, Aa ( + ε) Aa ( ) > Aa ( ) Aa ( ε ) and only one constraint can bind. To induce the manager's actions with the lowest payments necessary, it is the constraint for 8
the high state that binds (otherwise the shareholders would pay the manager more than necessary when i = H). Thus, the optimal contract maximizes the shareholders' expected return subject to the incentive compatibility constraint for the high state and the reservation utility constraint for the low state, so that the Lagrangian is L L L H H H max L=. 5( c + ε + a w ) +. 5( c + ε + a w ) F < wi, ai> L L L H H H L L + θ ( w A( a ) u) + θ ( w A( a ) w + A( a ε)). RU 1 1 2 IC The first order conditions for w L and w H L yield θ RU for a H yields = 1 and θ IC H =.5, and the first order condition H H H L/ a =. 51 ( A ( a )) = 0 A ( a ) = 1, illustrating that the optimal contract induces the first best action if i = H, a H = a FB. However, it induces a lower level of the action in the bad state, as seen from the first order condition for a L so that L L L L/ a =. 5 A ( a ) +. 5A ( a ε ) = 0, L L L L 1 A ( a ) = A ( a ) A ( a x) A ( a ) < 1 (1) The optimal contract sets a L < a FB L L since this reduces the information rent Aa ( ) Aa ( ε ) required to satisfy the incentive compatibility constraint for the high state, as above. The information rent decreases when a L is reduced because Aʺ = k > 0. The manager s second period information advantage therefore leads to contracting costs that consist of two components: (i) the inefficiency cost of a L FB < a, denoted α( a L ) ( a FB A( a FB )) ( a L A( a L )), and (ii) the manager s information rent if i = H, denoted ρ( a L, ε) A( a L ) A( a L ε). The optimal contract is designed to minimize the expected contracting costs, denoted κ( a L, ε). 5α( a L ) +. 5 ρ( a L, ε), as seen by writing the expression for the optimal value of a L in (1) as 9
κ α = + ρ.( 5 ) = 0. (1') L L L a a a The optimal value of a L in (1) characterizes the value-maximizing second period compensation contract in our analysis and is denoted a L* (i.e. a L* characterizes the contract that maximizes the cash flow available for investors, given the unavoidable managerial information advantages). This is the dynamically consistent value of a L when F 2 is risk free (as above), so that maximizing shareholder wealth is equivalent to maximizing firm value. Such low debt levels, however, leave the manager with an asset substitution incentive in the first period, as seen next. I.2 The Asset Substitution Choice As discussed above, asset substitution is modeled as a mean preserving spread in project outcomes such that ε increases from x to x + y. In contrast to standard analyses, however, the decision to unilaterally add risk reflects a positive association between risk and the manager s information advantages, which arises in our model because the manager asymmetrically observes ε. Asset substitution therefore alters the value-maximizing compensation contract characterized by (1). In particular, asset substitution increases the cost of contracting with an asymmetrically informed manager, and therefore lowers firm value, as stated formally in lemma 1. Lemma 1: A mean preserving spread in investment outcomes (asset substitution) increases the level of contracting costs under the value-maximizing second period compensation contract to K( x+ y) > K( x), thereby reducing firm value. Lemma 1 can be seen by totally differentiating the contracting costs K( ) ( a L * ε κ ( ε), ε), while recognizing that da L* /d ε = -1 (from differentiation of (1) with A (a) = ka). This adjustment in a L* reflects that, ceteris paribus, the increased information asymmetry increases the marginal benefit of reducing the manager s rents but not the marginal inefficiency cost of a L < a FB, so that a L* is optimally decreased as in (1 ). The increase in expected contracting costs K( ε) is therefore 6 L* L* L* L* L* dκ( a, ε) κ( a, ε) a κ( a, ε) κ( a, ε) L* =. A ( a ε). L* d ε a ε + = = 5 > 0 ε ε 10
Despite the adverse effect on firm value, the manager may pursue asset substitution to increase the information rents she receives under the value-maximizing second period L* L* L* compensation contract, ρ( a, ε) A( a ) A( a ε)). The effect of ε on the manager s information rents is given by L* L* da L* L* L dρ/ d ε = A ( a ε) + ( )( A ( a ) A ( a ε)) = A ( a ε)) k ε. d ε The first term represents the direct effect of ε, which increases the manager s rents, and the second term represents the effect of the offsetting adjustment in a L* to maintain the optimality condition (1) (i.e. da L* /d ε = -1). In contrast to firm value (which is monotonically decreasing in ε), the manager s rents are concave in ε (i.e. d 2 ρ/d ε 2 = -3k), reaching a maximum at ε = 1/(3k). To maintain focus, we restrict attention to the case where the direct effect of the additional information asymmetry dominates, so that asset substitution increases the manager s rents (a sufficient condition is that x + y 1/(3k)). Thus, when F 2 is risk-less and the incentive contract is designed to maximize t = 1 shareholder wealth (i.e. characterized by (1)), the manager pursues asset substitution, as stated in lemma 2. Lemma 2: When the debt level F 2 remains risk-less, the manager pursues the riskier investment in the first period, increasing ε from x to x + y. Lemma 2 illustrates that the manager will pursue a sub-optimal investment strategy if the firm has low (risk-less) levels of debt. Higher debt levels, however, alter this investment incentive, because risky debt introduces the familiar agency conflicts between shareholders and bondholders. This alters the shareholders compensation design problem, and therefore the manager s first period investment incentives, as seen next. 11
I.3 Risky debt and Under-investment in a L We now illustrate the case where the debt level F 2 is risky in the analysis above. Risky debt levels leave no residual in the low state, so that the shareholders are primarily concerned with value in the high state and the standard shareholder-bondholder agency conflicts arise (Myers (1977), Jensen and Meckling (1976)). Since the manager in our model makes the operating decisions, the effects of shareholderbondholder conflicts manifest through the effects on managerial incentives. In particular, the opportunity to expropriate bondholder wealth distorts the shareholders contract design problem at t = 1, since the incentive contract that maximizes shareholder wealth now induces highly inefficient actions when low value is realized (a L = 0) to increase the return when high value is realized. This expropriation incentive is similar to the under-investment incentive in Myers (1977) where shareholders forego profitable projects because part of the return would accrue to debt holders. Here, the shareholders forego a profitable ex-post "investment" of w L since the benefit, an increase in a L, accrues to the bondholders. The effect of risky debt on the incentive contract designed by shareholders is presented in lemma 3. Lemma 3: When the second period debt payment F 2 is risky, the dynamically consistent compensation contract offered by the shareholders induces a highly inefficient level of a L, i.e. a L = 0. This reduces firm value despite reducing managerial rents to zero. The formal explanation (proof) of lemma 3 follows from the change in the shareholders objective in the contract design problem, which becomes L max i i H H H =. 5( c 1 + ε + a w F 2 ) < w, a > L L L H H H L L + θ ( w A( a ) u) + θ ( w A( a ) w + A( a ε). RU IC The first order conditions for w i and a H L now yield θ RU =.5 and θ IC H =.5, A ( a H ) = 1, and L L L L/ a =. 5( A ( a ) A ( a ε )) = 0 a L = 0. (2) 12
The shareholders now prefer to reduce a L because this decreases ρ(a L, ε) as above (they are unconcerned with the corresponding increase in α(a L ) since their payoffs are insensitive to inefficiency costs when i = L). As illustrated above, however, firm value (i.e. the value of equity plus debt) is maximized at a L* (i.e. κ(a L*, ε) < κ(0, ε) as in (1 )). Thus, setting a L = 0 expropriates bondholder wealth but reduces firm value. Although the creditors bear the t = 1 cost of the under-investment in a L, they anticipate the possibility at t = 0, so that the original owners ultimately bear any residual loss (Jensen and Meckling (1976)). The owners therefore issue t = 0 debt only to the extent that there are offsetting benefits. In our model, these offsetting benefits stem from the interaction between the first period asset substitution incentive and the second period under-investment incentive, as seen next. I.4 The Interaction Between the Asset Substitution and Under-investment Incentives The analysis above illustrates how capital structure affects dynamically consistent managerial compensation contracts in our model. In particular, lemma 2 illustrates that the dynamically consistent compensation contract will induce the manager to pursue asset substitution if the second period debt payment F 2 remains risk-less. Lemma 3 illustrates, however, that the manager has an incentive to avoid asset substitution if the riskier investment makes F 2 risky, since the dynamically consistent compensation scheme then leaves the manager with no rents. These results imply that the manager s first period investment choice depends on whether asset substitution makes the second period debt payment risky. As discussed above, there are three factors that determine whether F 2 is risky at t = 1: the level of F 2 chosen at t = 0, the first period realization of c 1 and the first period asset substitution choice ε. In this section, we develop the manager s asset substitution choice as a function of c 1, given the (potentially risky) value of F 2. 7 To do so, we first determine the realizations of c 1 for which F 2 becomes risky if the manager pursues asset substitution, but not otherwise. For these realizations, the manager refrains from asset substitution to deter the shareholders from the underinvestment compensation scheme in lemma 3. Indeed, when the manager refrains from asset substitution following these realizations, it is dynamically consistent for the shareholders to choose the value-maximizing contract (induce a L* ), so that the second period debt level produces efficient corporate decisions at no additional cost. 13
To show this formally, we identify the value of c 1 that just deters the shareholders underinvestment incentive. For lower realizations of c 1, the second period debt payment is risky and the shareholders prefer under-investment (a L = 0), as in lemma 3. This reduces managerial rents to zero in the high state, so that w H FB = A( a ) and expected shareholder wealth is H FB FB.[ 5 c + ε + a A( a ) F ] +.[ 5 0]. 1 2 With higher values of c 1, however, the shareholders receive a residual in the low state if they induce a L* rather than a L = 0, and expected shareholder wealth is H FB FB L* L L* L*. 5[ c+ ε + a Aa ( ) ρ( a, ε) F] +. 5[ c+ ε + a Aa ( ) F]. 1 2 1 2 The value of c 1 at which the shareholders are indifferent between the value-maximizing (a L = a L* ) and under-investment (a L = 0) solutions is found by equating (3) and (4). This level of cash flow, denoted!c, is given by L FB FB c!( ε) = F2 ε a + A( a ) + 2 K( ε) (3) L L where again K( ε) =. 5α( a ( ε)) +. 5 ρ( a ( ε), ε) as above. For c < c!, shareholder wealth is maximized by offering the under-investment contract (inducing a L = 0), and for c 1 c!, shareholder wealth is maximized by offering the value-maximizing contract inducing (a L = a L* ). 1 As seen from (3), the range of first period cash flows that produce the value-maximizing contract depends on the manager s asset substitution choice, ε. A mean preserving spread in ε from x to x + y increases!c for two reasons. First, because y is mean preserving, y L < 0 and y H > 0, so that ε L decreases from x L to x L + y L. Second, adding y increases the contracting costs from K( x) to K( x+ y) as in lemma 1. The effect of asset substitution on the range of cash flows that produce the value-maximizing contract is therefore given by φ c!( x+ y) c!( x) = 2( K( x+ y) K( x)) y L > 0. (4) Equation (4) implies that, upon observing c!( x) c1 c!( x+ y), the manager will refrain from asset substitution; otherwise the dynamically consistent compensation contract will expropriate bondholder wealth to reduce the manager s rents. When the manager refrains from asset substitution, the shareholders offer the value-maximizing second period contract and L* therefore positive managerial rents of ρ( a ( x), x) >0. This result is stated formally as proposition 1: 14
Proposition 1: When the first period cash flow realization satisfies c!( x) c1 c!( x+ y), the second period debt level F 2 deters asset substitution in the first period and produces the value maximizing incentive contract in the second period. For lower realizations, c1 < c!( x), the shareholders pursue under-investment, a L =0, and for higher realizations, c1 > c!( x+ y), the manager pursues asset substitution, y. Proposition 1 illustrates that, for a particular range of first period cash flows, the longterm debt payment F 2 can simultaneously control the asset substitution and under-investment incentives, thereby increasing firm value. The optimal capital structure exploits this benefit of long-term debt, while accounting for the incentive problems associated with any other realizations of c 1, as seen next. II. Optimal Capital Structure In this section, we present the optimal capital structure in our analysis. To do so, we first illustrate the optimal second period debt payment in the absence of first period debt or dividend payments as above. We subsequently extend the analysis to illustrate how first period debt and dividend payments can reduce the cost of any incentive problems that remain. Proposition 1 illustrates that a long-term debt payment can induce value-maximizing decisions at no additional cost over a range of first period cash flows given by c!( x) c1 c!( x+ y). The optimal F 2 (and more generally the optimal t = 0 capital structure) therefore depends on the set of possible values of c 1, as given by the support c uniform density function g(c 1 ) = g. (, C) with 1 0 The long-term debt payment F 2 cannot produce value-maximizing incentives for all first period realizations when C > φ, where φ c!( x+ y) c!( x) as in (4), and we focus on this case for the remainder of the analysis. In this case, if the firm sets F 2 sufficiently low to avoid underinvestment for all c 1, i.e. such that c!( x) =0, the manager will invest opportunistically when the highest realizations obtain. Alternatively, if the firm sets F 2 sufficiently high to avoid asset 15
substitution for all c 1, i.e. c!( x+ y) = C, the shareholders will pursue under-investment when the lowest realizations obtain. The optimal choice of F 2 therefore depends on the relative cost of asset substitution and under-investment. The cost of asset substitution is given by AS κ(a L* ( x+ y), x+ y) κ(a L* ( x), x) K( x+ y) K( x), and the cost of under-investment is given by UI κ(0, x) κ(a L* ( x), x). Since κ(0, x) = κ(0, x+ y) > κ(a L* ( x+ y), x+ y), asset substitution is less costly in our model. Thus, a capital structure that includes only a second period debt payment optimally sets a low debt level to deter under-investment, allowing high managerial rents for the highest realizations of c 1. This result is presented formally in proposition 2. Proposition 2. When C > φ, a capital structure that includes only a second period debt payment F 2 allows either under-investment for the lowest realizations of c 1, or asset substitution for the highest realizations. In the absence of first period debt or dividend payments, the latter is optimal since asset substitution is less costly than under-investment. Proposition 2 implies that the long-term debt payment in fact increases firm value. With no debt, the manager pursues asset substitution for all c 1 as in lemma 2. The debt level in proposition 2, however, prevents asset substitution for 0 c1 φ, thereby reducing expected contracting costs by g φ AS. Since C > φ, however, significant costs (equal to g (C-φ) AS) remain. These costs can be reduced, however, by incorporating a short-term debt and dividend payments to help control suboptimal investment incentives, as seen next. Short-term debt Introducing a short-term debt payment, F 1, has two effects on the analysis above. First, when the payment is made, less cash flow is available for the second period debt payment F 2. This implies that, ceteris paribus, the under-investment incentive arises for more values of c 1, whereas the asset substitution incentive arises for fewer values. Specifically, the under- 16
investment incentive now arises for c < c!( x) + F, whereas the asset substitution incentive arises for c > c!( x+ y) + F. 1 1 1 1 Second, short-term debt creates the possibility of default at t = 1, which occurs when c 1 < F 1. Default can be costly due to the opportunity cost of each party s time, reputation damage, and legal costs. Default, however, is also beneficial in our model, as it can facilitate a renegotiation to deter sub-optimal investment. For example, default may reduce the free-rider and hold-out problems associated with disperse claimants, and take advantage of the strong bondholder incentive to deter under-investment (e.g., the legal right to seize collateral would produce a financial restructuring in which the bondholders receive an equity payment in return for reducing F 2 to deter under-investment). 8 To maintain focus, we do not formally model the process of default, and restrict attention to the case where default produces the value-maximizing managerial incentive contract at a cost γ that is less than the cost of sub-optimal investment (i.e. γ < AS < UI). Specifically, we assume that if c 1 < F 1, the shareholders and bondholders renegotiate the second period debt level to F r 2, such that F r x L a FB + A( a FB ) + 2K( x) c F r x L y L a FB + A( a FB ) + 2K( x+ y), 2 1 2 which deters both asset substitution and under-investment as in proposition 1. 9 Since the cost of default (including debt contract restructuring) is less than that of suboptimal investment, a short-term debt payment can be designed to increase firm value. To do so, the first period debt level F 1 is designed such that it causes default if (and only if) the underinvestment incentive exists, as shown in lemma 4. Lemma 4: The optimal combination of short and long-term debt is designed to place the firm in default (force renegotiation) whenever the under-investment incentive arises. In the absence of dividend payments, default is optimal for the lowest realizations of c 1, as it is less costly than asset substitution. Lemma 4 implies that the first period payment F 1 can be designed to effectively reduce the cost of the under-investment incentive to γ, and therefore increase value when default is less costly than asset substitution, i.e. when γ < AS. The relevant comparison is between γ and AS 17
because asset substitution is less costly than under-investment (i.e. AS < UI as above), so that the firm optimally avoids under-investment even without short-term debt (i.e. when F 1 = 0) as in proposition 2. That is, in proposition 2 the firm sets F 2 such that c!( x) =0, allowing asset substitution for the highest cash flow realizations, φ < c 1 < C. Adding the short-term debt payment increases the probability of default but reduces the probability of asset substitution, and since γ < AS, the optimal F 1 reduces the probability of asset substitution to zero. In particular, the optimal combination of F 1 and F 2 causes default for the lowest cash flow realizations and produces efficient incentives for the highest realizations. This is accomplished by augmenting the same F 2 with a first period debt payment equal to F 1 = C - φ. The firm then defaults when the under-investment incentive arises, i.e. when 0 < c 1 < C - φ, and the combination of F 1 and F 2 deters asset substitution for the remaining realizations, C - φ c 1 < C. This reduces the expected cost of the incentive problems from AS g (C-φ) in proposition 2 to γ g (C-φ), where again g (C-φ) is the ex-ante probability of realizing a value of c 1 for which an incentive problem remains in proposition 1. The solution with debt only in lemma 4, however, leaves significant costs when default costs are substantial (e.g. when firm is doing well so that the costs of managerial time and reputation are higher). In this case, it is possible to reduce costs further by integrating capital structure with dividend policy, as seen next. Dividends The introduction of first period dividends, D 1, also has two effects on the analysis above. First, similar to F 1, the disbursement of a dividend further reduces the cash flow available to make the second period debt payment, such that the under-investment incentive arises for c < c!( x) + F + D and the asset substitution incentive arises for c > c!( x) + φ + F + D. 1 1 1 1 1 1 The second effect differs from that of debt payments, however, reflecting the discretionary nature of dividend payments (F 1 and F 2 are, by definition, fixed payments). In particular, a dividend need not be paid when it creates the under-investment incentive, so that the increase in the set of realizations causing under-investment can be avoided. And since default costs are optimally incurred only to deter under-investment (lemma 4), this discretion can relax the trade-off between asset substitution and default described above. Specifically, a dividend payment equal to D = c c!( x) φ F that is paid only when c > c!( x) + φ + F deters asset 1 1 1 1 1 18
substitution without exacerbating the under-investment incentive (and therefore without imposing additional default costs). 10 The discretionary nature of dividends, however, can impose costs of its own. Specifically, it can be costly to induce the manager to disburse a dividend that restricts his investment choice (and therefore reduces his utility). The cost of inducing such a dividend depends on the dynamically consistent penalty for choosing a sub-optimal dividend, which in turn depends on the cost of managerial replacement. 11 In this section, we focus on the case where replacement costs are substantial and the manager can choose a low dividend without being replaced (lower replacement costs are discussed in the extensions). This implies that the manager will pay a dividend that deters asset substitution only if he is compensated for his lost rents. Specifically, the dividend is incentive compatible only if the manager is offered additional compensation equal to the foregone rents of.5 ρ, where ρ ρ (a L* ( x+ y), x+ y) ρ (a L* ( x), x) > 0 denotes the reduction in the manager s rents in the high state (which occurs with probability.5). It is optimal for the shareholders to offer the additional compensation of.5 ρ because it is less than the cost of asset substitution, and as usual the residual accrues to the shareholders. That is, the cost of asset substitution includes both the increase in rents and the increase in inefficiency costs, α(a L* ( x+ y)) α(a L* ( x)) >0, so that dividends reduce the cost of controlling the asset substitution incentive, as seen in lemma 5. Lemma 5: It is optimal for the shareholders to induce a dividend payment to deter asset substitution whenever the incentive arises. Lemma 5 implies that the shareholders can employ dividends to effectively reduce the cost of the asset substitution incentive to.5 ρ. Again, by recognizing this possibility at t = 0, the initial owners can design a capital structure that further increases firm value. Indeed, the optimal capital structure reflects the firm s ability to employ first period debt that effectively reduces the cost of the under-investment incentive to γ, and dividends that effectively reduce the cost of the asset substitution problem to.5 ρ, as follows. 19
The optimal combination of debt and dividend payments The optimal t = 0 capital structure specifies the combination of first and second period debt payments that, together with the dynamically consistent dividend payments at t = 1, minimizes the cost of the corporate incentive problems. As seen above, without dividends it is optimal is optimal for F 1 to cause default for the lowest realizations and F 2 to produce efficient incentives for higher realizations (lemma 4). Lemma 5 implies that default costs of γ can be avoided by reducing F 1 and offering additional compensation of ρ/2 if the manager disburses a dividend when the asset substitution incentive arises (i.e. disburses D c c!( x) φ F when c > c!( x) + φ + F). 1 1 1 1 1 The optimal combination of first period payments therefore depends on the cost of default relative to the cost of inducing the dividend: dividends are preferable when γ >.5 ρ and debt is preferable when γ <.5 ρ. Since default costs are likely to be higher when the firm is doing well (especially reputation costs, the cost of managerial time, and hold-up costs), we allow for the possibility that γ is a function of c 1, and present the results for the simplest case where γ(c 1 ) = λ c 1 0. 12 The optimal combination of debt and dividend payments is therefore given by proposition 3. Proposition 3: The optimal capital structure includes both short and long-term debt payments and is jointly determined with dividend policy. The optimal second period debt level is L FB FB F = x + a A( a ) K( x). 2 2 The optimal first period debt payment depends on the cost of default relative to the cost of inducing dividends. Specifically, a. When γ(c-φ).5 ρ, it is optimal to set F 1 = C-φ and D 1 = 0, b. When.5 ρ < γ(c-φ), it is optimal to set F 1 =.5 ρ/λ and D 1 = c 1 -F 1 -φ for F 1 +φ < c 1 < C. The optimal capital structure in proposition 3 reflects the firm s ability to use first period debt and dividend payments to control the incentive problems that remain in proposition 2. In each case, the debt payments (F 1 and F 2 ) alone produce efficient incentives for F 1 c 1 < F 1 + φ, the first period debt payment produces efficient incentives via renegotiation for 0 < c 1 < F 1, and the optimal dividend produces efficient incentives for F 1 + φ c 1 < C. 20
The optimal mix of first period debt and dividend payments is determined by their relative costs. In particular, when default costs are relatively low as in part a, dividends are suboptimal and the incentive problems are optimally controlled with debt payments alone. In the special case where default costs are zero (i.e. λ = 0), the incentive problems that remain in proposition 2 are also controlled without cost. When default costs increase with firm performance as in part b, dividends are substituted for F 1 at the point where γ(f 1 ) λf 1 =.5 ρ, since at this point the cost of controlling the under-investment incentive begins to exceed the cost of controlling the asset substitution incentive. Proposition 3 therefore illustrates how the optimal capital structure in our model is related to the firm s dividend policy. It also illustrates the determinants of the firm s optimal short and long-term debt levels, and provides new insight into the literature on optimal maturity structure (i.e. the optimal percentage of total leverage that is comprised of long term debt). For example, in their pioneering study, Barclay and Smith (1995) argue that maturity structure reflects the cost of controlling the adverse incentives of debt overhang as in Myers (1977). In developing their empirical hypotheses, Barclay and Smith point out that, since short-term debt avoids the debt overhang incentives, its use must be limited by unspecified costs, such as (i) flotation costs, (ii) the opportunity cost of the management time (required to roll over short term debt), and (iii) reinvestment risk and potential costs of illiquidity. Our analysis, however, predicts an optimal combination of short and long-term debt even in the absence of such costs. In our analysis, substituting short-term for long-term debt is sub-optimal because it removes the credible threat required to control the asset substitution incentive i.e., short term debt is limited because debt overhang can help motivate managers. Further, short-term debt is limited by the substitutability of dividends as in part b of proposition 3. The empirical implications of our analysis, as well as some interesting extensions, are presented next. 21
III. Extensions and Empirical Implications In this section, we relate our analysis to the empirical literature on capital structure, and discuss extensions regarding replacement costs, contractible variables and security design. Proposition 3 has a number of implications that are consistent with the empirical literature. First, part b of proposition 3 shows that short-term debt and dividend payments can serve as substitutes to control the effects of interim cash flow realizations, such that capital structure and dividend policy are jointly determined. This is consistent with the empirical findings of Jensen, Solberg and Zorn (1992), Barclay Smith and Watts (1995), and Fama and French (2002). Second, contracting costs are a major determinant of optimal debt and dividend payments. The optimal long term payment, F = x L + a FB A( a FB ) K( x), decreases in the 2 2 equilibrium level of contracting costs, K( x). This is because, ceteris paribus, higher contracting costs reduce the second period debt levels that avoid under-investment. The optimal first period payments also depend on contracting costs. When both D 1 and F 1 are optimal (part b of proposition 3), F 1 decreases with equilibrium contracting costs, as determined by the manager s information advantage x in section I. This is because the relative cost of inducing dividends (.5 ρ) decreases with x, reflecting that the manager s information rents ρ are concave in x as in section I.2. In contrast, for the zero dividend firms in part a of proposition 3, the short term debt level F 1 = C - φ increases because the range of cash flows for which F 2 alone can provide efficient incentives, i.e. φ, decreases with x. In this latter case, however, the decrease in F 2 dominates, so that total leverage (F 1 + F 2 ) again decreases. In each case, therefore, our analysis predicts a negative relationship between leverage and contracting costs that is consistent with the empirical literature (Titman and Wessels (1988), Barclay, Smith and Watts (1995), Rajan and Zingales (1995)). This is proven formally in proposition 4: Proposition 4: Optimal leverage (F 1 + F 2 ) is negatively related to contracting costs, as determined by x. Third, the maturity structure implied by proposition 3 is consistent with the empirical literature. Barclay and Smith (1995) find that debt maturity (defined as the proportion of debt 22
with a maturity of at least three years) decreases with contracting costs (defined as the market to book ratio). In contrast, Stohs and Mauer (1996) find only weak evidence of this relationship. Our model predicts that the proportion of total payments comprised of long-term debt, i.e. F 2 /(D 1 + F 1 + F 2 ), decreases with contracting costs, since F 2 decreases and F 1 + D 1 increases with x. Specifically, in the case without dividends, F 1 = C - φ increases because φ decreases with x as above. In this case, therefore debt maturity, F 2 /(F 1 + F 2 ) decreases with contracting costs as in Barclay and Smith. With dividends, as in part b proposition 3, F 1 + D 1 = c 1 - φ increases, but F 1 =.5 ρ decreases with x (as above), which implies that the effect on debt maturity is ambiguous, as in Stohs and Mauer. That is, since both F 1 and F 2 decrease with contracting costs, the effect on debt maturity is determined by the relative percentage changes, and is in general ambiguous. Our model suggests, however, how this ambiguity might be resolved. In particular, it implies that the (absolute) percentage change in F 1 is relatively high when there is little potential for asset substitution (i.e. when y is small), since then dividends are less costly so that F 1 is low but still sensitive to costs. This suggests that a negative relationship between maturity and contracting costs is more likely in firms with greater potential for asset substitution. These results are presented in proposition 5. Proposition 5: The optimal maturity structure of the firm s capital structure depends on contracting costs as follows: a. For zero dividend firms (part a of proposition 3), debt maturity F 2 /(F 1 + F 2 ) is decreasing in equilibrium contracting costs, as determined by x. b. For firms combining first period debt and dividends (part b of proposition 3), the maturity structure of the total payments, i.e. F 2 /(D 1 + F 1 + F 2 ), is decreasing in equilibrium contracting costs. The effect of x on debt maturity F 2 /(F 1 + F 2 ) is ambiguous, but decreases with the potential for asset substitution, as determined by y. Proposition 5 illustrates that our model can reconcile the findings of Barclay and Smith (1995) with the ambiguous results of Stohs and Mauer (1996). In addition, propositions 4 and 5 are consistent with the findings of Stohs and Mauer (1996) and Barclay, Marx and Smith (2001) that leverage and maturity are jointly determined, and support the latter authors conjecture that the inconsistency between their leverage and maturity regressions reflects omitted dividend or compensation variables, and the difficulty of obtaining proxies for the relevant exogenous variables. 23