Finance Articles

The Theory of Capital Structure 311

Brennan and Kraus, Constantinides and Grundy, and Noe demonstrate that allowing firms a wider range of financing choices can invalidate the Myers-Majluf results in some cases. Whether the type of examples identified in these papers are more important empirically than those of Myers-Majluf is an open question. We note, however, that Noe shows that the average quality of firms issuing debt is higher in equilibrium than that of firms issuing equity. Therefore, like Myers-Majluf, Noe's model predicts a negative stock market response to an announcement of an equity issue. Noe also predicts a positive market response to an announcement of a debt issue. Moreover, when Constantinides and Grundy further extend the model to allow different firm types to have different optimal investment levels and assume that investment is observable, they show that firms can fully separate using

investment and the size of a straight bond issue (with some share repurchase) as signals. Thus, in this situation straight debt is a preferred financing tool, although the reason here is that it helps to signal a firm's true type while in Myers-Majluf, debt is a device to avoid signaling. Also in this variant of the model, the market reaction to a stock repurchase financed by debt is more favorable the larger is the transaction.

B. Signaling with Proportion of Debt

In the previous subsection, capital structure emerged as part of the solu- tion to problems of over- and underinvestment. We turn now to models in which investment is fixed and capital structure serves as a signal of private insider information.

The seminal contribution in this area is that of Ross (1977). In Ross' model, managers know the true distribution of firm returns, but investors do not. Firm return distributions are ordered by first order stochastic dominance. Managers benefit if the firm's securities are more highly valued by the market but are penalized if the firm goes bankrupt. Investors take larger debt levels as a signal of higher quality.17 Since lower quality firms have higher marginal expected bankruptcy costs for any debt level, managers of low quality firms do not imitate higher quality firms by issuing more debt.

The following is a simple formal model. Suppose that the date-one returns

x of a firm of type t are distributed uniformly on [0, t]. The manager is privately informed about t. He chooses the face value of debt D to maximize a weighted average of the market value of the firm at date zero and the expected value at date one, net of a penalty L for bankruptcy.18 We denote by

17 An equivalent approach is to assume that managers can commit to paying dividends and suffer a penalty if the promised dividend is not paid. Ravid and Sarig (1989) consider a

combination of debt and dividend commitment. They show that both dividends and debt level increase with firm quality.

18 This objective function reflects the implicit assumptions that the manager's welfare is increasing in the current and future stock price and decreases in the event of bankruptcy. This

"bankruptcy penalty" could result from loss of reputation or search costs of finding a new position. The penalty is not a bankruptcy cost since it effects only the manager's welfare and not firm value.

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312 The Journal of Finance

VO(D) the value assigned to the firm at date zero by the market if the debt level is D. The manager's objective function is then

(1 - -y)Vo(D) + y(t/2 - LD/t).

The parameter -y is a weight. The expected payoff at date one, given the manager's information is simply t/2. He evaluates the bankruptcy probabil- ity as D/ t. If investors infer that t = a(D) when the manager issues debt of face value D, then

Vo(D) =a(D)/2.

Substituting this into the objective function and taking the derivative with respect to D gives the first order condition. In equilibrium, investors cor- rectly infer t from D, i.e., if D(t) is the manager's optimal choice of debt level as a function of the firm type t, then a(D(t)) t. Using this in the first order condition and solving the resulting differential equation gives

D(t) = ct2/L + b,

where c and b are constants.

The main empirical result is that firm value (or profitability) and the debt-equity ratio are positively related.19 It is also easily seen from the above formula that increases in the bankruptcy penalty, other things equal, de- crease the debt level and the probability of bankruptcy. Ross also shows that this probability is increasing in firm type t. Thus firm value, debt level, and bankruptcy probability are all positively related in this model.

Heinkel (1982) considers a model similar to Ross but does not assume that firm returns are ordered by first order stochastic dominance. Instead, the return distribution is assumed to be such that "higher" quality firms have higher overall value but lower quality bonds (lower market value for given face value), hence higher equity value. This allows firms to separate cost- lessly when insiders maximize the value of their residual claim subject to raising a given amount of external capital.20 The reason is that any firm attempting to convince the market that it is a type other than its true type will gain from overvaluation of one security and lose from undervaluation of the other. In equilibrium, the amounts issued of the two securities for each

type firm are such that the gains and losses balance at the margin. High value firms issue more debt. To imitate a high value firm, a lower value firm must issue more underpriced debt and reduce the amount of overpriced equity. Similarly, to imitate a low value firm, a higher value firm must issue

19 This can be seen by calculating the value of the debt and equity as functions of D(t) and t, taking the ratio, and showing that this ratio is increasing in t (see Ross (1977, p.37)). As will be seen below, many other models also imply a positive relation between firm profitability and leverage. Interestingly, Chang (1987), using an agency model, obtains the opposite results. Since

Chang derives optimal securities, his paper is considered in our companion survey, Harris and

Raviv (1990b).

20 See also Franke (1987) for a similar financial signaling model with costless separation of

firms.

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The Theory of Capital Structure 313

less overpriced debt and more underpriced equity. Since higher quality firms have higher total value, the result that they issue more debt is consistent with Ross' result.21

Another model that uses debt as a signal is that of Poitevin (1989) which involves potential competition between an incumbent firm and an entrant. The entrant's marginal costs are privately known by the entrant.22 In equilibrium, low cost entrants signal this fact by issuing debt while the incumbent and high cost entrants issue only equity. The cost to a firm of issuing debt is that it makes the firm vulnerable to predation by the other firm, possibly resulting in bankruptcy of the debt-financed firm. The benefit of debt is that the financial market places a higher value on the debt financed firm since it believes such a firm to be low cost. High cost entrants will not issue debt since the resulting probability of bankruptcy due to predation by the incumbent renders the cost of misleading the capital market too high (incumbents prey equally on all debt-financed firms, even if thought to be low cost). The main result, like the other models in this subsection, is that issuance of debt is good news to the financial market. Since predation is used only to drive one's rival into bankruptcy, there will be predation only against debt-financed firms.

C. Models Based on Managerial Risk Aversion

Several studies exploit managerial risk aversion to obtain a signaling equilibrium in which capital structure is determined. The basic idea is that increases in firm leverage allow managers to retain a larger fraction of the (risky) equity. The larger equity share reduces managerial welfare due to risk aversion, but the decrease is smaller for managers of higher quality projects. Thus managers of higher quality firms can signal this fact by having more debt in equilibrium.23

A simple formal model based on Leland and Pyle (1977) is as follows.

Consider an entrepreneur whose project returns x = It + e with Es = 0 and

21 Another signaling model that obtains this result is John (1987). 22 Glazer and Israel (1990) also consider a model in which capital structure is used to signal

costs of production. Unlike in Poitevin, in Glazer and Israel, an incumbent monopolist signals his cost to prevent entry. The incumbent's manager is assumed to be compensated based on the terminal value of equity, not including any dividends. Glazer and Israel assume that the proceeds of any debt issued are paid out in dividends. Therefore, leverage increases are costly for the manager. In equilibrium, potential entrants interpret more debt as indicative that the incumbent has lower marginal production costs. It is optimal for managers of low cost incum- bents to issue more debt since for them the benefit of preventing entry exceeds the cost of debt. Managers of high cost incumbents will not imitate since for them the value of entry prevention is lower. Note, however, that signaling could work equally well using dividends financed by retained earnings or preferred stock instead of by debt. The authors recognize this point and do not claim that their results constitute a theory of capital structure. Gertner, et al. (1988) also consider a model in which firms use capital structure as a signal in the output market (as well as in the capital market). Their main result is that whether the equilibrium will involve pooling or separation depends on what is best for the informed firm.

23 In addition to the papers discussed below, see Blazenko (1987).

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314 The Journal of Finance

who must raise I from external sources. The entrepreneur observes expected

return it, but investors do not. He chooses the fraction of the equity he retains a and the face value of default-free debt D to maximize his expected

utility of end-of-period wealth Eu(W) where:24

W= a(x - D) + (1 - a)(V(a) - D) + D = ax + (1 - a)V(a), subject to the constraint that I of external funds must be raised.

(1 - a)[V(a) -D] +D = I. Here V(a) is the market's assessment of the value of the firm given that the entrepreneur retains the fraction a of the equity. We have also assumed that there is no investment required (K = 0 in Leland and Pyle's notation) since this does not affect the results. Although the debt level D does not affect the entrepreneur's objective directly, his choice of a implies a debt level through the external-funds constraint.25 It is clear from the formula for W that increases in the entrepreneur's share a increase the riskiness of his portfolio (since V(a) is riskless cash) but also increase the amount he obtains for the share sold to outsiders through signaling (since V is increasing in a, in equilibrium).

The first order condition for a is obtained by differentiating Eu(W) with

respect to a, substituting the equilibrium condition that V(a(tt)) = it (where a(,t) is the entrepreneur's optimal ownership share if his expected return is

it), and setting the result equal to zero. It can be shown from this condition that the entrepreneur's equilibrium ownership share a increases with firm quality. To translate this into a capital structure theory, we must calculate the effect on the debt level D of changes in firm quality using the external-

funds constraint. Increases in it result in increases in a as just shown; however, the increase in a has two opposing effects on D. The increased ownership of the entrepreneur, other things equal, would require that more funds be raised by debt. Firm value V is, however, larger for larger a, so that equity holders may pay more for the smaller fraction of the firm they receive. Consequently, D may not need to increase to finance the increased ownership share of the entrepreneur. Leland and Pyle (1977) derive some conditions on the parameters of an example that guarantee that debt increases with a. Under these conditions, firms with larger debt also have a larger fraction of the equity owned by insiders and are of higher quality.26

24 This expression reflects the assumption that the amount raised externally, (1 - c)[ V(cx) - D] + D, is invested in a riskless asset with zero return.

25 In fact, the debt level determined in the Leland and Pyle model is the total debt issued by the corporation and the entrepreneur on personal account. The results can be interpreted as a

theory of corporate capital structure only if personal debt is costly.

26 Darrough and Stoughton (1986) incorporate moral hazard into the Leland and Pyle formula- tion. The manager is assumed to choose an effort level after securities are issued. The marginal product of effort ,u and the standard deviation of returns a are known only to the entrepreneur, but investors know that a = .2 In this model, the fraction of equity retained by the en-

trepreneur is both a signal of It and a and an incentive device. The entrepreneur retains a smaller fraction the more risky are the returns. There are no specific results linking debt level or capital structure to observable characteristics of the firm.

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The Theory of Capital Structure 315

D. Summary of Section II

The main predictions of asymmetric information theories concern stock price reactions to issuance and exchange of securities, the amount of lever- age, and whether firms observe a pecking order for security issues.

Stock Price Effects of Security Issues

. Debt: Myers and Majluf (1984) and Krasker (1986) predict the absence of price effects upon issuance of (riskless) debt. Noe (1988) and Narayanan (1988) predict a positive price effect of a (risky) debt issue.

. Equity: Myers and Majluf (1984), Krasker (1986), Noe (1988), Korajczyk, et al. (1990c), and Lucas and McDonald (1990) predict a negative price effect of an equity issue. This price drop will be larger the larger is the informational asymmetry and the larger is the equity issue. Moreover, Lucas and McDonald (1990) show that, on average, equity issues will be preceded by abnormal stock price increases.

Stock Price Effects of Exchange Offers

. Debt Increasing Offers: Constantinides and Grundy (1989) predict a positive stock price reaction that is larger the larger the exchange.

. Equity Increasing Offers: Brennan and Kraus (1987) predict a positive stock price reaction.

Is There a Pecking Order?

. Yes: Myers and Majluf (1984), Krasker (1986), and Narayanan (1988). . No: Brennan and Kraus (1987), Noe (1988), Constantinides and Grundy

(1989) dispute the pecking order result in models similar to that of Myers and Majluf. Other signaling models, such as Ross (1977), Leland and Pyle (1977), and Heinkel (1982) do not obtain a pecking order result.

Leverage

Myers and Majluf (1984) implies that leverage increases with the extent of the informational asymmetry. Ross (1977), Leland and Pyle (1977), Heinkel (1982), Blazenko (1987), John (1987), Poitevin (1989), and Ravid and Sarig (1989) all derive a positive correlation between leverage and value in a cross

section of otherwise similar firms. Ross (1977) also predicts a positive correla- tion between leverage or value and bankruptcy probability, while Leland and Pyle (1977) predict a positive correlation between value and equity owner- ship of insiders.

III. Models Based on Product/Input Market Interactions

Models of capital structure that use features of the theory of industrial organization have begun to appear in the literature. These models can be classified into two categories. One class of approaches exploits the relation- ship between a firm's capital structure and its strategy when competing in

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316 The Journal of Finance

the product market. A second class of approaches addresses the relationship between a firm's capital structure and the characteristics of its product or inputs. These two literatures are surveyed in the next two subsections.

A. Debt Influences Strategic Interaction Among Competitors

Until recently, the industrial organization literature has assumed that in choosing its competitive strategy the firm's objective is to maximize total profits. The finance literature, on the other hand, has focused on maximiza- tion of equity value while generally ignoring product market strategy. The new literature linking capital structure and product market strategy adopts

the finance view that managers generally have incentives to maximize equity value as opposed to profits or total value. In these papers, leverage changes the payoffs to equity and thus affects the equilibrium product market strategies.

One of the initial papers in this line of research was Brander and Lewis (1986).27 They use the basic idea of Jensen and Meckling (1976) (see Section I) that increases in leverage induce equity holders to pursue riskier strate- gies. In the Brander and Lewis model, oligopolists increase risk by a more aggressive output policy. Thus, to commit to pursuing a more aggressive strategy in a subsequent Cournot game, firms choose positive debt levels.

To see how this process works in somewhat more detail, consider the following formal model based on Brander and Lewis. There are two firms, i = 1, 2. The two firms first commit simultaneously to a debt level Di, then choose simultaneously an output level qi. Profits to firm i are given by Ri(qi, qj, zi) where z1 and z2 are independent and identically distributed shocks to the firms' profits. We assume that firm i's profits are decreasing in

the other firm's output and increasing in the random shock zi. Also, firm i's marginal profit (aR/daqi) is increasing in the random shock zi and decreas- ing in the other firm's output.

These assumptions are fairly standard in Cournot-equilibrium models ex- cept for the assumption that marginal profit increases with the random component.28 This assumption states that the marginal "product" (profit) of output is large in "good" states (when z is large). If the marginal product of output is high, the firm will optimally choose higher output than if it is low. But in this model the firm must choose output before its marginal product is known. Since levered equity holders receive payoffs only in good states (because of limited liability), however, they ignore the possibility that the marginal product of output is low. Consequently, leverage creates an incen- tive to increase output. Moreover, in Cournot oligopoly models, firms have an incentive to commit to producing large outputs since this causes their rivals

27 Two other treatments that are contemporaneous with Brander and Lewis (1986) are Allen (1985) and Maksimovic (1986). For a similar treatment, see Maksimovic (1989).

28 Brander and Lewis consider both this case and the case in which the marginal profit is decreasing with z. They consider the increasing case to be the most important empirically, since, in the other case, firms will be unlevered in equilibrium.

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The Theory of Capital Structure 317

to produce less. Leverage thus provides a device that allows firms to commit to producing more in the Cournot oligopoly. Therefore, in equilibrium, both firms will choose a positive debt level. Notice that the firms are worse off in this equilibrium than they would be in an all-equity Cournot equilibrium since, with leverage, firms produce more than the Cournot output.29

When oligopolies persist over time, tacit collusion is possible through the use of punishment strategies triggered when a rival deviates from the collusive output level. It is well known (see Green and Porter (1984)) that the monopoly solution can be achieved in an infinitely repeated Cournot oligopoly by a subgame perfect equilibrium in which each firm reverts to the Cournot output forever in the period after any firm deviates from its share of the monopoly output. The condition that is required for this result is that the present value of monopoly profits exceeds the value of deviating for one period, then obtaining Cournot profits forever. If we denote monopoly profits per period by 7rm, Cournot profits per period by 7rc, the one-period profit from deviating by 7rd, and the discount rate by r, the condition required for supporting the monopoly solution is

7rm + rm / r > 7rd + 7rc/r.

Maksimovic (1988) points out that if managers are assumed to maximize the value of equity (as opposed to the value of the firm) this condition must be modified. In particular, suppose the firm has issued debt that promises to pay b per period forever, where b> 7r_ (otherwise, the debt has no effect since it will be paid even if the firm reverts to the Cournot equilibrium). Now, if the firm deviates, equity holders receive 7rd - b for one period, then nothing thereafter since the assets will be transferred to bondholders (who will then follow the Cournot strategy forever). The condition for supporting the monopoly solution is therefore

7rm - b + (wm- b)/r > wd- b or b < wm + (m- 7d)r.

Maksimovic interprets this as a debt capacity, i.e., the maximum amount of leverage that firms in such industries can support without destroying the possibility of tacit collusion.

By modeling profits explicitly in terms of demand and cost functions and number of firms, Maksimovic is able to derive comparative static results on debt capacity as a function of industry and firm characteristics. He shows that debt capacity increases with the elasticity of demand and decreases with the discount rate. Assuming some advantage for debt (e.g. taxes), so that the firm's actual debt will be at capacity, makes these implications potentially testable.30

29 Glazer (1989) shows that when long run considerations are taken into account in a Brander and Lewis type model, firms have an incentive to issue long term debt which helps in enforcing a form of tacit collusion.

30 Maksimovic (1990) extends this analysis to the case in which firms are privately informed about their own productivity.

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318 The Journal of Finance

B. Debt Influences Interaction with Customers and / or Suppliers

The second industrial-organization-based approach to capital structure de- termination is to identify product (input) or product market (input market) characteristics that interact in a significant way with the debt level. The examples included here are customers' need for a particular product or service, the need for workers to invest in firm-specific human capital, product quality, and the bargaining power of workers or other suppliers.

Titman (1984) observes that liquidation of a firm may impose costs on its customers (or suppliers) such as inability to obtain the product, parts, and/or service.31 These costs are transferred to the stockholders in the form of lower prices for the firm's product. Consequently, the stockholders would like to commit to liquidate only in those states in which the net gains to liquidation exceed the costs imposed on customers. Unfortunately, when the firm's investors make the liquidation decision, they ignore these costs. Titman shows that capital structure can be used to commit the shareholders to an optimal liquidation policy. Specifically, capital structure is arranged so that stockholders never wish to liquidate, bondholders always wish to liquidate when the firm is in bankruptcy, and the firm will default only when the net gain to liquidation exceeds the cost to customers. It is shown that firms for

which this effect is more important, e.g., computer and automobile compa- nies, will have less debt, other things equal, than firms for which this effect is less important, e.g., hotels and restaurants. In general, for unique and/or durable products, the cost imposed on customers when a producer goes out of business is higher than for nondurable products or those made by more than one producer.

Maksimovic and Titman (Forthcoming) show that producers of nonunique and nondurable goods may also be subject to a similar effect. Consider a firm that can produce goods of high or low quality in any period, and suppose that consumers cannot distinguish quality until after consuming the good. Even though high quality costs more to produce, it may be worthwhile for the firm to produce high quality if it can establish a reputation for being a high quality producer. If, however, this reputation is lost (at least to stockholders) when the firm goes bankrupt, then the incentive to produce high quality is diminished by debt. Consequently, one would expect firms that can easily switch from high to low quality output but whose customers cannot distin- guish quality without purchasing the good, to have less debt, other things equal.

Another advantage of debt is that debt strengthens the bargaining position

of equity holders in dealing with input suppliers. Sarig (1988) argues that bondholders bear a large share of the costs of bargaining failure but get only a small share of the gains to successful bargaining. That is, bondholders insure stockholders to some extent against failure of negotiations with sup-

31 Allen (1985) also focuses on bankruptcy costs emanating from the product market. He points out that firms in financial distress may postpone investments, thus giving an advantage to their competitors. See also John and Senbet (1988).

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