5. Reputation Effects on Corporate Financing Policies
5.2 Equilibria of the Corporate Financing Policies
The Bayesian equilibrium concept is used to derive the set of equilibria in the financing model. A Bayesian equilibrium is a set of conditional probabilities, dqt, eqt , t{G,B} and {1,2}; and a set of the outsiders beliefs, pd ,
} , {ID IE
d and {1,2}; such that dqt, eqt maximizes the expected value for the existing shareholders and pd satisfies Bayes’ rule. The set of Bayesian equilibria are consistent with any kind of beliefs and this article is going to discuss the main features of each equilibrium.
Lemma 5.1 For each historical performance 1{S,F}, no firms go for debt financing - that is, dqt 0t.
Proof
Suppose that, by observing a firm issuing debt, the outsiders believe the firm to be of bad management quality; by observing a firm issuing equity, the outsiders believe the firm to be of good management quality. That is, pID 0 and pIE 1. It follows that
From (5.5), DSG (1)(1c)Z (A5.1) From (5.6), DSB (1)Z c (A5.2)
From (5.7), ESG Z (A5.3)
From (5.8), ESB Z (A5.4)
Thus, (A5.3)-(A5.1)>0 and (A5.4)-(A5.2)>0. A pooling equilibrium at dqt 0 emerges. No firm will choose to finance by issuing debt.
Q.E.D.
Next, the other pooling equilibrium is considered.
Lemma 5.2 For each historical performance 1{S,F}, no firms go for equity financing - that is, eqt 0t.
Proof
Suppose that, by observing a firm issuing equity, the outsiders believe the firm to be of bad management quality; by observing a firm issuing debt, the outsiders believe
the firm to be of good management quality. That is, pIE 0 and pID 1. It follows that
From (5.1), DSG Z (1)c (A5.5)
From (5.2), DSB Zc (A5.6)
From (5.3), ESG 1Z (A5.7)
From (5.4), ESB 1Z (A5.8)
For both types of firms, the probability to issue equity is decreasing as increases.
When 1, a pooling equilibrium at eqt 0 emerges and no firm will choose to finance by issuing equities.
Q.E.D.
Lemma 5.1 and Lemma 5.2 are common results in the reputation model. When there are zero-probability events, Bayesian equilibria are consistent with any kinds of beliefs. In Lemma 5.1, issuing debt is a zero-probability event, and we can infer such an event with the belief that the firm is of the bad management quality, thus making “no issuing debt”an equilibrium. Applying the same deduction to Lemma 5.2, while issuing equities is a zero-probability event, the firm makes “no issuing equities”an equilibriumsince an equity-issuing firm will be regarded as a firm of bad management quality. The equilibria under the investors’degenerate beliefs are also regarded as the degenerate equilibria. In this chapter, the author is going to exclude the degenerate equilibria and focus on two non-degenerate equilibria under investors’
non-degenerate beliefs. Propositions 5.1 and 5.2 will show the features of these two equilibria.
Proposition 5.1 For a given level of the firm’s reputation, as c1, there exists a non-degenerate separating equilibrium where the firm of good management quality goes for debt financing and that of bad management quality goes for equity financing.
Proof
Let MB be the difference of the marginal benefit for each type of firms when choosing between debt and equity financing. As c1, we have MB0 showed
as follows. Since the pooling equilibria are excluded in Lemma 5.1 and Lemma 5.2,
0 historical performance matters the most, that is, the case when the outsiders concern aboutfirm’saccumulated reputation most. In thiscase,theoutsidersconcern less about the information the financing policies convey. Instead, if the firm has a successful history, the outsiders are more likely to perceive it as a firm of good management quality. Next in Proposition 5.2, the firm’s financing policiesare characterized when the outsiders concern the firm’s past reputation most.
Proposition 5.2 As long as the past reputation dominates and 1, the firm of good management quality can choose between debt and equity;
while the firm of bad management goes for equity financing only.
Proof
Suppose that, no matter which financing decision the firm made, by observing a firm with a successful history, the outsiders believe the firm to be of good management quality. At the same time, if a firm has a failed history, the outsiders believe the firm to be of bad management quality. Then, pSd 1 and pFd 0
We compare the firm’s expected value under different financing policies and
make a financing decision as follows.
Firm Issuing Debt Firm Issuing Equity Financing Decision Z
1 Issuing Equity
c
This implies that a bad management firm with a successful history will choose to issue equity, while it makes no difference for a good management firm with a successful history to choose between issuing debt and equity.
Q.E.D.
5.3 Main Reputation Effects and Empirical Evidence
Table 5.2 shows the analyses from the equilibria of the financing policies and three information effects are proposed in the corporate financing decision.
Table 5.2 Decision Matrix of Financing and Investing
Reputation
5.3.1 The Feedback Reputation Effect and the Signaling Effect
From the result of Proposition 5.1, we find that if (DSG ESG)0, then,
IE S ID
S p
p1 1 . This implies that, on the one hand, for a given historical performance, the firm of good management quality is more likely to observe an S signal in the new project, thus, higher firm’s value will be expected. We call this a feedback reputation effect.
On the other hand, the result also implies that the feedback reputation effect favors firm issuing debt more than that issuing equity. Thus, a good firm will choose to issue debt rather than equity. We call this a signaling effect. As for
0 )
(DSB ESB , this implies that pIDF c pIEF
1
1
. Since the financial distress cost, c is high and a bad firm is more likely to fail, a bad firm will be better off to issue equity rather than debt. This coincides with the signaling effect.
The result of Proposition 5.1isconsistentwith Stien’sstudy in 1992. Stien’s study proposed that if costs of financial distress are high enough, good firms issue debt and bad firms issue equity. Donaldson’s(1961)study found that management strongly favors internal generation as a source of new funds. Majluf and Myers (1984) also proposed that, according to the pecking order hypothesis, firms prefer internal finance. If external finance is required, firms start with debt, then possibly hybrid securities such as convertible bonds, then equity as a last resort. In the reputation model where firm also takes internal funds as the first priority, we find that for a good firm, it follows the pecking order theory to raise funds needed for a new project. While, for a bad firm, due to the high cost of financial distress, it cannot help to deviate from the pecking order theory to issue equity instead.
5.3.2 The Direct Reputation Effect
The third reputation effect proposed in this section is the direct reputation effect. Proposition 5.2 shows that if the outsiders believe that a firm with a successful history is more likely to be a good firm, then a good firm with a successful history could choose eitherto issuedebtorequity. Firm’sreputation makesagood firm more flexible in financing operations. Again due to the financial distress cost, a bad firm with a successful history could choose to issue equity only. We call this a direct reputation effect.
The equilibrium where a good firm may choose to go for debt financing and a bad firm goes for equity financing only again coincides with the signaling effect.
While, since we get the other equilibrium where both types of firms may pool at equity financing, we are curious to know why a good firm would deviate from the pecking order theory to issue equity. Hovakimian, Opler and Titman (2001) suggested thatafirm’shistory may play an importantrolein determining itscapital structure. Studies by Masulis and Korwar (1986), Asquith and Mullins (1986) showed that firms tend to issue equity following an increase in stock prices, implying that firms that perform well subsequently reduce their leverage.
In addition, Stulz (1990), Hart and Moore (1995) and Zwiebel (1996) proposed that firms should use relatively more debt to finance assets in place and relatively more equity to finance growth opportunities. As a result, firms may choose to issue equity rather than debt in response to an increase in their value, if the change in value is generated by an increase in the perceived value of their growth opportunities.
Baker and Wugler (2002) also proposed that low leverage firms are those that raised funds when their market valuations were high, while high leverage firms are those that raised funds when their market valuations were low. Kayhan and Titman (2007) confirmed that history does in fact have a major influence on capital structure. Their empirical results showed that the cumulative stock return as well as the cumulative profitability has negative impact on the change in leverage, which implies that a firm with a good past will decrease its leverage ratio. Thus, current capital structure is strongly related to historical market values, that is, capital structure is the cumulative outcome of past. The reputation model here proposes that if the firm possesses a good name, the outsiders will be more likely to perceive the firm to be a good firm.
The past performance as well as the potential growth opportunity makes a good firm issuing equity more profitable.
While for a bad firm with a successful history, it cannot help to deviate from the pecking order theory to issue equity since a bad firm will be more likely to face the financial distress cost. In this case, the equity market would be subjected to offering funds to a firm of bad management quality and sustains a bad firm in the economy.
The direct reputation effect here makes bad firms over issue equity and over invest in projects as well.
Finally, the case when the firm needs to discontinue a project is discussed. In this model, if the firm fails in the 1st stage, the outsiders would be more likely to perceive the firm to be of bad management quality and consequently, to perceive negative expected value of the firm. In this case, firm’s optimal decision is to discontinue the project at time 1. Thus, the direct reputation effect makes the good firm under invest in projects, while it screens the bad firm with a poor past off the economy.