The announcement effect of debt forgiveness

Transcription

1 Working Paper Series No The announcement effect of debt forgiveness Konari Uchida and Naohisa Goto Faculty of Economics and Business Administration The University of Kitakyushu Kitagata, Kokuraminami-ku, Kitakyushu, Japan Phone and Fax +81 (93) Faculty of Economics and Business Administration The University of Kitakyushu Kitagata, Kokuraminami-ku, Kitakyushu, Japan Phone and Fax +81 (93) First Draft, August 004 Comments Welcome 1

2 1. Introduction It is an occasionally observed fact that financial institutions like banks rescue a financially distressed firm by providing debt forgiveness. Especially since the late 1990, Japanese economy has experienced several cases that huge amount of debt forgiveness is provided to a large company. It reflects the recent serious non-performing loan problem in the Japanese banking sector. Corporate finance theory can offer a rational explanation about the reason why banks provide debt forgiveness which is tended to be considered as a non-profitable project for banks. As Jensen and Meckling (1976) point out, shareholders of a firm with high leverage have a risk-shifting incentive and prefer a more risky project to a safer project even when the safer project is more profitable. In such a case, the debt forgiveness raises bank s loan value, since it weakens the shareholders risk-shifting incentive. This explanation implies that the stock prices of a borrowing firm and a lending bank positively respond to the news of debt forgiveness. owever, we observe a different pattern of the stock price reaction when debt forgiveness is announced in Japan. Using a standard event study methodology, Uchida and Goto (00) show that the main bank experiences negative but insignificant abnormal return when the news of debt forgiveness is released. Isagawa and Yamashita (003) report that when the agreement of debt forgiveness is announced the lending bank experiences negative and significant abnormal return. This paper explores theoretically and empirically the stock price reactions of a lending bank and a borrowing firm to the announcement of debt forgiveness. The basic idea of our theoretical model is that a bank may provide debt forgiveness when the debt level of a financially distressed firm is higher than that which maximizes its expected return. In other words, the debt forgiveness adjusts the debt level of a financially distressed firm, usually too high, into the optimal one for the lending bank. Supposing an information asymmetry in which the manager and the bank can identify the real quality of the distressed firm whereas outside investors can not, this idea leads to the conclusion that debt level after the debt forgiveness reveals the real quality of the distressed firm to outside investors. Overall, our model predicts that the stock price reactions of a borrowing firm and a lending bank are positively correlated with debt level after the forgiveness. We empirically test this prediction by a standard event study methodology. Using recent Japanese data, we compute the abnormal returns of the borrowing firm and the lending bank to the announcement of debt forgiveness. The firm s stock price reactions

3 have positive and significant correlation with the debt-to-sales ratio after the forgiveness. This evidence supports the main implication of our model. Our argument is also consistent with a stream of previous studies on the optimal capital structure. A stream of previous studies on the capital structure argue that the debt level serves as a signal of firm s quality and the market values a company with higher level of debt better (Narayanan, 1988; Ross, 1977). Our primary idea is essentially identical with that of those studies, except that the debt level chosen by a lending bank serves as a signal of firm s type in our model whereas that chosen by a manager does so in the previous studies. The remainder of this paper is organized as follows. Section explains our basic model. Section 3 extends the basic model and draws a theoretical conclusion regarding the relation between the debt level after the forgiveness and stock price reactions of a borrowing firm and a lending bank. Section 4 presents empirical test on the main implication of our model. Finally, this paper is summarized in Section 5.. The basic model.1. Basic environments et us consider a three dates model (t=0,1,) with two agents: a bank and a firm manager (See Figure 1). For a purpose of simplification, we assume that all economic agents are risk neutral and risk-free rate is zero. The firm has existing assets at t=0 and they earn random return at t=1 and, and respectively. y takes on a value y1 y of y with the probability of p and y with the probability of 1 p ( y < y ). Throughout this paper, we assume y y a (a is constant). The firm issues bank debt at t=0 with the face value of repay D 1 to the bank. = D 1. This debt is matured at t=1 and the firm must Suppose that happens to be zero at t=1 and thus the firm can not meet the repayment of. The liquidation value of the firm is zero and then the bank preliminarily delays the repayment of profitability of the firm. At t=1.1, the certain value of y to t= and starts to evaluate the future (t=) is realized and thus that of is also realized. This information is available to the manager and the bank. At the same time, the bank can revise the loan face value so as to maximize its expected return. owever, we assume that the bank can not increase the loan face value at that moment. We denote the revised loan face value as. takes on a value of D or ( D ). We refer the bank s decision to decrease the loan face value into D as debt forgiveness. y 1 D 1 D 1 y D D 1 DF < 1 F 3

4 At t=1., the manager chooses his/her effort level e ( 0 e 1). The manager s effort level affects p, the probability of realizing higher return, y, at t=. Specifically, we assume p = p(, p ( > 0, p ( < 0, p ( 0) = 0 and p ( 1) = 1. We also postulate that the effort is costly for the manager. e/she must bear cost c = c( and c( has the following characteristics; c ( > 0, c ( > 0 and c ( 0) = 0. The manager M chooses his/her effort level so as to maximize his/her expected utility, U. We define M the U as U M M = E{max( 0, y D )} c(. The first term of the U represents the firm s expected return after the payment of the revised face value to the bank... Manager s effort level First, we should analyze the effort level chosen by the manager at t=1.. When the bank revises the loan face value from into D at t=1.1, the following lemma is held. D1 emma 1 (manager s effort level): The effort level chosen by the manager is: (1) e if 0 D < y. The e is the effort level satisfying the following condition. p'( e )( y y ) c'( e ) = 0. () a decreasing function of D when y D < y. (3) zero if y < D. Overall, the function e(d) takes a form shown in Figure. [Proof] See Appendix A. It would be useful to analyze the form of e( D ) in the range of y D < y. Second derivation of e( D ) is computed as follows. e''( D ) p''( e' ( D ){( y D ) p''( c''( } p'( {( y D = {( y D ) p'( c''( } ) p'' '( e'( D ) p''( c'' '( e'( D )} Since the third derivations of p ( and c( appear in the numerator, we can not specify the sign of e '( D ). For a purpose of simplification, we focus on the case of e ''( D ) < 0 ' 4

5 throughout the rest of this paper. 1 Thus, the manager s effort level is a concave function of, when D ranges between y and y. After all, e D ) takes the form shown D in Figure. (.3. Bank s decision y Next, we analyze the bank s choice at t=1.1, the bank knows the realized values of and y. At this time, it may have an incentive to revise the face value, if doing so maximizes its expected return. We show the following lemma about the loan face value maximizing the bank s expected return. emma (optimal face value for the bank): There is an optimal face value D for the bank in the range between y and. If D <, the bank can maximize its expected return by reducing the loan face value into y D1 D (debt forgiveness). In the debt forgiveness case, the bank s expected return amounts to π = )) D + {1 p( e( D y p ( e( D ))}. [Proof] See Appendix B. emma offers a reason why a lending bank provides debt forgiveness to a financially distressed firm. The debt forgiveness has two conflicting effects on the bank s loan value. One is the reduction of the amount which the bank has a right to collect from the firm. It obviously reduces the bank s loan value. owever, the debt forgiveness has another effect on the loan face value. That is, it increases the manager s effort level (emma 1) and thus lifts up the loan face value. The relation between the revised face value and the loan value is determined by the trade off between these two conflicting effects (Figure 3). As shown in Figure 3, there is a unique level of D maximizing the bank s expected return. If, therefore, the bank provides debt forgiveness, reducing the face value into. If D, on the other hand, the bank does not provide debt forgiveness. D > D 1 D 1 D 1 When p' ''( 0 and c '''( 0, the e '( D ) certainly becomes negative. ' 5

6 3. The extension of the basic model 3.1. Setting This section presents an extended model of the Section for a purpose of analyzing market reaction to an announcement of debt forgiveness. Suppose a three dates model similar to that in the former section. In this section, we postulate that is subject to the distribution function, F ( ), y y, y ]. Since y equals to y + a, the level [ of realized y represents quality of the firm. That is, higher y corresponds to a better type of a firm. et us denote the density function for distribution function of manager and the bank. y y y as f ( ). All agents know the, but they can not observe its realized value except the Suppose that the existing assets happen to earn zero return at t=1. The bank preliminarily delays the repayment of into t=. The level of D and the bank s decision to delay the repayment of value of y are common knowledge. At t=1.1, the certain realizes and only the manager and the bank can have access to this information. At this time, the bank can calculate D 1 D1 1, the loan face value maximizing the loan value. If D 1 > D, the bank decides to provide debt forgiveness and announces the amount of debt forgiveness to public. D 3.. Firm type and the loan face value chosen by the bank In this setting, we derive the following lemma regarding the relation between the firm quality (level of y ) and the loan face value maximizing the bank s loan value. emma 3 (firm quality and loan face value maximizing bank s expected return): As shown in Figure 4, the loan face maximizing bank s expected return becomes higher as the firm quality improves. That is, D = D ( y ), > 0. dy [Proof] See Appendix C. emma 3 has an important implication for examining the market reaction to the announcement of debt forgiveness. The bank which knows the realized value of can choose the loan face value maximizing its expected return. For outside investors y 6

7 who can not have access to the realized value of, emma 3 means that they can rationally identify its realized value (firm typ by observing the revised face value when debt forgiveness is announced. Figure 4 illustrates the implication of emma 4. The upper-right (downer-left) lines correspond to bank s expected return lines when the firm type is better (wors. Better the firm type becomes, higher the loan face value maximizing bank s expected return becomes. Using Figure 4, outside investors can rationally identify firm type when they know firm s debt level after the debt forgiveness. We denote the outside investor s belief function about the realized value of y as y = dy y ( D ). It satisfies 1 < (See Appendix C). The idea that the loan face value after the debt forgiveness reveals firm type to outside investors is similar to that of a stream of previous studies on optimal capital structure (Ross, 1977; Narayanan, 1988). These studies argue that firm s debt level coveys its quality to the market. When a manager chooses higher debt level, the market considers that the manager believes his/her firm to have enough profitability to repay the high level of debt. As a result, they identify that the firm quality is high. This argument is identical with that of our model except that firm s debt level chosen bank conveys the firm s type to the market in our model. y D 3.3. The change in the firm s shareholder value and the bank s loan value At t=1 when the firm defaults, no agent knows the certain value of y ) D ( y ) < 1 y. For a purpose of simplification, we assume D ( < D. This assumption assures that the bank certainly provide debt forgiveness at t=1.1. Thus, all agents predict that the loan face value will be reduced to D ( y Thus, the shareholder value of the firm at t=1, y SV = f ( y )[ p( ( y + a D )] dy BF y Similarly, the bank s loan value at t=1, V BF y y ) at the moment of the default.. V BF = f ( y )[ p( D + (1 p( ) y ] dy. At t=1.1, the bank knows the realized value of forgiveness, F 1 maximizing the bank s expected return, SV BF, is evaluated as follows., is evaluated as follows. and announces the amount of debt. Therefore, outside investors rationally identify the realized value of y through the belief function, ( ), at t=1.1. The y = D D. At this time, outside investors know the loan face value D y D 7

8 firm s shareholder value after the announcement of debt forgiveness, follows. SV, becomes as SV = p( ( y ( D ) + a D ). Thus, the change in the firm s shareholder value before and after the announcement of debt forgiveness, CSV, is computed as follows. CSV = p( ( y ( D ) + a D ) V BF Similarly, the bank s loan value after the announcement of debt forgiveness, evaluated as follows. V = p( D + (1 p( ) y ( ). D. V Thus, the bank s loan value change before and after the announcement of debt forgiveness is expressed as follows. CV = p( D + (1 p( ) y ( D ). These calculations derive the following proposition., is Proposition 1 The changes in firm s shareholder value and bank s loan value before and after the announcement of debt forgiveness is positively correlated to the loan face value after the debt forgiveness. [Proof] See Appendix C. The loan face value after the debt forgiveness affects the firm s shareholder value through several ways (Figure 5); First, higher face value enables the lending bank to explore a larger part of firm s return and thus decreases the firm s shareholder value (expropriation effect). Second, higher face value reduces the shareholder value by decreasing manager s effort level (incentive effect of loan face valu. Third higher face value reveals that the firm type is better (announcement effect). Finally, we should note that a manager of a better type of a firm with higher loan face value chooses higher effort level (incentive effect of firm typ. A key point in considering the relation between and the firm s shareholder value is that y increases by more than one unit when D increases by one unit ( dy > 1 ). This assures that the positive announcement effect on the shareholder value exceeds the negative expropriation effect when D D increased by one unit. It is also confirmed that the positive incentive effect achieved by better firm type associated with higher D 8

9 outperforms the negative incentive effect induced by the higher. Overall, we can present a conclusion that the firm s shareholder value is positively correlated with the loan face value after the debt forgiveness. For the same reason, the bank s loan value is also positively associated with the loan face value after the debt forgiveness. These arguments obviously mean that the changes in firm s shareholder value and bank s loan value before and after debt forgiveness are positively related to the loan face value after the debt forgiveness. Finally, it would be worth noting that our model does not offer a clear prediction about the direction in the market reaction of firm s stock price and bank s loan value. We argue that the market will positively (negatively) respond to the news of debt forgiveness when the loan face value after the debt forgiveness conveys that the realized y is higher (lower) than the ex ante expected value of D. All we can insist is that the loan face value after the debt forgiveness serves a signal of firm type and it is positively correlated with the changes in the firm s shareholder value and the bank s loan value. y 4. Empirical evidence 4.1. Sample selection and methodology Our model demonstrates that the firm s stock price reaction to the announcement of debt forgiveness is positively correlated with the debt level after the forgiveness. It is also shown that the change in the bank s loan value and therefore the bank s stock price reaction are positively related to the debt level after the forgiveness. This section empirically tests this hypothesis, using Japanese data. In recent years, Japanese banks sometimes provide debt forgiveness to financially distressed firms. We collect stock price data of the firms provided with debt forgiveness and the banks forgiving loans during the period from 1995 to 00. Our main concern is not to investigate the sign of stock price reactions of the firm and bank but to test whether the stock price reactions have positive correlations with the debt level after the debt forgiveness. Our sample selection procedure is as follows. First, we search news paper articles whose key words are debt forgiveness using Nihon Keizai Shimbun CD-ROM Of the searched articles, we pick up those on out-of-court debt forgiveness between Japanese private banks and a listed company. 3 Non-listed companies are The Nihon Keizai Shimbun is the most popular economic newspaper in Japan. 3 For example, articles on debt forgiveness by non-financial institutions, debt forgiveness provided to foreign national projects, debt forgiveness induced by lender s 9

10 generally small so that debt forgiveness to them may not have enough impact on bank s share prices. The articles appearing in regional pages are also excluded. We collect stock price data of the firm provided with debt forgiveness and its main bank. We define the main bank as the first described bank in the article among those with which the firm deals. The stock price data is obtained from Stock Price CD-ROM of Toyo Keizai Data Bank. For analyzing the stock price reaction, we use a standard methodology of event study (Brown and Warner, 1980; Brown and Warner, 1985; MacKinlay, 1997). Throughout the paper, day t means t days after the event day (day 0), and day t means t days before the event day. Specifically, we compute abnormal returns of the firm and bank during the period from day -10 to day 10 (event window). When the stock price data is missing on a day or days during the event window, the firm or bank is deleted from the sample. The abnormal return is defined as the difference between actual return and expected return estimated by the market model. The parameters of the market model are estimated using stock price data from day -0 to day -1 (estimation window). When the stock price data does not begin available at day -0, the firm or bank is excluded from the sample. We use Tokyo Stock Price Index (TOPIX) as a proxy for the market portfolio. We also compute cumulative abnormal return defined as the sum of abnormal returns during the days in the event window. et us denote the abnormal return on day t as AR(t) and the cumulative abnormal return from day t 1 and day t as CAR t, t 1 ). ( A difficult task in the event study on the debt forgiveness is to specify the event day. Especially when a large company is provided with debt forgiveness, the news about it is usually released several times following the next steps. First, the company asks debt forgiveness to its principal banks. The amount of debt forgiveness which the firm asks is also released in this step. Second, the main bank of the firm announces that it accepts the request and is negotiating with other banks for each bank s share of debt forgiveness. Finally, the agreement by the distressed firm and all lending banks on the debt forgiveness is announced. It occasionally takes a few months to reach agreement by all lending banks from a day when a financially distressed firm asks debt forgiveness to its principal banks. For example, Kumagaigumi, a general contractor, announced agreement on debt forgiveness with all lending banks on December 8, 00 whereas it released its restructuring plan which includes debt forgiveness of 450 billion yen on September 19, 00. In this case, thus, there was 3-months lag between the firm s first request for debt forgiveness and financial distress are deleted from this analysis. 10

11 final agreement with all lending banks. For the above reasons, we define the event day as follows: a) a day when a distressed firm announces its restructuring plan including a request for debt forgiveness or b) a day when a distressed firm asks debt forgiveness to its principal banks. Stock prices are likely to reflect the information of debt forgiveness at the moment that a firm asks debt forgiveness. The most important problem in this method is that the firm is not secured to be provided with debt forgiveness since all banks do not agree with that at this time. owever, it would be a plausible inference that at least principal banks agree with the distressed firm on the debt forgiveness under the surface when the firm announces its policy of asking debt forgiveness. 4 If the news that a principal bank or all lending banks agree (decid to provide debt forgiveness are released as the first news on the debt forgiveness, we set that day as the event day. We have to stress that the amount of debt forgiveness is important in this research, because that figure is necessary in computing the debt level after the debt forgiveness. If no information is announced about the amount of debt forgiveness on a day when a distressed firm announces its restructuring plan including a request for debt forgiveness or asks debt forgiveness to its principal banks, we set the event day as the first day when the amount of debt forgiveness is released. Through these procedures, we have 36 cases of debt forgiveness as our entire sample. Panel A of Table 1 exhibits the year and industry distribution of the entire sample. ooking at the year distribution, the cases of debt forgiveness have heavily increased since The top rank industry regarding the number of firms provided with debt forgiveness is construction industry. This reflects the fact that the Japanese construction companies borrowed huge amount of land-collateral loans in the late 1980s and thereafter experience serious downturn of land prices in the 1990s. The construction industry is followed by the wholesale industry. Panel B of Table 1 describes the size of debt forgiveness. The amount of debt forgiveness is over 100 billion yen on average. In half cases, however, debt forgiveness of less than 50 billion yen is provided. The financially troubled firms reduce approximately 40 percent of their financial liabilities through the debt forgiveness. Panel B also shows the firm s debt-to-total assets ratio before and after the debt forgiveness. The firms provided with debt forgiveness uniformly have extremely high debt-to-assets ratio and in most cases it exceeds 90 percent. The firm reduces the 4 In many cases, principal banks of a financially distressed firm announce that they will support the firm as much as possible on the day when the distressed firm announces its policy of asking debt forgiveness. 11

12 debt-to-assets ratio into about 75 percent on average through the debt forgiveness. The ratio after the debt forgiveness is more widely ranged and 75 percent of the sample ranges between percent. In 4 cases of the entire sample, stock price data of the borrowing firms is not available on a day or days during their event windows. We delete these companies from the sample and thus 3 companies are adopted as our sample for borrowing firms. In six cases, bank s stock price data does not begin available at day -0. We also exclude these banks from the research and then 30 banks are adopted as our sample of banks providing debt forgiveness. 5 Table summarizes the firm s and bank s stock price reaction for the entire sample. It indicates that CAR ( 1,0) and CAR( 1,1 ) of the firm are significantly positive, suggesting that firm s stock price positively reacts to the news of debt forgiveness. On the other hand, it shows that bank s CAR are not significantly different from zero. 4.. Stock price reaction and firm s debt level after the forgiveness This subsection tests the hypothesis that the firm s and bank s stock price reactions are positively correlated with the debt level after debt forgiveness. Specifically, we investigate the relation between the firm s debt level after the debt forgiveness and CAR of both borrowing firm and lending bank. An important problem here is what would be an appropriate measure of the firm s debt level. The most common measure of firm s debt level would be the debt-to-assets ratio. owever, adopting the debt-to-assets ratio as a measure of the debt level might be misleading for testing the implication of our theoretical model. As described before, the debt-to-assets ratios before the debt forgiveness of our sample are uniformly high (mean is 99.6%) and three-fourth of the sample concentrate on the range between 91.5% and 99.8%. As a result, the debt-to-assets ratio after the debt forgiveness shows high correlation with the size of debt forgiveness, which might affect the stock price reaction for some reasons beyond our model. Therefore, we afraid that adopting the debt-to-assets ratio as a proxy for debt level might bias our results. Given that firms provided with debt forgiveness tend to have large amount of non-profitable assets due to the collapse of the asset babble, a measure which divides debt level by sales or cash flow would offer a more appropriate proxy for the degree of firm s burden of liabilities. Actually, recent Japanese economists frequently use such measures when examining the excess debt problem in the industrial sector (e.g., 5 Some mergers or integrations between large Japanese banks occurred in the late 1990s make it difficult to collect long-term stock price data of the banks. 1

13 Economic Survey of Japan, 000). Since the cash flow of a firm provided with debt forgiveness is likely to be negative, we adopt debt-to-sales ratio as a proxy for the debt level. It is computed as the debt at the latest fiscal year end before the event day subtracted by the amount of debt forgiveness divided by sales during the latest fiscal year before the event day. Using two definitions about the debt, all liabilities and financial liabilities, we analyze the relation between two kinds of debt-to-sales ratio and the stock price reaction. Specifically, we equally divide the sample into two groups based on the debt-to-sales ratio after the debt forgiveness and compare the stock price reactions between the two groups. We also present correlation coefficient between the debt-to-sales ratio andcar. Considering that the sample size is small, we adopt not only the usual correlation coefficient (Pearson s correlation coefficient) but also non-parametric correlation coefficient (Spearman s correlation coefficient). Table 3 shows the empirical result for the firm s stock price reaction. Panel A exhibits the empirical result when using the all liabilities-to-sales ratio as a measure of debt level after the debt forgiveness. It finds that firms with low debt-to-sales ratios experience negative stock price reactions and their CAR(0,1) is significantly negative. On the other hand, CAR of the firms with high debt-to-sales ratio are systematically positive and significant. We also find that CAR is significantly different between the two groups. Furthermore, the non-parametric correlation coefficient (Spearman) shows that CAR ( 1,0) and CAR(0,1) have positive and significant correlations with the debt-to-assets ratio. Panel B which describes the empirical result when adopting the financial liabilities-to-sales ratio as a proxy for the debt level after the debt forgiveness shows similar findings. The firm with low debt level after the debt forgiveness experiences negative stock price reaction on average, whereas that with high debt level after the debt forgiveness systematically has positive and significant CAR. The differences CAR are systematically significant between the two groups. These findings support the hypothesis that the firm s stock price reaction to the announcement of debt forgiveness is correlated with the debt level after debt forgiveness. Table 4 depicts the relation between firm s debt level after the debt forgiveness and bank s stock price reaction. Panel A exhibits the empirical result when using the all liabilities-to-sales ratio as a measure of debt level after the debt forgiveness. It finds that the bank s stock price reaction is not significantly different from zero when debt forgiveness makes firm s debt level lower. In the case of debt forgiveness in which firm s debt level after the debt forgiveness is higher, the bank s CAR s are systematically positive and one of them are statistically significant. We also find that 13

14 CAR (0,1) and CAR( 1,1) have significantly positive correlations with the all liabilities-to-sales ratio (Pearson correlation coefficient). Panel B shows results for the relation between firm s debt level after the debt forgiveness and the bank s stock price reaction when adopting the financial liabilities-to-sales ratio as a measure of the debt level. It reveals that debt forgiveness which makes firm s debt level lower provides negative stock price reaction to the lending bank. owever, the stock price reactions in the case of debt forgiveness which makes firm s debt level higher are positive and two of them are statistically significant. We also find the differences in CAR (0,1) and CAR ( 1,1 ) between the two groups to be statistically significant. Furthermore, non-parametric correlation coefficient shows that bank s CAR(0,1) has a significantly positive correlation with the financial liabilities-to-sales ratio. Overall, our empirical test supports the hypothesis that firm s and bank s stock price reactions to the announcement of debt forgiveness are positively related to firm s debt level after the forgiveness. 5. Concluding remarks This paper explores theoretically and empirically the stock price reactions of a borrowing firm and a lending bank to the announcement of debt forgiveness. The basic idea of our theoretical model is that a bank may provide debt forgiveness when the debt level of a financially distressed firm is higher than the level which maximizes its expected return. In other words, the debt forgiveness adjusts the debt level of a financially distressed firm, usually too high, into the optimal one for the lending bank. This idea leads to the theoretical prediction that debt level after the debt forgiveness reveals the real quality of the distressed firm to outside investors. Overall, our model predicts that the stock price reactions of a borrowing firm and a lending bank are positively correlated with the debt level after the debt forgiveness. Using recent Japanese data, we empirically test this prediction by a standard event study methodology. Our empirical test shows that the stock price reactions of financially distressed companies and lending banks when debt forgiveness is announced have positive and significant correlation with the debt-to-sales ratio after the forgiveness. This evidence supports the main implication of our model. Our argument is also consistent with a stream of previous studies on the optimal capital structure. Some authors argue that the debt level serves as a signal of firm s quality and the market values more a company with higher level of debt (Narayanan, 1988; Ross, 1977). Our primary idea is essentially identical with that of these studies, 14

15 except that the debt level chosen by a lending bank serves as a signal of firm s quality in our model whereas the debt level chosen by a manager does so in the previous studies. 15

16 References Brown, S. J., Warner, J. B., Measuring security price performance. Journal of Financial Economics 8, Brown, S. J., Warner, J. B., Using daily stock returns: The case of event studies. Journal of Financial Economics 14, Isagawa, N., Yamashita, T., 003. Debt forgiveness and stock price reaction of lending bank: Theory and evidence from Japan. Discussion Paper Series 003.8, Kobe University. Jensen, M. C., Meckling W.., Theory of the firm: Managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3, MacKinlay, A. C., Event studies in Economics and Finance. Journal of Financial Economics 5, Myers, S. C., Determinants of corporate borrowing. Journal of Financial Economics 5, Myers, S. C., Majluf, N. S., Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics 13, Narayaman, M. P., Debt versus equity under asymmetric information. Journal of Financial and Quantitative Analysis 3, Ross, S. A., The determination of financial structure: The incentive-signaling approach. Bell Journal of Economics 8, Uchida, K., Goto, N., 00., Economic role of forgiving loans. JCER Economic Journal 45, (in Japanes. 16

17 Appendix A M (1) In the case of D < y, U = p( ( y D ) + (1 p( )( y D ) c(. The first order condition of the expected utility maximization is p ( ( y y ) = c (. () In the case of y D <, U = p( ( y D ) c(. The first order condition y m of the expected utility maximization is p ( ( y ) D c ( = 0. Then, we can obtain the following relation between the revised face value and the manager s effort. de = ( y D p' ( '' ) p ( c '' < 0. ( (3) In the case of y < D, U m = c( and thus the manager obviously makes no effort. Q.E.D Appendix B If the bank sets the revised face value to D satisfying 0 < D < y, it certainly collects D at t=. In this case, the obviously maximizes its expected return to y by setting D to. When y < D, the manager must make no effort (see emma 1) y and thus the bank certainly collects When the D rangs between y and y,the bank s expected return equals to y. π = ( e( D )) DAR + {1 p( e( D p ))} y specifying the form of π D ), we calculate the following equations. dπ = ( y ) p ( e' ( D ) + ( D p(.. For The form of π D ) is specified through the following calculations, though we cannot ( specify the sign of lim D y dπ. dπ = p( e( y )) = p( e ) > 0, 17

18 lim D y dπ dπ = ( y y ) p'( e'( y ) < 0, = p'( e'( D ) + ( D y ){ p''( e' ( D ) + p'( e( D ) e''( D )} < 0, π ( y ) = π ( y ) = y. ( D Therefore, π ) takes a form as shown in Figure.3. There is an optimal level of D = D which maximizes the bank s expected return in the range of y D < y. Q.E.D. Appendix C The loan face value maximizing the bank s expected return, condition. ' ( D y ) p ( e( D )) e ( D ) + p( e( D )) 0. Then, = < D y y < D, meets the following dy = p'( e'( D ) + ( D y p'( e'( D ) p''( { e'( D ) )} + ( D y ) p'( e''( D ) Thus, 0 < < 1. dy Q.E.D. Appendix D First, we demonstrate that the change in the firm s shareholder value has a positive correlation with the loan face value after the debt forgiveness. We have to pay attention that D has several ways of affecting SV. D has an impact on SV by affecting manager s effort level, by revealing Overall, effect of D on SV is computed as follows. dsv SV dy = + D SV y, y, and by reducing the amount of repayment. 18

19 SV D V y dy 1 <, e D e = p'( D e = p'( y = ( y Therefore, dsv > 0. Since ( y ( y + a D ) p(, + a D ) + p(, p'( e =. + a D ) p''( c''( y y e dy = ( 1) p'( ( y + a D ) + ( D y SV = D dy + SV y dsv SVBF is constant, > 0 1) p( obviously means that the firm s shareholder value change has a positive correlation with the loan face value after the debt forgiveness. Next, we show that the change in the bank s loan value has a positive correlation with the loan face value after the debt forgiveness. The loan value after the debt V forgiveness,, is also affected by through several ways. dv = p'( ( D = p'( ( D Since V = D y y dy + dy )( dy )( V y e y e 1) y e + D D dy ) + p( + dy + p( + dv VBF is constant, > 0 (1 p( ) (1 p( ) > 0. obviously means that the bank s loan value change before and after the announcement of debt forgiveness has a positive correlation with the loan face value after the debt forgiveness. Q.E.D 19

20 Figure 1 Time line t=0 t=1 t=1.1 t=1. t= y Existing assets Return and determined Return realizes 1 y Bank Debt issue Expiration of the loan or Face value D1 y y y Manager s chooses his/her effort level Bank can revise the face value Bank delays the repayment of D1 y 1 into t= if y 1 < D1 Figure Revised face value and manager s effort level e e 0 y y DAR 0

21 π Figure 3 oan face value and bank s expected return π y 0 D y D y 1

22 Figure 4 Firm type and bank s expected return line Better type (igher y ) 0 D y = y + a

23 Figure 5 oan face value and firm s shareholder value after the debt forgiveness oan face value Negative after the debt forgiveness( D ) Negative Positive Manager s effort level ( e ) Positive Shareholder value after the debt forgiveness ( SV ) Positive Firm type ( ) y Positive 3

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