- Email: [email protected]
The soft budget constraint, the debt overhang and the optimal degree of credit centralization
Japan and the World Economy 19 (2007) 187–197 www.elsevier.com/locate/econbase
The soft budget constraint, the debt overhang and the optimal degree of credit centralization Kenji Tsuji * Graduate School of Economics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan Received 11 April 2003; received in revised form 1 August 2005; accepted 19 September 2005
Abstract The paper analyzes the optimal degree of credit centralization in the situation where the soft budget constraint and the debt overhang problems may occur. The paper characterizes the optimal range of credit centralization, and shows that the entrepreneur with a greater endowment or higher credit quality is likely to choose a lower degree of credit centralization. # 2005 Elsevier B.V. All rights reserved. JEL classification: G30 Keywords: The soft budget constraint; The debt overhang; The degree of credit centralization
1. Introduction The soft budget constraint and the debt overhang problems, which were originally posed by Kornai (1980) and Myers (1977) respectively, are important in corporate finance, since the former induces overinvestment and the latter induces underinvestment. Studies on the former include Kornai (1980), Dewatripont and Maskin (1995), Berglo¨f and Roland (1995, 1997), Maskin (1996, 1999) and Kornai et al. (2003). Studies on the latter include Myers (1977), Lamont (1995) and Snyder (1998). In the previous literature, both problems have been treated separately, but this paper provides a framework for analyzing both problems simultaneously and analyzes the optimal degree of credit centralization. Several studies have been undertaken on credit concentration. For example, assuming that asymmetric information exists between entrepreneurs and creditors, Dewatripont and Maskin
* Tel.: +81 6 6609 5169; fax: +81 6 6605 3066. E-mail address: [email protected]. 0922-1425/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2005.09.002
188
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
(1995) show that since credit decentralization offers a way for creditors to commit not to refinance unprofitable projects, it tends to deter unprofitable projects, thus providing financial discipline, but it may also discourage profitable projects that are slow to pay off. Bolton and Scharfstein (1996) show that it is optimal for firms with low credit quality to borrow from just one creditor, and for firms with high credit quality to borrow from multiple creditors. Their basic idea is that while borrowing from multiple creditors disciplines managers, it can reduce efficiency by lowering liquidation value in a liquidity default, and an optimal contract must balance these two effects. These papers do not consider the optimal degree of credit centralization, which I investigate. In this paper, the entrepreneur has insufficient capital, so he has to depend on outside lenders to finance a project requiring a sequence of investments. Since the initial loan is sunk as in Dewatripont and Maskin (1995), if it is made by only one lender, then the soft budget constraint problem may occur, that is, the entrepreneur may extract ex post a larger loan than would have been considered efficient ex ante. Decentralizing credit allocation to many lenders improves the financial discipline of the entrepreneur and alleviates the soft budget constraint problem; however, it may induce the debt overhang problem due to the incentive for lenders to free-ride. Returns from a project refinanced by a lender are beneficial to all lenders, not just to that lender alone. That is, refinancing is a public good, from the individual lender’s viewpoint, and thus the free-rider problem may occur in refinancing the project, leading to the possibility that later investment with positive values will be abandoned; that is, the debt overhang problem may occur. This paper shows that there is an optimal range of credit centralization under which neither the soft-budget constraint nor the debt overhang problems occur. If the degree of credit centralization is above the upper bound of the optimal range, the soft budget constraint problem occurs, and if it is below the lower bound of the optimal range, the debt overhang problem occurs. In addition, this paper shows that the entrepreneur with a greater endowment or higher credit quality is likely to choose the lower degree of credit centralization. Japanese firms depend heavily on debt finance, and particularly depend on their largest respective lenders—main banks. This fact is consistent with the results of this paper. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks. The rest of the paper is structured as follows. Section 2 describes the basic model. Section 3 derives the optimal contracts and the optimal range of credit centralization. Section 4 presents the major conclusions. 2. A basic model An entrepreneur undertakes a project requiring a sequence of investments. The entrepreneur can choose only one project among N(>1) projects indexed by i = 1, 2, 3, . . ., N. All projects require an investment I1 in period 1. The entrepreneur is endowed with W(>0), which is less than I1, so the entrepreneur must borrow I1 W from lenders to undertake a project. If investment is undertaken in period 1, then at the end of period 2, project i generates return Ri(>0) with probability 1 if the state is good. The same return is generated with probability L2 =I2i if the state is bad, and no return occurs with probability 1 if the state is very bad. Here, L2 ð 2 I2i Þ is the amount actually invested by the entrepreneur in period 2, and I2i ð > 0Þ is the sufficient amount of investment which project i require in period 2 if the state is bad. In period 2, since the entrepreneurs have no endowment, L2 is equal to the total amount of loans granted by lenders.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
189
Note that all projects require no period 2 investment if the state is good or very bad. For all projects, the probability that the state is good is p1(>0, <1), that it is bad is p2(>0, <1) and very bad is 1 p1 p2(>0, <1). The entrepreneur chooses a project, after the initial loan contract is made in period 1. The state is realized at the start of period 2. The project choice, the realized state and the realized return from the project are observed by both the entrepreneur and lenders, but are not verifiable to outsiders, e.g. courts. The parameters I1, I2i , p1 and p2 are considered to be common knowledge. The amount actually invested and the amount actually paid to the lenders are assumed to be freely observable by the entrepreneur and lenders, and be verifiable to outsiders. I assume that if the entrepreneur defaults on debt contracts, then lenders together obtain all residual value and the entrepreneur receives nothing, thus the entrepreneur pays the promised amount as long as he can do so. Both the entrepreneur and lenders are assumed to be risk-neutral. The entrepreneur obtains a non-monetary, non-transferable private benefit, B, such as reputation, specific human capital, etc., if and only if a project is undertaken and completed successfully, that is, generates the return Ri. The entrepreneur maximizes the sum of his expected monetary returns and his private benefit, which is henceforth called expected total revenue. The entrepreneur borrows I1 W for two periods from lenders at the start of period 1. Lenders are assumed to be competitive at the contracting stage, so each lender makes zero expected profits. Furthermore, they are ready to provide funds as long as they break even on their loans. The risk-free market interest rates are certain and normalized to zero. To consider the case where it can be profitable ex post for a lender or lenders to grant a loan of I2i to a financially distressed entrepreneur, it is assumed that Eq. (1) holds: I2i < Ri < ðI1 WÞ þ I2i :
(1)
In the remainder of this section, I assume that the entrepreneur borrows funds from only one lender in period 1, called the incumbent lender. The incumbent lender grants a loan of I1 W to the entrepreneur at an interest rate of r1 in period 1. The maximum expected monetary surplus for project i is Si ¼ ð p1 Ri I1 Þ þ p2 ðRi I2i Þ:
(2)
Suppose that the project indexed by larger number has a larger maximum expected monetary surplus, i.e. Si < Sj, if i < j. For simplicity, assume that Si > 0 for all i 2 {1, 2, 3, . . ., N}. Suppose that project i is undertaken and the state is bad. In this case, potential lenders grant no loan in period 2, since Eq. (1) holds. Assume that the incumbent lender has all the bargaining power in the negotiation phase of period 2 loan, i.e. the lender presents the entrepreneur with a take-it-or-leave-it-offer and so appropriates all the verifiable returns. The incumbent lender grants a loan of I1 W in period 1 and L2(30) in period 2, and acquires Ri with probability L2 =I2i at the end of period 2. Hence, the expected profit of the incumbent lender, pi(L2), is given by
pi ðL2 Þ ¼
L2 Ri L2 ðI1 WÞ: I2i
(3)
190
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
Differentiating Eq. (3) with respect to L2, I get dpi 1 ¼ ðRi I2i Þ > 0: I2i dL2
(4)
From Eq. (4), the incumbent lender grants a loan of I2i in period 2, i.e., L2 ¼ I2i , and so the return of project is Ri with certainty. Given that L2 ¼ I2i , the entrepreneur’s expected revenue, Pi, is P i ¼ p1 ðRi PÞ þ ð p1 þ p2 ÞB;
(5) i
where P is the promised payment to the incumbent lender. In equilibrium, P is equal to be Si, since P is determined so that the incumbent lender acquires zero expected profits. Differentiating Pi with respect to Ri, I have dP i ¼ p1 > 0: dRi
(6)
If project N has the largest project return, then the entrepreneur undertakes project N since dPi/dRi > 0, and there is no efficiency loss. Suppose that project N does not have the largest project return. The project with the largest project return is denoted by project M. Assume that the lender cannot commit himself not to make a loan larger than I2N , because such a commitment can be renegotiated if renegotiation is profitable ex post. The entrepreneur undertakes project M and the expected efficiency loss, SN SM(>0), occurs. This implies that the entrepreneur chooses the project with the largest project return regardless of the amount of funds required in period 2; consequently the project with the largest expected surplus may not be chosen, and the expected efficiency loss may occur. This leads to the following proposition. Proposition 1. Suppose that the entrepreneur borrows from one lender, and that the project with the largest expected surplus does not have the largest project return. Then, the entrepreneur undertakes an inefficient project and an expected efficiency loss occurs. From Eq. (2), it is clear that I2M > I2N since SN > SM and RN < RM. When the entrepreneur undertakes project M and the state is bad, period 2 loan is larger than if project N is undertaken. Namely, the entrepreneur extracts ex post a larger loan than would have been considered efficient ex ante. This is the soft budget constraint problem. 3. Optimal contracts Suppose that the entrepreneur can borrow the necessary funds, I1 W, from K(>1) lenders at the start of period 1. The lenders who grant loans to the entrepreneur in period 1, called the incumbent lenders, are assumed to have all the bargaining power in the negotiation phase of period 2 loan and so acquire all residual value if the state is bad, as assumed in the previous section. Assume that many lenders cannot co-operate in period 2, since lenders have an incentive to free-ride. Under these assumptions, the following proposition is obtained. Proposition 2. Suppose that ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ > L1j > 0;
for all j 2 c
(7)
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
191
and X
L1j ¼ I1 W;
(8)
j2c
where C is the set of the incumbent lenders. Then, none of lenders grant loans in period 2. Proof. I need only consider the situation where the state is bad, since refinancing is not required if the state is good or very bad. Suppose that project i is undertaken and the state is bad. First, consider the case where each lender acquires the same share of revenue from the project as the share of his loan. I denote period 1 loan and period 2 loan which incumbent lender j grants to the entrepreneur by L1j and L2j respectively, the total loan granted to the entrepreneur in period 2 by L2, total promised payment on period 1 loan by P1(3I1 W, 2Ri) which is determined at the start of period 1, and an interest rate on period 1 loan granted by lender j by r1j. Since incumbent lender j acquires L1j ð1 þ r1j Þ2 þ ðL2j =L2 ÞðRi P1 Þ with probability L2 =I2i at the end of period 2, the expected profit of incumbent lender j in the bad state, pi j ðL2j Þ, is given by ij
p
ðL2j Þ
L2j i ¼ þ þ ðR P1 Þ L2j L1j L2 j L2 L2 j j 2 ¼ L1 ð1 þ r1 Þ þ ðRi P1 Þ L2j L1j : I2i I2i L2 I2i
L1j ð1
r1j Þ2
(9)
Differentiating Eq. (9) with respect to L2j , the following equation is obtained.
1 fL1j ð1 þ r1j Þ2 þ ðRi P1 Þg 1 j i I dL2 2 i 1 1 R ðI1 WÞ L1j j j 2 i ¼ ½R fP1 L1 ð1 þ r1 Þ g 1 2 i 1 I2i I2 ð p1 þ p2 Þ 1 fð p1 þ p2 ÞðRi I2i Þ ðI1 WÞ þ L1j g: ¼ i I 2 ð p1 þ p2 Þ
dpi j
¼
(10)
The inequality follows from the non-negative profit condition of lenders besides lender j; i.e., ð p1 þ p2 ÞfP1 L1j ð1 þ r1j Þ2 g 3 ðI1 WÞ L1j . Since dpi j =dL2j < 0 from Eqs. (7) and (10), incumbent lender j does not grant a loan to the entrepreneur in period 2; i.e., L2j ¼ 0. For any lender who acquires the same share of revenue as the share of his loan, the same argument holds, so that none of the incumbent lenders lend anything to the entrepreneur in period 2. Second, consider the case where lender j acquires a smaller share of revenue than the share of his loan. The expected profit of incumbent lender j, pi j ðL2j Þ, is given by L2j ðRi P1 Þ L2j L1j L2 j L2 L ¼ L1j ð1 þ r1j Þ2 þ b i2 ðRi P1 Þ L2j L1j ; I2i I2
pi j ðL2j Þ ¼
L2 I2i
L1j ð1 þ r1j Þ2 þ b
(11)
192
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
where 1 > b > 10. Differentiating Eq. (11) with respect to L2j , the following equation holds: dpi j dL2j
¼
1 1 j j 2 i fL1 ð1 þ r1 Þ þ bðR P1 Þg 1 2 i fL1j ð1 þ r1j Þ2 þ ðRi P1 Þg 1: I2i I2 (12) dpi j =dL2j
From Eqs. (10) and (12), lender j grants no loan to the entrepreneur, since < 0 when Eq. (7) is satisfied. For any lender who acquires a smaller share of revenue than the share of his loan, the same argument holds, so they do not lend anything to the entrepreneur in period 2. Finally, consider the case where lenders acquire a larger share of revenue than the share of his loan. It is clear that the budget constraint is not satisfied, so this case is not feasible. Consequently, incumbent lenders do not lend anything to the entrepreneur in period 2. It is clear that potential lenders offer nothing to the entrepreneur in period 2. & From the left-hand side inequality of Eq. (7), I have Ri
fðI1 WÞ L1j g I2i < 0: p1 þ p2
(13)
If the return, Ri, is realized at the end of period 2, then lender j acquires at most ½Ri fðI1 WÞ L1j g=ð p1 þ p2 Þ, since the other lenders acquire at least fðI1 WÞ L1j g=ð p1 þ p2 Þ from the non-negative profit conditions. Eq. (13) means that lender j decreases his profits if he lends I2i to the entrepreneur in period 2. Hence, if Eq. (7) holds, then lender j does not grant period 2 loan. Also, Eq. (13) implies that as the loan granted by lender j, L1j , decreases, a leakage of return into the other lenders gets larger, and lender j acquires less return in period 2 and has less incentive to grant period 2 loan. Proposition 2 implies that if L1j ð j 2 cÞ is small, then refinancing is not undertaken and inefficiency occurs since Ri > I2i . This is the debt overhang problem, because later investment with positive values is abandoned after the initial investment is financed by debt. Suppose that the entrepreneur borrows Lk1 ð > 0; 2 I1 WÞ at an interest rate of r1k from lender k and I1 W Lk1 at an interest rate of r1o from the other lenders in period 1. The following proposition then holds. Proposition 3. Suppose that project i is undertaken and that ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ > L1j > 0;
for all j 2 fxjx 2 c and x 6¼ kg;
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1; r1o ¼ p1 þ p2
ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ < Lk1 2 I1 W;
(14)
(15)
(16)
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
r1k
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lk1 p2 fRi ððI1 WÞ Lk1 Þ=ð p1 þ p2 Þ I2i g ¼ 1; p1 Lk1
193
(17)
and X
L1j ¼ I1 W:
(18)
j2c
Then, the entrepreneur borrows the full amount of the necessary funds, I2i , from lender k in period 2, if the state is bad. Proof. From the proof of Proposition 2, if condition (14) holds, it is easy to show that L2j ¼ 0 for j 2 {xjx 2 C and x 6¼ k}, that is, none of lenders besides lender k grant loans in period 2. Since lenders besides lender k acquire fðI1 WÞ Lk1 g=ð p1 þ p2 Þ from the zero profit conditions, the expected profit of lender k in the bad state, pik ðLk2 Þ, is given by ik
p
ðLk2 Þ
¼
Lk2 I2i
ðI1 WÞ Lk1 R Lk2 Lk1 : p1 þ p2 i
(19)
Differentiating Eq. (19) with respect to Lk2 :
ðI1 WÞ Lk1 R 1 p1 þ p2 1 fð p1 þ p2 ÞðRi I2i Þ ðI1 WÞ þ Lk1 g: ¼ i I2 ð p1 þ p2 Þ
dpik ¼ dLk2
1 I2i
i
(20)
The right-hand side of Eq. (20) is positive from Eq. (16). Therefore, lender k grants a loan of I2i in period 2, that is, Lk2 ¼ I2i , in the bad state. Given that Lk2 ¼ I2i , the expected profit of lender k is fðI1 WÞ Lk1 g I2i ; p1 ð1 þ r1k Þ2 Lk1 Lk1 þ p2 Ri (21) p1 þ p2 which is equal to zero due to competition among lenders. Then, r1k is given by Eq. (17). Furthermore, Eq. (15) is obtained from the zero profit conditions of the other lenders. & Eq. (14) is the same as Eq. (7), except that the former does not include lender k. The left-hand side of Eq. (16) is the same as that of Eqs. (7) and (14). As easily inferred from the explanation of Eq. (13) which is derived from Eq. (7), the left-hand side inequality in Eq. (16) means that lender k increases his profits if he lends I2i to the entrepreneur in the bad state. Hence, if Eq. (16) holds, then lender k grants period 2 loan if the state is bad. Also, Eq. (16) implies that as a loan granted by lender k, Lk1 , increases, a leakage of return into the other lenders gets smaller, and lender k acquires more return in period 2 and has more incentive to grant period 2 loan. The right-hand side inequality in Eq. (16) means that the amount of loan granted by lender k, Lk1 , is limited by the full amount of necessary funds. Now, I turn from the behavior of lenders to that of the entrepreneur. If the entrepreneur undertakes project i and lender k grants a loan of I2i in period 2 in the bad state, then the expected total revenue of the entrepreneur is given by
194
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
P ic ¼ p1 ðRi P1 Þ þ ð p1 þ p2 ÞB:
(22)
The suffix ‘‘c’’ means that the project is continued in the bad state since the entrepreneur gets the necessary funds in period 2. If project Z is undertaken and is not refinanced in the bad state, then the entrepreneur’s expected total revenue is given by P Zt ¼ p1 fðRZ P1 Þ þ Bg:
(23)
The suffix ‘‘t’’ means that the project is terminated in the bad state since the entrepreneur has no funds in period 2. Since PZt takes the maximum value if RZ is equal to RM which is assumed to be the largest project return, the entrepreneur undertakes project M if the project is not refinanced in the bad state. Hence, I replace ‘‘Z’’ by ‘‘M’’ in Eq. (23). From Eqs. (22) and (23): P ic P Mt ¼ p1 ðRi RM Þ þ p2 B
(24)
From Eq. (24), if p1(Ri RM) + p2B > 0, then Pic > PMt. Suppose that another project, denoted by project X, gives the largest value of expected monetary surplus among projects included in [i 2 {1, 2, 3, . . ., N}jp1(Ri RM) + p2B > 0].1 For simplicity, assume that V 6¼ f where V = [i 2 {1, 2, 3, . . ., N}jRi 3 RX and i 6¼ X]. From Proposition 3, the following proposition then holds. Proposition 4. Suppose that ðI1 WÞ þ ð p1 þ p2 ÞðI2X RX Þ > L1j > 0; sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1; r1o ¼ p1 þ p2
for all j 2 fxjx 2 c and x 6¼ kg;
(25) (26)
ðI1 WÞ þ ð p1 þ p2 ÞðI2X RX Þ < Lk1 < min½ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ; ði 2 VÞ; (27) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lk1 p2 fRX ððI1 WÞ Lk1 Þ=ð p1 þ p2 Þ I2X g 1 (28) r1k ¼ p1 Lk1 and
X
L1j ¼ I1 W:
(29)
j2c
Then, the entrepreneur undertakes project X, borrows the full amount of the necessary funds from lender k if the state is bad, and acquires SX + (p1 + p2)B, which is the largest expected profit that the entrepreneur can obtain.
1
For simplicity, I assume that the private benefit of the entrepreneur, B, is so large that it holds that p1(Ri RM) + p2B > 0 for some i 2 {1,2,3, . . ., N}.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
195
Proof. It is clear from Eq. (6) that if Ri < RX for all i 6¼ X, then project X is undertaken. If Ri 3 RX, for some i 6¼ X, that is, i 2 V, then Si < SX from the definition of project X. There are some values of Lk1 that satisfy Eq. (27), since I2X RX < I2i Ri from Si < SX and Ri 3 RX. If Eqs. (25) and (27) are satisfied, then if project i 2 V is undertaken, it is not refinanced in the bad state from Proposition 2 and Eq. (20). From Eq. (24), the entrepreneur obtains more expected revenue by undertaking project X than project i 2 V, since p1(RX RM) + p2B > 0. Therefore, the entrepreneur undertakes project X. From Proposition 3, if project X is undertaken, then the entrepreneur borrows the full amount of the necessary funds from lender k if the state is bad. Since lenders are assumed to be competitive at the initial contracting stage, they obtain zero expected profits and the entrepreneur acquires SX + ( p1 + p2)B. By definition, project X gives the entrepreneur the largest expected revenue which he can acquire. & Eq. (25) is the same as Eq. (14), except that the former replaces project i with project X. As easily inferred from the explanation of Eq. (16), the left-hand side inequality of Eq. (27) means that lender k increases his profits if he lends I2X to the entrepreneur when project X is undertaken. Hence, if the left-hand side inequality of Eq. (27) holds, then lender k grants period 2 loan when project X is undertaken. The right-hand side inequality of Eq. (27) means that lender k decreases his profits if he lends I2i to the entrepreneur when project i is undertaken. Hence, if the right-hand side inequality of Eq. (27) holds, lender k does not grant period 2 loan when project i is undertaken. Since PXc > Pit for all i 6¼ X from the definition of project X, the entrepreneur undertakes project X which is the most efficient feasible project. Proposition 4 implies that if the optimal degree of credit centralization is chosen, then the project undertaken is successfully completed when the state is good or bad, and default occurs only when the state is very bad. Also, if it holds that p1(RN RM) + p2B > 0, then project X coincides with project N, which is a project with the largest expected monetary surplus, and there is no efficiency loss. Furthermore, from Eq. (27), the optimal range of credit centralization, defined by the lending share of the largest lender, is given by RX I2X Lk1 Ri I2i 1 ð p1 þ p2 Þ < < min 1 ð p1 þ p2 Þ ; ði 2 VÞ : I1 W I1 W I1 W
(30)
The second term in the left-hand side of Eq. (30), ðð p1 þ p2 ÞðRX I2X ÞÞ=ðI1 WÞ, represents the expected rate of return for period 2 investment in project X. As the expected rate of return decrease, lender k has less incentive to grant period 2 loan. Hence, in order for project X to be refinanced in period 2, the lending share of lender k in period 1, Lk1 =ðI1 WÞ, has to be raised so as to increase the share acquired by lender k in return realized in period 2 and strengthen incentive to refinance. Similar arguments show that the lending share of lender k in period 1, Lk1 =ðI1 WÞ, has to be reduced so as to weaken incentive to undertake project i which is less efficient than project X. If the right-hand side inequality of Eq. (30) is violated, then an inefficient project with a larger investment is undertaken, and efficiency loss occurs due to the soft budget constraint problem. If the left-hand side inequality of Eq. (30) is violated, then even if project X is undertaken, period 2 investment with positive net present value is not undertaken, and efficiency loss occurs due to the debt overhang problem. From Eq. (30), the lower bound of the optimal range decreases, as the endowment of the entrepreneur, W, increases and the probability that the state is not very bad, that is, default does
196
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
not occur, p1 + p2, increases. The same is true for the upper bound of the optimal range. Consequently, the entrepreneur with a greater endowment is likely to choose the lower degree of credit centralization. The entrepreneur with a lower probability of default, i.e. higher credit quality, is also likely to do so. The former result implies that a firm that relies more on debt financing for financing investment than internal funds and equity financing has a higher degree of credit centralization to avoid the debt overhang problem. On the contrary, a firm that relies more on internal funds and equity financing than debt financing has a lower degree of credit centralization to avoid the soft budget constraint problem. In general, Japanese firms depend heavily on debt finance, and particularly depend on each firm’s largest respective lenders, which are called their main banks. This fact is consistent with the above results. In fact, Hoshi et al. (1991) find that group financing arrangements (so-called main bank system) relax financial constraints. However, the more recent works show that Japanese firms significantly face financial constraints. For example, Motonishi and Yoshikawa (1999) find that financial constraints significantly affect investment of small firms. Kang and Stulz (2000) find that firms which depended more on bank borrowing cut investment back more substantially than did other firms in the early 1990s when banks were doing poorly. We should note that the existence of financial constraints doesn’t necessarily mean that the debt overhang problem has occurred. Financial constraints may be caused not because of prior debt financing but because of other reasons such as the health of banks. Gibson (1995) find that firms with unhealthy main banks invested less than other firms for the period from 1991 to 1992. It is a remaining issue to study empirically whether the debt overhang problem has occurred. Since the high dependence of Japanese firms on the main bank leads to a high degree of credit concentration (Berglo¨f (1990)), the soft budget constraint problem may be likely to occur in Japan. As some previous studies, e.g. Sheard (1989, 1994) and Hoshi and Kashyap (2001, Chapter 5), show, the main bank has frequently refinanced borrowers when they are in financial distress. The refinance may induce moral hazard on the part of entrepreneurs. In future work, it would be interesting to empirically examine whether soft budget constraint is a pervasive phenomenon in Japanese economy. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks. 4. Conclusions The paper has analyzed the optimal degree of credit centralization in the situation where the soft budget constraint problem and the debt overhang problem may occur. The paper has found the optimal range of credit centralization under which neither the soft budget constraint nor the debt overhang problems occur. It has been shown that if the degree of credit centralization is above the upper bound of the optimal range, the soft budget constraint problem occurs, and if it is below the lower bound of the optimal range, the debt overhang problem occurs. In addition, the entrepreneur with a greater endowment or higher credit quality is likely to choose a lower degree of credit centralization. Furthermore, the results support the fact that Japanese firms depend heavily on debt finance, and particularly depend on their respective main banks. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
197
References Berglo¨f, E., 1990. Capital structure as a mechanism of control: a comparison of financial system. In: Aoki, M., Gustafsson, B., Williamson, O.E. (Eds.), The Firm as a Nexus of Treaties. SAGE Publications, London, pp. 237–262. Berglo¨f, E., Roland, G., 1995. Bank restructuring and soft budget constraints in financial transition. Journal of the Japanese and International Economies 9, 354–375. Berglo¨f, E., Roland, G., 1997. Soft budget constraints and credit crunches in financial transition. European Economic Review 41, 807–817. Bolton, P., Scharfstein, D.S., 1996. Optimal debt structure and the number of creditors. Journal of Political Economy 104, 1–25. Dewatripont, M., Maskin, E., 1995. Credit and efficiency in centralized and decentralized economies. Review of Economic Studies 62, 541–555. Gibson, M.S., 1995. Can bank health affect investment? Evidence from Japan. Journal of Business 68, 281–308. Hoshi, T., Kashyap, A.K., 2001. Corporate Financing and Governance in Japan. The MIT Press. Hoshi, T., Kashyap, A., Scharfstein, D., 1991. Corporate structure, liquidity, and investment: evidence from Japanese industrial groups. Quarterly Journal of Economics 106, 33–60. Kang, J.-K., Stulz, R.M., 2000. Do banking shocks affect borrowing firm performance? An analysis of the Japanese experience. Journal of Business 73, 1–23. Kornai, J., 1980. The Economics of Shortage. North-Holland, New York. Kornai, J., Maskin, E., Roland, G., 2003. Understanding the Soft Budget Constraint. Journal of Economic Literature 41, 1095–1136. Lamont, O., 1995. Corporate-debt overhang and macroeconomic expectations. American Economic Review 85, 1106– 1117. Maskin, E.S., 1996. Theories of the soft budget-constraint. Japan and the World Economy 8, 125–133. Maskin, E.S., 1999. Recent theoretical work on the soft budget constraint. American Economic Review 89, 421–425. Motonishi, T., Yoshikawa, H., 1999. Causes of the long stagnation of Japan during the 1990s: financial or real? Journal of the Japanese and International Economies 13, 181–200. Myers, S.C., 1977. Determinants of corporate borrowing. Journal of Financial Economics 5, 147–175. Sheard, P., 1989. The main bank system and corporate monitoring and control in Japan. Journal of Economic Behavior and Organization 11, 399–422. Sheard, P., 1994. Main banks and the governance of financial distress. In: Aoki, M., Patrick, H. (Eds.), The Japanese Main Bank System. Oxford University Press, New York, pp. 188–230. Snyder, C.M., 1998. Loan commitments and the debt overhang problem. Journal of Financial and Quantitative Analysis 33, 87–116.
The soft budget constraint, the debt overhang and the optimal degree of credit centralization Kenji Tsuji * Graduate School of Economics, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan Received 11 April 2003; received in revised form 1 August 2005; accepted 19 September 2005
Abstract The paper analyzes the optimal degree of credit centralization in the situation where the soft budget constraint and the debt overhang problems may occur. The paper characterizes the optimal range of credit centralization, and shows that the entrepreneur with a greater endowment or higher credit quality is likely to choose a lower degree of credit centralization. # 2005 Elsevier B.V. All rights reserved. JEL classification: G30 Keywords: The soft budget constraint; The debt overhang; The degree of credit centralization
1. Introduction The soft budget constraint and the debt overhang problems, which were originally posed by Kornai (1980) and Myers (1977) respectively, are important in corporate finance, since the former induces overinvestment and the latter induces underinvestment. Studies on the former include Kornai (1980), Dewatripont and Maskin (1995), Berglo¨f and Roland (1995, 1997), Maskin (1996, 1999) and Kornai et al. (2003). Studies on the latter include Myers (1977), Lamont (1995) and Snyder (1998). In the previous literature, both problems have been treated separately, but this paper provides a framework for analyzing both problems simultaneously and analyzes the optimal degree of credit centralization. Several studies have been undertaken on credit concentration. For example, assuming that asymmetric information exists between entrepreneurs and creditors, Dewatripont and Maskin
* Tel.: +81 6 6609 5169; fax: +81 6 6605 3066. E-mail address: [email protected]. 0922-1425/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2005.09.002
188
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
(1995) show that since credit decentralization offers a way for creditors to commit not to refinance unprofitable projects, it tends to deter unprofitable projects, thus providing financial discipline, but it may also discourage profitable projects that are slow to pay off. Bolton and Scharfstein (1996) show that it is optimal for firms with low credit quality to borrow from just one creditor, and for firms with high credit quality to borrow from multiple creditors. Their basic idea is that while borrowing from multiple creditors disciplines managers, it can reduce efficiency by lowering liquidation value in a liquidity default, and an optimal contract must balance these two effects. These papers do not consider the optimal degree of credit centralization, which I investigate. In this paper, the entrepreneur has insufficient capital, so he has to depend on outside lenders to finance a project requiring a sequence of investments. Since the initial loan is sunk as in Dewatripont and Maskin (1995), if it is made by only one lender, then the soft budget constraint problem may occur, that is, the entrepreneur may extract ex post a larger loan than would have been considered efficient ex ante. Decentralizing credit allocation to many lenders improves the financial discipline of the entrepreneur and alleviates the soft budget constraint problem; however, it may induce the debt overhang problem due to the incentive for lenders to free-ride. Returns from a project refinanced by a lender are beneficial to all lenders, not just to that lender alone. That is, refinancing is a public good, from the individual lender’s viewpoint, and thus the free-rider problem may occur in refinancing the project, leading to the possibility that later investment with positive values will be abandoned; that is, the debt overhang problem may occur. This paper shows that there is an optimal range of credit centralization under which neither the soft-budget constraint nor the debt overhang problems occur. If the degree of credit centralization is above the upper bound of the optimal range, the soft budget constraint problem occurs, and if it is below the lower bound of the optimal range, the debt overhang problem occurs. In addition, this paper shows that the entrepreneur with a greater endowment or higher credit quality is likely to choose the lower degree of credit centralization. Japanese firms depend heavily on debt finance, and particularly depend on their largest respective lenders—main banks. This fact is consistent with the results of this paper. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks. The rest of the paper is structured as follows. Section 2 describes the basic model. Section 3 derives the optimal contracts and the optimal range of credit centralization. Section 4 presents the major conclusions. 2. A basic model An entrepreneur undertakes a project requiring a sequence of investments. The entrepreneur can choose only one project among N(>1) projects indexed by i = 1, 2, 3, . . ., N. All projects require an investment I1 in period 1. The entrepreneur is endowed with W(>0), which is less than I1, so the entrepreneur must borrow I1 W from lenders to undertake a project. If investment is undertaken in period 1, then at the end of period 2, project i generates return Ri(>0) with probability 1 if the state is good. The same return is generated with probability L2 =I2i if the state is bad, and no return occurs with probability 1 if the state is very bad. Here, L2 ð 2 I2i Þ is the amount actually invested by the entrepreneur in period 2, and I2i ð > 0Þ is the sufficient amount of investment which project i require in period 2 if the state is bad. In period 2, since the entrepreneurs have no endowment, L2 is equal to the total amount of loans granted by lenders.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
189
Note that all projects require no period 2 investment if the state is good or very bad. For all projects, the probability that the state is good is p1(>0, <1), that it is bad is p2(>0, <1) and very bad is 1 p1 p2(>0, <1). The entrepreneur chooses a project, after the initial loan contract is made in period 1. The state is realized at the start of period 2. The project choice, the realized state and the realized return from the project are observed by both the entrepreneur and lenders, but are not verifiable to outsiders, e.g. courts. The parameters I1, I2i , p1 and p2 are considered to be common knowledge. The amount actually invested and the amount actually paid to the lenders are assumed to be freely observable by the entrepreneur and lenders, and be verifiable to outsiders. I assume that if the entrepreneur defaults on debt contracts, then lenders together obtain all residual value and the entrepreneur receives nothing, thus the entrepreneur pays the promised amount as long as he can do so. Both the entrepreneur and lenders are assumed to be risk-neutral. The entrepreneur obtains a non-monetary, non-transferable private benefit, B, such as reputation, specific human capital, etc., if and only if a project is undertaken and completed successfully, that is, generates the return Ri. The entrepreneur maximizes the sum of his expected monetary returns and his private benefit, which is henceforth called expected total revenue. The entrepreneur borrows I1 W for two periods from lenders at the start of period 1. Lenders are assumed to be competitive at the contracting stage, so each lender makes zero expected profits. Furthermore, they are ready to provide funds as long as they break even on their loans. The risk-free market interest rates are certain and normalized to zero. To consider the case where it can be profitable ex post for a lender or lenders to grant a loan of I2i to a financially distressed entrepreneur, it is assumed that Eq. (1) holds: I2i < Ri < ðI1 WÞ þ I2i :
(1)
In the remainder of this section, I assume that the entrepreneur borrows funds from only one lender in period 1, called the incumbent lender. The incumbent lender grants a loan of I1 W to the entrepreneur at an interest rate of r1 in period 1. The maximum expected monetary surplus for project i is Si ¼ ð p1 Ri I1 Þ þ p2 ðRi I2i Þ:
(2)
Suppose that the project indexed by larger number has a larger maximum expected monetary surplus, i.e. Si < Sj, if i < j. For simplicity, assume that Si > 0 for all i 2 {1, 2, 3, . . ., N}. Suppose that project i is undertaken and the state is bad. In this case, potential lenders grant no loan in period 2, since Eq. (1) holds. Assume that the incumbent lender has all the bargaining power in the negotiation phase of period 2 loan, i.e. the lender presents the entrepreneur with a take-it-or-leave-it-offer and so appropriates all the verifiable returns. The incumbent lender grants a loan of I1 W in period 1 and L2(30) in period 2, and acquires Ri with probability L2 =I2i at the end of period 2. Hence, the expected profit of the incumbent lender, pi(L2), is given by
pi ðL2 Þ ¼
L2 Ri L2 ðI1 WÞ: I2i
(3)
190
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
Differentiating Eq. (3) with respect to L2, I get dpi 1 ¼ ðRi I2i Þ > 0: I2i dL2
(4)
From Eq. (4), the incumbent lender grants a loan of I2i in period 2, i.e., L2 ¼ I2i , and so the return of project is Ri with certainty. Given that L2 ¼ I2i , the entrepreneur’s expected revenue, Pi, is P i ¼ p1 ðRi PÞ þ ð p1 þ p2 ÞB;
(5) i
where P is the promised payment to the incumbent lender. In equilibrium, P is equal to be Si, since P is determined so that the incumbent lender acquires zero expected profits. Differentiating Pi with respect to Ri, I have dP i ¼ p1 > 0: dRi
(6)
If project N has the largest project return, then the entrepreneur undertakes project N since dPi/dRi > 0, and there is no efficiency loss. Suppose that project N does not have the largest project return. The project with the largest project return is denoted by project M. Assume that the lender cannot commit himself not to make a loan larger than I2N , because such a commitment can be renegotiated if renegotiation is profitable ex post. The entrepreneur undertakes project M and the expected efficiency loss, SN SM(>0), occurs. This implies that the entrepreneur chooses the project with the largest project return regardless of the amount of funds required in period 2; consequently the project with the largest expected surplus may not be chosen, and the expected efficiency loss may occur. This leads to the following proposition. Proposition 1. Suppose that the entrepreneur borrows from one lender, and that the project with the largest expected surplus does not have the largest project return. Then, the entrepreneur undertakes an inefficient project and an expected efficiency loss occurs. From Eq. (2), it is clear that I2M > I2N since SN > SM and RN < RM. When the entrepreneur undertakes project M and the state is bad, period 2 loan is larger than if project N is undertaken. Namely, the entrepreneur extracts ex post a larger loan than would have been considered efficient ex ante. This is the soft budget constraint problem. 3. Optimal contracts Suppose that the entrepreneur can borrow the necessary funds, I1 W, from K(>1) lenders at the start of period 1. The lenders who grant loans to the entrepreneur in period 1, called the incumbent lenders, are assumed to have all the bargaining power in the negotiation phase of period 2 loan and so acquire all residual value if the state is bad, as assumed in the previous section. Assume that many lenders cannot co-operate in period 2, since lenders have an incentive to free-ride. Under these assumptions, the following proposition is obtained. Proposition 2. Suppose that ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ > L1j > 0;
for all j 2 c
(7)
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
191
and X
L1j ¼ I1 W;
(8)
j2c
where C is the set of the incumbent lenders. Then, none of lenders grant loans in period 2. Proof. I need only consider the situation where the state is bad, since refinancing is not required if the state is good or very bad. Suppose that project i is undertaken and the state is bad. First, consider the case where each lender acquires the same share of revenue from the project as the share of his loan. I denote period 1 loan and period 2 loan which incumbent lender j grants to the entrepreneur by L1j and L2j respectively, the total loan granted to the entrepreneur in period 2 by L2, total promised payment on period 1 loan by P1(3I1 W, 2Ri) which is determined at the start of period 1, and an interest rate on period 1 loan granted by lender j by r1j. Since incumbent lender j acquires L1j ð1 þ r1j Þ2 þ ðL2j =L2 ÞðRi P1 Þ with probability L2 =I2i at the end of period 2, the expected profit of incumbent lender j in the bad state, pi j ðL2j Þ, is given by ij
p
ðL2j Þ
L2j i ¼ þ þ ðR P1 Þ L2j L1j L2 j L2 L2 j j 2 ¼ L1 ð1 þ r1 Þ þ ðRi P1 Þ L2j L1j : I2i I2i L2 I2i
L1j ð1
r1j Þ2
(9)
Differentiating Eq. (9) with respect to L2j , the following equation is obtained.
1 fL1j ð1 þ r1j Þ2 þ ðRi P1 Þg 1 j i I dL2 2 i 1 1 R ðI1 WÞ L1j j j 2 i ¼ ½R fP1 L1 ð1 þ r1 Þ g 1 2 i 1 I2i I2 ð p1 þ p2 Þ 1 fð p1 þ p2 ÞðRi I2i Þ ðI1 WÞ þ L1j g: ¼ i I 2 ð p1 þ p2 Þ
dpi j
¼
(10)
The inequality follows from the non-negative profit condition of lenders besides lender j; i.e., ð p1 þ p2 ÞfP1 L1j ð1 þ r1j Þ2 g 3 ðI1 WÞ L1j . Since dpi j =dL2j < 0 from Eqs. (7) and (10), incumbent lender j does not grant a loan to the entrepreneur in period 2; i.e., L2j ¼ 0. For any lender who acquires the same share of revenue as the share of his loan, the same argument holds, so that none of the incumbent lenders lend anything to the entrepreneur in period 2. Second, consider the case where lender j acquires a smaller share of revenue than the share of his loan. The expected profit of incumbent lender j, pi j ðL2j Þ, is given by L2j ðRi P1 Þ L2j L1j L2 j L2 L ¼ L1j ð1 þ r1j Þ2 þ b i2 ðRi P1 Þ L2j L1j ; I2i I2
pi j ðL2j Þ ¼
L2 I2i
L1j ð1 þ r1j Þ2 þ b
(11)
192
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
where 1 > b > 10. Differentiating Eq. (11) with respect to L2j , the following equation holds: dpi j dL2j
¼
1 1 j j 2 i fL1 ð1 þ r1 Þ þ bðR P1 Þg 1 2 i fL1j ð1 þ r1j Þ2 þ ðRi P1 Þg 1: I2i I2 (12) dpi j =dL2j
From Eqs. (10) and (12), lender j grants no loan to the entrepreneur, since < 0 when Eq. (7) is satisfied. For any lender who acquires a smaller share of revenue than the share of his loan, the same argument holds, so they do not lend anything to the entrepreneur in period 2. Finally, consider the case where lenders acquire a larger share of revenue than the share of his loan. It is clear that the budget constraint is not satisfied, so this case is not feasible. Consequently, incumbent lenders do not lend anything to the entrepreneur in period 2. It is clear that potential lenders offer nothing to the entrepreneur in period 2. & From the left-hand side inequality of Eq. (7), I have Ri
fðI1 WÞ L1j g I2i < 0: p1 þ p2
(13)
If the return, Ri, is realized at the end of period 2, then lender j acquires at most ½Ri fðI1 WÞ L1j g=ð p1 þ p2 Þ, since the other lenders acquire at least fðI1 WÞ L1j g=ð p1 þ p2 Þ from the non-negative profit conditions. Eq. (13) means that lender j decreases his profits if he lends I2i to the entrepreneur in period 2. Hence, if Eq. (7) holds, then lender j does not grant period 2 loan. Also, Eq. (13) implies that as the loan granted by lender j, L1j , decreases, a leakage of return into the other lenders gets larger, and lender j acquires less return in period 2 and has less incentive to grant period 2 loan. Proposition 2 implies that if L1j ð j 2 cÞ is small, then refinancing is not undertaken and inefficiency occurs since Ri > I2i . This is the debt overhang problem, because later investment with positive values is abandoned after the initial investment is financed by debt. Suppose that the entrepreneur borrows Lk1 ð > 0; 2 I1 WÞ at an interest rate of r1k from lender k and I1 W Lk1 at an interest rate of r1o from the other lenders in period 1. The following proposition then holds. Proposition 3. Suppose that project i is undertaken and that ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ > L1j > 0;
for all j 2 fxjx 2 c and x 6¼ kg;
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1; r1o ¼ p1 þ p2
ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ < Lk1 2 I1 W;
(14)
(15)
(16)
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
r1k
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lk1 p2 fRi ððI1 WÞ Lk1 Þ=ð p1 þ p2 Þ I2i g ¼ 1; p1 Lk1
193
(17)
and X
L1j ¼ I1 W:
(18)
j2c
Then, the entrepreneur borrows the full amount of the necessary funds, I2i , from lender k in period 2, if the state is bad. Proof. From the proof of Proposition 2, if condition (14) holds, it is easy to show that L2j ¼ 0 for j 2 {xjx 2 C and x 6¼ k}, that is, none of lenders besides lender k grant loans in period 2. Since lenders besides lender k acquire fðI1 WÞ Lk1 g=ð p1 þ p2 Þ from the zero profit conditions, the expected profit of lender k in the bad state, pik ðLk2 Þ, is given by ik
p
ðLk2 Þ
¼
Lk2 I2i
ðI1 WÞ Lk1 R Lk2 Lk1 : p1 þ p2 i
(19)
Differentiating Eq. (19) with respect to Lk2 :
ðI1 WÞ Lk1 R 1 p1 þ p2 1 fð p1 þ p2 ÞðRi I2i Þ ðI1 WÞ þ Lk1 g: ¼ i I2 ð p1 þ p2 Þ
dpik ¼ dLk2
1 I2i
i
(20)
The right-hand side of Eq. (20) is positive from Eq. (16). Therefore, lender k grants a loan of I2i in period 2, that is, Lk2 ¼ I2i , in the bad state. Given that Lk2 ¼ I2i , the expected profit of lender k is fðI1 WÞ Lk1 g I2i ; p1 ð1 þ r1k Þ2 Lk1 Lk1 þ p2 Ri (21) p1 þ p2 which is equal to zero due to competition among lenders. Then, r1k is given by Eq. (17). Furthermore, Eq. (15) is obtained from the zero profit conditions of the other lenders. & Eq. (14) is the same as Eq. (7), except that the former does not include lender k. The left-hand side of Eq. (16) is the same as that of Eqs. (7) and (14). As easily inferred from the explanation of Eq. (13) which is derived from Eq. (7), the left-hand side inequality in Eq. (16) means that lender k increases his profits if he lends I2i to the entrepreneur in the bad state. Hence, if Eq. (16) holds, then lender k grants period 2 loan if the state is bad. Also, Eq. (16) implies that as a loan granted by lender k, Lk1 , increases, a leakage of return into the other lenders gets smaller, and lender k acquires more return in period 2 and has more incentive to grant period 2 loan. The right-hand side inequality in Eq. (16) means that the amount of loan granted by lender k, Lk1 , is limited by the full amount of necessary funds. Now, I turn from the behavior of lenders to that of the entrepreneur. If the entrepreneur undertakes project i and lender k grants a loan of I2i in period 2 in the bad state, then the expected total revenue of the entrepreneur is given by
194
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
P ic ¼ p1 ðRi P1 Þ þ ð p1 þ p2 ÞB:
(22)
The suffix ‘‘c’’ means that the project is continued in the bad state since the entrepreneur gets the necessary funds in period 2. If project Z is undertaken and is not refinanced in the bad state, then the entrepreneur’s expected total revenue is given by P Zt ¼ p1 fðRZ P1 Þ þ Bg:
(23)
The suffix ‘‘t’’ means that the project is terminated in the bad state since the entrepreneur has no funds in period 2. Since PZt takes the maximum value if RZ is equal to RM which is assumed to be the largest project return, the entrepreneur undertakes project M if the project is not refinanced in the bad state. Hence, I replace ‘‘Z’’ by ‘‘M’’ in Eq. (23). From Eqs. (22) and (23): P ic P Mt ¼ p1 ðRi RM Þ þ p2 B
(24)
From Eq. (24), if p1(Ri RM) + p2B > 0, then Pic > PMt. Suppose that another project, denoted by project X, gives the largest value of expected monetary surplus among projects included in [i 2 {1, 2, 3, . . ., N}jp1(Ri RM) + p2B > 0].1 For simplicity, assume that V 6¼ f where V = [i 2 {1, 2, 3, . . ., N}jRi 3 RX and i 6¼ X]. From Proposition 3, the following proposition then holds. Proposition 4. Suppose that ðI1 WÞ þ ð p1 þ p2 ÞðI2X RX Þ > L1j > 0; sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 1; r1o ¼ p1 þ p2
for all j 2 fxjx 2 c and x 6¼ kg;
(25) (26)
ðI1 WÞ þ ð p1 þ p2 ÞðI2X RX Þ < Lk1 < min½ðI1 WÞ þ ð p1 þ p2 ÞðI2i Ri Þ; ði 2 VÞ; (27) sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Lk1 p2 fRX ððI1 WÞ Lk1 Þ=ð p1 þ p2 Þ I2X g 1 (28) r1k ¼ p1 Lk1 and
X
L1j ¼ I1 W:
(29)
j2c
Then, the entrepreneur undertakes project X, borrows the full amount of the necessary funds from lender k if the state is bad, and acquires SX + (p1 + p2)B, which is the largest expected profit that the entrepreneur can obtain.
1
For simplicity, I assume that the private benefit of the entrepreneur, B, is so large that it holds that p1(Ri RM) + p2B > 0 for some i 2 {1,2,3, . . ., N}.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
195
Proof. It is clear from Eq. (6) that if Ri < RX for all i 6¼ X, then project X is undertaken. If Ri 3 RX, for some i 6¼ X, that is, i 2 V, then Si < SX from the definition of project X. There are some values of Lk1 that satisfy Eq. (27), since I2X RX < I2i Ri from Si < SX and Ri 3 RX. If Eqs. (25) and (27) are satisfied, then if project i 2 V is undertaken, it is not refinanced in the bad state from Proposition 2 and Eq. (20). From Eq. (24), the entrepreneur obtains more expected revenue by undertaking project X than project i 2 V, since p1(RX RM) + p2B > 0. Therefore, the entrepreneur undertakes project X. From Proposition 3, if project X is undertaken, then the entrepreneur borrows the full amount of the necessary funds from lender k if the state is bad. Since lenders are assumed to be competitive at the initial contracting stage, they obtain zero expected profits and the entrepreneur acquires SX + ( p1 + p2)B. By definition, project X gives the entrepreneur the largest expected revenue which he can acquire. & Eq. (25) is the same as Eq. (14), except that the former replaces project i with project X. As easily inferred from the explanation of Eq. (16), the left-hand side inequality of Eq. (27) means that lender k increases his profits if he lends I2X to the entrepreneur when project X is undertaken. Hence, if the left-hand side inequality of Eq. (27) holds, then lender k grants period 2 loan when project X is undertaken. The right-hand side inequality of Eq. (27) means that lender k decreases his profits if he lends I2i to the entrepreneur when project i is undertaken. Hence, if the right-hand side inequality of Eq. (27) holds, lender k does not grant period 2 loan when project i is undertaken. Since PXc > Pit for all i 6¼ X from the definition of project X, the entrepreneur undertakes project X which is the most efficient feasible project. Proposition 4 implies that if the optimal degree of credit centralization is chosen, then the project undertaken is successfully completed when the state is good or bad, and default occurs only when the state is very bad. Also, if it holds that p1(RN RM) + p2B > 0, then project X coincides with project N, which is a project with the largest expected monetary surplus, and there is no efficiency loss. Furthermore, from Eq. (27), the optimal range of credit centralization, defined by the lending share of the largest lender, is given by RX I2X Lk1 Ri I2i 1 ð p1 þ p2 Þ < < min 1 ð p1 þ p2 Þ ; ði 2 VÞ : I1 W I1 W I1 W
(30)
The second term in the left-hand side of Eq. (30), ðð p1 þ p2 ÞðRX I2X ÞÞ=ðI1 WÞ, represents the expected rate of return for period 2 investment in project X. As the expected rate of return decrease, lender k has less incentive to grant period 2 loan. Hence, in order for project X to be refinanced in period 2, the lending share of lender k in period 1, Lk1 =ðI1 WÞ, has to be raised so as to increase the share acquired by lender k in return realized in period 2 and strengthen incentive to refinance. Similar arguments show that the lending share of lender k in period 1, Lk1 =ðI1 WÞ, has to be reduced so as to weaken incentive to undertake project i which is less efficient than project X. If the right-hand side inequality of Eq. (30) is violated, then an inefficient project with a larger investment is undertaken, and efficiency loss occurs due to the soft budget constraint problem. If the left-hand side inequality of Eq. (30) is violated, then even if project X is undertaken, period 2 investment with positive net present value is not undertaken, and efficiency loss occurs due to the debt overhang problem. From Eq. (30), the lower bound of the optimal range decreases, as the endowment of the entrepreneur, W, increases and the probability that the state is not very bad, that is, default does
196
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
not occur, p1 + p2, increases. The same is true for the upper bound of the optimal range. Consequently, the entrepreneur with a greater endowment is likely to choose the lower degree of credit centralization. The entrepreneur with a lower probability of default, i.e. higher credit quality, is also likely to do so. The former result implies that a firm that relies more on debt financing for financing investment than internal funds and equity financing has a higher degree of credit centralization to avoid the debt overhang problem. On the contrary, a firm that relies more on internal funds and equity financing than debt financing has a lower degree of credit centralization to avoid the soft budget constraint problem. In general, Japanese firms depend heavily on debt finance, and particularly depend on each firm’s largest respective lenders, which are called their main banks. This fact is consistent with the above results. In fact, Hoshi et al. (1991) find that group financing arrangements (so-called main bank system) relax financial constraints. However, the more recent works show that Japanese firms significantly face financial constraints. For example, Motonishi and Yoshikawa (1999) find that financial constraints significantly affect investment of small firms. Kang and Stulz (2000) find that firms which depended more on bank borrowing cut investment back more substantially than did other firms in the early 1990s when banks were doing poorly. We should note that the existence of financial constraints doesn’t necessarily mean that the debt overhang problem has occurred. Financial constraints may be caused not because of prior debt financing but because of other reasons such as the health of banks. Gibson (1995) find that firms with unhealthy main banks invested less than other firms for the period from 1991 to 1992. It is a remaining issue to study empirically whether the debt overhang problem has occurred. Since the high dependence of Japanese firms on the main bank leads to a high degree of credit concentration (Berglo¨f (1990)), the soft budget constraint problem may be likely to occur in Japan. As some previous studies, e.g. Sheard (1989, 1994) and Hoshi and Kashyap (2001, Chapter 5), show, the main bank has frequently refinanced borrowers when they are in financial distress. The refinance may induce moral hazard on the part of entrepreneurs. In future work, it would be interesting to empirically examine whether soft budget constraint is a pervasive phenomenon in Japanese economy. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks. 4. Conclusions The paper has analyzed the optimal degree of credit centralization in the situation where the soft budget constraint problem and the debt overhang problem may occur. The paper has found the optimal range of credit centralization under which neither the soft budget constraint nor the debt overhang problems occur. It has been shown that if the degree of credit centralization is above the upper bound of the optimal range, the soft budget constraint problem occurs, and if it is below the lower bound of the optimal range, the debt overhang problem occurs. In addition, the entrepreneur with a greater endowment or higher credit quality is likely to choose a lower degree of credit centralization. Furthermore, the results support the fact that Japanese firms depend heavily on debt finance, and particularly depend on their respective main banks. This paper also suggests that the soft budget constraint problem is one of the reasons why Japanese firms do not borrow the full amount of necessary funds from their respective main banks.
K. Tsuji / Japan and the World Economy 19 (2007) 187–197
197
References Berglo¨f, E., 1990. Capital structure as a mechanism of control: a comparison of financial system. In: Aoki, M., Gustafsson, B., Williamson, O.E. (Eds.), The Firm as a Nexus of Treaties. SAGE Publications, London, pp. 237–262. Berglo¨f, E., Roland, G., 1995. Bank restructuring and soft budget constraints in financial transition. Journal of the Japanese and International Economies 9, 354–375. Berglo¨f, E., Roland, G., 1997. Soft budget constraints and credit crunches in financial transition. European Economic Review 41, 807–817. Bolton, P., Scharfstein, D.S., 1996. Optimal debt structure and the number of creditors. Journal of Political Economy 104, 1–25. Dewatripont, M., Maskin, E., 1995. Credit and efficiency in centralized and decentralized economies. Review of Economic Studies 62, 541–555. Gibson, M.S., 1995. Can bank health affect investment? Evidence from Japan. Journal of Business 68, 281–308. Hoshi, T., Kashyap, A.K., 2001. Corporate Financing and Governance in Japan. The MIT Press. Hoshi, T., Kashyap, A., Scharfstein, D., 1991. Corporate structure, liquidity, and investment: evidence from Japanese industrial groups. Quarterly Journal of Economics 106, 33–60. Kang, J.-K., Stulz, R.M., 2000. Do banking shocks affect borrowing firm performance? An analysis of the Japanese experience. Journal of Business 73, 1–23. Kornai, J., 1980. The Economics of Shortage. North-Holland, New York. Kornai, J., Maskin, E., Roland, G., 2003. Understanding the Soft Budget Constraint. Journal of Economic Literature 41, 1095–1136. Lamont, O., 1995. Corporate-debt overhang and macroeconomic expectations. American Economic Review 85, 1106– 1117. Maskin, E.S., 1996. Theories of the soft budget-constraint. Japan and the World Economy 8, 125–133. Maskin, E.S., 1999. Recent theoretical work on the soft budget constraint. American Economic Review 89, 421–425. Motonishi, T., Yoshikawa, H., 1999. Causes of the long stagnation of Japan during the 1990s: financial or real? Journal of the Japanese and International Economies 13, 181–200. Myers, S.C., 1977. Determinants of corporate borrowing. Journal of Financial Economics 5, 147–175. Sheard, P., 1989. The main bank system and corporate monitoring and control in Japan. Journal of Economic Behavior and Organization 11, 399–422. Sheard, P., 1994. Main banks and the governance of financial distress. In: Aoki, M., Patrick, H. (Eds.), The Japanese Main Bank System. Oxford University Press, New York, pp. 188–230. Snyder, C.M., 1998. Loan commitments and the debt overhang problem. Journal of Financial and Quantitative Analysis 33, 87–116.