Microsoft Word - cet-01.docx


 

 CHEMICAL ENGINEERING TRANSACTIONS  
 

 VOL. 46, 2015 

A publication of 

 

The Italian Association 
of Chemical Engineering 

Online at www. aidic. it/cet 

Guest Editors: Peiyu Ren, Yanchang Li, Huiping Song 
Copyright © 2015, AIDIC Servizi S. r. l.,  
ISBN 978-88-95608-37-2; ISSN 2283-9216  

The Research on the Impact of Institutional Environment on 
Debt Maturity Structure 

Yi W ua, Xiangjun W anga, Xiani Yang*b 
aFaculty of Management and Economics, Kunming University of Science and Technology, 650093, Kunming, Yunnan, 
China, 
b Faculty of Economics and Management, Yunnan Agricultural University, 650201, Kunming, Yunnan, China.  
xianiyang@126.com 

As an important part of the debt financing decision, the choice of debt maturity structure will not only affect 
investment and financing cost, corporate governance and liquidity risk, but also be directly related to the 
distribution of interests between the creditor and debtor. In fact, debt maturity structure can be regarded as an 
endogenous result of one social economic system in a particular development stage. Therefore, it owns 
important theoretical significance and application value to study the effect of institutional environments on debt 
maturity structure. Using theoretical analysis, this paper introduces institutional environments into the standard 
debt maturity model established by Holmstrom and Tirole (1998, 2000). And then, this paper constructs a 
theoretical model under this situation and examines the influence of institutional environment on debt maturity 
structure, through solving the mathematical model, theoretical derivation, comparative static analysis and 
numerical simulation. The theoretical research results show that, debt maturity structure is shortened with the 
improvement of institutional environment. 

1. Introduction 

Debt financing has always been the most important channel for the enterprise's funding. As one of the most 
important content of debt financing decisions, the corporate choice for debt maturity structure is destined to 
become a hot academic issue. So it is particularly important to study the various factors influencing debt 
maturity structure, based on its nature. Foreign scholars have studied the debt maturity structure from the 
perspective of the enterprise’s internal microscopic features since the 1990s, and some representative 
theories were formed, such as the matching principle hypothesis (Lopes and Caetano (2015)), agency cost 
theory (Brockman and Unlu (2009)), tax hypothesis (Blouin et al. (2010)) and information asymmetry 
hypothesis(Cheng and Milbradt (2012)). However, financing contract signing is not only the enterprise's own 
behavior, to a great extent; it would be led by the institutional environments. 
From a macro perspective, the enterprise's debt maturity structure and its institutional environm ent would be 
bound together in a common cause. Through the empirical research, lots of scholars find that all sorts of 
institutional environment would affect the corporate choice for debt maturity (Fan et al. (2012), Zheng et al. 
(2012), Diamond and He (2014)). Liu et al. (2015) accurately demonstrate the debt maturity is negatively 
related to the degree of institution developing and perfecting. Ben-Nasr (2015) believed that short-term debt is 
positively related to labor protection. Taking Chinese listed companies as samples, Tu (2014) finds that debt 
maturity structure is negatively related to institutional environment. However, few scholars expla in the 
relationship using theoretical research. 
Holmstrom and Tirole (1998, 2000) examine the influence of the enterprise's own factors on debt maturity 
through the theoretical analysis. And they assume that the investors’ claims on long -term income can be fully 
implemented. But considering the reality in China, the imperfect institutional environment will surely affect this 
kind of right of investors. When analyzing the importance of property rights system, Acemoglu et al.  (2005) 
point out that difference in institutional environment will change creditor's claims on final income. And both of 
Frieden (2015) and Holmstrom and Tirole (2011) use the similar assumption in their theoretical analysis. 
Now that, the hypothesis that the institutional environment could affect investors' claims on income has strong 
practical significance and theoretical basis. Then, how will the change of institutional environment affect the 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1546102

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Wu Y., Wang X.J., Yang X.N., 2015, The research on the impact of institutional environment on debt maturity 
structure, Chemical Engineering Transactions, 46, 607-612  DOI:10.3303/CET1546102  

607



debt contract? Will the change of institutional environment influence debt maturity structure? If it is, what kind 
of relationship would be between them? This article will further expand the benchmark model of debt maturity 
structure built by Holmstrom and Tirole (1998, 2000), and then answer these questions one by one.  

2. Assumption 

This paper introduces institutional environments into the standard debt maturity model , in the contest of the 
variable-investment framework. The basic assumptions are as follows: 
• Participants: an entrepreneur and investors. 

• Three periods: date 0 , date 1  and date 2 . At date 0 , the entrepreneur has a project requiring variable 

investment I . He initially has “assets” A  and needs to borrow I A  from investors. 
• At date 1 , the investment yields deterministic and verifiable income rI ; at the same time, the firm meets a 

new investment chance requiring an amount I , where   is ex ante unknown and has cumulative 

distribution function ( )F   with density ( )f   on [0, )  . The realization of   is learned at date 1 . 

• If the entrepreneur would not get enough money for reinvestment, he will face bankruptcy liquidation, and 
liquidation value LI  belongs to outside investors.  

• If the firm reinvests I , then it yields, at date 2 , RI  with probability p  and 0  with probability 1 p . 

• Influenced by institutional environment factors, such as laws and regulations, transparency of market, 

protection of small and medium-sized investors, effectiveness of the court, and so on, investors cannot get all 
earnings of the claims on final profits. That is, the investors recoup the profit with probability e  at date 2 . 
Where e  means how well the institutional environments, in fact increasing of e  shows that institutional 
environment improves. 
• The probability of success p  is affected by the effort degree of the entrepreneur which is unobservable. 

Behaving yields probability 
H

p p  of success, and misbehaving results in probability 
L H

p p p   of 

success and private benefit 0BI  . Let 0
H L

p p p    . 

• The project has positive NPV if the entrepreneur behaves, but negative NPV, even if one includes the 

borrower’s private benefit, if she does not. Let (1 ) /e R B p   . 

• Both the entrepreneur and investors are risk neutral. The entrepreneur is protected by limited liability, and 

the riskless rate is taken to be 0 . Investors behave competitively in the sense that the loan, if any, makes 
zero profit. W e summarize the timing in figure 1:  

in
v

e
sto

rs

e
n

tre
p

re
n

e
u

r

e1-e

• Failure (profit 0)

• Success(Profit RI)

Moral hazard

Invest

Financing 

contract
Eventual  profits

• The entrepreneur

   has wealth A 

• The entrepreneur

   borrows I−A from

   investors

Reinvest

Not reinvest

Date 0 Date 1 Date 2

orHpp  Lp•Short-term 
income

•New 

investment 

chance 

rI

Liquidation

Value LI

I

 

Figure 1: Figure of the timing 

608



3. Optimal Model 

Suppose that the financing contract takes the following state-contingent form:  

{ ; ; (0, , 0); ( , , 0)}
c

b b
I R rI RI R   

The contract specifies investment level I , and c  is a cutoff of reinvestment. Only if 
c

  , the firm 

reinvests. The entrepreneur gets nothing at date 1 , and, If the project success, the entrepreneur and investors 

get 
b

R  and 
b

RI R  respectively; if the project fail, both of them get 0 . The outside investors can only get 

b
RI R with probability e ; the entrepreneur can get 

b
R  with probability e  and 

b
R  with probability 1 e . 

According to the contract, the probability of reinvestment is Pr ob{ } ( )
c c

F    . So the optimization 

problem becomes 

, ,

0

max ( ) [ (1 e)RI]

. . ( 1) ( ) [ (1 ) ] ( ){ [ (1 ) ] }

( 1) ( ) ( ) [1- ( )] ( )

c
b

c

c

H b
R I

c c

H b L b

c c

H b

F p eR A

s t a F p eR e RI F p eR e RI BI

b rI F p e RI R F LI I If d A







 

    

   



     

      
 

      (1)

 

 

Where the objective function is the entrepreneur’s utility; (a1) is the entrepreneur’s incentive -compatibility 
constraint, and it could be simplified as 

(1 )
b

eR e RI BI p                                                                  (2) 

and because (1 ) /e R B p   , equation (2) must be established; (b1) is the investors’ individual-rationality

 constraint, and it could be simplified as 

0
( )( ) [1 ( ) ]

( ) ( )

c

c H

b

c H c H

F p eR L f d L r A
I R

F p e F p e



   

 

    
 

             (3) 

 So the optimal model (1) will be simplified as 

0, ,

0

max ( )( ) [ ( ) ]

. . ( )[ ( ) ] [ ( ) ]

c

c
b

c

c

H
R I

c

H b

rI F p R L I LI I If d

s t rI F p e RI R LI LI I If d A







   

   


    



       






   (4) 

4. Optimal Contract 

Next, the model (4) could be solved in three steps.  

Step one: Solve *
b

R  for a given 
c

  and I . In fact, the model (4) can be simplified further as 

, ,

0

max ( )

. . ( 1) ( ) ( ) [1 ( )] [ ( ) ]

c
b

c

c

R I

c c

H b

m I

s t a rI F p e RI R F LI I If d A







    




       
 

  (5)

 

Where 
0

( ) ( )( ) 1 ( )
c

c c

H
m F p R L f d L r



           
is the margin per unit of investment. And 

it could be easy to get that 
*

0
b

R  . 

609



Step two: Find the optimal *I  for a given c . Actually, take 
*

0
b

R   into the problem (5). And as investors 

makes zero profit, (a1) in (5) holds with equality. And then it could be get that  

*
( ) ( ) ;

c c
I k A   * ( ) ( ) ( )c c c

b
U m k A   ; 

1

0
( ) [1 ( ) ] L-r [ ( ) e )] 0

c

c c

H
k f d F p R L



           （  

Step Three: Consider the optimal *c . 

Corollary 1: If the threshold liquidity shock *
c

  is equal to the expected unit cost of effective investment, the 

entrepreneur’s welfare reaches its maximum, and 
*

c
  lies between the expected pledgeable income and the 

expected income, that is: * *( ) ;
c c

c    *
0 1

c
    , where  

0
( ) [1 ( ) ] / ( )

c

c c
c f d L r F



        . 

Proof: In fact 

1
0 1

0
0

0

( ) [1 ( ) ] ( )
( )

( )
1 ( ) ( )

c

c

c
c

c

b c
c

F f d L r c
U A A

c
f d L r F





      


     

    
 


   





 

So max ( ) min ( )
c

c

c c

b
U c



  . The first-order condition is 

0

2

( ) ( ) ( )[1 ( ) ]
0

[ ( )]

c

c c c c

c

f F f f d L r

F



      



   


  

that is:  
0

( ) 1
c

F d L r


                                                 (6)
 

then from (6) it can be got that 
* *

* *

* *0 0

* *

1 ( ) 1 ( ) ( )
( )

( ) ( )

c c

c c

c c

c c

f d L r F F d L r
c

F F

 

      
 

 

      
  

          (7) 

Because of 
*

* 1

*

0

c

b c
U A

 

 





, It may be achieved that: *

0 1

c
    . 

Corollary 2: The “first-best cutoff” of reinvestment *c  has nothing to do with e , that is  

*
/ 0

c
e     

The expression of *c  is (7), so it is very easy to get that 
*c

  has nothing to do with e . 

Corollary 3: The optimum investment scale 
*

I  is increasing with the improvement of institutional 

environment, that is 
*

/ 0I e   .
 

Proof: To simplify the proof process, set 

610



*

* * *

0
( ) 1 ( ) ( )( )

c

c c

H
M f d L r F p eR L



                                                                        
(8) 

taking partial derivative on both sides and combine with (8), it can be got that 
* * *
( ) / ( ) 0

c c

H
M e F p R      . And because * * *

* *
( ) ( )

( )

c c

c

A
I k A

M
 


  , easy to draw that 

* * * *
*

1* * 2 * * 2

( ) ( )
( ) 0

[ ( )] [ ( )]

c c
c

c c

I A M A
F

e M e M

 
 

 

 
    

 
 

5. Comparative Analysis 

Definition 1: The debt maturity structure can be measured by the ratio of long -term debt to total debt, 

nam ely: / ( )DM LD LD SD  , where * * * * *
0 0

( ) ;
c

b
SD r I LD RI R I        . 

Proposition 1: The short-term debt increase with improvement of institutional environment, that is

/ 0SD e   . 

Proof: The short-term debt is * *
0

( )
c

SD r I    , where 
0 H

p eR L   , so 

*
* *

0 1
( )

cSD I
r I

e e
  

 
   

 
 

From corollary 3, it can be got that * / 0I e   , and SD  is positive means *
0

0
c

r     , so 

*
/ 0SD e    

Proposition 2: The long-term debt increase with improvement of institutional environment, that is 

/ 0LD e   . 

Proof: The long-term debt is * * *
0b

LD RI R I   , and * 0
b

R  , so 

* * *

0 * *

( )
[ ( )] ( )

( )

c H
H c

R p eR L
LD RI I R p eR L k A A

M
 



 
       

And because * * *( ) / ( )c c
H

M e F p R     , it can be got that 

*

*

0

* * 2

{ ( ) [1 ( ) ]}
0

[ ( )]

c

c

H

c

p R RF f d L rLD
A

e M



   



   
 



  

Proposition 3: The debt maturity structure reduce with improvement of institutional environment, that is 

/ 0DM e   . 

Proof: The debt maturity structure, 
*

0

* * *

0 0

( )

[( ) ( )]

H

c c

R I R p eR LLD
DM

LD SD R r I R r



   

  
  

      
 

*c
  has nothing to do with e  from corollary 3, so DM  is decreasing with the increase of e . 

611



5. Conclusions  

Signing of financing contract is not just kind of the enterprise's independent behavior; it will be led by the 
institutional environment to a great extent. As an important content of corporate debt financing, the choice of 
debt maturity structure is bound to affect by the institutional environment.   
This paper analyzes the impacting process and influencing result of institutional environment on debt maturity, 
by constructing theoretical model. And finally get that, as the improvement of the institutional e nvironment, the 
short-term debt and long-term debt will increase; meanwhile, the debt maturity structure will become shorter.  

Acknowledgements 

The authors acknowledge the financial support of three projects: Philosophy and Social Science Fund of 
Yunnan Province, China, project No. YB2015032; Faculty of Economics and Management fund of Kunming 
University of Science and Technology, China, project No. QY2015003; Personnel Training fund of Yunnan 
Province, China, project No. KKSY201508009. 

References 

Acemoglu D., Johnson S. and Robinson J. A., 2005, Institutions as a fundamental cause of long-run growth 
[J], Handbook of Economic Growth, 1: 385-472, DOI: 10.1016/S1574-0684(05)01006-3. 

Ben-Nasr H., 2015, Labor protection and government control: Evidence from pri vatized firms [J], Economic 

Modelling, In Press, DOI: 10.1016/j.econmod.2015.09.029. 
Blouin J., Core J. E. and Guay W., 2010, Have the tax benefits of debt been overestimated? [J], Journal of 

Financial Economics, 98(2): 195-213, DOI: 10.1016/j.jfineco.2010.04.005.  
Brockman P. and. Unlu E., 2009, Dividend policy, creditor rights, and the agency costs of debt [J], Journal of 

Financial Economics, 92(2): 276-299, DOI: 10.1016/j.jfineco.2008.03.007. 
Cheng H., and Milbradt K., 2012, The hazards of debt: Rollover freezes, incentives, and bailouts [J], Review of 

Financial Studies, 25(4): 1070-1110. DOI: 10.1093/rfs/hhr142. 
Diamond D. W. and He Z., 2014, A theory of debt maturity: the long and short of debt overhang [J], The 

Journal of Finance, 69(2): 719-762, DOI: 10.1111/jofi.12118. 

Fan J. P., Titman S. and Twite G., 2012, An international comparison of capital structure and debt maturity 
choices [J], Journal of Financial and quantitative Analysis, 47(1): 23-56, DOI: 

10.1017/S0022109011000597. 
Frieden J, 2015, The political economy of adjustment and rebalancing [J], Journal of International Money and 

Finance, 52(C): 4-14, DOI: 10.1016/j.jimonfin.2014.11.010. 
Holmstrom B. and Tirole J., 1998, Private and public supply of liquidity [J], Journal of Political Economy 

106(1): 1–40, DOI: 10.1086/250001. 
Holmstrom B. and Tirole J., 2000, Liquidity and risk management [J], Journal of Money, Credit and Banking 

32(3): 295-319, DOI: 10.2307/2601167. 

Holmstrom B. and Tirole J., 2011, Inside and outside liquidity [M], Cambridge: Massachusetts Institute of 
Technology Presse. 

Liu Q., Luo T. and Tian G. G., 2015, Family control and corporate cash holdings: Evidence from China [J], 
Journal of Corporate Finance, 31: 220-245, DOI: 10.1016/j.jcorpfin.2015.02.007. 

Lopes A. I. and Caetano T. T., 2015, Firm-level conditions to engage in public-private partnerships: What can 
we learn? [J], Journal of Economics and Business, 79(C): 82-99. DOI: 10.1016/j.jeconbus.2015.01.001. 

Tu R., 2014, The ultimate ownership structure, institutional environm ent and dynamic adjustment of financing 
structure [D], Cheng Du: Southwest Jiaotong University, DOI: 10.7666/d.Y2576742. 

Zheng X., Ghoul S. E., Guedhami O., Kwok C., 2012, National culture and corporate debt maturity [J], Journal 

of Banking & Finance, 36(2): 468-488, DOI: 10.1016/j.jbankfin.2011.08.004. 

612