THE PRICING MECHANISM OF SUPPLIERS IN

RISK-SHARING IN EXTERNAL FINANCING

Zhenyi Wang ,Yihong Ru

School of Economics and Management, Beijing Jiaotong University, Haidian District, Beijing 100044, China

Hanqing Li

School of Economics and Management, Beijing Jiaotong University, Haidian District, Beijing 100044, China

Keywords: Supply chain, External financing, Risk-sharing, Utility function.

Abstract: In the background of retailers financing to financial institutions because of lacking of fund, assume that

suppliers are risk-averse and it costs much to rebuild the network of retail outlets, the paper uses utility

function to deduce the best wholesale prices for suppliers in risk-sharing. Research shows that suppliers will

avoid financing risks at high wholesale price in risk-sharing. And it also shows the influence mechanism of

the wholesale price.

1 PREFACE

1.1 About External Financing

It is an important puzzle in current supply chain

management that how to coordinate the relationship

between logistics, funding flow and information

flow effectively. Modigliani and Miller(1958)

pointed that financial decision making was irrelevant

to production capability/decision to produce in

complete competition environment, so financial

decision making and operating decision making

could separate. So it concentrates in the coordination

between material flow and information flow such as

Lee and Whang (1992)

.Those conclusions are based

on amply supported with funds. But in a competitive

global economy and national market competition, it

is hard to fulfill, Thomus (2002)

pointed the capital

restraint would affect operating decisions, price and

production of the enterprise. But without

consideration of the interaction of decision making

in financial and operation, meanwhile, the

conclusion that financial decision making and

operating decision making can separate may not be

tenable(Chen and Wan(2008)).As a result, more and

more scholars begin to pay attention to

codetermination of financial and operation. The

financing in supply chain caused wide attention.

In model study, past studies have focused on an

individual company such as Hu and Sobiel (2005)

used dynamic newsboy model to study the

interaction of capital composition and operating

decision. Xu and Brige (2005)

used newsboy to

analyze the best output decision of enterprise under

limitation of funds and incentive mechanism to

manager. Chen and Wan (2007) used merchant

agreement and loan agreement to study the influence

of financing service on supply chain enterprise

operating decision and value. Caldentey and Chen

(2008)

studied financing service value in purchasing

contract and the influence of financing service on

the value of financing enterprise. Chen Xiangfeng

studied the best ordering policy and the profit of

supply chain enterprise of which the retailers borrow

money from financial institutions in lacking

sufficient funds. But he only considered the

allocation of risks between retailers and financial

institution without considering suppliers. The paper

has considered suppliers to share risks based their

studies and calculated the best wholesale price and

the influence mechanism of wholesale price.

1.2 The Necessary of the Research and

Relevant Conclusions

In developing countries, medium-sized and small

145

Wang Z., Ru Y. and Li H..

THE PRICING MECHANISM OF SUPPLIERS IN RISK-SHARING IN EXTERNAL FINANCING.

DOI: 10.5220/0003431601450149

In Proceedings of the 13th International Conference on Enterprise Information Systems (ICEIS-2011), pages 145-149

ISBN: 978-989-8425-55-3

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

enterprises usually face shortage of funds. Financing

becomes the survival guarantee of medium-sized

and small enterprises. Financing can be divided into

external financing and internal financing. This paper

mainly considers external financing. In external

financing, most papers focus on retailers and

financing institutions need undertake the risk of

indeterminacy demand. Obviously, it is unfair to

retailers. In the operation of supply chain, only in

equitable and efficient allocation of risks can the

supply ensure high-efficient development.

It costs large manual labor and material

resources to rebuild the network of retail outlets,

leading that under normal circumstances suppliers

don’t want to see the retailers go broke. Assume that

suppliers are rational agents and risk-averse.

Suppliers will help the retailers share risks to avoid

the retailers going broke because these risks are

insignificant to key suppliers and it can achieve win-

win.

This paper is under the two background

conditions. Consider suppliers as rational agents to

share financing risks of retailers to calculate

equation and influence mechanism of wholesale

price and contrast with that of non-risk-taking.

2 PROBLEM DESCRIPTIONS

AND MODEL HYPOTHESES

2.1 Problem Descriptions

Considering secondary structure of supply chain, a

single supplier serves a single retailer. In the initial

sale, if retailers appear limitation of funds, they can

attain financing service from competitive capital

market. Chen Xiangfeng’s study demonstrated that

suppliers are the biggest beneficiaries when

cooperation and risk-taking between retailers and

financing institutions are only considered. And he

deduced the best wholesale price of suppliers and its

influence mechanism. On that basis, considering the

large cost of rebuilding of regional retail network,

suppliers will initiatively share financing risk in

external financing to avoid the bankruptcy risk of

retailers.

2.2 Model Hypotheses and

Nomenclature

Assume that a single supplier provides a single kind

of product to a single retailer newsboy charactered,

wholesale price is

, import price of the suppliers

; there is limitation of funds in adoption process

for retailers and its own purchase fund is

B .Market

demand

D is uncertain, its density function is set as

()

D .CDF(cumulative distribution function) is

()

D , and ()

D is continuous, derivable and strict

increase. And

() 1 ()FD FD=−

.Assume that ()

has a certain mean value

, ()

D accords with a

distribution of increasing failure rate.

At the beginning of the sales cycle, cash-strapped

retailers can attain financing service in the

competitive capital market and accept the merchant

agreement from suppliers through ordering

and

paying

. Then, retailers sell on the market at the

fixed retail price

≤

, and the profit is

min[ ; ]

DQ⋅ .

At the end of the sales cycle, the retailers will

return principal and interest of financing to the

financial institution who offered financing service to

them.

In order to explain the model clearer, the paper

assumes as follows,

Assumption 1, goods have little marketable value

after sales cycle.

Assumption 2, financial institutions especially

banks face drastic market competition, so many

financial institutions will offer financing service to

cash-strapped enterprises so as to achieve financing

profit, and the financing rate is

Assumption 3, financial institutions that offer

financing service are investors that pursue risk

neutral and are in competitive capital market. The

average market rate of return on investment in

capital market is

, or risk-free rate of the capital

market. And it is determined by the competition of

market. The more intense the competition of market

is, the smaller

is.

Assumption 4, the suppliers and the retailers are

both rational agents. To suppliers, if the retailers go

broke, it is necessary to rebuild the regional retail

net. And the reproduction cost is

K it is high in

general.

Assumption 5, the suppliers are risk-averse and

HARA rate is

Figure 1 states that the retailers and the fund

raising institutions share the financing risks. The

dotted line states that the suppliers, the retailers and

the fund raising institutions share the financing risks.

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

146

Figure 1.

3 RISK-SHARING PRICING

STRATEGIES FOR SUPPLIERS

According to assumptions made before, at the

beginning of sales cycle, the retailers with

inadequate capital could afford

to suppliers

with capital of amount B from themselves as well as

wQ B=−

from financing; At the end of the sales

cycle, the retailers will get profits of amount

min[ ; ]

DQ⋅ , and clear the debts in the bank

account by paying back min

[min[;];]

DQ L⋅ ,

where

(1 )LL r=+.

Therefore, retailers should order the optimal

amount for sales to optimize their benefits, and the

expected earnings should be:

[

]

min , ( )(1 )

Ep DQ wQ B r

⎡⎤

=−−+

⎣⎦

;

From the formula above we can see that under

the assumption of existence of financial service, the

retailers’ net income will be positive while the

profits from sales “

min[ ; ]

DQ⋅ ” is larger than the

amount of principal and interest owed to the

financial institute. Otherwise, the company would

end up with bankruptcy, after which the profits will,

of course, be zero. The optimal-ordering strategy

and the corresponding probability of bankruptcy of

retailers can be described by Proposition 3.1.

Proposition 3.1

The optimal-ordering amount for a capital-limited

retailer who can finance in the competitive capital

market is

(1 )

−

⎡

⎤

⎢

⎥

⎣

⎦

Under this optimal-ordering amount the

bankruptcy probability of the retailer is

()(1)

wQ B r

⎡⎤

−+

⎢⎥

⎣⎦

Proof:

The proof for optimal-ordering amount was

given by Chen X.(2008). And under this optimal-

ordering amount, the profit of the retailer is:

[

]

min , ( )(1 )

Ep DQ wQ B r

⎡

⎤

=−−+

⎣

⎦

(1)

If the retailer comes to bankruptcy, obviously

we have

[

]

min , ( )(1 ) 0pDQwQBr

−

−+≤

(2)

The retailer will not apply the sale plan if the

retailer would still end up with bankruptcy even

while the real sales amount reaches the optimal-

ordering amount. So this is not realistic and from (2)

we can get

()(1)WQ B r

−

≤

(3)

So the bankruptcy probability is

()(1)

wQ B r

⎡

⎤

−+

⎢

⎥

⎢

⎥

⎣

⎦

Proved.

Obviously, this probability is an increasing

function with respect to the risk-free interest rate and

a decrease function with respect to the capital B

owned by the retailer.

Now, the expectation of profits for the retailer is:

()( )(1 ) ( )

FF F

EwcQFFwcQK

⎡⎤

=− −+ − −

⎣⎦

()

wcQ FK=− −

(4)

The variance of profits is:

*222

111

()(1 )()( )

()( )

FFF

Var F E w c Q

EwcQkFKFK

ππ

⎡⎤

=− − −

⎣⎦

⎡⎤

+−−+=+

⎣⎦

(5)

Proposition 3.2

While the distribution function of market demand

()

D satisfies the property of failure-rate-increase,

with the competitive financial market that is able to

serve for retailers of inadequate funds, the pricing

strategy of a risk averse supplier while considering

to reestablish the network for sales after bankruptcy

of the retailers should be a fixed value

, which

should be larger than the value

obtained without

taking into consideration the reestablishment of the

network.

Proof:

Without considering the reestablishing of network,

the pricing equation (see Xiangfeng, 2008) should



THE PRICING MECHANISM OF SUPPLIERS IN RISK-SHARING IN EXTERNAL FINANCING

147

1(1)

()

=−

(6)

Here

()

HQ Q

is the general failure

rate.

The supplier is risk averse, and satisfies the mean-

variance utility function, which is

() ()

UE Var

=−

(7)

Obviously

∂

, so there must exist

, such

that (7) has maximum value.

Is the solution of the

equation?

(1 ) 1

()

()(1)(1)

(1 ) 0

()

FfFf

wwHQ

wQ B r Q r

ppHQ

⎡⎤

∂

=− − − −

⎢⎥

∂

⎣⎦

⎡⎤

−+ +

−=

⎢⎥

⎣⎦

(8)

Here

11 1

(,)

fK K K F

==+−

()

HQ Q

Set

()(1)(1)

wQ B r r

Mff

⎡⎤

−+ +

⎢⎥

⎣⎦

Then we have

1(1)

()

−= −−

(9)

Without considering the network for sales after

bankruptcy of retailers, the price

w satisfies

1(1)

()

=−

(10)

For the sake of convenience, assuming that

()

D follows an exponential distribution, we can

easily get

ww> .Proved.

The research shows that while the suppliers take

into account the cost for the reestablishment of sales

network, they may control the ordering amount of

retailers as well as avoid the potential over storage

problem resulted from the shrinking of demand by

setting a higher wholesale price. Then they can

hedge for the risk of bankruptcy of retailers. In this

process, the suppliers get involved in the financing

step of retailers. So the optimal wholesale price will

be determined by the capital amount

B owned by

retailers and by the competitive level of the capital

market, denoting by



Proposition 3.3

While suppliers take into account the cost of

reestablishment of sales network, the optimal

wholesale price aiming at hedging for the risk of

bankruptcy of retailers will be negative related with

the funds amount

B owned by retailers, and be

positive related with the competitive level of the

capital market, denoting by



. And it will also be

positive related with the absolute risk-aversion

coefficient



of suppliers.

Proof:

Since w is the solution of

1(1)

()

−= −−

After calculation we can easily get

∂

;

∂

；

∂

So the optimal price designed while considering

the share of financing risk should be negative related

with the funds amount

B owned by retailers, and be

positive related with the competitive level of the

capital market, denoting by



. And it will also be

positive related with the absolute risk-aversion

coefficient



of suppliers.

4 CONCLUSIONS AND

PROSPECT

Based on ideas of utility function, we discussed the

pricing strategies for suppliers in a double supply

chain while the suppliers have to share the financial

risk from the retailers with inadequate funds. We

concluded that the optimal-ordering amount for a

capital-limited retailer who can finance in the

competitive capital market is a fixed value. And we

also find that taking the high cost for

reestablishment of sales network into consideration,

a risk adverse supplier will push the rational retailers

to cut off their order by setting a high wholesale

price, by which they can hedge for the risk of

bankruptcy of retailers. At the same time, our

calculation shows that the optimal price should be

negative related with the funds amount

B owned by

retailers, and be positive related with the competitive

level of the capital market, denoting by



. And it

will also be positive related with the absolute risk-

aversion coefficient



of suppliers.

ICEIS 2011 - 13th International Conference on Enterprise Information Systems

148

There are still some limitations in our paper. We

assume the market demand following an exponential

distribution, which is not necessarily true. And in

reality, suppliers always try to increase their sales to

gain market share, so the suggestion of hedging for

risk by setting higher wholesale price may not be

realistic. The upcoming research may consider the

strategies of sharing the financial risk of retailers

with other suppliers, such as recycling the unsold

goods or economic assistance to the bankrupted

retailers. What’s more, we only make our discussion

under the secondary supply chain structure. To

extend the results into a three-tier (or more) supply

chain structure, the adjustments for production and

sale according to financing activities from different

levels of the supply chain may deserve further

discussion.

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Thomus L, 2002. Non-linear Pricing with Budget

Constraint. Economic Letters. 75: 257-263.

Chen, Xiang-Feng&Guo-Hua, Wan, 2008. The Impact of

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