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A model of adaptive relationship between the entrepreneur and the bank

The case of french vineyards entrepreneurs

Julien Cadot Conference

Small business banking and financing: a global perspective

May 25th-26th, 2007, Cagliari

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Introduction

• A demand from the Crédit Agricole (main agricultural bank)

• Changes in the wine business/ Changes in the bank practices

A new relationship between the bank and the vineyards entrepreneurs ?

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Financial specificities

• Small Family Business (capital limited)• Capital-intensive• Natural risk, risk of prices• Non depreciable assets (land) High leverage, good solvency but…… a risk of chronic liquidity crisis (Barry,

2001)

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Bank relationship specificities(Barry, 2001)

• Close-ties relationship• US banks but also Crédit Agricole: « local

community entrenchment »• An alignment of preferences instead of

« pure » credit rationing • Investment flexibility

An adaptive relationship

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Evolution du chiffres d'affaires et de l'endettement après l'installation

0

50

100

150

200

250

300

2-3 ans (33) 4-5 ans (39) 6-7 ans (38)

Années post installation

Sales

1000€

Debt

2-3 years 4-5 years 6-7 yearsYears after business start-up

A long phase of very high leverage

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The research question

• What is the influence of the bank financing on the investment process?

• Information asymmetry and underinvestment (initiated by Myers (1977))

• Liquidity risks and reputation (Diamond (1991)) A role of debt maturity on the investment process

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The modelHypothesis

• Entrepreneur limited in capital• Project of different scales (« prudent » and

« ambitious » project)• Value/Investment and Risk are constant along project

scale• Access to long term finance depends on the initial

demand and bank rating• The spread between investment and long term finance

can be filled by short term debt Liquidity risks

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The modelDefinition

• θ: project scale• V(θ): value• I(θ): investment• p: probability of

success• : bank rating • : long term

debt

• γ: Short term interest rate• S(D;I): Short term debt• Φ(S): Cost of a liquidity

crisis• C(S): Total expected costs

of short term debt• VR: Readjusted value

(value less expected costs of short term debt)

p~

LIpdD );~(

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I

LIpdD);~( S

The modelEquation

• The entrepreneur decides to undertake θ• Balance sheet at t=0

• Profit at t=1

• Expected profit:

ISVS In case of success : p

In case of failure : (1-p) DSVF )(

)))~(()(1())~(()1( 111 DpSpIpSpVpp FS

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The modelEquation

• Readjusted Value ISapSpV )]()(1((1

IVR 1

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Optimal project scale under long term finance limitations

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0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

VR

D

I

V

$

θθ*

S

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A dynamic setting

D a te 0 D a te 1 D a te 2 B a n k ra tin g 1

~p im p lie s th a t th e e n tre p re n e u r c h o o se s th e p ro je c t s c a le : i

1

S ta te re a liz e d (S u c c e ss ) 12

~~ pp a n d

2~p d e p e n d s o n S 1

(F a ilu re ) 12~~ pp a n d th e

e n tre p re n e u r h a s to p a y )(S . T h e e n tre p re n e u r is m o d ify in g h is p ro je c t , g iv e n th a t h e o p tim iz e s h is n e w re a d ju s te d v a lu e : *2

i .

T h e e n tre p re n e u r p ro fits a m o u n t to : )(* *

22ii

R IV .

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-5

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

$

θ1* θ2*

Vr1

I

V

Vr2

D2

D1

θ

Optimal projects in a two-period setting

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The entrepreneur dilemmawhen he has the choice between two projects

a

b

The « prudent » project•Optimal at the first period•No renegotiation of short term debt•No bank rating revision when state realized

The « ambitious » project•Optimal at the second period•Reputation due to renegotiation of short term debt•Bank rating revision when state realized

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Bank’s rating

Entrepreneur’s choice

First-period entrepreneur’s profit p

1-p1

~p

a

b

aa IVr )(1

bb IVr )(1

aaa IVr )(2

)()(2aaaa ScIVr

)()(2baaa ScIVr

bbb IVr )(2 p

1-p

Second-period entrepreneur’s profit

The entrepreneur dilemmawhen he has the choice between two projects

The decision tree

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The solution

atbt

)(11)()])(1()([1

1)( 21121 IVIVIVpIVpIV aR

aaR

aaR

bbR

bbR

)]()[( 11)()( 2211

aaR

bbR

bbR

aaR IVIVpIVIV

Is it profitable to be ambitious and take liquidity risks?Yes, if…

First period loss < Time preference*Quality*Second-period gain

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The solutionThe second-period expected gain

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

)()(

2222

22

aabbaabb

aaR

bbR

SapSpSapSpIVIV

IVIV

“Absolute” Value Differential

)~;()~;( 22aabb pIcpIcc

pdpcdII

cdC ~ ~

The trade-off between liquidity risk and reputation building

Total expected costs of the short term debt surplus

>0 <0

-

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Managerial implicationsDifferent trajectories

• Role of renegotiation as a condition of « growth »• Information sharing (in the course of the bank

relationship or at the time of short term debt revolving or conversion in long term debt) : a necessary condition for renegotiation

• Three trajectories :The “prudent” trajectory The “growth” trajectoryThe “go-back ” trajectory

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Managerial ImplicationsThe determinants of the “growth” trajectory

• The liquidity crisis costs• The time preference• The entrepreneur’s quality• The information shared in the interim

period• The ability of the bank to revise its rating

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Value and debt for youngest business (2-4 years after start-up)

y = 85880x + 106383

y = 72932x - 27388

y = 49403x - 5180,5

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

Grape growers Wine makers Independent Vineyards

V

D+S

D

Part of short term debt linearity test: significant at 0,015%

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Value and debt for oldest business (5-7 years after start-up)

y = 85880x + 106383

y = 72649x - 29644

y = 56690x - 17864

0

50000

100000

150000

200000

250000

300000

350000

400000

450000

Grape growers Wine makers Independent Vineyards

D

D+S

V

Part of short term debt linearity test: significant at 0,012%

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Evolution of the part of short term debt in total debt

Project scale Part of short

term debt N Oldest Grape growers 3% 78 Wine makers 8% 39 Independent

Vineyards 9% 20

Total 5% 137 Youngest Grape growers 4% 58 Wine makers 19% 28 Independent

Vineyards 12% 17

Total 10% 103

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…work-in-progress…

…variables specification and further quantitative or qualitative evidences have to come…

Thanks for your attention!