Corporate Finance: Credit rationing - TAU · Corporate Finance 5 Credit rationing Creditor’s...

Corporate Finance:Credit rationing

Yossi Spiegel

Recanati School of Business

Tirole 2006

The Theory of Corporate Finance

Corporate Finance 3

The model� The timing:

� Effort raises the prob. of success from pL to pH� ∆p ≡ pH – pL� The project is viable only if there’s effort:

An entrepreneur has A dollars and needs to invest in a project that costs I > A

The entrepreneur exerts effort to boost the prob. of success.If he does not exert effort he gets private benefits B

Period 0 Period 2Period 1

If the project succeeds it yields R; if it fails, it yields 0

BpRBIRpIRp LH >∆⇒+−>>−+4342143421

Benefits NPVNPV

0

Corporate Finance 4

The loan agreement

� The loan can be debt or equity (the model cannot distinguish between them)

� Incentive compatibility (to ensure effort):

� Creditor’s individual rationality:

p

B

pp

BRBRpRp

LH

bbLbH ∆≡

−>⇒+>

4342143421321

MH ofCost effortwithout payoff expected

sur'Entreprene

effortwith payoff expected

sur'Entreprene

( ) {funds Required

)(income pledgeable Maximal

AIp

BRpRRp HbH −≥

∆−≡−

+43421

43421

Corporate Finance 5

Credit rationing

� Creditor’s individual rationality:

� An entrepreneur must have Ā to get funds

� When A < Ā, we get credit rationing: the creditor gets too little ex post to agree to give the entrepreneur I-A

� Credit rationing is “more severe” when B is large: there’s more agency problem or MH

( )444 3444 21

48476

assumptionby )(

effort with NPV

+

−−∆

≡≥⇒−≥

∆− IRp

p

BpAAAI

p

BRp HHH

Corporate Finance 6

Entrepreneur’s payoff� When A < Ā, the project is not funded so U = 0

� When A ≥ Ā, the project is funded; if the entrepreneur has all the bargaining power, the creditor simply breaks even:

� The entrepreneur’s net payoff (above and beyond A which he can consume anyway by not investing):

� Since the creditor breaks even, the entrepreneur captures the entire NPV

( )43421

effort with NPV

IRpAp

AIRpARRpU H

H

HlH −=−

−−=−−=

321321

effortgiven creditor payment toMin

payoffexpected

sCreditor'H

llHp

AIRAIRp

−=⇒−=

Corporate Finance 7

The entrepreneur’s net payoff (above and beyond A) - illustration

� The entrepreneur either gets all the NPV or nothing ⇒the entrepreneur is indifferent to A above Ā

A

pHR-I

Ā

Creditrationing

Norationing

Corporate Finance 8

Overborrowing

� Suppose the firm can ↑ the prob. of success by τ by investing J which it borrows from a new creditor

� Assumption: the investment is inefficient: J > τR

⇒ No point in investing if effort stays the same (investment ↓NPV and hence ↓ the entrepreneur’s payoff); the investment’s role is to transfer value from the original creditor

� The entrepreneur invests J only if it induces him to exert no effort (the alternative is to forgo J and exert effort):

( )32144 344 21

effort andmentoverinvest No

even breakscreditor new n theeffort whe w/o

payoff sur'entreprene The

bHbL RpBJRp >+−+τ

Corporate Finance 9

Overborrowing� The condition for overborrowing:

� Overborrowing is worthwhile only if it transfers enough value from the initial creditor to compensate for the resulting inefficiencies

� If the condition holds, the initial creditor must impose a no-extra investment/loan covenant

� Rl↑⇒ overborrowing is more tempting

� But Rl = (I-A)/pH; hence, A↓ ⇒ Rl↑ ⇒ overborrowing is more likely when A is low and hence covenants are needed more

( )( ) ( ) ( )( ){

44 844 76

321

444 8444 76

44 344 214342143421

Cost

investment new of

costNet

effort oflack todue Loss

Benefit

creditor initial theof payoff expected in the

RJpRBRppRRpBJRRP lLH

R

lH

R

lL

BB

τττ −+∆>++−⇒−>+−−+↓

Corporate Finance 10

Debt overhang

� Suppose the firm has initial secured debt with face value D ≤ A

� The creditor’s IR constraint:

� D makes investment less likely

{loan of Size

income pledgeableNet

AIDp

BRpH −≥−

∆−

44 344 21


Debt restructuring

� Suppose that R is large enough so the entrepreneur can get a loan without debt but not with the debt:

� Absent restructuring, the investment is not made and the creditor gets A

� To induce investment D must be lowered to d such that

∆−≤−<−

∆−

p

BRpAID

p

BRp HH

AIdp

BRpH −=−

∆−


Multiple projects� 2 identical projects� Suppose that the entrepreneur gets R2 if both projects

succeed and gets 0 otherwise (can also pay R1 is one project succeeds and R0 if none succeeds but R2 is sufficient since the entrepreneur is risk neutral)

� Incentive compatibility:

� The first IC constraint implies the second

( ) BRpppp

BRpRp

p

LHLH

LH >−

+⇒+>

∆

2

effortwithout payoff sur'Entreprene

2

2

projectsboth on effort with payoffsur'Entreprene

2

2

22

4342143421321

BpRpBRppRp HLHH >∆⇒+> 2

projectssingle aon effort with

payoff sur'Entreprene

2


2

2

43421321


The creditor’s IR� Creditor’s individual rationality (IR):

� From entrepreneur’s IC:

� Substituting from IC into creditor’s IR:

( ) ( )AIRpRpRpRppRp HHHHHH −≥−=−−+ 22122 2

2

payoffsur'Entreprene

2

2

return Expected

2

3214444 34444 21

p

B

ppR

LH ∆+≥

212

( )( ) AI

p

B

pp

pRpAI

ppp

BpRp

LH

HH

LH

HH −≥

∆

+−⇒−≥

∆+− 2

22

2


The effect of multiple projects on financing

� The condition for financing:

∆

+−−≡≥

p

B

pp

pRpIAA

LH

HH

A

pHR-I

Ā

Creditrationing

NorationingĀ↓

Financing is easier


Multiple projects with perfect correlation

� Entrepreneur’s IC:

� Creditor’s individual rationality (IR):

� From entrepreneur’s IC:

p

BRBRpRp LH ∆

>⇒+>2

2 2

effortwithout payoff sur'Entreprene

2


2 43421321

[ ] ( )AIRRpRpRp HHH −≥−=− 222 2

payoffsur'Entreprene

2

return Expected

321321

( ) ( )IRpp

BpAAAI

p

BRp HHH −−

∆≡≥⇒−≥

∆− 2

22


The creditor’s IR under perfect correlation

� Under perfect corr. we are back to the single project case

� Diversification helps because the projects are not perfectly correlated

� Imperfect correlation effectively lowers B to pHB/(pL+pH)


Correlation or independence?� Suppose the entrepreneur can choose whether

projects will be correlated or independent but his choice is hidden from the creditor

� Given R2, the entrepreneur’s payoff:

� Correlation: pHR2

� Independence: pH2R2

⇒ The entrepreneur will choose perfect correlation. Why is that?

� Asset substitution: correlation is riskier than independence. The entrepreneur is the residual claimant and likes risk


Continuous investment� I ∈ [0,∞) is a choice variable; the entrepreneur chooses I and whether

to exert effort

� Return is RI and private benefit is BI

� IC for the entrepreneur:

� IR for the creditor:

� Rewriting:

p

BIRBIRpRp bbLbH ∆

>⇒+>

( ) AIp

BIRIpAIRRIp HbH −≥

∆−⇒−≥−

444 3444 21multiplier

1

1

p

BpRp

AIH

H ∆+−

≡⇒≤ κκ


Continuous investment – optimal investment

� In a competitive capital market, the lenders must break even given their anticipation that the entrepreneur will exert effort: pHRl = I-A

� The entrepreneur’s utility above and beyond A:

� Assumption 1: pHR > 1 – investment has a positive NPV with effort

� Implication: the entrepreneur would like to invest as much as he can

� But if I is high, the IC constraint is violated

� Optimal investment is determined by the multiplier equation: I = κA

� “Invest up to κ times your wealth” or “Borrow κ-1 times your wealth”

( ) ( )IRpAp

AIRIpARRIpU H

H

HlH 1−=−

−−=−−=


Continuous investment - multiplier� Assumption 1: pHR > 1 – investment has a positive NPV with effort

� Assumption 2: pLR + B < 1 – investment has a negative NPV w/o effort

� Assumption 1 + 2 imply: pHR > 1 > pLR + B ⇒ ∆pR > B ⇒ R > B/∆p

� Assumption 3: pHR1 – 1 < pHB/∆p – NPV is lower than the cost of MH

� Since R > B/∆p and given Assumption 3, κ > 1

� Implication: κ is a “multiplier” – each dollar of equity leads to κ dollars of investment

� κ is smaller if B is large


Continuous investment - leverage

� The optimal investment is κA

� The entrepreneur needs to borrow (κ-1)A, where

∆

−−

∆

−

=−

∆+−

=−

p

BRp

p

BRp

p

BpRp

H

H

HH 1

1

1

11κ

Corporate Finance: Credit rationing - TAU · Corporate Finance 5 Credit rationing Creditor’s...

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Transcript of Corporate Finance: Credit rationing - TAU · Corporate Finance 5 Credit rationing Creditor’s...