Moral Hazard and Costly External Finance This section is based on1 – Chapter 3 of Tirole which itself is based on Holmstrom, B. and J. Tirole (1997) “Financial Intermediation, Loanable Funds, and the Real Sector”, Quarterly Journal of Economics, 112, pp. 663-691. – Chapter 5 of Tirole, which itself is based on Holmstrom, B.. and J. Tirole (1998) “Private and Public Supply of Liquidity”, Journal of Political Economy, 106, pp. 1-40. A moral hazard model to understand costly external …nancing and credit rationing. Intuition: – Borrowers (Managers) may mismanage a project. This takes the form of a private bene…t B that reduces the probability of project success (or alternatively, it is costly for the borrower to ensure project success). – The private bene…t is ine¢ cient in that its value to the borrower is less than the NPV of the project. Yet the borrower receives the entire B and must share the project return with the lender. – Thus, the borrower must keep a su¢ cient stake in the project in order not to waste money. – Since the project’s income cannot be fully pledged to lenders, it may not get funding even if the NPV is positive (i.e. credit rationing). Since the framework is so simple, there isn’t really debt vs equity just external …nance. Recall in the data notes, I introduced a reduced form convex cost of external …nance function C(e) where e = I A (actually in the other notes, internal funds was denoted w; but here it is denoted A). This chapter derives an endogenous cost function where C(e) =

0 for A A 1 for A < A

where A is an endogenously derived cuto¤ which respects incentive constraints. 1 Subsections

with “*” will be covered in class.

1

1 1.1

A Simple Model of Credit Rationing (T3.2) A Fixed Investment Environment Firm (or entrepreneur) has a project which requires a …xed level of investment I: Firm only has cash (internal funds) A < I: Thus to implement project, …rm must obtain I

A funding from lenders.

Project either yields R > 0 if it succeeds with probability p or 0 if it fails. Moral hazard. Firm can choose p = pH probability of success but with no private bene…t or he can choose p = pL < pH but with private bene…t B 0: – One can interpret these as probabilities conditional on the amount of e¤ort chosen by the entrepreneur: if he puts in high e¤ort H, he gets a higher probability of success but it is costly (relative to low e¤ort). – Let p = pH pL : Firm (borrower) and investor (lender) are risk neutral = 1 so expected rate of return equals 0. Limited Liability on part of …rm (can’t pay anything in failure state). Lenders behave competitively (i.e. loans make zero pro…t)2 Loan contract speci…es Rb goes to borrower and Rl goes to lender. Timing: – Competitive lenders post contract3 (Rb ; Rl ) – Investment I – E¤ort choice H or L (unobservable) – Outcome R (observable) Parameterization (I; A; R; pH ; pL ; B): Assume the project has positive NPV only if the good action is taken pH R

I>0

(1)

but negative NPV (even if the private bene…t is included) if the bad action taken pL R I + B < 0: (2) 2 Some economists don’t include statements about markets or competition in the “environment”. An environment is a list: (1) population; (2) preferences; (3) technologies; (4) information structure; and (5) timing. Then they solve for a (constrained) optimal allocation. Markets can come back in when they try to implement (or decentralize) that allocation. 3 Alternatively, we could implement this by having the borrower make take-it-or-leave-it o¤ers to any of the large number of lenders.

2

1.2

Equilibrium (First Best) Suppose B = 0; so there is no moral hazard problem (i.e. the cost of choosing pH is the same as the cost of choosing pL ). The solution to the …rst best problem maximizes the borrower’s utility subject to lender participation. Perfect competition drives the lenders participation constraint down to their zero pro…t condition: pH Rl + (1

pH ) 0

(I

A) = 0 =) Rl =

I

A pH

(3)

Because the NPV with good behavior is positive, the project should be funded in which case the borrower receives Rb

= R = R

Rl I

A pH

:

(4)

While the return the borrower receives is increasing in A; whether or not he/she receives it is independent of A in the …rst best.

1.3

Equilibrium (Second Best) Suppose B > 0: Because the project has negative NPV with misbehavior, the loan agreement must be careful to preserve enough of a stake for the borrower. The borrower will behave if the following IC constraint is satis…ed: p H Rb

pL Rb + B ()

pRb

B

If investment is undertaken, the optimal contract maximizes the entrepreneur’s expected compensation subject to entrepreneur incentive compatibility and lender participation given by max pH Rb

Rb 2[0;R]

subject to

pH (R

pRb

B

Rb )

I

3

(5) A

(6)

The zero pro…t condition (6) with equality (solving for Rb ) into incentive compatibility (5) implies a necessary condition for equilibrium is pH

B p

I

(pH R

I)

R

A:

(7)

But (7) can be rearranged to A

pH

B p

A(B)

(8)

To make things interesting, assume that parameters (I; R; B; pH ; pL ) are such that the asset threshold A > 0; otherwise even a borrower without cash would get funding. I will call A A(B) the “…nancing constraint”. The key result in the second best environment is that if A < A; then even a project with positive NPV doesn’t get funded. In that case, we say there is credit rationing. This is what I meant in the introduction that “the borrower must keep a su¢ cient stake in the project in order not to waste money.”If the borrower has a su¢ cient stake in the project, then they don’t want to see it fail because in that state they do not recoup the stake. Hence they have an incentive to behave and raise the probability of success. If A A (i.e. (8) is satis…ed), then the …rm gets funding and since there is perfect competition among lenders, the zero pro…t condition in (6) holds with equality or (I A) Rb = R pH Importantly, note that this is the same level as in the …rst best (4). Existence: The key issue is that this allocation need not exist if A < A whereas the same allocation existed for all A in the …rst best. The entrepreneur’s net utility (subtracting A since he had to put that stake up if funded) is given by Ub =

A pH Rb

A=0 A = pH R

I

if A < A if A A

(9)

i.e. the borrower receives the entire social surplus or NPV if the project is funded.4 4 To

see this, p H Rb

A

=

pH R

=

[pH R

A) pH (I A)]

=

pH R

I:

4

(I

A A

Note that (1) and (9) implies that the entrepreneur with enough internal funds would prefer to undertake the project than simply eat his A (i.e. maxfpH Rb ; Ag = pH Rb ). This is why I wrote the programming problem as I did above. Two factors may make a …rm credit-constrained (i.e. violate the necessary and su¢ cient condition (8)): – Low cash on hand A – High Agency Cost pH Bp : Note that not only high private bene…t B but also a high value of pH = p: If we de…ne p=pH as the likelihood ratio as Tirole does5 , then a lower likelihood ratio implies less information about the e¤ort choice by the borrower, a higher agency cost, and makes it harder to get outside funding. Note it was WLOG that the borrower invested all their cash in the project (i.e. it was optimal). This is because no matter what, the borrower got all the social surplus and investing less just makes it less likely to get funded. Note it was WLOG that there were no transfers to the borrower when the project is unsuccessful (risk neutrality is important for this result). If the borrower got something T > 0 in the failure state, then it makes it harder to satisfy incentive compatibility (5) since: pH Rb + (1 p (Rb

pH )T

pL Rb + (1

T)

pL )T + B

B

Note that total value is pR while investor value is pRl (often the empirical literature uses the phrase “value” for what Tirole calls “investor value”). Note that moral hazard refers to the possibility that the borrower takes an action that reduces investor (and total) value. See EXERCISE 3.15, 3.16 for ways to introduce risk taking.

1.4

Debt or Equity? (T3.5) With just 2 outcomes f0; Rg; the lender’s claim can either be thought of as equity (Rl =R is outside equity while Rb =R is inside equity) or risky debt (which pays lender Rl in successful state and bankruptcy in failure state).

5 There are many di¤erent de…nitions of likelihood ratio, including p =p , which is inH L creasing in pH : But so is Tirole’s de…nition since p=pH = 1 (pL =pH ) is also increasing in pH :

5

1.5

Sensitivity of Investment to Cash Flow (T3.2.7) The MM theorem says that investment depends only on fundamentals (measured by market to book value termed Q in the literature) and not on capital structure. Fazzari, Hubbard, and Peterson (1988, BPEA) tested whether a …rm’s investment was sensitive to its capital structure after controlling for Q: In particular, they ran regressions of the form Iit = Kit

C 0

+

C 1

Qit +

C 2

CFit + "t

where CFit was cash ‡ow at …rm i in a particular agency cost class (e.g. 3 classes of …rms that could depend on such observables like dividend payout practices, size, age, etc. where class 1 was supposed to have the highest agency costs and class 3 the lowest). They found that unlike MM, C 2 6= 0 and that 12 > 22 > 32 > 0: We now consider the sensitivity of investment to cash ‡ow in the context of Tirole’s …xed investment model. Note that any aggregate e¤ects in the …xed investment environment will only come from the “extensive margin”. Recall from (8) that the borrower is not rationed if A where “pledgeable income” is de…ned as 0

pH

R

B p

A( 0 ) = I

0

;

while those whose cash lies A < A(B) will be rationed. Then, the lower is 0 the higher are agency costs. Note that since I is …xed and exogenous, an increase in I raises the required amount of cash and makes it less likely to invest for a given amount of cash (i.e. dA dI > 0). Suppose there is heterogeneity in A and 0 : Let G(A) denote a continuous distribution function and g(A) its associated density. As an example suppose A U (0; I) so that G(x) = xI and g(x) = I1 : Because only …rms with cash-in-hand A satisfying A A( 0 ) receive …nancing, aggregate investment for …rms with pledgeable income 0 is I( 0 )

I

Z

I

A(

g(A)dA = 1

G(A( 0 ))

I:

(10)

0)

Note that aggregate investment in this …xed I case only changes through a change in the extensive margin A( 0 ): 6

In the uniform case: I( 0 )

I

Z

I

A(

0)

1 I A dA = I: I I

Consider a small change dA = in cash for all …rms. The entire distribution shifts right, but the cuto¤ I 0 does not (since 0 does not depend on A). In that case, the change in investment for a small change in A is given by dI( 0 ) = g(A) I dA: Intuitively, the mass of people just below A will be shifted over the threshold and start to invest given the helicopter cash drop. This result is consistent with Fazzari, et. al. where an increase in cash raises investment. For example in the uniform case U ( ; I + ):6 I+ ( 0 )

I

dI( 0 )

=

Z

I+

A(

0)

I+ 1 dA = I I

A

I

so that

= =

I+ ( 0 ) I+

I

I( 0 )

A

I

I

A I

I

1 I I

Furthermore, the sensitivity of investment to cash ‡ow increases is a¤ected by agency costs. Consider a decrease in agency costs (i.e. a decrease in B) which leads to an increase in 0 . Then d

dI( 0 ) dA

d

= g 0 (A( 0 ))

0

dA I: d 0

(11)

0) where ddA = 1: Thus, the sensitivity of investment to cash ‡ow dI( dA 0 depends on agency costs and can be increasing or decreasing depending on the sign of g 0 (A( 0 )):

– If g 0 (A( 0 )) > 0; the sensitivity of investment to cash ‡ow is lower for …rms with a low agency cost (as in Fazzari, et. al.). – If g 0 (A( 0 )) < 0; the sensitivity of investment to cash ‡ow is higher for …rms with a low agency cost (as in Kaplan and Zingales (1997, QJE)). 6 Note

that the uniform distribution may not be the best to illustrate this phenomenon dI( ) since it generates dA0 independent of 0 :

7

2 2.1

Borrowing Capacity: The Equity Multiplier (T3.4) A Continuous Investment Environment In the previous model, the required investment size I was discrete (and exogenously given). In that case, the borrower needed a large amount of cash A to get funding. In contrast, in this section investment is continuous and endogenously chosen. In the continuous (endogenous) investment case, for even small amounts of cash, investment can always be chosen to respect the IC constraint. Assume constant returns to scale in the investment technology. Exercise 3.5 considers DRS. I 2 [0; 1) yields – income RI in the case of success – income 0 in the case of failure Private bene…t also proportional to I – if behave, get 0 but prob of success is pH – if misbehave, get BI but prob of success is pL < pH : Now Rl + Rb = RI Assume project has positive NPV per unit of investment if borrower behaves but negative NPV if the borrower misbehaves, i.e. pH R 1

> 1; >

(12)

pL R + B:

To guarantee a …nite level of investment with a linear technology, assume expected per-unit net revenue is lower than expected per-unit agency cost: pH R

1<

pH B p

(13)

Assume perfect competition. Exercise 3.13 considers a lender with market power.

8

2.2

Equilibrium Incentive compatibility for the borrower (to behave): pH Rb

pL Rb + BI ()

pRb

BI

(14)

Participation constraint for lender pH (RI

Rb )

I

A

(15)

Since lending is competitive, (15) implies that borrowers net utility is Ub

= p H Rb

A

= p H Rb

[I

=

1) I

(pH R

pH (RI

Rb )] (16)

In that case it is optimal for the borrower to invest as much as possible. The upper bound on I is determined by the IC and participation constraints. In particular, since the lender participation constraint is binding, then (15) implies pH RI + A I Rb = pH which upon substituting into (14) yields the modi…ed IC constraint p [pH RI + A

I]

pH BI ()

pH R

()

A

1

()

kA

I

where k

1

h 1

(17)

1 pH R

pH B I +A 0 p B I pH R p

B p

i;

(18)

Hence I is bounded above by kA (these are all parameters). That k > 0 follows from (13), from which k > 1 follows. This is important. The fact that k > 1 shows the borrower can “lever up” his wealth. They call k the equity multiplier. Borrowers are better able to lever their wealth to be able to borrow more if:

9

– private bene…ts B are small since dk =h dB

1

p pH

– likelihood ratio dk d

1

< 0:

is big since wrt its inverse

=h

pH p

B p

pH R

pH p

i2

1 1

pH R

B p

pH p

i2

< 0:

Given that utility is increasing in I in (16) since pH R > 1, we know that the outside …nancing capacity constraint (17) is binding, in that case it is optimal to borrow I Let d

(k

A () kA

A () (k

1)A:

1):

The maximum loan d A is called the “borrowing capacity”.7 Note also that “debt over inside equity” ratio is just d: Another important concept, which will be used in computing the value of retained earnings in dynamic models, is the shadow or marginal value (denoted v) of equity (in this case cash or retained earnings A). Letting the borrower’s gross utility be given by Ubg

Ub + A =

(pH R

=

[(pH R 1) k + 1] A h 0 (pH R 1) + 1 pH R @ h i B 1 pH R p 0 1 pH pB @ AA B 1 pH R p

=

=

1) kA + A B p

i1

AA

vA

where the …rst equality follows from (16) and a binding constraint in (17). dU g It is clear then that the marginal value of cash is just dAb = v: With constant returns, the shadow value of equity (or internal cash) is 7 The

“gearing ratio” is de…ned as g = d=k:

10

– independent of A (Does this change in the second problem of problem set 2?) – increases with R since dv = dR

pH B p

1

pH

– decreases with B since nh 1 pH R dv = h dB 1 =

Using the notation from before, 1 > 1 > 0 ; then – k = 1=(1 –d = – Ubg

0 =(1

=(

1

– Ub = (

1

B p

pH R 1

i

( pH ) > 0

pH p

pH R

pH R) pHp

(1

h 1

B p

2

B p

R

B p

h

pH pB i2

i

pH p

o

i2 < 0:

pH R and

0

pH R

B p

where

0) 0) 0 ) A=(1

1) A=(1

0) 0)

Exercise 3.17 shows that the bounding condition in (13) is unnecessary if the price of the …rm’s output depends negatively on industry investment (or output). Intuitively, in that case more investment reduces pledgeable income. Sensitivity of Investment to Cash Flow. – In the …xed (exogenous) investment case, A A(I; 0 ) = I 0 dA and dI > 0 so that the extensive margin changes with a change in exogenous I given by Z I I(I; 0 ) I g(A)dA: A(I;

0)

and for a small increase in cash to all …rms gives dI( 0 ) = g(A) I dA: – In the continuous (endogenous) investment case, for even small amounts of cash, investment can always be chosen to respect the IC constraint. Hence in this case, it is “intensive margin”e¤ects that matter in the aggregate. 11

– In this case, I = k( 0 )A; so that I must be in the integral given by Z 1 I( 0 ) k( 0 ) Ag(A)dA = k( 0 )E[A]: 0

– In that case, a small change dA to all …rms raises the mean by dA so that dI( 0 ) = k( 0 )dA and d

dI( 0 ) dA

d

0

=

dk( 0 ) = d 0 (1

1

2( 0)

1) > 0:

so there is a de…nite prediction independent of the distribution unlike (11). Firms with a low agency cost (i.e. high 0 ), which are therefore less …nancially constrained, exhibit a higher investment sensitivity. That is consistent with Kaplan and Zingales, not Fazzari, et. al.

3

Debt Overhang (T3.3) Starting with Myers (1977, JFE), papers have studied situations where a borrower is debt ridden (say amount D) and unable to raise funds for an otherwise pro…table project. In this case, the borrower is said to su¤er from debt overhang. One big question is where did D come from? In a static model, it is taken as exogenous. But in a dynamic model, it was chosen last period. If there is credit rationing, would debt be chosen so as not to violate the “…nancing constraint”? This is just to say that these debt overhang models are a bit ad hoc. Here we will return to the …xed investment case since that is simpler.

3.1

Rationing without Renegotiation Suppose – the entrepreneur has A in cash and a positive NPV project, but owes D from previous borrowing (say from some initial investors). – the initial investors had a convenant specifying that the borrower cannot raise more funds without consent – the borrower’s assets A are pledged to initial investors as collateral in case of default If A>A>A

12

D

0;

the project is not …nanced. This just says that even though it would be …nanced in the absence of the debt, it is not …nanced in the presence of debt. Why? – Because initial investors can secure D; they must receive an expected payment at least equal to D: – Since pledgeable income net of investment is pH

B p

R

I;

new investors obtain at most pH

B p

R

(I

A)

D=

since A = pH Bp (pH R I) : Note that the “slack” in pledgeable income.

3.2

A+A

D<0

A can be thought of as

Renegotiation One could think about this subsection as applying to what happens if renegotiation-proof contracts are not o¤ered or that it is a situation o¤the-equilibrium path. Recall that in the previous …xed investment section, the borrower received all the surplus due to the perfect competition assumption (i.e. the borrower made a t-i-o-l-i o¤er to lenders). Ex-post renegotiation could put the creditor in a di¤erent bargaining position than in ex-ante case when originally negotiating the loan. Suppose – the entrepreneur has no cash A = 0: – the project is su¢ ciently pro…table to attract funds even if the borB rower has zero cash (0 < pH R I () A < 0). p – the borrower already owes D on a long run debt obligation (which is senior to any other claims) that is to be paid o¤ in the successful state provided the project is funded. – the slack in pledgeable income (recall pledgeable income is pH R is smaller than what needs to be paid back to previous investors pH

R

B p

I < pH D () 13

A < pH D:

B p

(19)

)

Timing: – Borrower enters period with A = 0 and previous D owed to initial investors – (re)-Negotiate contract – Investment undertaken – Action taken – Outcome Note that because the borrower has no cash, initial investors receive nothing if the project is not …nanced.8 Hence initial investors are willing to …nance as long as they receive at least 0. We will consider two cases and several possible outcomes. There may be many other outcomes in the renegotiation subgame. 1. Case 1: Initial investors have su¢ cient funds to …nance I and the opportunity to make a take-it-or-leave-it (counter)o¤er to the entrepreneur (i.e. they have some bargaining power, say due to their seniority). Then they could forgive the debt (what’s sunk is sunk) and demand the slack from pledgeable investment receiving pH

B p

R

I

A > 0:

The borrower is willing to go along with this since he gets pH Bp instead of 0 (recall A = 0). Note that this allocation is di¤erent from the …rst best, since there the initial investor actually got zero. 2. Case 2: Initial investors have insu¢ cient funds to …nance I. The borrower then needs to turn to new investors, who we will assume have no bargaining power as before. Are new investors willing to …nance the project? – Because initial debt is senior, at most R

D

B p

can be pledged, so new investors participate if pH

R

D

B p

I

0 ()

A

pH D

0 () pH D

A

which contradicts assumption (19). 8 As in most problems in renegotiation (an ex-post concept), it is not speci…ed why the initial investors are owed D (i.e. why the lack of payment was not anticipated).

14

Thus, the borrower cannot raise funds from new investors unless he renegotiates some debt forgiveness from initial investors. Suppose even though initial investors have no funds, they negotiate a reduction in the face value from D to d < D in the event of success where A + pH d = 0: – Then new investors can expect to get pH

R

d

B p

I ()

A

pH d = 0

so they are willing to invest. – Initial investors get pH d =

A > 0; so they are better o¤.

– The borrower expects to get pH B= p; so he is better o¤. Thus, renegotiating debt yields an ex-post pareto improvement (not necessarily ex-ante though since the “bargaining power” in the renegotiation subgame is di¤erent in these examples).

4

Liquidity and Risk Management (T5.2) A key issue in the design of long-term …nancing (solvency) is to ensure that, at intermediate stages, there is su¢ cient liquidity to pay operating expenses, etc. Liquidity planning is central to the practice of corporate …nance. The previous sections were about Solvency (the ability of the …rm to meet its long term commitments). This section introduces Liquidity (the ability of the …rm to meet short term commitments). To model solvency (Section 3.2) we focused on a single stage problem. To model liquidity (Section 5.2) we focus on multistage …nancing by introducing an interim stage with an exogenous liquidity shock.9 The capital market may ex-post rationally, but ine¢ ciently (since the …rm must terminate the e¢ cient (pro…table) project), deny funds to …rms to continue a project. Thus, even though agents are risk neutral there is a need for interim insurance. A …rm has two ways of facing urgent liquidity needs: – Cash retentions (e.g. …rm could overborrow at t = 0 and then hold cash to self insure). – Secure a line of credit in event shock arrives. 9 Section

5.5 studies the case when liquidity shocks are endogenous.

15

Lenders do not internalize the loss incurred by the borrower when the project is stopped. A concession by the borrower to induce lenders to keep the project going (i.e. to internalize the externality) may not be acceptable by lenders in the presence of moral hazard .

4.1

Environment Same as …xed investment environment of Section T3.2 with one key difference, an interim stage in timing where: – After initial investment of I A as in T3.2, the investment yields deterministic income r 0 but to continue the project requires reinvesting a random amount (unknown at initial investment time) drawn from distribution function F ( ) (density function f ( )) on [0; 1):

– If the …rm does not reinvest liquidation value is 0:

; then the …rm is liquidated. The

– If the …rm does reinvest, it receives the same returns as in Section T3.2 (i.e. R with probability p and 0 otherwise where p 2 fpH ; pL g where pL choice brings private bene…t B: As before, both borrower and lender are risk neutral. Timing: – t = 0; Competitive lenders post contract10 (rb ; rl ; Rb ; Rl ) where rb + rl = r and Rb + Rl = R Investment I –t = 1 Short term Income r and cost drawn from density f ( ) realized Continuation decision E¤ort choice H or L (unobservable) –t = 2 Long term income R (observable) realized Thus this model nests Section T3.2 with r = 0 and a degenerate distribution on = 0: 1 0 Alternatively, we could implement this by having the borrower make take-it-or-leave-it o¤ers to any of the large number of lenders.

16

4.2

Equilibrium A heuristic description of the optimal contract. Assume there is a cuto¤ rule whereby continue only if interim cost is below an endogenously determined threshold :There is no constraint that the cost has to be funded out of the …rm’s t = 1 income (i.e. r). Borrower Incentive compatilibity at date t = 1 remains pRb

B

(20)

Lender participation at t = 0 under the assumed cuto¤ rule is F ( )pH (R

Rb ) + (r

rb )

I

A+

Z

f ( )d

(21)

0

In equilibrium, the lender gets all the t = 1 income ( rb = 0). To see why, assume to the contrary that the borrower gets some rb > 0: Then the contract could eliminate rb and increase Rb by Rb to satisfy F ( )pH Rb = rb : This does nothing to expected utility and helps on the IC constraint. In that case, competition (i.e. (21) binding) implies " Z F ( )pH Rb = F ( )pH R + r I A+

f ( )d

0

#

Thus, the borrower receives net utility given by Ub ( )

=

F ( )pH Rb

A

=

F ( )pH R + r

Z

f ( )d

I

(22)

f ( )d

(23)

0

Pledgeable income under these assumptions is given by P( ) = F ( )pH R

B +r p

Z

0

How does net-utility and pledgeable income change with an “exogenous” change in the cuto¤? –

dUb ( d

)

0 provided f ( )pH R > f ( ) and decreasing thereafter which implies one cuto¤ U = pH R. This cuto¤ maximizes borrower utility.

17

–

dP( d

)

h > 0 provided f ( )pH R

B p

thereafter which implies another cuto¤ o¤ maximizes borrowing capacity.

i

>

P

f ( ) and decreasing h i B = pH R p : This cut-

– Thus P < U : Given continuation occurs for < , this means that …rst best continuation is more frequent than second best continuation. This delineates 3 regions based on lender participation which depends on where I A lies in relation to pledgeable income (see Figure T5.2)11 . – Region I) P( U ) I A (i.e. plenty of pledgeable income say due to cash rich …rms). Can attain the “…rst best”level of investment.12 – Region II) P( U ) < I A P( P ) (i.e. enough pledgeable income to support reinvestment). The constrained optimal contract speci…es rb = 0 and Rb = B= p (i.e. the IC constraint binds). The cuto¤ 2 [ P ; U ] solves the IRL constraint P( ) = I

A:

In this case, credit rationing applies to the continuation decision. In order to be able to invest more ex-ante, the borrower accepts a level of reinvestment below the ex-post e¢ cient level (i.e. < pH R). Note further that in this region, d =dA > 0 since the lhs (i.e.P( )) is independent of A while the rhs (i.e. I A) is decreasing in A: – Region III) I A > P( P ) (i.e. insu¢ cient pledgeable income to support initial investment, so the …rm is credit rationed). Since P < U ; less pro…table projects are being …nanced in Region II than Region I. Figure T5.3 shows the e¤ect of moral hazard on the continuation region: – Higher B shifts the P( ) down but not Ub ( ): For a given level of A; this implies drops (i.e. more moral hazard, less continuation. – Higher A, implies uation).

4.3

rises (i.e. more skin in the game, more contin-

Term Structure of Cash Rich Firms Implementation of the above problem provides a simple theory of maturity structure. Recall that r is the cash in‡ow and

1 1 Figure

is the cash out‡ow at time t = 1:

T5.2 graphs aggregate utility Ub ( ) + I which includes the lender utility (i.e. I). It is simple to see from (22) and (23) that Ub ( ) + I is everywhere higher than P( ): 1 2 The terms of the contract (r ; R ) are indeterminate since the IC constraint is not binding. b b

18

Suppose r >

; in which case we can call a continuing …rm cash rich.

Then the optimal contract can be implemented by a combination of payments to the lender in the event of continuation of: – short term debt: d = r – long term debt: D = R

B=( p)

Given d =dA > 0; then a …rm with a strong balance sheet (i.e. big A) needs to borrow less short term (i.e. dd=dA < 0). Conversely, a …rm with a weak balance sheet (i.e. small A) needs to borrow more short term. This helps us understand whey highly indebted …rms are more likely to borrow on a short-term basis.

4.4

Credit Lines for Cash-Poor Firms (Insurance Arrangement) Suppose r = 0: Then the entrepreneur must raise funds at t = 1 to pay thereby diluting the t = 0 lenders. As an example, suppose the entrepreneur receives a shock B p

=

1 2 P

where

pH R (i.e. pledgeable income). Since pledgeable income was promised to the t = 0 investors, the borrower needs to issue double those shares (so that the value of each share is halved). P

– Are the t = 0 investors willing to dilute their shares? If not, they receive nothing so they are willing to accept the dilution. Is there an upper bound to how much initial investors are willing to accept? The investors will never allow dilution more than 0 : What happens if

2(

P ; U )?

– Need a nonrevokable line of credit of size pH R revokable, the creditor may revoke it ex-post.

5

B p

: If it is

Related Models of Credit Rationing (T3.5) Tirole provides three more models which di¤er on the basis of what is assumed about the veri…ability of income. The earlier sections assumed that the outcome was observable, but the action was not (moral hazard). At the other extreme, the outcome is unobservable. So for instance, even if the borrower gets R; they can say it was 0 and keep all of R: Why would anyone lend in that case? Collateral? Punishment by future exclusion? 19

More generally, these two extremes are just one parameterization of a costly state veri…cation model: observable outcome at zero cost; unobservable outcome at in…nite cost; and CSV at intermediate cost. The optimal contracts in the 3 models of Section 3.5 are implemented via inside equity and outside (risky) debt.

5.1

Veri…able Income (T3.6) This case is closest to the previous analysis in Chapter 3 and based on Innes. It has a very strange monotonic reimbursement assumption, so I will not spend time on it.

5.2

Semi-Veri…able Income - Costly State Veri…cation (T3.7) Townsend, R. (1979) “Optimal Contract and Competitive Markets with Costly State Veri…cation”, Journal of Economic Theory, Vol. , p.265-93. If we restrict attention to deterministic veri…cation, the optimal contract will look like debt (a …xed payment in high income realization states and chapter 7 default in low states).

5.2.1

Environment Unlike the previous sections, the agency cost is not that the agent (entrepreneur) makes an e¤ort choice which privately bene…ts him at the expense of revenue to the principal (investor). Here the action is to hide revenue (i.e. if R is realized, he reports 0 and eats R all himself). Technology: After investing I A, the technology yields a random revenue R distributed on say S = [0; 1) according to density p(R): Information: While R is costlessly observed by borrower, the lender must incur cost K to observe it. Both entrepreneurs and investors are risk neutral. There is limited liability. b R) specifying Punishment Technology: There is a penalty function P (R; a punishment on the borrower after the outcome of the audit, depending b The on the result of the audit R and on the report of the borrower R. b utility loss on the borrower for reporting R 6= R after an audit is taken to be arbitrarily large and zero otherwise. As will be seen, this is only necessary to cover o¤-the-equilibrium path events associated with untruthful reporting in the audit region. Timing: 20

– Lenders o¤er a contract contingent on the borrower’s revenue report b R – Investment I

A

– Outcome realized R b – Report R

– Lender chooses whether to audit – Allocation disbursed 5.2.2

Equilibrium In the above section, we applied the revelation principle when talking about the contract. The revelation principle states that, in designing the loan agreement, there is no loss of generality involved in focusing on contracts that require the entrepreneur to report revenue, and furthermore, the contract can be structured, again WLOG, so that the entrepreneur has an incentive to report b = R.13 the true realized revenue R b: A general contract speci…es for each report R

b 2 [0; 1] of no audit – a probability y(R) b R) in the case of no audit. – borrower return w0 (R; b R) in the case of an audit. – borrower return w1 (R;

In the no audit region, the lender return cannot depend on R but only b (i.e. Rl (R) b + w0 (R; b R) = R) but it can in the audit region (i.e. on R b b Rl (R; R) + w1 (R; R) = R). b R) Limited liability implies wa (R;

0:

Denote the borrower’s conditional return under truthtelling w(R) (1 y(R))w1 (R; R):

y(R)w0 (R; R)+

The key question addressed by Townsend is whether the information constrained optimal allocation from the above general contract can be implemented as a standard debt contract. Recall that a standard debt contract speci…es a debt level D; no audit if D is repaid, and an audit and no reward if it is not. So – y(R) = 1 if R

D

– y(R) = 0 if R < D; 1 3 In

the appendix to these notes we de…ne and prove the revelation principle.

21

b = minfR; Dg just as in the …rst D; 0g and Rl (R)

– w(R) = maxfR set of notes.

The optimal contract maximizes the borrower’s expected income subject to the incentive constraint that the borrower reports the truth and the breakeven constraint for investors. That is Z 1 w(R)p(R)dR max y( );w0 ( );w1 ( )

0

subject to b 0 (R; b R) + (1 w(R) = max y(R)w Z

[R

b R

w(R)

(1

b b y(R))w 1 (R; R);

y(R))K] p(R)dR

I

A:

(24) (25)

Notice that as in the simple moral hazard problem of the …rst section, the objective and lender individual rationality (25) constraints are written under the action (i.e. truthtelling) implied by the incentive compatibility constraint (24). Note that since the lender participation constraint is met with equality, we can re-write (25) as Z Z [R (1 y(R))K] p(R)dR (I A) = w(R)p(R)dR which upon substitution into the objective yields the equivalent programming problem: Z 1 min (1 y(R))Kp(R)dR (26) y( );w0 ( );w1 ( )

0

subject to (24) and (25) since R the other terms in the objective were not choice variables (i.e. Rp(R)dR (I A) ). Thus the problem amounts to choosing the optimal IC region of reports that minimizes veri…cation costs. b 2 [0; 1]; we Instead of solving the problem with stochastic auditing y(R) b will constrain the problem to deterministic auditing y(R) 2 f0; 1g:

The deterministic audit assumption divides the set of feasible revenues into two regions: no audit R0 and audit R1 where R0 \ R1 = ? and R0 [ R1 = [0; 1): b 2 R0 ; Rl (R) b =D Lemma 1. Incentive compatibility requires that for R (a constant). 22

– To see why, suppose not. WLOG suppose that Rl (R0 ) > Rl (R00 ) for R0 ; R00 2 R0 .

– Then the borrower would report R00 (the revenue which makes his reimbursement to the lender as small as possible) since then he gets more (i.e. w0 (R00 ; R) = R Rl (R00 ) > R Rl (R) = W0 (R0 ; R)). b sub– In fact, the borrower would (almost) always report minRb Rl (R) b ject to Rl (R) R independent of the realization of R consistent with resource feasibility. That is, he would misreport with probability one. – Since the lender doesn’t audit, he is unable to detect misrepresentation. – Thus, a contract with variable reimbursement in the no audit region cannot be incentive compatible (the required contradiction). – The only way to get him to report truthfully is if no report contingent reimbursement is smaller than another report contingent reimbursement (i.e. the reimbursement is independent of the report). Since the payment is independent of the report, the borrower might as well report the truth.

b 2 R1 ; Rl (R) b Lemma 2. Incentive compatibility requires that for R

D.

b > D; then the borrower would – To see why, suppose not. If Rl (R) b 2 R0 and since he is not audited would receive w0 ( instead report R b b 2 R1 ) = w1 (R b 2 R1 ; R): R 2 R0 ; R) = R D > R Rl (R b 2 R1 ) > D is inconsistent with incentive – Thus, a contract with Rl (R compatibility.

Proposition CSV. The solution to (26) subject to (24) and (25) is a standard debt contract where 8R 2 R1 ; Rl (R) = minfR; D g and R1 = fRjR < D g: See Figure CSVDebt.pdf. – Consider any other IC contract (R01 ; Rl0 ( )) associated with the same probability of auditRbut with a di¤erent audit region R01 6= R1 (so R that R0 p(R)dR = R p(R)dR). 1

1

– By Lemma 1, this contract is associated with a constant payment on 0 R00 ;say Rl (R) = D0 for R 2 R00 :

– Limited liability implies that R

D0 ; 8R 2 R00 .

– Since R01 6= R1 but with the same probability of audit, there is at least one element R0 2 R1 that does not belong to R01 (i.e. R0 2 = R01 () R0 2 R00 ).

– Therefore D0 R0 < D where the …rst inequality follows from the above LL result and the second inequality follows from the de…nition of R1 = fRjR < D g: 23

– While the new contract does not help lower costs in the objective (since the audit probabilities are identical), it results in less expected return for the lender from the new contract since D0 < D:14 – Given that there is a higher surplus for the lender under the contract, it is possible to raise the borrower’s utility without violating the lender’s participation constraint. Random audits can do a little better, but it no longer looks like a standard debt contract.15 Renegotiation? Gale and Hellwig (1989) conclude that the possibility of renegotiation can undo the optimality of debt contracts. Suppose that the borrower says he cannot repay D but o¤ers to repay D K: The lender should be happy because he will never be able to receive more if he audits. Suppose the distribution of shocks is U (0; R): Then using the Propostion we have from the lender’s participation constraint Z

D

(R

0

Z R 1 1 dR + D dR R R D R2 D K D D R j0 Rj0 + RjD 2R R R 1 2 KD D D + R D 2R R R D2 2KD + 2RD 2D2

K)

= I

A ()

=

I

A ()

= I

A ()

=

2R (I

A) ()

D2 + 2 R

f (D)

K D

2R (I

a quadratic in D: – Note that at D = 0; f (0) =

2R (I

0

– Note that f (D) = 2D + 2 R max occurs at D > 0:

A) < 0:

K = 0 () D = R

K so the

– Thus, the quadratic looks like (see Figure CSVSolution.pdf) an upside down bowl with 2 positive solutions where D1 < R K < D2 : The latter obviously violates feasibility, so the …rst one is the constrained e¢ cient allocation. In that case, an increase in audit costs actually increases D : To see this, df 2D < 0; so the upside down bowl shifts down and dD dK jD>0 = dK > 0: The intuition is that since the lender bears the audit cost, he must be compensated for it with a higher reimbursement. Further note that if K gets too big, the upside down bowl may have no “real”solutions. That is, if audit costs are too big, we are back to autarky. Lemmas 1 and 2 and LL imply Rl0 (R) = minfR; D0 g; 8R: J. and B. Smith (1994) “How good are standard debt contracts? Stochastic versus nonstochastic auditing in a costly state veri…cation model”, Journal of Business, 67, p. 539-61. 1 4 Since

1 5 Boyd,

24

A) = 0

5.3

Non-Veri…able Income - Threat of Termination (T3.8) Based on Bolton, P. and D. Scharfstein (1990) “A Theory of predation based on agency problems in …nancial contracting”, American Economic Review, 80, p. 93-106 and Hart, O. and J. Moore (1998) “Default and Renegotiation: A Dynamic Model of Debt”, Quarterly Journal of Economics, 113, p. 1-42.16 If R 2 [0; 1) is unobservable to the lender at any cost, then in a static b = 0: model, there can be no lending since the borrower will always report R

However, if there is more than one period, then a borrower who does not repay can be terminated (i.e. no future projects are …nanced).

5.3.1

Environment Two dates 1 and 2: No discounting between periods. Date 1 investment I yields R1 with probability p and 0 otherwise At date 2; initial investment yields R2 with probability p if not liquidated by lender. If liquidated at the end of date 1, the lender receives L 2 [0; I A) and the entrepreneur receives 0 at date 2: Assume further that L < R2 so liquidation is ine¢ cient (from a societal point of view). Limited liability. Timing – Date 1 Contract o¤ered (R1l ; R2l ; R1b ; R2b ) Investment undertaken Realization R1 (Report contingent) liquidation decision (given by probability 1 y) and allocation – Date 2 Realization R2 (Report contingent) allocation Parameterization (so that LL is not binding): (I A) R2 pR2 + (1 p)L

R1

(27)

1 6 For one of the earliest papers on how dynamic contracts can help with private information, see Townsend, R. (1982), “Optimal Multiperiod Contracts and the Gain from Enduring Relationships under Private Information,” Journal of Political Economy, 90, 1166-86.

25

5.3.2

Equilibrium Again, we will look for an optimal contract which maximizes borrower expected payo¤ subject to incentive compatibility and lender participation. First note that since there are only 2 periods, there can be no payment by the borrower to the lender at date 2: Due to non-veri…able income b2 = 0: In that case, limited liability/feasibility the borrower will report R l implies R2 = 0:

Let y0 2 [0; 1] be the probability of continuation when there is no repayment at date 1 (so 1 y0 is the probability of liquidation/termination). The “stick”. Let y1 2 [0; 1] be the probability of continuation when there is repayment at date 1 (so 1 y1 is the probability of liquidation/termination). The “carrot”. Let the lenders return R1l = D limited liability/feasibility.

R1 where the inequality follows from

Incentive compatibility for the borrower at t = 1 requires (by the …rst bullet point the only IC allocation at t = 2 is (R2l = 0; R2b = R2 )): R1

D + y1 R2

R1 + y0 R2 () (y1

y0 )R2

D

(28)

b1 = 0; then limited liability/feasibility since if the borrower reports R l b1 = R1 > 0; then limited liabilrequires R1 = 0 but if he reports R ity/feasibility ensures R1l = D: Lender participation requires p [D + (1

y1 )L] + (1

p) [(1

y0 )L]

I

A

(29)

An optimal contract solves max

y0 ;y1 ;D R1

p [R1

D + y1 R2 ] + (1

p) [y0 R2 ]

subject to (28) and (29). First, it is not optimal to liquidate in the event of repayment. That is, y1 = 1: – To see why, suppose y1 < 1 while y1 > y0 : – Increase y1 by " and increase D by "L to keep the IR constraint (29) unchanged (i.e. [D + "L + (1 (y1 + "))L] – The IC constraint (28) remains satis…ed since R2 > L (i.e. (y1 + " y0 )R2 D + "L) 26

– Then the borrowers utility increases since R2 > L (i.e. p [R1

(D + "L) + (y1 + ") R2 ]).

Second, the IC (28) must bind – To see why, …rst note that y0 < 1; otherwise the IC (28) is violated in non-autarkic cases (i.e. where D > 0). This simply says that no borrower would repay if there was no punishment to not repay. – If (28) doesn’t bind, then increase y0 by a small amount " and increase D by "L(1 p)=p so as to keep IR (29) satis…ed. That is, p

D+

p [D + (1

"(1

p)L

p y1 )L] + "(1

+ (1

y1 )L + (1

p)L + (1

p) [(1

p) [(1

y0 )L]

(y0 + "))L] (1

=

I

A ()

p)"L =

I

A

– Since the IC constraint doesn’t bind, the increase in " respects IC, IR and increases borrower welfare since

() because

"(1

p R1

D+

p [R1

D + R2 ]

"(1

p)L + (1

p)L + R2 + (1 p) [(y0 + ") R2 ] p "(1 p)L + (1 p) [y0 R2 ] + (1 p)R2 "

p)R2 " () (1

p)"(R2

L) > 0:

Given that the IC (28) and IR (29) constraints bind, then D and y0 must solve

pD + (1

(1

y0 )R2

=

D

p) [(1

y0 )L]

=

I

(30) A

(31)

Solving (30) for D and plugging into (31) gives the probability of liquidation when the borrower doesn’t repay is p(1

y0 )R2 + (1

p) [(1

y0 )L] (1

y0 )

= I =

A () I A >0 pR2 + (1 p)L

(32)

Thus, the threat of termination provides incentives for repayment when income is nonveri…able (or in the case of sovereign countries, nonattachable). Note that (30) and (32) implies we need the following parameterization to respect limited liability (i.e. (27)): D=

(I A) R2 pR2 + (1 p)L

R1

Comparative statics for the probability of liquidation (1 27

y0 ) in (32):

– termination is increasing in the size of the loan (I debt, more likely to default)

A) (i.e. more

– termination is decreasing in expected future earnings R2 (this is the borrower’s future reward when they repay and are not terminated) – termination is decreasing salvage value L (this makes the debt repayment smaller since the lender recoups this in the event of “default”). – termination is decreasing in the …rst period probability of success p (since lenders are more likely to get repaid)

6 6.1

Appendix Dilution and Overborrowing Real world debt contracts sometimes have covenants included to restrict new issues of debt. – lenders don’t want more senior debt since this reduces what they can get if there is default. – the issue of new securities may alter managerial incentives and the size of the pie. Next example illustrates the 2nd reason using the model of this section. So assume that if Rl is promised to …rst lenders if R is realized, then they get it even after, potentially, second contract is taken.

6.1.1

Change in Environment: Suppose there is an opportunity for a deepening investment which costs an extra J and increases the probability of success by (that is, the prob of success is pH + if …rm behaves and pL + if it doesn’t). Obviously it decreases the probability of failure to (1 p ): Assume the deepening investment is ine¢ cient in the sense that the “direct” cost is greater than the expected bene…t (i.e. C1 J R > 0). Timing – First lenders o¤er contract (Rb ; Rl ) – Investment I bb ; R bl ) – Second lenders o¤er contract (R – Deepening investment J – E¤ort Choice bb ; Rl ; R bl ) – Outcome (R

28

6.1.2

Equilibrium It is not in the interest to issue new debt unless it leads to a di¤erent level of e¤ort. – Why? New investment reduces total value by C1 ; so someone must lose. – But the …rst investors actually gain since now they expect to get (pH + )Rl : – So either the borrower or the second lender must lose. In that case, the contract wouldn’t be signed by one side. So assume the new contract disincentivizes the borrower (i.e. instead of choosing H; the borrower chooses L). bb and R bl be the new returns to the borrower and the second lender Let R bb + R bl = Rb : where by assumption that Rl doesn’t change, then R

Assuming competitive loans, the new cost J is passed along to the second lender. In that case bl J = 0: (pL + )R (33)

The entrepreneur gains from overborrowing i¤

bb + B > pH Rb : (pL + )R

bb = Rb Using R

(34)

bl and (33), now (34) can be written R (pL + )Rb

J + B > pH Rb

After some manipulations17 , this condition can be written [pH where C2

[(pH + )

(pL + )] Rl > C1 + C2

(pL + )] R

B=

pR

(35)

B:

Condition (35) provides insight as to why overborrowing can arise. 1 7 Using

the fact that C1

J

R and C2

J + B0 =

pR

B 0 so that

(C1 + R) + ( pR

C2 );

manipulation yields (pL + )Rb (pL + ) (R (pL R

pL Rl ) + ( R

Rl )

Rl )

J + B0

(C1 + R) + ( pR

R + (pH

pL )R [pH

which is (35) above.

29

>

C2 )

>

p H R + p H Rl

>

(pL + )] Rl

>

pH Rb () pH (R

Rl ) ()

C1 + C2 ()

C1 + C 2

– The rhs is the total cost of re…nancing: “direct”cost plus “incentive” cost – The lhs is the externality on the initial investors (remember the …rst investors only get Rl in a successful state). – Thus, the total cost must be less than the loss of value for initial investors. – If the borrower’s balance sheet declines (say because A is falls), Rl increases and so the inequality is more likely to hold.

6.2

Reputational Capital Boosts the Ability to Borrow (T3.2.5) Based on Diamond (1991). Can think of a …rm’s reputation as intangible capital. Suppose there are 2 di¤erent borrowers; one with private bene…t b < B: Then the asset threshold in (8) is lower where A(b) = pH Since A(B)

A(b) =

pH (B p

b p

(pH R

I) :

b) > 0;

then a more “reliable” borrower is more likely to get a loan. Now suppose that private bene…t B or b is not observable. Then with enough observations of success or failure, the lender’s posterior should be able to tell who is the more “reliable” borrower. Since this entails a dynamic setting (i.e. a learning story), we will wait to introduce it (see also Section 2.5.2 of Freixas and Rochet).

6.3

Collateral Values: Outside Debt and the Maximal Incentives Principle The indeterminacy of the …nancial structure (debt or equity) is an artifact of the absence of pro…t in the case of failure. Recall that a debt contract gives the borrower nothing maxfR the event of “failure” (i.e. low R).

D; 0g in

Here we will show that the optimal contract will set borrower rewards to zero in the event of “failure” in order to reward (incentivize) “success”. Assume revenue in the case of success is RS I and RF I in the case of failure (i.e. this could in fact be salvage value which is more likely to be high in liquid secondary markets) where RF > 0 and de…ne R RS RF > 0:

30

The generalization of the …rst condition in (12) is pH RS + (1

pH )RF

pH R + RF > 1

(36)

and the condition in (13) that pledgeable income per unit of investment is negative given by pH RS + (1

pH )RF

1<

pH B , pH p

B p

R

+ RF < 1:

(37)

A contract speci…es an investment level I and rewards for each outcome RbS ; RbF : The optimal contract maximizes the entrepreneur’s expected compensation subject to entrepreneur incentive compatibility and lender participation given by max pH RbS + (1 fI;RbS ;RbF g

Ub =

pH )RbF

A

subject to pH RbS + (1 S

RbS

pH R I

+ (1

pH )RbF F

pL RbS + (1

RbF

pH ) R I

I

pL )RbF + BI ()

A

The lender’s breakeven constraint is binding. If not, you could increase RbS and RbF by some amount, say " > 0, without violating the constraint and raise the objective. That is, pH RS I S

pH R I

RbS + (1 (RbS

pH ) RF I

+ ") + (1

RbF F

pH ) R I

(I (RbF

A) + ")

= =

" ()

(I

A)

Substituting the participation constraint pH RS I + (1

pH )RF I

(I

A) = pH RbS + (1

pH )RbF

into the objective we have Ub

= pH RS I + (1 S

=

pH R + (1

=

pH (RS

pH )RF I pH )RF

(I

A)

A

1 I

RF ) + RF I

By (36), we know the entrepreneur will choose the highest possible I: Since the entrepreneur wants to choose the highest possible I; the incentive compatibility constraint must bind or p RbS 31

RbF = BI:

p RbS

RbF

BI

Finally, at an optimum RbF = 0: Suppose not. That is, RbF > 0 (this was not possible in the previous sections where RF = 0): – Consider a small increase + RbS and small decrease the lender’s participation constraint is unchanged pH RS I S

RbS

pH R I

F

+ (1

+

RbS (1 +

pH ) R I

pH ) R F I

) + (1

RbF (1

RbF such that

)

pH

+

RbS

RbF (1

+ (1

pH )

in which case we need pH + RbS + (1 pH ) RbF = 0: That is how we incentivize “success” at the expense of “failure”. – This small change, which is only feasible if RbF > 0; also keeps the objective unchanged (no surprise since this didn’t change the lender’s participation constraint and we substituted that into the objective). – But now the incentive constraint doesn’t bind, which is inconsistent with optimality, yielding a contradiction. Since RbF = 0 < RF in an optimum, an all-equity …rm is not optimal (i.e. in an all equity …rm, an entrepreneur with some bargaining power - in this case, 100% - gets all the returns, while the entrepreneur gets nothing here while the lender gets the entire failure return as in a debt contract). Rewriting the binding lender participation constraint pH RS I S

pH RbS

pH R I F

R I + pH R

RbS + (1 F

pH R I S

R

F

I

pH ) RF I

+ pH RbF pH RbS

F

+R I RbF

RbF RbF RbF

=

I

=

I

=

I

A ()

A () A

But then substituting the binding IC into the expression and using the result that RbF = 0 we have R F I + pH R S

RF I

R F I + pH

BI RbF p B I 0 p

pH R

I

=

I

A ()

=

I

A ()

1

h

=

1 pH R

B p

+ RF

i(38) A

Equation (38) is the analogue of (17). That is, now k 0 includes RF : By (37), k 0 > 1 and k 0 > k (i.e. there is even more leverage in this case). Predictions: – Firms with lower agency costs borrow more (i.e. as in the previous section, dk 0 =dB < 0). 32

)

= I

RbF

= I

A () A

– Investors holding safe debt plus some equity maximizes the entrepreneur’s stake in the project and thereby her incentives ( RbF = 0 forms the basis of this prediction). Decompose the lender’s claim into safe debt (which repays RF I) and risky equity (which repays in expectation pH (R B= p) I), then we can de…ne the leverage ratios RF I RF debt = = totalequity pH RI pH R and debt RF I RF = = outsideequity pH (R B= p) I pH (R B= p) are both constant.

33