Diversification: more than one project. It may be beneficial for a firm, in terms of getting hold of external funds, to have several projects.

Transcription

1 Further determinants of orrowing caacity: oosting ledgeale income Diversification: more than one roject Collateral: ledging real assets Liquidity: a first look uman caital Diversification It may e eneficial for a firm, in terms of getting hold of external funds, to have several rojects. Equivalently, it may e eneficial for multile roject owners to merge into one firm. Previous analysis: constant returns to scale in investment technology Exansion in investment roject equivalent to an increase in the numer of rojects whose outcomes are erfectly correlated. Consider the oosite extreme: Several rojects are availale, and they are statistically indeendent. Cross ledging: Incomes on one successful roject can e offered as collateral for other rojects. Model: Two identical rojects. Otherwise: as in the fixedinvestment model Entrereneur s initial wealth er roject: A; i.e., total wealth: A. Tore Nilssen Cororate Governance Set 4 Slide 1

2 A enchmark: roject financing. For each of the two rojects: o orrower receives if success, 0 otherwise. o Incentive constraint: o reakeven constraint: I A, or: A A. o Project financing not viale if A < A. Cross ledging o The two rojects financed in comination o Contract: orrower receives 0, 1, or when 0, 1, or rojects are successful. o Exected return to orrower: o Two incentive constraints: Working on two rojects referred to working on only one L L L 1 L 0 Working on two rojects referred to working on none L L L 1 L 0 o Clearly, 0 = 0 in equilirium, as efore. Tore Nilssen Cororate Governance Set 4 Slide

3 o Full cross ledging: We also have 1 = 0 in equilirium. In order to increase the orrowing caacity, the orrower offers all returns that are availale in those cases where only one roject succeeds. We can simlify the incentive constraints. Working on oth rojects etter than on none: ( + L ) L ( + L ) L Working on oth rojects etter than on a single one: L + This one is always satisfied when the revious one is. It follows that, in equilirium, L Minimum exected ayoff to orrower: L = (1 d ), 1 L where d = 0, is an agency-ased measure L of the economies of diversification into two indeendent rojects. Tore Nilssen Cororate Governance Set 4 Slide 3

4 The reakeven constraint: o Exected ledgeale income investors exenses (1 d ) I A (1 d ) I A A A, where A I d o ecall: A I 1 < A = I Diversification and cross ledging facilitates financing: A < A Statistical indeendence of rojects similarly facilitates financing. Variale investment: Diversification increases the orrowing caacity, rather than giving etter access to financing. Extension to n indeendent rojects: Let orrower have net worth na. reakeven constraint for investors now ecomes: (1 d n ) I A, n1 n1 L where d n L = Limits to diversification n n L increases with n. o Endogenous correlation: The orrower has an incentive to choose correlated rojects, if she can. This decreases the value of cross ledging. Asset sustitution. o Limited exertise. o Limited attention. Tore Nilssen Cororate Governance Set 4 Slide 4

5 Sequential rojects o Sulementary section 4.7 o Variale investment in two rojects. o enchmark: simultaneous rojects Investment I i in roject i {1, }. eturn I i if success in roject i, 0 otherwise Proaility of success ( L ) if the orrower ehaves (misehaves) Private enefit from misehaving in roject i: I i. Total investment: I = I 1 + I. o Otimal with reward only when oth rojects succeed:. o inding incentive constraint: misehavior on oth rojects L I We disregard misehavior on one roject for now o Total net resent value: ( 1)I o Investors reakeven constraint: I I = I A o In equilirium, A I, where ˆ 1 0 L ˆ 0 1 L d, and U = ( 1)I = ˆ 0 A Tore Nilssen Cororate Governance Set 4 Slide 5

6 o Checking the other incentive constraint: misehavior on roject i: L I i o Comining with the other incentive constraint: I i I L This constraint does not ind if total investment is slit relatively equally among the two rojects o Sequential rojects: Short-term loan agreements Financing one roject at the time. Increased incentives early on: success at the first roject rovides the orrower with extra funds for the second roject. Think ahead and reason ack. Project : the single-roject variale-investment case, with the orrower entering date with assets A. Exected ayoff er unit of investment: 1 = Exected ledgeale income er unit of investment: 0 orrower s gross utility from roject : 1 0 A = A 1 0 > 1 is the shadow value of equity: If you can increase your assets at the start of date with 1 unit, then you increase your utility with. Tore Nilssen Cororate Governance Set 4 Slide 6

7 Project 1: orrower s initial assets A. eturn if success: I 1 = + l Investors reakeven constraint P l I 1 + A I1 orrower s incentive constraint: Exected ledgeale income er unit of investment ~ = Det caacity at date 1: I 1 = k 1 A, where k1 k 1 ~ Assume 1; otherwise, det caacity is infinite. ecall earlier assumtion: 1 > 1 > 0. The orrower invests in roject if and only if roject 1 is successful. She then invests: k I = ka = k = I = v I 1 = 1 1 I 1 = I 1 Exected investments in the rojects are the same: I = I 1 Stakes increase over time: I > I 1 Tore Nilssen Cororate Governance Set 4 Slide 7

8 o Sequential vs simultaneous rojects seq U = A A = ( v k 1 1)A seq U = A > A = 1 ˆ sim U 0 1 ˆ 0 d = L L 1 Note error in Tirole, o Sequentiality is etter: The orrower has no chance to misehave on roject if roject 1 fails, so the moral hazard rolem is less serious. o Long-term loan agreements One agreement for oth rojects isk neutrality and constant returns to scale imly that short-term agreements fair equally well. Tore Nilssen Cororate Governance Set 4 Slide 8

9 Collateral Assets = cash + roductive assets Productive assets = quasi-cash, since they may e ledged as collateral to lenders edeloyaility of roductive assets o Fixed-investment model, with one new feature. o Suose, after investment is made ut efore effort is ut in, it ecomes ulicly known whether the roject is viale o With roaility x, the roject is viale and the model roceeds as efore o With roaility (1 x), the roject is not viale, and assets can e sold at a given rice P I. o Economic distress, as oosed to financial distress. o New assumtion on NPV: x + (1 x)p > I. o The entrereneur chooses to ledge the resale rice in full. o reakeven constraint for investors: x 1 xp I A o Threshold level of net worth: A x x 1 xp Decreases with asset redeloyaility o orrowing atterns across industries: The more liquid assets, the easier it is for firms orrow. o Endogenous redeloyaility: fire sale externalities further aggravating credit rationing. I Tore Nilssen Cororate Governance Set 4 Slide 9

10 Collateral is costly A deadweight loss associated with collateralization: assets may have lower value for lenders than for the orrower o Transaction costs o orrower s rivate enefit from ownershi: sentimental values, secific skills o Prosects of future credit rationing makes the asset of higher value to the orrower than to investors o isk aversion o Collateralized assets may receive oor maintenance Costly collateral and contingent ledging Suose first collateral would not exist without the investment. orrower has no cash initially, needs to orrow I. Asset has residual value o A to the entrereneur o A A to the lenders o Deadweight loss if asset is seized: A A Contract: {, l, y S, y F } o y S roaility that the orrower kees the asset if success o y F if failure o stochastic ledging: needed in a simle model Otherwise, fixed-investment model. Tore Nilssen Cororate Governance Set 4 Slide 10

11 The equilirium contract is the one that maximizes orrower s utility, suject to orrower s incentive-comatiility constraint and lenders reakeven constraint. Max U = ( + y S A) + (1 )y F A suject to [ + (y S y F )A], and [ l + (1 y S )A ] + (1 )(1 y F )A I orrower wants to ledge as little collateral as ossile The outcome deends on the strength of the alance sheet of the orrower o Strength of alance sheet deends on Investment level I ( ) Agency costs, measured y ( ) Any initial cash, Ã (+) o Strong alance sheet no collateral y S = y F = 1; > 0. o Intermediate alance sheet collateral if failure: y S = 1, y F 1; 0. o Weak alance sheet orrower gets a share of the asset if success: y S 1, y F = 0; = 0. Contingent ledging: orrower gets a contingent share of the asset rather than of income. Solution: derivative of the Lagrangian with resect to y S is ositive if that with resect to or that with resect to y F is. Some of the three regimes may not exist. Tore Nilssen Cororate Governance Set 4 Slide 11

12 Weak orrowers ledge more collateral than strong orrowers o Pledging collateral in lack of cash o Oosite rediction from adverse-selection theories, where strong firms ledge collateral to show strength. Pledging existing assets Suose next that the entrereneur has existing wealth Contingent ledging o If success, the entrereneur kees the asset. o If failure, the investors receive the collateral. Continuous collateral: the entrereneur chooses an amount C [0, C max ] to ledge as collateral in case of failure. o We need an uer limit on C max ; see elow. Costly collateral: Value C to investors, where < 1. orrower s net utility: Project s NPV without collateral minus exected deadweight loss from ledging collateral. U = I (1 )(1 )C o To ensure that U 0 for any feasile C, we assume I 1 C max 1 Collateral costly C = 0 if A A. Tore Nilssen Cororate Governance Set 4 Slide 1

13 The orrower s incentive comatiility constraint (1 )C L (1 L )C + C o The orrower loses oth the reward and the collateral when she fails o Limited liaility: In order to ensure that 0 for any feasile C, we assume: C max The investors reakeven constraint ( ) + (1 )C I A ( ) + C + (1 )C I A Collateral has two ways of affecting ledgeale income o Directly: + (1 )C o Indirectly through a lower reward to orrower: + C orrower ledges the minimum collateral necessary to satisfy the investors reakeven constraint: I A C 1 o excet if this exression gets too ig, in which case collateral cannot solve the funding rolem. dc Weaker firms ledge more collateral: 0. da Conditional collateral referale to unconditional. More astract forms of collateral: Putting one s jo at stake. Tore Nilssen Cororate Governance Set 4 Slide 13

14 The liquidity-accountaility tradeoff When should the orrower receive her comensation? o Towards the end: good for accountaility, ecause more information aout the roject is availale o Along the way, ecause of her need for liquidity Consumtion New rojects Outside investment oortunities not oservale for investors o A scoe for strategic exit, escaing sanctions following oor erformance The other side of the coin: the liquidity of investors o The more control you have, the less liquid your assets are Model: an extension of the fixed-investment one New feature: A new, fleeting investment oortunity at an intermediate date Initial investment I, entrereneur s assets A < I. Tore Nilssen Cororate Governance Set 4 Slide 14

15 Moral hazard: misehavior means a lower success roaility ( L < ) ut also a rivate enefit. Project returns at final date: or 0 (whether or not an intermediate investment oortunity shows u). Limited liaility, risk neutrality. Project would have een financed in the asence of the intermediate liquidity needs: A > A Liquidity shock: With roaility, a new investment oortunity arises. o Investing x returns x, where > 1. Contract: {r, }. orrower receives o r on the intermediate date and nothing on the final date, in the case of a liquidity shock. o on the final date if success (0 if failure) and nothing on the intermediate date, in the case of no liquidity shock. What if the liquidity shock is not verifiale? Exit vs vesting: what aout artial vesting? Some cash at the intermediate date and some ayment at the final date (if success). Imlementation: where does r come from? Needs to e sutracted from ledgeale income. Tore Nilssen Cororate Governance Set 4 Slide 15

16 enchmark case: Verifiale liquidity shock orrower s incentive comatiility constraint r + (1 ) r + (1 ) L + (1 )( ) 1 1 o No incentive effect from r. o Only effect of the liquidity shock is that the orrower s stake must e increased, since final date is reached only with roaility (1 ). orrower receives r with roaility. So this is similar to no liquidity shock, ut the entrereneur having availale A r. Exected ledgeale income: 1 {r + (1 ) 1 } = r. Cometition among investors ensures that the orrower gets the NPV from the roject. So her total exected net utility is U = I + ( 1)r. It is otimal to have r as high as ossile suject to incentive comatiility: r = I A In equilirium: r = I A 1 ; 1. 1 Tore Nilssen Cororate Governance Set 4 Slide 16

17 Non-verifiale liquidity shock A two-dimensional moral-hazard rolem. Incentives needed for orrower o to ehave in carrying out the roject, and o to reort truthfully aout the liquidity shock The two forms of moral hazard interact o Strategic exit: A misehaving orrower may want to exit even without a liquidity stock efore the consequences are disclosed. Simlifying assumtion: L = 0 = o A misehaving orrower would indeed want to cash out early, since there is nothing to e had later: L = 0. orrower s incentive constraint r + (1 ) [ + (1 )]r + (1 )[ r ] (1 )[( ) r ] r 1 1 Comare with the case of verifiale liquidity shock: the ossiility of a strategic exit makes the incentive constraint stricter (for a given r > 0). When there is no liquidity shock, the orrower strictly refers to continue: > r. ut would the orrower want to cash out when there is a liquidity shock? Is r? Suose first that it is. Tore Nilssen Cororate Governance Set 4 Slide 17

18 Again, cometition among investors ensures that all NPV of the roject accrues to the orrower. So, given r, her exected net utility is: U = I + ( 1)r. ut the incentive constraint is stricter, so ledgeale income is smaller. Therefore r is lower when liquidity shock is nonverifiale. Exected ledgeale income for a given r : r 1 r 1 = r 1 In equilirium: 1 r = I A 1 r ; 1 Comared to the case of verifiale liquidity shock: r is lower, is higher. o The ossiility of strategic exit hurts the orrower, since she is allowed less liquidity. If the aove contract does not oey r : o aens when A is low. o Solution: artial vesting. Only imlementation changes. Total comensation has two comonents: One, a asis comensation,, ayed out in case of success. 0 At the intermediate date, the orrower receives cash r. She can choose to uy shares for this, which would ay in case of success, where + = 0 Tore Nilssen Cororate Governance Set 4 Slide 18

19 Inalienaility of human caital Is there a scoe for the loan contract to e renegotiated as the roject roceeds? A renegotiation must mean that the existing contract is not efficient for the arties involved that a new contract exists that is weakly etter for oth orrower and lender, and strictly etter for at least one of them. old-u: Suose the entrereneur is indisensale the roject cannot e comleted without her. The entrereneur may want to renegotiate the initial contract in order to otain a etter deal. o The inalienaility of human caital. Model: no moral hazard: = 0; no cash: A = 0. Otherwise, fixed-investment model. The act of comleting the roject cannot e contracted uon until after investment has een made: enegotiation is needed. o enegotiation relaces effort as the source of the incentive rolem. Incomlete roject returns 0. Comlete roject returns [ro ] or 0 [ro (1 )]. Disregarding renegotiation, the roject can e financed y a det contract: orrower ays investors D in case of success, such that D = I. o l = D, = D, and U = ( D) = I. enegotiation: argaining over I. Tore Nilssen Cororate Governance Set 4 Slide 19

20 Who has argaining ower? o No longer cometition among creditors: lender has.. o Entrereneur is indisensale: orrower has.. o oth receive 0 in case of noncomletion of roject Lender s argaining ower: o In the renegotiation, lender receives in case of success, and orrower receives (1 ). o Lender willing to invest if I. o If > D/, then the orrower refers to simly ski the renegotiation and comlete the roject. o If < D/, then < D = I: the roject will not e financed. o If the orrower is too indisensale, the roject is not carried out. Determinants of argaining ower o eutations on oth sides o Disersion of lenders o Outside otions If ossile, the orrower may want to give the lenders the right to seize the firm s assets in order to secure some external finance. A arallel to collateral the value of the collateral may deend on how indisensale the entrereneur is. Tore Nilssen Cororate Governance Set 4 Slide 0