Corporate Finance: Credit rationing. Yossi Spiegel Recanati School of Business

Transcription

1 Cororate Finance: Credit rationing Yossi Siegel ecanati School of usiness

2 Tirole 006 The Theory of Cororate Finance

3 The model The timing: Period 0 Period 1 Period n entrereneur has dollars and needs to invest in a roject that costs I > The entrereneur exerts effort to boost the rob. of success. If he does not exert effort he gets rivate benefits If the roject succeeds it yields ; if it fails, it yields 0 Effort raises the rob. of success from L to L The roject is viable only if there s effort: I > 0 > L I + > NPV NPV + enefits Cororate Finance 3

4 The loan agreement The loan can be debt or equity (the model cannot distinguish between them) Incentive comatibility (to ensure effort): b > Lb + b > Entrereneur's exected ayoff with effort Entrereneur's exected ayoff without effort 1 Creditor s individual rationality: L 443 Cost of M ( b ) I{ 1443 Maximal ledgeable income 1443 ( + ) equired funds Cororate Finance 4

5 Credit rationing Creditor s individual rationality: I NPV with effort ( I ) ( + ) by assumtion n entrereneur must have Ā to get funds When < Ā, we get credit rationing: the creditor gets too little ex ost to agree to give the entrereneur I- Credit rationing is more severe when is large: there s more agency roblem or M Cororate Finance 5

6 Entrereneur s ayoff When < Ā, the roject is not funded so U = 0 When Ā, the roject is funded; if the entrereneur has all the bargaining ower, the creditor simly breaks even: The entrereneur s net ayoff (above and beyond which he can consume anyway by not investing): U = l 13 exected Creditor' s ayoff ( ) = I = I 1443 l NPV with effort Since the creditor breaks even, the entrereneur catures the entire NPV l I = I 13 Min ayment to creditor given effort = Cororate Finance 6

7 The entrereneur s net ayoff (above and beyond ) - illustration Credit rationing No rationing -I Ā The entrereneur either gets all the NPV or nothing the entrereneur is indifferent to above Ā Cororate Finance 7

8 Overborrowing Suose the firm can the rob. of success by τ by investing J which it borrows from a new creditor ssumtion: the investment is inefficient: J > τ No oint in investing if effort stays the same (investment NPV and hence the entrereneur s ayoff); the investment s role is to transfer value from the original creditor The entrereneur invests J only if it induces him to exert no effort (the alternative is to forgo J and exert effort): ( +τ ) L b J + > The entrereneur's ayoff w/o effort when the new creditor breakseven b 13 No overinvestment and effort Cororate Finance 8

9 Overborrowing The condition for overborrowing: ( PL + τ )( l ) J + > ( l ) ( ( L + τ )) l + > { Overborrowing is worthwhile only if it transfers enough value from the initial creditor to comensate for the resulting inefficiencies If the condition holds, the initial creditor must imose a no-extra investment/loan covenant l overborrowing is more temting enefit in theexectedayoff of the initialcreditor Cost J τ Lossdue to lack of effort Net cost of new investment ut l = (I-)/ ; hence, l overborrowing is more likely when is low and hence covenants are needed more Cororate Finance 9

10 Debt overhang Suose the firm has initial secured debt with face value D The creditor s I constraint: D Net ledgeable income I { Size of loan D makes investment less likely Cororate Finance 10

11 Debt restructuring Suose that is large enough so the entrereneur can get a loan without debt but not with the debt: < bsent restructuring, the investment is not made and the creditor gets To induce investment D must be lowered to d such that D I d = I Cororate Finance 11

12 Multile rojects identical rojects Suose that the entrereneur gets if both rojects succeed and gets 0 otherwise (can also ay 1 is one roject succeeds and 0 if none succeeds but is sufficient since the entrereneur is risk neutral) Incentive comatibility: + L > L + L > Entrereneur's ayoff with effort on both rojects Entrereneur's ayoff without effort > L + > Entrereneur's ayoff with effort on both rojects Entrereneur's ayoff with effort on a single rojects The first IC constraint imlies the second ( ) Cororate Finance 1

13 Cororate Finance 13 The creditor s I Creditor s individual rationality (I): From entrereneur s IC: Substituting from IC into creditor s I: ( ) ( ) I = + 1 ayoff Entrereneur's Exected return L + 1 ( ) ( ) I I L L + +

14 The effect of multile rojects on financing The condition for financing: I + L Ā Financing is easier Credit rationing No rationing -I Ā Cororate Finance 14

15 Multile rojects with erfect correlation Entrereneur s IC: > L Entrereneur's ayoff with effort on both rojects Entrereneur's ayoff without effort Creditor s individual rationality (I): From entrereneur s IC: > [ ] ( I ) = Exected return Entrereneur's ayoff ( I ) ( I ) Cororate Finance 15

16 The creditor s I under erfect correlation Under erfect corr. we are back to the single roject case Diversification hels because the rojects are not erfectly correlated Imerfect correlation effectively lowers to /( L + ) Cororate Finance 16

17 Correlation or indeendence? Suose the entrereneur can choose whether rojects will be correlated or indeendent but his choice is hidden from the creditor Given, the entrereneur s ayoff: Correlation: Indeendence: The entrereneur will choose erfect correlation. Why is that? sset substitution: correlation is riskier than indeendence. The entrereneur is the residual claimant and likes risk Cororate Finance 17

18 Continuous investment I [0, ) is a choice variable; the entrereneur chooses I and whether to exert effort eturn is I and rivate benefit is I IC for the entrereneur: I for the creditor: ewriting: b > L b + I b > I I ( I ) I I I I b κ 1 κ multilier Cororate Finance 18

19 Continuous investment otimal investment In a cometitive caital market, the lenders must break even given their anticiation that the entrereneur will exert effort: l = I- The entrereneur s utility above and beyond : U = I ( I ) = I = ( )I l 1 ssumtion 1: > 1 investment has a ositive NPV with effort Imlication: the entrereneur would like to invest as much as he can ut if I is high, the IC constraint is violated Otimal investment is determined by the multilier equation: I = κ Invest u to κ times your wealth or orrow κ-1 times your wealth Cororate Finance 19

20 Continuous investment - multilier ssumtion 1: > 1 investment has a ositive NPV with effort ssumtion : L + < 1 investment has a negative NPV w/o effort ssumtion 1 + imly: > 1 > L + > > / ssumtion 3: 1 1 < / NPV is lower than the cost of M Since > / and given ssumtion 3, κ > 1 Imlication: κ is a multilier each dollar of equity leads to κ dollars of investment κ is smaller if is large Cororate Finance 0

21 Cororate Finance 1 Continuous investment - leverage The otimal investment is κ The entrereneur needs to borrow (κ-1), where = + = κ