inside equity and outside equity.Example: If the pro°t in case of success is 10, a claim of4 can be interpreted either as a 40 percent equity stake,or as a risky debt claim with nominal value 4 which isdefaulted upon in case of failure.Remark:Indeterminacy no longer true if there is a left-over value in case of failure.
1.1ConclusionsIn summary:°Because of moral hazard there is a limit to pledgeableincome°Projects with positive NPV may not be funded°The entrepreneur needs to have enough assets to be°nanced°Higher private bene°ts, higher threshold for °nanc-ingThis model can also explain the ³credit rationing´puzzle:
°Lenders are not willing to raise interest rates evenif the demand for loans exceeds their supply at theprevailing rates°Loan markets are personalised because of private in-formationExplanation:°Higher interest rates reduces the stake of the entre-preneur°Reduced stake may demotivate the entrepreneur andlower the probability of repayment (moral hazard).
2The variable investment model°Technology with constant returns to scale: invest-mentI2[0;1)giving returnRIin case of success,and0in case of failure.°The entrepreneur can work or shirk: if shirk, privatebene°tBI:BIpLLow0pHHighPrivatebenefitsProbabilityof successEntrepreneur’seffort:°The entrepreneur has internal fundsAand needs toborrowI±Ato °nance the project.
A °nancial contract speci°esIand a sharing rule:´in case of failure:0for both;´and in case of success:Rb; Rl, for entrepreneur and°nanciers respectively, whereRl+Rb=RI:De°ne:°1µpHR;exp. income per unit of investment;°0µpH°R±B°p±;exp. pledgeable income per unit ofinvestment.Assume°1>1> °0i.e.:°1>1!the project hasNPV >0if the entre-preneur behaves (°1>1);°0<1!the net return per unit of investimentpHR±1is lower than the agency rentpHB°p.
Financial contract: choose a level of investmentIand asharing rule (Rb; Rl) thatmaxUb=pHRb±A=pH(RI±Rl)±Awhile satisfying the investors±break even constraint (whichholds with equality with competitive capital mkt)pHRl=I±Aand the entrepreneur±s IC°pRb²BISolvingPCforRland substituting out inUbandICbmaxI(pHR±1)Ist"pHR±B°p!±1#I+A²0!@Ub@I=°1±1>0 :want to maximiseI:
How much high?Not in°nitely high, because entrepreneur has °nite assets,and so too much investment relative to his own sharewould destroy incentives!Analytically,@ICb@I=°0±1<0!cannot raiseItoomuch, otherwise violateICb:Thus, raiseIuntilICbinds.!I¶solvesICbAlsoICbbinds.
More precisely,I¶=1h1±pH°R±B°p±iA=11±°0A=kAwherek=11±°0>1:the manager investsk >1timeshis wealth.How much does he borrow?I¶±A=kA±A(k±1)A=dAd= (k±1)times his wealth, whered=°01±°0The max loan he gets,dA;is hisdebt capacity(or out-side °nancing capacity, or borrowing capacity) and is amultiple of his assets.
Last, the entrepreneur±s utility coincides withNPVUb=pHRb±A= (pHR±1)I¶while the gross utilityUgb=Ub+AisUgb=(pHR±1)I¶+A=[(°1±1)k+ 1]A=vAwherev >1is de°ned as the shadow value of equity,and expresses the sensitivity of gross utility to changes inA:@Ugb@A= (°1±1)k+ 1>1An increase inAincreases gross utility directly, and indi-rectly through the increase in borrowing capacity.