Οικονομικό Πανεπιστήμιο Αθηνών
Τμήμα Οικονομικής Επιστήμης
Άνοιξη 2012
Χρηματοοικονομικές αγορές και εταιρική διακυβέρνηση
Lectures 6 & 7: Credit rationing and the role of net worth.
A borrower is rationed if he cannot obtain the loan that he wants even though he is
willing to pay the interest that the lenders are asking.
Lenders do not increase interest rates even though Dloans > Sloans at that interest rate.
Explanation: Information asymmetries between borrowers and lenders
A high interest rate reduces the borrower’s stake in the project. An interest rate increase
has no effect on the borrower in the event of bankruptcy, but it lowers the borrower’s
income in the absence of bankruptcy. Thus, a moral hazard issue: The reduced stake may
demotivate the borrower (i.e. the borrower pursues projects with high private benefits and
ignores profitable projects when r increases. That is, if r increases, the prob. of
reimbursement decreases through reduced performance.
Also, an adverse selection issue if we can not separate good from bad borrowers: Higher
r attract low-quality borrowers (with high prob. of default and therefore less affected by a
rise in r).
The fixed-investment model (Holstrom and Tirole (1997)).
An entrepreneur has a project that requires a fixed investment I. He has assets A < I. He
must borrow I – A from lenders.
The project succeeds with prob. p and yields income R or fails with prob. (1-p) and yields
no income.
The project is subject to moral hazard. The borrower may mismanage the project: He
may not work hard, thus receiving a private benefit (and reduce the probability of
success). The private benefit is less than the total profit. However, the borrower receives
only part of the profit may choose not to work hard. The amount the borrower receives
should induce him to work hard. Thus, the project’s income cannot be fully pledged to
outside investors even if it has positive NPV. That is we have credit rationing.
The effort the entrepreneur puts may vary. If the entrepreneur works hard, the prob. of
success is pH and there is no private benefit for the entrepreneur. If the entrepreneur does
not work hard, the prob. of success is pL and there is private benefit B > 0 for the
entrepreneur. We have Dp = pH - pL.
Assumptions.
The borrower and the lenders are risk neutral.
There is no time preference. Value of money now or in the future.
Lenders behave competitively (they make zero profits).
The loan contract.
Both sides receive zero in case of failure (borrower’s limited liability).
In the case of success both parties (the borrower and the lenders) share the profit R. R =
Rb + Rl.
We assume: The project is viable in the absence of moral hazard. That is:
pH R - I > 0 whereas
pL R - I + B < 0 (no loan that gives an incentive to the borrower to misbehave will be
granted).
As a result, the zero profit constraint for the lender assuming that he contract induces the
borrower to work hard: pH Rl = I – A.
The rate of interest is given by: Rl = (1 + i) (I - A) or 1 + i = 1/ pH.
We can rewrite pL R - I + B < 0 (add and subtract A) as:
PL Rl - ( I – A) + [ pL Rb + B – A] < 0
In case of misbehavior, either the lenders must lose money or the borrower would be
better off if he does invest but consume A, or both.
The lender’s credit analysis.
The contract should take into account that after the loan, the entrepreneur receives B if he
does not work and he reduces the prob. of success. We should therefore have (incentive
compatibility constraint):
pH Rb  pL Rb + B or Dp Rb  B.
(IC)
That is lenders get at most (in the case of success): Rl = R - Rb < R – B/Dp their expected
income is (assuming the borrower will work hard):
P = pH Rl = pH (R – B/Dp).
Lenders should have nonnegative profits (lender’s individual rationality constraint):
P = pH (R – B/Dp)  I – A.
(L1)
Or A  Abar = pH ( B/Dp) – (pH R - I)
we assume Abar > 0.
Abar is the minimum amount the borrower should have to find lenders.
(1)
Or,
(pH R - I) < pH ( B/Dp)
That is, the NPV is smaller than the minimum expected rent that must be left to the
borrower to provide her with an incentive to behave. I.e. the borrower must have enough
assets in order to be granted a loan.
If A  Abar the entrepreneur is able to secure financing.
When A < Abar a positive NPV project is not financed… There is credit rationing.
(1) is a necessary and sufficient condition for financing.
Lenders do not enjoy surplus. They receive: pH Rl = I – A
(L)
Borrower receives: Rb = R – Rl =R – (I – A)/ pH from above. We have,
R – (I – A)/ pH  R – (I – Abar)/ pH from (1) and
R – (I – Abar)/ pH = B/ Dp (from (1)).
pH B/Dp The agency rent (the min amount to borrower to preserve incentives).
Utility of borrower:
0
if A < Abar
pH Rb - A = pH (R - Rl ) – A = pH R – I (from (L))
if A  Abar
From the zero profit condition for the lenders, the borrower receives the entire NPV (exp.
Revenues - investment) if the project is funded.
Factors for credit rationing:
Low amount of cash (low A)
High agency cost: combination of B with Dp/ pH.
What happens if the borrower invests part of his entire wealth?
What happens if the entrepreneur receives income in the case of failure?
Overborrowing
Debt contracts include negative covenants prohibiting the dilution of creditors’ claims
through the issue of new securities especially ones with equal or higher seniority.
(a) Creditors do not want the borrower to issue claims that have a higher or the same
seniority as theirs as this reduces the amount they can collect if the firm defaults.
(b) The issue of new securities may alter managerial incentives and the size of the pie.
Suppose in our example there is an opportunity for more investment. The investment
costs J and increases the prob. of success by t.
Prob. of success is pH + t or pL + t in the two cases. Also, assume the expected increase
in profits is smaller than the cost of the investment J.
(1) C1 = J – tR > 0. [A positive cost]
New financing is allowed as in such case, initial lenders keep their stake Rl in success
when the borrower contracts with new lenders.
(A) Value of initial investors’ claim is now: ( pH + t) Rl
With (1) and (A) it is not in the interest of the borrower to contract with new investors if
this results in the same effort:
The new investment reduces the total value by C1 and the borrower is not willing to
undertake it if he still puts the same effort (the value of initial investors’ claim is
increased and since C1>0 either the entrepreneur or the new lenders must loose which is
impossible).
If we add the incentive constraints:
pH R - I > 0
pL R - I + B < 0 which implies: - pL R + I - B > 0
We have an additional cost as the entrepreneur puts less effort now:
C2 =(Dp)R - B > 0. [A positive cost]
The amount of the borrower and the amount of the new lenders:
We have Rb’ + Rl’ = Rb .
By competition between lenders, ( pL + t) Rl’ = J.
(2)
The entrepreneur gains from overborrowing if and only if: ( pL + t) Rb’ + B > pH Rb
Or, using (2) ( pL + t) Rb – J + B > pH Rb
or
[ pH - ( pL + t)] Rl > C1 + C2.
The total cost of additional financing (direct cost plus incentive cost) must be smaller
than the loss of value for the initial investors (externality on initial investors).
What happens if the borrower’s benefit from misbehaving decreases?
Debt overhang
A borrower can not raise funds for a profitable project.
There is need for renegotiating past liabilities in order to enable new investments.
The entrepreneur has A in cash but owes D from previous borrowing to “initial
investors.” The entrepreneur can not raise more funds without the consent of “initial
investors.” A are pledged to the initial investors as collateral in case of default.
If A > Abar > A – D > 0
The project could have been financed in the absence of previous borrowing.
If all agree for the project:
As initial investors can secure themselves D by seizing the collateral, they should receive
at least D (the collateral). The new investment requires I - A funds.
The pledgeable income net of the investment cost is:
pH ( R –( B/Dp)) – I
from (L1)
New investors should obtain (see the first model we examined) at most:
pH ( R –( B/Dp)) – I – D + A = A – D – Abar < 0.
I.e. New investors do not break even.
Lack of Renegotiation.
The project is sufficiently profitable to attract funds even if the borrower has zero net
worth: Abar < 0,
The borrower had a loan D which must pay at the end of the project (senior debt).
The borrower has no cash: A = 0
Serious overhang problem. –Abar is smaller to what has to be paid back to previous
investors pH D if the project is funded. If the new project is funded previous investors
receive pH D, and -Abar < pH D I.e.
Abar + pH D > 0
(R)
As A = 0 initial investors receive nothing if the project is not financed.
Initial investors agree for the project and finance the investment I as long as they break
even on this new investment. When initial investors get the entire cash-flow rights
attached to external shares, i.e. R –( B/Dp) in the case of success. Initial investors obtain:
pH (R –( B/Dp)) – I = - Abar > 0.
(R1)
The borrower (entrepreneur) obtains rent pH B/Dp in expectation rather than 0 if the
project is not financed.
What happens if initial investors can not finance the investment?
Since initial debt is D, and the borrower receives ( B/Dp)
New investors will receive in case of success at most: (R –( B/Dp)) – D
New investors finance the project when pH [(R –( B/Dp)) – D]  I or (by R1)
Abar + pH D  0 which contradicts (R)
If initial investors accept a reduction in the face value of their debt from D to d < D
where
Abar + pH d = 0
The new investors receive ( R –( B/Dp) – d) in case of success, and are willing to invest
since pH (R –( B/Dp) – d) = I
This is equivalent with the break even constraint (1) [Abar = pH ( B/Dp) – (pH R - I)]:
pH (R –( B/Dp)) = I – Abar = I - pH d [I.e. new investors break even]
Initial investors benefit as they get now pH d = - Abar > 0.
The borrower can undertake the project and obtain rent pH B/Dp > 0.
Reference
Jean Tirole, “The theory of corporate finance,” Princeton University Press 2006, Chapter
3, pages 113 - 126.
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