8. Moral Hazard Term Structure & Adverse Selection Flashcards
What does liquidity management consider?
We consider the optimal financing problem when entrepreneurs face uncertain liquidity needs. In particular, we consider an environment where at the time that a contract is agreed there is uncertainty about the future liquidity needs of the firms
Main conclusions of liquidity management
Cash- rich firms issue short term debt, long term debt and also use retentions (retained profits)
Cash-poor firms finance their projects with credit lines (loan commitments)
Timing of the model
Date 0: contract and investment
Date 1: short term income- random investment need
Date 2: moral hazard
Date 3: outcome
This is a simple extension of the fixed investment model where an intermediate step has been added
What is F(rho) and f(rho)
Cumulative distribution function and density of reinvestment
What happens if the entrepreneur doesn’t reinvest?
The firm is liquidated
What is the liquidation value of the firm?
0
How much lower is pledgable income than the corresponding revenue in the case of success?
B/delta P less which is the min amount that the entrepreneur must receive so that he has incentives to exert effort
When should the investment be salvaged?
When the cost, rho, of a rescue is less than the expected payoff PhR of continuing
What is the most investors can claim?
Ph(R-B/delta P) given that they need to give incentives to the entrepreneur to exert effort in the case of continuation
When is utility and pledgable income increasing/decreasing?
It is increasing for low values of rho* and decreasing for high values of rho*
When does utility reach its highest value relative to pledgable income and why?
Utility reaches its highest value at a higher value of the continuation threshold since the marginal benefit of continuation is lower for pledgable income than for utility while the marginal costs are the same
What happens in case 1 and case 3?
In case 1 the contract is indeterminant and in case 3 there is no contract
Proposition 1 how can the optimal contract be implemented when r>=rho*
The optimal contract can be implemented through a combination of short term debt d= r-rho* and long term debt D=R-B/delta p
Proposition 2 how can the optimal contract be implemented when r=0?
The optimal contract can be implemented by an initial loan I-A and a nonrevokable credit line at level rho*
Why must the credit line be nonrevokable?
If rho> ph(R-B/delta p) the investor has an incentive not to rescue the firm. The reason is that in expectation the investor breaks even which implies that if liquidity needs are high but lower than rho* the investor expects to make losses
Types of adverse selection
Asymmetric info between insiders and investors. Investors might have imperfect info of
- firms prospects
- the value of assets in place
- the value of pledged collateral
- the issuers potential private benefit
Consequences of adverse selection
-Market breakdown
-cross subsidisation
-over investment
-underinvestment
Summarise the privately known prospects model assumptions
-entrepreneur: risk neutral, limited liability, A=0
-credit market: competitive, lenders are risk neutral, risk free interest rate equals 0
-project: requires investment I, yields R in the case of success and 0 in the case of failure
Probability of good entrepreneur succeeding
P
Probability of bad entrepreneur succeeding
q
What are the two subcases of the privately known prospects model?
-PR>I>qR (only good type is credit worthy)
-PR>qR>I (both types are credit worthy)
What is the probability that the entrepreneur is a p-type or q-type
Alpha for p-type
1-alpha for q-type
What is m equal to?
m= alpha x p + (1- alpha)q
This is the lenders prior probability of success
What is Rb^G given by in symmetric info model?
The lenders break even condition
P(R-Rb^G)=I
When does the bad entrepreneur obtain finance in the symmetric info model?
If qR>I the bad entrepreneur obtains finance and Rb^B is given by
q(R-Rb^B)= I
Why isn’t the symmetric info outcome robust to asymmetric info?
Because the bad entrepreneur can pretend to be a good entrepreneur and derive greater utility
Proposition 1 adverse selection
If mR<I the market breaks down. Good entrepreneur don’t obtain finance (underinvestment)
Proposition 2 adverse selection
Lenders make money on the good type (p(R-Rb)>I) and lose money on the bad type (q(R-Rb)<I) there is cross subsidisation when the bad entrepreneur isn’t credit worthy there is overinvestment
Pecking order hypothesis
There is no distinction between debt and equity when the return of the investment is either R or 0. Project yields R^F in the case of failure and R^s in the case of success where R^s-R^F=R
What is the break even condition?
m(R^s-Rb^s)+(1-m)(R^F-Rb^F)>=I
What does the good entrepreneur maximise?
PRb^s+(1-p)Rb^F
What does the adverse selection discount increase and decrease with?
Increases with Rb^F and decreases with Rb^s
Proposition 3 adverse selection
Optimal capital structure: the entrepreneur issues safe debt equal to the salvage value R^F and issues risky equity with payoffs R^s-Rb^s in the case of success and 0 in the case of failure
Why does safe debt minimise cross subsidisation?
Because it is a low info intensity claim and it isn’t sensitive to the entrepreneurs private info
How can good types separate from bad types?
By introducing distortions that are costly to them but would be even costlier to bad types.
-certification
-collateral pledging
-short term maturities
-payout policy (dividends)
What is rho?
Reinvestment unknown at date 0, known at date 1
What is r?
Deterministic and verifiable income
What is the cutoff value?
Cutoff value of rho, rho, such that it is optimal to continue if rho<=rho. The probability of continuation is Pr(rho<=rho)=F(rho)
Why does the contract for cash poor firms stipulate that the loan commitment is non-revocable?
In expectation the lender makes zero profits. In some cases the bank will make negative profits but it must commit to this and can’t revoke it
Suppose B=0. How would this change affect the results?
When B=0, pledgable income and utility become exactly the same so you try to maximise utility
When does underinvestment occur?
mR<I
This case can only arise when the bad entrepreneur is not creditworthy and alpha<alpha*
When does overinvestment occur?
When the bad isn’t creditworthy and alpha>=alpha*
What is the lenders profit in the asymmetric case?
(Alpha p + (1- alpha)q)(R-Rb)-I=m(R-Rb)-I
How is the value of alpha* determined?
Let alpha* such that
alpha(pR-I)+(1-alpha)(qR-I)=0
