3. Moral Hazard- Variable Investment

Question 1

How does investment yield income?

Answer 1

Yields income RI proportional to investment (CRS) in the case of success and 0 in the case of failure

Question 2

When does the project have positive NPV?

Answer 2

If the entrepreneur exerts effort PhR>1

Question 3

When does the project have negative NPV?

Answer 3

When the entrepreneur doesn’t exert effort
1>PlR+B

Question 4

Which condition ensures that investment is finite and states that the pledgeable income per unit of investment is less than 1?

Answer 4

PhR< 1+ PhB/delta P

Question 5

What is the entrepreneurs incentive comparability constraint?

Answer 5

Delta P x Rb>= BI

Question 6

What is the lenders break even condition?

Answer 6

Ph(IR-Rb)>= I-A

Question 7

What is the entrepreneur’s net utility equal to?

Answer 7

The investments social surplus

Ub = (PhR-1)I

Question 8

What imposes a limit on investment and thus on borrowing capacity of the entrepreneur?

Answer 8

The incentive compatibility constraint and the participation constraint

Question 9

Proposition 1. How can wealth be levered?

Answer 9

k>1 wealth can be levered
PhR<1+ PhB/delta P
implies that the denominator of
k=1/(1-Ph(R-B/delta P)) is positive.
PhR>1 and 1>PlR+ B imply that delta PR>B and therefore the denominator is less than 1

Question 10

Proposition 2. What does the multiplier depend on?

Answer 10

The multiplier depends on the two measures of agency costs (a) the private benefit B (negatively) and (b) the likelihood ratio delta P/ Ph (positively)

Question 11

In the variable investment model which firms exhibit a higher sensitivity of investment to cash flow?

Answer 11

Those with a low agency cost (these firms have a higher multiplier)

Question 12

What is IR^s and IR^F?

Answer 12

Investment yields IR^s in the case of success and IR^F in the case of failure (salvage value of assets). Let RI= (R^s-R^F)I

Question 13

What does the optimal contract do?

Answer 13

Maximise the entrepreneur’s expected compensation subject to the entrepreneur’s incentive constraint and the investors break even constraint

Question 14

Proposition 3. Optimal contract

Answer 14

The optimal contract is Rb^s, Rb^F = ((PhR+ R^F -1)I+A)/Ph, 0
This can be derived from the fixed investment model as long as the projects salvage value when it fails is positive

Question 15

What does proposition 1 imply about contracts?

Answer 15

That an all equity contract isn’t optimal. The optimal financial structure requires that investors hold debt D>= IR^F

Question 16

Proposition 4. What dictates a firm’s capacity for outside financing?

Answer 16

Firms with lower agency costs (as measured by either the private benefit B or the inverse of the likelihood ratio delta P/Ph keeping Ph and therefore profitability constant) have higher outside financing capacities

Question 17

How does the project yield private benefit?

Answer 17

BI>0 proportional to investment

Question 18

How is k related to investment and cash?

Answer 18

I<=kA

Where k= 1/(1-Ph(R-B/delta P))

Question 19

Give the equation specifying sensitivity of investment to cash flow

Answer 19

dk/dpo= 1/(1-Ph(R-B/delta P))^2

Question 20

What is the NPV per unit of investment and the pledgable income per unit of investment?

Answer 20

The NPV per unit of investment is positive while the pledgable income per unit of investment is negative

PhR + R^F > 1 > Ph(R-B/delta P) + R^F

Question 21

Steps of finding the optimal contract

Answer 21

1. Suppose breakeven constraint isnt binding. Increase Rb^s and Rb^F an equal amount. This change increases entrepreneurs payoff therefore original contract can’t be optimal.
2. Suppose incentive constraint isn’t binding. Then optimal investment would be infinite violating the two constraints combined.
3. Rb^F=0. Suppose it is positive. Can make a small increase in Rb^s and a small decrease in Rb^F keeping the objective function and breakeven constraint constant but the incentive is now slack.
4. To derive Rb^s set 1 and 2 equal and Rb^F=0

Question 22

Suppose that pledgable income per unit of investment is greater than 1. How would this change affect the results of the model?

Answer 22

The constraint is not binding. There isn’t moral hazard so the size of the project is infinite