13

Problem 4 (25 Points)

Please read carefully:

There are 2 firms, Firm B ("Bad) and Firm G ("Good"), that each have $50 in cash but need to borrow an

additional $200 in order to finance a one-period investment project. The firms are limited liability

corporations and exist for only one period, after which they will be dissolved. You are a loan officer at

the Seattle Lemon Bank. The only way for the firms to finance their project is to borrow from your bank.

While you are unable to identify the type of firm (B or G), you have the following additional information:

The payoffs of firm B's investment one year from now would be either $1000 with 30%

probability or $0 with 70% probability.

The payoff of firm G's investment would be $350 for sure.

You can assume that the expected return requirement for any loans you make are zero (i.e., no

need to discount payoffs)

Once the firm obtains the loan of $200 it must invest the entire $250 into the project. However, the

firm can always opt to not take the loan and thus forgo the investment opportunity, in which case it

simply returns the $50 cash in one year.

(Note: You may find it useful to sketch out what is going on.)

a. Suppose both firms had enough cash to finance the investment of $250, compute the net

present values of the investment opportunities for firm B and for firm G (you can ignore

discounting). Which of the two projects should be undertaken from an NPV perspective?

[5 points]

14

b. Now suppose the firms approach your bank. In return for the loan of $200 today, you require a

fixed loan repayment of $D one period from now (a standard debt contract). While you cannot

identify the firm types, first assume that both firms will take your loan offer. What must be the

promised repayment $D such that the bank just breaks even? (Note that because there are only

2 firms, they are equally likely). [5 points]

c. Using the promised payment $D you computed in part (b), re-analyze the project opportunity

from each firm's perspective (Remember that each firm can choose to forgo the investment

opportunity). For each firm type, what are the firm values of doing the project and how does

this compare with not doing the project? [5 points]

15

d. Which of the two firms would take the bank's offer ($200 in return for the promised payment of

$D you computed in parts (b) and (c)) and what would this mean for the bank's profits?

Assuming that the bank must break even, in equilibrium, who will be financed and at what

promised amount $D? Explain. [7 points]

e. Now suppose that the two firms are run and owned by wealthy, risk-neutral CEOs. While the

firms are limited liability corporations, you require the CEOs to personally guarantee any loan

you provide to the firm (the CEOs are unwilling to provide direct financing to the firm). Assume

that the CEOs have sufficient personal funds at the end of the period to make whole on the loan.

How does this personal guarantee affect the information problem? That is, which of the firms

will want to contract with your bank and what loan terms are being offered, if any? Explain. [3

points]