There are 2 firms, Firm B (“Bad) and Firm G (“Good”), that each have $10 in cash but need to borrow an additional $40 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 $200 with 30% probability or $0 with 70% probability.
• The payoff of firm G’s investment would be $70 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 $40 it must invest the entire $50 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 $10 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 $50, 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?

b. Now suppose the firms approach your bank.  In return for the loan of $40 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). 

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?