Suppose you are the sole shareholder of a bank with deposits of $1,200,000 and a

Question

Suppose you are the sole shareholder of a bank with deposits of $1,200,000 and assets of $1,000,000. There is no reserve requirement. Your liability in the bank is limited by law to your investment (if it fails, you needn't make up losses to depositors). You are risk neutral.

A. What is the net worth of the bank?

B. Suppose you may reinvest your assets into one but only one of the following projects before the examiners audit your books: Project A; pays a certain return of 7%. Project B; has a 50% chance of a 21% net return and a 50% chance of a -21% net return. Project C; has a 10% chance of doubling your assets and 90% chance of losing everthing. Rank the projects according to which will benefit you personally.

C. How would your ranking change if the assets of the bank were $1,200,000?

D. How would your ranking change if the assets of the bank were $2,000,000?

E. If you have the chance to abscond with $100,000 at the cost of losing ownership in the bank, would you do it? How does your answer depend on the net worth of the bank?

F. If banks are covered by governemnt deposit insurance, why should the government take an active role in closing down failed banks as soon as they can be discovered?

Explanation / Answer

(A) The bank has asset of 1,000,000 and deposit of 1,200,000 which is nothing but bank's liability. It indicates that bank has more liability than its asset. The net worth of the bank is Zero (0), in fact won't be able to pay its debt of 200,000 if all depositors decided to withdraw money and eventually declare bankruptcy for debt retructuring.

(B)

The expected payoff from project A is

E(A) = 1,000,000 at 7% = 1,000,000*1.07 = 1,070,000

The expected payoff from project B is

E(B) = 1,00,000*1.21*0.5 + 1,000,000*0.79*0.5 = 1,000,000

The expected payoff from project C is

E(C) = 1,000,000*2*0.1 + 1,000,000*0*0.9 = 200,000

The Project A will benefit me personally followed Project B and C.

(C) The rank would remain same as the outcomes from project A, B and C using above method will be 1,284,000, 1,200,000 and 240,000

(D) The rank would remain same as the outcomes from project A, B and C using above method will be 2,140,000, 2,000,000 and 400,000

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