Exercises 12.1 Suppose you are the sole shareholder of a savings and loan with d

Question

Exercises 12.1 Suppose you are the sole shareholder of a savings and loan with deposits of $1,200,000 and assets of $1,000,000. There is no reserve requirement. Your liability in the S&Lis; 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 S&L;? 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 percent. Project B: has a 50 percent chance of a 21 percent net return and a 50 percent chance of a net return of-21 ent Exercises 229 Project C: has a 10 percent chance of doubling your assets and a 90 percent chance of losing everything. Rank the three projects according to which will benefit you personally c. How would your ranking change if the assets of the S&L; were $1,200,000? d. How would your ranking change if the assets of the S&L; were $2,000,000? e. If you have the chance to abscond with $100,000 at the cost of losing ownership in the S&L;, would you do it (setting aside questions of morality)? How does your answer depend on the net worth of the S&L;? f. IfS&Ls; are covered by government deposit insurance, why should the government take an active role in closing down failed S&Ls; as soon as they can be discovered? Answer with references to the e xample s in this exercise.

Explanation / Answer

Solution:

a) Net worth = value of assets - value of liabilities

= $1,000,000 - $1,200,000 = -$200,000

b) As per the given information: By investing principal amount of $1,000,000, final return amount by investing in

Project A = 1000000*(1 + 0.07) = $1,070,000

Project B = 0.5*1000000*(1 + 0.21) + 0.5*1000000*(1 + (-0.21))

= 605000 + 395000 = $1,000,000

Project C = 0.10*2(1000000) + 0.90*0 = $200,000

So, we can rank the above projects in this way (from most beneficial to least beneficial)

1) Project A 2) Project B 3) Project C

c) Principal amount = $1,200,000. Then, final return amount by investing this amount in

Project A = 1200000*(1 + 0.07) = $1,284,000

Project B = 0.5*1200000*(1 + 0.21) + 0.5*1200000*(1 + (-0.21))

= 726000 + 474000 = $1,200,000

Project C =  0.10*2(1200000) + 0.90*0 = $240,000

So, again we can rank the above projects in this way (from most beneficial to least beneficial)

1) Project A 2) Project B 3) Project C

d) Principal amount = $2,000,000. Then, final return amount by investing this amount in

Project A = 2000000*(1 + 0.07) = $2,140,000

Project B = 0.5*2000000*(1 + 0.21) + 0.5*2000000*(1 + (-0.21))

= 1,210,000 + 790,000 = $2,000,000

Project C =  0.10*2(2000000) + 0.90*0 = $400,000

So, again we can rank the above projects in this way (from most beneficial to least beneficial)

1) Project A 2) Project B 3) Project C

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