Suppose a bank pools the money of two investors (A and B), each contributing $10

Question

Suppose a bank pools the money of two investors (A and B), each contributing $100. There is a 5% chance that either one of the investors needs cash after year 1. The probability that they need cash after year 1 is independent of each other. Otherwise, they will need money in year 2. The bank keeps $100 in cash that earns zero interest rate, and it lends the remaining $100 to a borrower who promises to pay $120 at time 2. Assume there is no default risk with the borrower. However, if the borrower's project gets liquidated at year 1, the project gets only $40 back (called liquidation value) at year 1.

Please answer the following questions based on this information. Only numbers, rounded to two decimal places when applicable, are necessary.

1-)What is the probability (in %) that only A needs money at year 1? 2-) What is the probability (in %) that only B needs money at year 1? 3-) What is the probability (in %) that no one needs money at year 1? 4-) What is the probability (in %) that both need money at year 1? 5-) What is the expected cash flow to both investors combined at time 1? 6-) What is the expected cash flow to both investors combined at time 2? 7-) Assuming a discount rate of 5%, what is the NPV of these cash flows? 8-) What is the minimum payoff in year 2 that the borrower would have to promise to pay in order to make this a zero-NPV project to the bank?

Explanation / Answer

1)      Amount Weighs Investment by A = $100 0.5 Investment by B = $100 0.5 Total $200 1 probability (in %) that only A needs money at year 1 =weight of A* Probabilty that A need money in year 1 =0.5*5% = 2.5% 2) Like in the above solution, probability that B need money in year 1 = 2.5% 3) Probability that no one needs money in year 1= 100% -2.5%-2.5% = 95% 4) Probability that both needs money in year 1= 100- 95% = 5% 5) What is the expected cash flow to both investors combined at time 1 Investor Probability of flow to investor (a) Weight (b) Amount © Out Flow (a*b*c) A 5% 0.25 100 1.25 B 5% 0.25 100 1.25 A & B 10% 0.5 140 7 Total 1 9.5 6) The expected cash flow to both investors combined at time 2 Investor Probability of flow to investor in year 2 (a) Weight (b) Amount © Out Flow (a*b*c) A 95% 0.25 110 26.125 B 95% 0.25 110 26.125 A & B 90% 0.5 220 99 Total 1 151.25 The expected cash flow to both investors combined at time 2 = $151.25 7) Assuming a discount rate of 5%, NPV of these cash flows year Amount PVIF @5% Present Value 1 9.5 0.952381 9.047619 2 151.25 0.907029 137.1882 Net flow to investor 146.2358 Cash Invested 200 Net NPV -53.7642 therefore NPV of these cash flows = ($53.76) 8) Current NPV (a) -53.7642 PVIF (5%, 2) (b) 0.907029 Future Value (a/b) -59.275 Therefore NPV need to be increased by 59.275

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