An investor has two prototypes for invention, A and B, and needs the same amount of loan L for each. It is expected that either one of these prototypes will take a year to develop and will yield a reward of either RA or 0 for prototype A and either RB or 0 for prototype B. The probabilities of positive payoff are given by Prob(RA)=PA Prob (RB) =PB And these probabilities are known to the bank. The bank will only lend if the expected repayment at the end of the year generates a yield of i. If the prototype given a 0 reward, then the bank receive no repayment. Assuming risk neutrality on the part of the bank, explain why the repayments when either prototype is a success are given by (1+i) LPA, (1+i) LPB for A, B respectively. If the loan were granted, show that the expected payoff for the inventor after the bank has been repaid is given by PARA-(1+i) LPBRB-(1+i)L for A, B respectively. Under what conditions the inventor would definitely not submit prototype B to the bank, but would submit prototype A? Now suppose that the bank grants the loan for A, but does not continue to monitor the inventor. What will be the payoff to the bank if the inventor is successful? Under what conditions will the bank now suffer moral hazard I-e the inventor will now choose to go for prototype B.? The bank now wishes to create incentive comparability, to ensure that the inventor work on prototype A. What is the minimum level of collateral required to guarantee this?
An investor has two prototypes for invention, A and B, and needs the same amount of loan L for each. It is expected that either one of these prototypes will take a year to develop and will yield a reward of either RA or 0 for prototype A and either RB or 0 for prototype B. The probabilities of positive payoff are given by Prob(RA)=PA Prob (RB) =PB And these probabilities are known to the bank. The bank will only lend if the expected repayment at the end of the year generates a yield of i. If the prototype given a 0 reward, then the bank receive no repayment. Assuming risk neutrality on the part of the bank, explain why the repayments when either prototype is a success are given by (1+i) LPA, (1+i) LPB for A, B respectively. If the loan were granted, show that the expected payoff for the inventor after the bank has been repaid is given by PARA-(1+i) LPBRB-(1+i)L for A, B respectively. Under what conditions the inventor would definitely not submit prototype B to the bank, but would submit prototype A? Now suppose that the bank grants the loan for A, but does not continue to monitor the inventor. What will be the payoff to the bank if the inventor is successful? Under what conditions will the bank now suffer moral hazard I-e the inventor will now choose to go for prototype B.? The bank now wishes to create incentive comparability, to ensure that the inventor work on prototype A. What is the minimum level of collateral required to guarantee this?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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An investor has two prototypes for invention, A and B, and needs the same amount of loan L for each. It is expected that either one of these prototypes will take a year to develop and will yield a reward of either RA or 0 for prototype A and either RB or 0 for prototype B. The probabilities of positive payoff are given by
Prob(RA)=PA Prob (RB) =PB
And these probabilities are known to the bank. The bank will only lend if the expected repayment at the end of the year generates a yield of i. If the prototype given a 0 reward, then the bank receive no repayment.
- Assuming risk neutrality on the part of the bank, explain why the repayments when either prototype is a success are given by (1+i) LPA, (1+i) LPB for A, B respectively.
- If the loan were granted, show that the expected payoff for the inventor after the bank has been repaid is given by PARA-(1+i) LPBRB-(1+i)L for A, B respectively.
- Under what conditions the inventor would definitely not submit prototype B to the bank, but would submit prototype A?
- Now suppose that the bank grants the loan for A, but does not continue to monitor the inventor. What will be the payoff to the bank if the inventor is successful? Under what conditions will the bank now suffer moral hazard I-e the inventor will now choose to go for prototype B.?
- The bank now wishes to create incentive comparability, to ensure that the inventor work on prototype A. What is the minimum level of collateral required to guarantee this?
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