Reference no: EM133046925

Questions -

Q1. A lender is willing to make a loan as long as a 12% expected rate of return is received. A borrower having no wealth but access to project A that requires $240 of initial financing applies for a loan. The bank screens the loan and predicts the following payoffs. Project A pays: {$320 with a probability of 0.65} {$182 with a probability of 0.35}

a) What interest should be charged? Show all calculations.

b) What occurs if the probability of the good outcome reduces to 0.6?

c) What is the maximum rate that you can charge the borrower? Why?

Q2. A lender is willing to make a loan as long as a 15% expected rate of return is received. A borrower having no wealth but access to a PROJECT A that requires $125.0 of initial financing applies for a loan. The bank screens the loan and predicts the following pay-offs:

PROJECT A pays: {$188.5 with probability 0.6} {$140.0 with probability 0.4}

a) What interest rate should be charged? Show all calculations.

PROJECT B requires $125.0 of initial financing and pays: {$210.0 with probability 0.4} {$105.0 with probability 0.6}

b) What interest rate should be charged? Show all calculations.

Unfortunately, the market is made up of 70% of PROJECT A's (from part 2(a)) and 30 % of PROJECT B's and the bank cannot identify the respective projects.

(c) Given the composition of the market what is the maximum interest rate that can be charged? [Hint: Both borrowers will participate in the loan if they can obtain at least $1 in the 'high' state and further assume that no project switching occurs.]

(d) Given this maximum rate, will the lender obtain their 15% expected rate of return given the loan market composition? Show all calculations.

(e) Unfortunately, Borrower A challenges your maximum rate - what argument(s) do you think that they will use to mount their challenge?

Q3. A lender is willing to make a loan as long as 13% expected rate of return is received. Borrowers having no wealth but access to two projects that require $3 million of initial financing, apply for a loan. The expected payoffs for each project are: PROJECT A pays: {$5.0 million with probability 0.6 {$3.0 million with probability 0.4 PROJECT B pays: {$6.1 million with probability 0.3 {$2.5 million with probability 0.7

(a) Calculate the fair rate for Project A.

(b) Calculate the fair rate for Project B.

(c) Calculate the maximum interest rate that can be charged? (Hint: Borrowers will participate in the loan if they can obtain at least $0.25 million in the 'high' state and further assume that no project switching occurs.) The market is made up of 40% of Project A's and 60% of project B's and the bank can not distinguish between the projects. (d) Given the maximum rate you calculated in (c), will the lender obtain their 13% expected rate of return, given the loan market composition?

Q4. A lender is willing to make a loan as long as 10% expected rate of return is received. Borrowers having no wealth but access to two projects that requiring $2.5 million of initial financing apply for a loan. From historical records the bank knows the payoffs for Project A and Project W are as follows: PROJECT A pays: { $4.5 million with probability 0.70 } { $1.5 million with probability 0.20 } { $1.2 million with probability 0.10 } PROJECT W pays: { $4.5 million with probability 0.70 } { $4.0 million with probability 0.20 } { $1.2 million with probability 0.10 }

(a) Calculate the fair rate of interest for Project A.

(b) Calculate the fair rate or interest for Project W.

Q5. A lender is willing to make a loan as long as a 15% expected rate of return is received. A Borrower having no wealth has access to two projects that each require $175 of initial financing. The bank screens the loan and predicts the following payoffs. From historical records the bank knows the payoffs for Project A and Project B are as follows: PROJECT A pays: { $280, 45% of the time } { $170, 55% of the time } PROJECT B pays: { $245, 60% of the time } { $198, 470% of the time }

(a) Calculate the fair rate of interest that should be charged for project A.

(b) Calculate the fair rate of interest that should be charged for project B.

(c) State which project would be considered the 'riskiest' and why.

(d) Explain the concept of 'moral hazard' in the context of this question. (Include calculations to support your answer.)

(e) Calculate the maximum interest rate that can be changed: (HINT: Both borrowers will participate in the loan if they can obtain at least $10 in the 'high' state. Assume that no project switching occurs.)

(f) Given the maximum rate you calculated in (e), will the lender obtain their 15% expected rate of return, given that the market is made up of 80% of project A's and 20% of Project B's, and the bank can not identify the respective projects?