A bank has made a two-year $20 million loan that pays annual interest of 10 per cent. The principal is due at the end of the second year. The bank is willing to sell this loan with recourse at an interest rate of 10.5 per cent. The bank expects a 5 per cent probability of default on this loan. It expects to receive no interest payments or principal if the loan defaults. What is the expected value for this loan when selling the loan with recourse? (Note: Pick the closest answer) (0.5 marks)Question 11Answera.19.24b.18.12c.17.56d.18.84e.17.79
Question
A bank has made a two-year $20 million loan that pays annual interest of 10 per cent. The principal is due at the end of the second year. The bank is willing to sell this loan with recourse at an interest rate of 10.5 per cent. The bank expects a 5 per cent probability of default on this loan. It expects to receive no interest payments or principal if the loan defaults. What is the expected value for this loan when selling the loan with recourse? (Note: Pick the closest answer) (0.5 marks)Question 11Answera.19.24b.18.12c.17.56d.18.84e.17.79
Solution
To calculate the expected value of the loan when selling it with recourse, we need to consider both the scenario where the loan does not default and the scenario where it does default.
-
If the loan does not default, the bank will receive interest payments for two years and the principal at the end of the second year. The present value of these payments can be calculated using the formula for the present value of an annuity:
PV = Pmt / r * (1 - (1 + r)^-n) + FV / (1 + r)^n
where:
- Pmt is the annual payment (in this case, the interest payment of $2 million)
- r is the discount rate (in this case, the interest rate of 10.5%)
- n is the number of periods (in this case, 2 years)
- FV is the future value (in this case, the principal of $20 million)
Substituting the given values into the formula, we get:
PV = 2 / 0.105 * (1 - (1 + 0.105)^-2) + 20 / (1 + 0.105)^2 PV = 18.12 million
-
If the loan does default, the bank expects to receive no interest payments or principal. Therefore, the present value of the loan in this scenario is $0.
-
The expected value of the loan is the sum of the present values of the two scenarios, each weighted by their probability of occurrence. In this case, the probability of the loan not defaulting is 95% and the probability of the loan defaulting is 5%.
EV = 0.95 * 18.12 + 0.05 * 0 EV = 17.21 million
Therefore, the expected value of the loan when selling it with recourse is approximately $17.21 million. The closest answer is (c) 17.56.
Similar Questions
A $10,000 loan is to be repaid at the rate of $200 per month, with an annual effective interest rate of 19.56% charged against the unpaid balance. What principal remains to be paid after the third payment? (a) 9500 (b) 9800 (c) 8900 (d) 9200
Select the correct answerA person takes a loan of Rs. 200 at 5% simple interest on the outstanding amount. He returns Rs. 100 at the end of one year. In order to clear his due at the end of 2 years, he would pay:
. Now that you are almost finished with school, you also have to start paying back your student loans. You borrowed a total of N$12,500. You plan to pay back the loan over 10 years at an interest rate of 9.4% interest, compounded monthly. How much will your monthly payments be?
A person takes a loan of Rs. 200 at 5% simple interest on the outstanding amount. He returns Rs. 100 at the end of one year. In order to clear his due at the end of 2 years, he would pay:OptionsRs. 125.50Rs. 115.50None of theseRs. 110
Sarah is planning to purchase a new house. To purchase the house, she will need to borrow $550,000 from the bank. The loan term is 30 years and the terms of the contract require monthly end of period payments (including interest and principle). The current interest rate offered by her bank is 3.5% per annum for a variable rate mortgage loan. If Sarah borrows the money from her bank and the interest rate decreases by 0.5% three years after the mortgage started, what would the new monthly repayment be?Question 1Select one:a.$1,375.00b.$2,469.75c.$2,500.00d.$2,331.00
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.