Essay on 3505 M2 Fall 2014 Soltn

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Management of Depository Institutions 3505 Fall 2014

Problems:
1. A bank is planning to make a loan of $5,000,000 with duration of 7.5 years to “Jumbo Manufacturing”, a young and aggressive firm. The loan rate is 12% and the servicing fee is 50 basis points. The bank estimates that with a probability of 95%, the risk premium on the loan will not increase by more than 4.2%. The average cost of funds for the bank is 10 percent. The bank manager wants to use the RAROC approach to make a decision on approval/rejection of the loan:
a. What is RAROC? Explain the concept theoretically.
b. How does this model use the concept of duration to measure the credit risk of a loan?
c. How is the expected change in the credit premium of the
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a. 0.50 years. b. 2.00 years. c. 4.40 years. d. 5.00 years. e. 4.05 years.
For zero coupon securities D =M

5. Consider an 18-month, 8 percent (semiannual) coupon Treasury note selling at par. What is the duration of this Treasury note? a. 1.500 years. b. 1.371 years. c. 1.443 years. d. 2.882 years. e. 1.234 years.

M = 18m. F= 10,000 (can be any amount), three cash flows: 400, 400, 10400. IR =4%. D = {[PV1 • 1 + PV2• 2 + …….+ PVn • n]/ P}= 1.443

6. Consider an 18-month, 8 percent (semiannual) coupon Treasury note selling at par. If interest rates increase by 20 basis points (i.e., R = 20 basis points), use the duration approximation to determine the approximate price change.

a. $0.000. b. -$0.2775 per $100 face value. c. $2.775 per $100 face value. d. $0.2672 per $100 face value. e. $2.672 per $100 face value.

M = 18m. F= 100 because the answers are per $100 face value.
Three cash flows: 4, 4, 104. IR =4%. D= 1.443 from the last question.
P = P x {-D[R/(1+R)]}= -100 x 1.443 x .0020/1.04 = -.2775

7. The duration of a consol bond is a. less than its maturity. b. infinity. c. 30 years. d. more than its maturity. e. given by the formula D=1/1-R.

8. If interest rates decrease 40 basis points (0.40 percent) for an FI that has a cumulative gap of -$25 million, the expected change in net interest income is a. +$100,000. b. -$100,000. c. -$625,000. d. -$625,000.

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