RES 3200: ARMs and REFI

1. A bank makes a 30 year Fully Amortizing FRM for $2,500,000 atan annual interest rate of 4.875% compounded monthly, with monthlypayments. What is the difference between the balance and the marketvalue of the loan after 36 monthly payments if the interest raterises to 5%?

(Give the absolute value of the difference, so the answer shouldbe a positive number.)

2. A bank makes a 30 year Fully Amortizing FRM for $2,500,000 atan annual interest rate of 5% compounded monthly, with monthlypayments. Suppose inflation is 2% per year, compounded monthly.What is the real value of the 120^th payment?

3. Assume the initial rate on a 1/1 ARM is 11.50%. The loan hasa margin of +265 basis points above Libor. In one year after theloan is originated, the Libor is 9.5%. What is the fully indexedrate on the loan in one year?

4. Suppose a bank pays depositors 0.40% on their checkingdeposits. The same bank makes mortgages at 3.50%. What is thebank’s Net Interest Margin (NIM)?

5. A bank originates a 30 year fully amortizing FRM at an annualinterest rate of 5.5%. 9 years later the bank’s cost of funds is12.50%. What is the bank’s NIM on this loan? (Your answer can bepositive or negative, use the correct sign!)

6. Tim wants to buy an apartment that costs $2,225,000 with an85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaserrate of 4.875%. The reset margin on the loan is 300 basis pointsabove 1 year CMT. There are no caps. Tim anticipates the index tobe 3.50% at the time of the 1^st reset. What is Tim’smonthly mortgage payment going to be during the 1^st 3years?

7. Tim wants to buy an apartment that costs $2,225,000 with an85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaserrate of 4.875%. The reset margin on the loan is 300 basis pointsabove 1 year CMT. There are no caps. Tim anticipates the index tobe 3.50% at the time of the 1^st reset. If the indexresets to 3.50% as Tim forecasts, what will his new mortgagepayment be in year 4?

8. Tim wants to buy an apartment that costs $2,225,000 with an85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaserrate of 3.75%. The reset margin on the loan is 300 basis pointsabove 1 year CMT. There are no caps. The index was 1% at the timeof origination. Tim also had to pay 6.5 points for this loan.Compute the true APR (annualized IRR) for this loan.

9. Tim wants to buy an apartment that costs $2,225,000 with an85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaserrate of 3.75%. The reset margin on the loan is 300 basis pointsabove 1 year CMT. There are no caps. The index was 1% at the timeof origination. Tim also had to pay 1 point for this loan.

Suppose the index rate will remain 1% for the life of the loan.Compute the annualized IRR for this loan assuming Tim will prepayin 5 years.

10. Bob got a 30 year Fully Amortizing FRM for $2,500,000 at 4%,except with non-constant payments. For the first 2 years Bob willpay $1,250 per month. The loan will become a fully amortizingmortgage after 2 years. What will be the balance on this mortgageafter 2 years?

(hint: see the option ARM slide in the ARM lecture)

11. Tom got a 30 year fully amortizing FRM for $1,500,000 at 8%,with constant monthly payments. After 3 years of payments ratesfall and he can get a 27 year FRM at 5%, but he must pay 2 pointsand $1000 in closing costs to get the new loan. Think of therefinancing decision as an investment for Tom, he pays a fee nowbut saves money in the future in the form of lower payments. Whatis the annualized IRR of refinancing for Tom assuming he staysuntil maturity?

12. Tom got a 30 year fully amortizing FRM for $1,500,000 at 8%,with constant monthly payments. After 3 years of payments ratesfall and he can get a 27 year FRM at 5%, but he must pay 2 pointsand $1000 in closing costs to get the new loan. Think of therefinancing decision as an investment for Tom, he pays a fee nowbut saves money in the future in the form of lower payments. Whatis the annualized IRR of refinancing for Tom assuming he prepaysthe new loan 5 years after refinancing?

(Clarification: Tom will prepay the new loan 3+5=8 years afterthe house is purchased)