Question

RES 3200: ARMs and REFI

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

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

2. A bank makes a 30 year Fully Amortizing FRM for $2,500,000 at an annual interest rate of 5% compounded monthly, with monthly payments. 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 has a margin of +265 basis points above Libor. In one year after the loan is originated, the Libor is 9.5%. What is the fully indexed rate on the loan in one year?

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

5. A bank originates a 30 year fully amortizing FRM at an annual interest rate of 5.5%. 9 years later the bank’s cost of funds is 12.50%. What is the bank’s NIM on this loan? (Your answer can be positive or negative, use the correct sign!)

6. Tim wants to buy an apartment that costs $2,225,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 4.875%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 3.50% at the time of the 1^st reset. What is Tim’s monthly mortgage payment going to be during the 1^st 3 years?

7. Tim wants to buy an apartment that costs $2,225,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 4.875%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. Tim anticipates the index to be 3.50% at the time of the 1^st reset. If the index resets to 3.50% as Tim forecasts, what will his new mortgage payment be in year 4?

8. Tim wants to buy an apartment that costs $2,225,000 with an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of 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 an 85% LTV mortgage. Tim got a 30 year, 3/1 ARM with an initial teaser rate of 3.75%. The reset margin on the loan is 300 basis points above 1 year CMT. There are no caps. The index was 1% at the time of 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 prepay in 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 will pay $1,250 per month. The loan will become a fully amortizing mortgage after 2 years. What will be the balance on this mortgage after 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 rates fall and he can get a 27 year FRM at 5%, but he must pay 2 points and $1000 in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he stays until 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 rates fall and he can get a 27 year FRM at 5%, but he must pay 2 points and $1000 in closing costs to get the new loan. Think of the refinancing decision as an investment for Tom, he pays a fee now but saves money in the future in the form of lower payments. What is the annualized IRR of refinancing for Tom assuming he prepays the new loan 5 years after refinancing?

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

Answer 1

(1) Mortgage Amount = $ 2500000, Interest Rate = 4.875%, Tenure = 30 years or (30 x 12) = 360 months, Payment Frequency: Monthly

Applicable Monthly Rate = 4.875 / 12 = 0.40625 %

Let the monthly repayments be $P

Therefore, 2500000 = P x (1/0.0040625) x [1-{1/(1.0040625)^(360)}]

2500000 = P x 188.962

P = 2500000 / 188.962 = $ 13230.21

Number of Repayments Remaining after 36 payments = 360 - 36 = 324 months

Outstanding Principal at the end of 36 payments = Total Present Value of remaining monthly payments discounted at the original interest rate = 13230.21 x (1/0.0040625) x [1-{1/(1.0040625)^(324)}] = $ 2381095.5

Market Value of Loan = Total Present Value of remaining monthly payments discounted at the higher prevailing interest rate

Higher Rate = 5 % , Monthly Rate = 5/12 = 0.41667 %

Therefore, Market Value of Loan = 13230.21 x (1/0.0041667) x [1-{1/(1.0041667)^(324)}] = $ 2349775.01

Difference between Market Value and Outstanding Value of Loan = 2381095.5 - 2349775.01 = $ 31320.49

NOTE: Please raise separate queries for solutions to the remaining unrelated questions as one query is restricted to the solution of only one complete question with up to four sub-parts.