In a market where interest rates are declining many homeowners face the decision to refinance an existing mortgage, particularly those homeowners who obtained mortgages when interest rates were historically at high levels. This effect was particularly evident during the late 1980's with homeowners who had obtained mortgages at interest rates as high as 16% in 1982 could refinance their mortgage as low as 8% in 1986. The decision to refinance is not that trivial since banks have closing costs which the homeowner must absorb upfront in order to obtain a new mortgage. The decision to refinance depends upon several factors including the level of closing costs, the amount of time the homeowner plans to hold the mortgage, and the difference in interest rates. 

Consider the following situation: Mr. Johnson obtained a 30 year fixed rate mortgage on January 1st, 1995 with the following characteristics:

Loan Amount = $300,000

APR = 100 (12) = 10.2%

Monthly Payment = $2,677.16

The first payment was made on February 1,1995.

In 2001, Mr. Johnson was faced with a refinance decision. He could obtain a 30 year fixed rate mortgage at an APR of 8.70%. His house was appraised at $600,000 in 1998 and he could have any loan amount up to 80% of the value of his property. The closing cost schedule is as follows:

Origination Fee = 3% of LOAN AMOUNT

Attorney's Fee = $500

Miscellaneous Costs = $1,000

1. Suppose that Mr. Johnson refinances his remaining loan balance on June 14, 2001 (just after making the June 1st payment on his existing mortgage). Compute his closing costs and his new monthly payment beginning on July 15, 2001, assuming that he pays his closing costs up front on June 14, 2001.

2. Compute the APR and the effective annual interest rate which actually apply on this refinance option taking into consideration the closing costs.

3. Suppose that Mr. Johnson refinances his remaining loan balance on June 14, 2001 (just after making the Jure 15 payment on his existing mortgage). Compute his new monthly payment beginning on July 1, 2001, assuming that he finances his closing costs over the life of the mortgage. By asking this

4. Suppose that Mr. Johnson refinances his mortgage but decides to keep his monthly payment at the same level as before, namely $2,677.16. Compute the loan amount and the amount of cash Mr. Johnson will receive from the bank.

5. Suppose Mr. Johnson decides to refinance the remaining loan balance on June 1, 2001. Compute the present value of the amount of savings Mr. Johnson will receive over the life of the mortgage. (Use i(12) = .087).

6. Suppose Mr. Johnson plans to sell his house in 2 years (on June 14, 2003).

a) Compute the present value of his obligations if he decides to refinance on June 1st, 2001 (use i(12) = .087).

b) Compute the present value of his obligations if he decides not to refinance (use i(12) = .087)

c) Should he refinance?

7. Repeat problem 6 if Mr. Johnson plans to sell his house in 1 year. Answer 6a, 6b, and 6c under this scenario.

8. If Mr. Johnson plans to sell his house in X months, he would be indifferent between refinancing on June 1, 2001 or holding his current mortgage. Determine the value of X to the nearest month.