Step 6: Considering Present Value
Compare Two Mortgages Using PV (Type 2)

Let us now consider an early termination to the loan from the previous step (Step 5) from the previous page.

So click here for COMPARE TWO MORTGAGES USING PV (Type 2). The default balances for the both the new loan and old loan are $100,000. The default "Mortgage Terms" for both loans is 30 years. The default rate for the new loan is 4.125% and the default rate for the old is 5.125%. The discount rate field has a default value of 5.125% and the "costs to close the loan" field has a default value of $2,500. The default value for "How Long Do You Expect To Live In The Home?" is 30, however change this to 8.

Generating the results will show 1) a difference in the rates of 1.00%, 2) a difference in the monthly payment of $59.84, 3) a difference in total interest payments over the life of the two loans of $7,841, 4) a difference in total payments (principal & interest) over the life of the two loans of $7,841, 5) a present value of $6,131, 6) a cost to refinance of $2,500, and 7) a net of $3,631. The schedule at the bottom will display the details relating to the differences in the annual payments and the present value of each of those differences.

Please note the following important assumptions:

1) Closing costs of the loan, which would include lawyer's fees, title insurance, loan application fees, appraisal fees and any other fees associated with closing and processing the loan.

2) In determining a discount rate we assume a flat yield curve. It would be much too complex to construct a yield curve using current treasury prices by applying a process referred to as cubic splining and then subsequently discounting the difference in the cash flows between the two mortgages using the various rates along the curve that coincide with the various cash flows. It is deemed sufficient for consumer purposes to assume a flat yield curve. If you are the average consumer and you read the above paragraph then your head is probably spinning, but if you are a professional trader of bonds then you have probably interpreted what I wrote.

This is a great little analysis. It is 1) clean, 2) straight forward, and 3) relatively easy to interpret.

However there are some limitations to this type of mortgage calculator; i.e.1) no ability to adjust for a loan which may have already begun amortizing.

The difference between the results in Step 5 and in Step 6 ($8,636 - $3,631) or $5,005 represents the lost opportunity benefit for closing out the loan early in the 8th year rather then holding the loan until maturity.

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