Questions that come up in scenarios related to buying or refinancing a home:
- Is mortgage A better than mortgage B?
- Each mortgage may be amortized over a different duration (e.g., 15 vs. 30 years)
- Given that I'm part-way through mortgage C, should I refinance to mortgage D?
Setting aside the emotional aspects, there is almost always a clear answer based on the Net Present Value (NPV) calculation of the cashflows related to the principal, interest, and loan fees.
For question #1, the Loan Estimate document would include an APR value that can be the basis for a comparison if the loan durations being compared are identical. It's not immediately obvious how to use the APR to compare loans of different durations. Also, the APR cannot be used to answer question #2 related to a refinance.
Sometimes the total (undiscounted) cashflow of interest payments over the span of the loan is used for the comparison, but as you'll see below that may give you the wrong answer.
I've made available a Mortgage Comparison Template.ods file that implements the calculations referred to in this post.
Discount rate
For the NPV calculation you'll need an appropriate discount rate (aka, opportunity cost). This would be the expected gains on an investment that you'd funnel your cash into if you didn't have to pay the mortgage.
I use a conservative 7.1 %/year (nominal rate which includes inflation).
If your investments are more aggressive, then a nominal rate of 9-10 %/year may be a reasonable choice.
Buying a house
Inputs needed:
- Starting principal
- Interest rate (%/year)
- Amoritization duration (years)
- Amortization period (usually monthly; to wit 12 periods/year)
- Loan fees (origination fees, title/insurance/deed fees, recording fees, etc.)
- Do not include any escrow amounts for home insurance and/or property taxes as they are not pertinent to the cost-benefit analysis
Set-up your amortization table for each mortgage and then calculate:
Present value of the loan =
NPV of cashflows for principal +NPV of cashflows for interest +Loan fees
Choose the loan that has the lowest present value. That's it.
