How to Compare Mortgage Refinancing Options

Comparing mortgage refinance options with varying terms is a unique mathematical challenge, and also one that consumers face often in a declining rate environment. Typically, borrowers must choose between a new 15- or 30-year fixed-rate mortgage, neither of which match the remaining duration of their current mortgage. While the interest rate may be lower on both options, a full analysis goes well beyond determining which mortgage has the lowest rate, or how much the borrower may save in total interest payments. Instead, one must determine which refinancing choice has the highest expected value to the borrower in today’s dollars. Why in today’s dollars? Because closing costs are paid with today’s dollars. Only by comparing the present value of refinancing to anticipated closing costs can the borrower answer the crucial question “Does it make sense to refinance at all?”

Consider the following example of a step-by-step approach to determine which mortgage refinancing option has the highest Net Present Value (NPV):

A borrower has a 30-year fixed mortgage at 4.25%, a balance of $355,247, and 24 years remaining. The scheduled monthly payment (principal + interest) is $1,965.79.

There are two refinancing options: a new 30-year fixed rate at 3.625% and a new 15-year fixed at 3.375%. For simplicity, ignore any “points” paid to obtain the new mortgage and assume that the borrower retains each mortgage option for the full duration.

Both options will save the borrower money, and the 15-year fixed should save even more because the interest rate is 0.25% lower. But exactly how much better is the 15-year than the 30-year in today’s dollars? Because the maturities are different, you can’t just compare total interest payments.

A mortgage refinance changes the stream of monthly payments and the future outstanding balances at any point in time. You must account for both differences using a discounted cash flow analysis.

Step 1: Using the full amortization schedule, determine the balance of the 30-year mortgage at the point when the current mortgage is paid off. Calculate the present value of that future balance by discounting it back to today at the refinance rate of 3.625%.

The balance of the new 30-year fixed option at the point the original mortgage is paid off in 24 years will be $103,389. The present value of $103,389 today at 3.625% is $43,597. This is a net negative to the borrower, relative to their current mortgage, because they’ll still have a balance left in 24 years.

Step 2: Calculate the Net Present Value of the difference in payments throughout the duration of the original (current) mortgage.

Current monthly payments are $1,965.79 vs. $1,620.11 on the new 30-year fixed option. Scheduled payments are therefore lower by $345.69 each month for the next 24 years. The NPV of this payment difference is worth $66,573 today at 3.625%. This is a net positive to the borrower, relative to the current mortgage, due to smaller monthly payments.

Step 3: Subtract the PV of the balance difference from the PV of the payment differences to calculate the net present value of refinancing.

The NPV of refinancing to the 30-year rate is therefore $66,573 - $43,597 = $22,976.

Note that total interest paid will actually be higher by approximately $15,100 on the new 30-year mortgage (because payments last six years longer), but the refinancing still has positive economic value.

Now you’ll perform the same three steps by comparing the current mortgage to the new 15-year fixed rate option.

Step 1: Again using the full amortization schedule, look up the future balance of the current mortgage in 15 years (when the 15-year fixed option would be paid off). This balance is expected to be $177,501 and the present value of that figure (this time using the 15-year rate of 3.375%) is $107,887. On that measurement, refinancing is a net positive to the borrower since the balance on the new mortgage will be zero in 15 years.

Step 2: The monthly payments on the new 15-year mortgage ($2,517.85) are notably higher than on the current mortgage ($1,965.79) since they are amortized over a much shorter timeframe. The difference is $552.05 per month, and the NPV of this payment differential is $77,890 at 3.375%. This time, the payment difference is a net negative to the borrower considering the 15-year refinancing option.

Step 3: Subtract the PV of the payment differences from the PV of the balance difference to calculate the net present value of refinancing on the 15-year option.

The NPV of refinancing to the 15-year rate is therefore $107,887 - $77,890 = $29,997.

With both NPVs in front of you, you can see that the 15-year refinancing option is worth $7,021 more in today’s dollars than the 30-year fixed. Both options should easily exceed closing costs, but if the borrower can afford the higher monthly payments, the 15-year fixed rate is the better choice.

Closing costs can be amortized over the life of the new loan, but they will still be expressed in today’s dollars. The method described above allows a direct “apples to apples” comparison of these costs to the present value of each refinancing option available to the borrower.

About the Author

Robert Fezekas, CFA, works as a financial advisor at Vickery Financial Services, Inc. in Athens, Georgia. Before joining Vickery, he worked as a portfolio manager for Dimensional Fund Advisors in Santa Monica, California, and as a securities analyst with the Principal Financial Group in Des Moines, Iowa. Robert has a BA in finance from the University of Iowa and an MBA from the University of Chicago Booth School of Business with concentrations in analytic finance, statistics, and economics. Robert is also a volunteer board member for the Athens Area Community Foundation. He writes a monthly investment blog at http://vickeryfinancial.com/resources/. Connect with Robert on LinkedIn.