BUSI 422 Week 3 Group Wiki Scenario 1 Example

Refinance, Re-Amortize or Switch to an ARM? A Group Analysis of One Household's Mortgage Decision

The Scenario and the Question

Our clients, a married couple, bought their home in 2023 with a 30-year fixed-rate mortgage at 7.25 percent. They now owe $320,000, with 27 years remaining. A lender offers three options, each with closing costs of $6,400, or 2 percent of the balance: a new 30-year fixed loan at 6.0 percent; a 27-year fixed loan at 6.0 percent, which keeps their payoff date; and a 5/6 adjustable-rate mortgage at an initial 5.5 percent, fixed for five years and then adjusting every six months. The couple expect to stay in the home about seven years, but are not certain. Their incomes are stable, one in public education and one in health care. The question is which option, if any, they should choose.

Comparing the Options

All payments below cover principal and interest only, computed with the standard mortgage payment formula.

The 30-year loan shows a larger saving, but part of that saving comes from adding three years of payments, not from the lower rate. The 27-year option isolates the benefit of the rate itself. Comparing balances makes the difference clear: after five years the current loan would have a balance of about $296,935, while the 27-year refinance would stand at about $292,319, and after seven years the figures are about $285,107 and $278,708. Refinancing at the same term both lowers the payment by about $257 a month and builds equity faster, so it wins on both measures rather than trading one for the other.

When Refinancing Pays

A simple break-even calculation ignores the option value of waiting, since rates might fall further. Agarwal et al. (2013) derived a closed-form rule for the optimal refinancing threshold that accounts for this option, for closing costs, for the borrower's tax rate and for the chance of moving. Under typical assumptions, their rule calls for a rate drop of well over one percentage point for modest loan sizes, with the threshold falling as the balance grows. A 1.25-point drop on a $320,000 balance with a seven-year expected stay clears that hurdle.

The research also warns that households often fail to act. Keys et al. (2016) studied U.S. borrowers in December 2010 who were in a position to refinance profitably and found that about 20 percent had not done so, with the median household leaving behind savings of roughly $11,500 in present value. Inattention, distrust of lenders and the hassle of paperwork appear to explain much of this. For our clients, the lesson is that waiting for a slightly better rate carries its own cost if it becomes not deciding at all.

The Adjustable-Rate Option

The 5/6 ARM has the lowest initial payment and the fastest break-even. Its risk is what happens after five years if rates rise, since payments then adjust every six months within the loan's caps. Campbell and Cocco (2003) modeled household mortgage choice and found that adjustable-rate loans are generally attractive, but less so for households that are risk averse, carry large mortgages relative to income, have uncertain income or expect to stay in the home a long time. Our clients' incomes are stable, which favors the ARM, but they may stay beyond five years and their mortgage is large relative to income, which weighs against it. If they do stay seven years, two years of adjusted payments are exposed to whatever rates prevail in 2030 and 2031.

Recommendation

The group recommends the 27-year fixed-rate refinance. It lowers the monthly payment by about $257, recovers its closing costs in about two years, reduces the balance faster than the current loan and keeps the original payoff date, all without exposing the couple to rate resets. The 30-year option would be reasonable only if the couple needed the lower payment for cash flow, and the ARM only if they were confident of moving within five years. We also recommend that the couple not let the decision slip: as Keys et al. (2016) show, the costliest refinancing choice is often no choice.

Group Contributions

One member built the payment and balance calculations in Excel, a second located and summarized the research, a third drafted the analysis and recommendation, and all three revised the page in the wiki, with comments resolving a disagreement over whether to include the 30-year option.

References

Agarwal, S., Driscoll, J. C., & Laibson, D. I. (2013). Optimal mortgage refinancing: A closed-form solution. Journal of Money, Credit and Banking, 45(4), 591-622. https://doi.org/10.1111/jmcb.12017

Campbell, J. Y., & Cocco, J. F. (2003). Household risk management and optimal mortgage choice. The Quarterly Journal of Economics, 118(4), 1449-1494. https://doi.org/10.1162/003355303322552847

Keys, B. J., Pope, D. G., & Pope, J. C. (2016). Failure to refinance. Journal of Financial Economics, 122(3), 482-499. https://doi.org/10.1016/j.jfineco.2016.01.031