A Closed-Form,After-Tax,Net Present Value Solution to the Mortgage Refinancing Decision

Refinancing one's mortgage is often an attractive, wealth-enhancing option for homeowners in a declining mortgage rate environment. In some respects the decision is simple to analyze because future cash flows are relatively easy to define for fixed-rate mortgages. In other respects, however, the decision is nuanced by option pricing and tax considerations. The analysis must first begin with accurate after-tax, net present value solutions for varying potential holding periods. This study improves upon previous studies, which either ignore tax implications or address them iteratively in spreadsheet model solutions, by introducing a closed-form model that incorporates the ever-changing tax shield of the interest portion of each mortgage payment. Further, unlike many previous studies, our model does not assume that the current and replacement mortgages have equal remaining terms.