Assumable Financing Redux: A New Challenge for Appraisal?

Abstract

Given the long term secular decline in interest rates, assumable financing has been of little concern for decades. But given both the growth of loans insured by the Federal Housing Administration (“FHA”) and recent increase in interest rates, this situation is likely to change very soon. Using data from California, we first document the dramatic increase in FHA-insured loans since 2007. We then derive the theoretical impact of capitalizing assumable financing into house prices as interest rates increase and simulate the effect on prices of homes sold with assumable FHA financing. Results are economically significant and likely to partially offset declines in house prices associated with higher mortgage rates. Findings imply that appraisers will need to adjust comparable sales to reflect FHA loan assumptions.

Appendices

Appendix 1

Proof

Suppose that an assumable loan has only one year term and annual payment, the payment of borrowing $1 assumable loan can thus be calculated as,

$$ PMT=\left(1+{i}_A\right) $$

(23)

If current interest rate becomes i_C, the present value of this assumable loan’s payment (PMT) becomes.

$$ PV=\frac{\left(1+{i}_A\right)}{1+{i}_C} $$

(24)

Therefore, the extent of the capitalization of one dollar of the assumable mortgage into the sales price on a before-tax basis can be expressed as:

$$ DP{V}_{BT}=1- PV=\frac{\left(1+{i}_C\right)-\left(1+{i}_A\right)}{\left(1+{i}_C\right)} $$

(25)

Equation (25) is exactly the same as Eq. (1). We can further show that Eq. (1) holds only when the assumable loan has only one year term with one annual payment.

Appendix 2

The tax rate of the home buyer will affect the home price premium because interest payments in U.S. are generally tax-deductible, particularly for higher income households. Generally speaking, a higher mortgage rate implies higher interest payments and thus greater tax-savings from the interest deduction. In other words, the home price premium should be higher as the marginal tax rate decreases. Two additional equations illustrate the relationships.

Suppose that pmt is denoted as the monthly payment for the remaining loan balance (Bal_t) at the higher market rate r_t. From Eq. (5), we thus have,

$$ \sum \limits_{n=1}^{N-t}\frac{pmt}{{\left(1+{r}_t\right)}^n}= Ba{l}_t=\sum \limits_{n=1}^{N-t}\frac{PMT}{{\left(1+{r}_0\right)}^n} $$

(26)

Since r_t > r₀, we have pmt > PMT. We can thus express the price premium for the FHA assumable mortgage on an after-tax basis as follows,

$$ \Pr emiu{m}_{\mathrm{t}}^{\mathrm{t}\mathrm{ax}}=\sum \limits_{n=1}^{N-t}\left(\frac{pmt-{\mathrm{interest}}_n\ast tax}{{\left(1+{r}_t\right)}^n}\right)-\sum \limits_{n=1}^{N-t}\left(\frac{PMT-{\mathrm{INTEREST}}_n\ast tax}{{\left(1+{r}_t\right)}^n}\right) $$

(27)

where tax is buyer’s marginal tax rate, interest_n and INTEREST_n are the portion of interest payments at time n for pmt and PMT, respectively.