## Wednesday, November 20, 2013

### The mortgage choice and taxes

This math problem in this post attempts to provide some insight into how the deductibility of mortgage interest on federal and state income taxes impacts the mortgage choice decision.

Question:  Consider a person with a combined federal and state marginal tax rate of 50%, a reasonable assumption for a high-income person in California.   Assume current rates of 4.35% for a 30-year fixed rate mortgage (FRM) and 3.35% for a 15-year FRM.  Rates are from the November 14 Primary Mortgage Market Survey published by Freddie Mac.

Analysis:  I am assuming a 15-year holding period and zero capital gains.  (Zero capital gains on a residential real estate purchase means the project is not profitable.  However, since the capital gain is independent of mortgage choice it does not affect the ranking of the financing options.)

Below are my financial comparisons:

Cumulative Interest Payments:

The cumulative interest payment over a 15-year period is \$108,969 for the 30-year FRM and \$82,071 for the 15-year FRM.  The after-tax interest payments are \$54,484 for the 30-year FRM and \$41,036 for the 15-year FRM.

Monthly Mortgage Payments:

The 30-year FRM comes with a monthly payment of \$1,493.  The 15-year FRM comes with a monthly payment of \$2,123.

Future Value of the Loan and House Equity After 15-Years:

After 15 years, the 30 year loan has an outstanding balance of \$197,000  and house equity of \$103,000 compared to an outstanding balance of \$0 and house equity of \$300,000 for the 15-year FRM.

The Internal Rate of Return (IRR) and the Net Present Value (NPV) of Cash Flows:

(Again, statistics are based on a 15-year holding period and 0 capital gains.  The capital gains assumption does not affect ranking of financing options.)

The IRR is -9.1% for the 30-year FRM and -1.8% for the 15-year FRM.

The NPV at a 5.0% cost of funds is -\$80,000 for the 30-year FRM and \$-95,000 for the 15-year FRM.

Concluding Thoughts:  What is preferable a 15-year FRM at 3.35% or a 30-year FRM at 4.35%???

The payment on the 15-year loan is a lot higher than the payment on the 30-year FRM.

The interest saved over 15-years after accounting for taxes is relatively small.   I also don’t consider tax issues as the primary factor, at least at low interest rates.  A future post will run the numbers at higher interest rates.

The difference in the build up in house equity is a primary concern.  The 15-year FRM is completely paid off after 15 years.  (this is of course a truism.)  By contrast, only around 1/3 of the loan balance for the 30-year FRM is paid off after 15 years.

The bottom line from the IRR analysis is that a 15-year FRM is better project than the 30-year FRM.  However, a person with a higher cost of capital due to other debts can maximize net present value by taking the 30-year FRM.

Summary Statistics Below:

 30-year FRM 15-year FRM Interest Rate Annual 4.35% 3.35% Interest rate Monthly 0.0036 0.0028 Term Months 360 180 Holding Period 180 180 Loan Amount \$300,000 \$300,000 Beginning period 1 1 ending Period 180 180 payment date in month 0 0 Cumulative Interest Paid -\$108,969 -\$82,071 Marginal Tax Rate 0.50 0.50 After-Tax Cost of Interest Payments -\$54,484 -\$41,036 monthly payment -\$1,493 -\$2,123 future value of loan -\$197,192 \$0 House Equity \$102,808 \$300,000 IRR -9.1 -1.8 NPV at 5.0% -\$80,670 -\$95,011

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