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 highincome person in California. Assume current rates of 4.35% for a 30year fixed rate mortgage (FRM) and 3.35% for a 15year FRM. Rates are from the November 14 Primary Mortgage Market Survey published by Freddie Mac.
Evaluate the advantages and disadvantages of the two mortgage financing options.
Analysis: I am assuming a 15year 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 15year period is $108,969 for the 30year FRM and $82,071 for the 15year FRM. The aftertax interest payments are $54,484 for the 30year FRM and $41,036 for the 15year FRM.
Monthly Mortgage Payments:
The 30year FRM comes with a monthly payment of $1,493. The 15year FRM comes with a monthly payment of $2,123.
Future Value of the Loan and House Equity After 15Years:
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 15year FRM.
The Internal Rate of Return (IRR) and the Net Present Value (NPV) of Cash Flows:
(Again, statistics are based on a 15year holding period and 0 capital gains. The capital gains assumption does not affect ranking of financing options.)
The IRR is 9.1% for the 30year FRM and 1.8% for the 15year FRM.
The NPV at a 5.0% cost of funds is $80,000 for the 30year FRM and $95,000 for the 15year FRM.
Concluding Thoughts: What is preferable a 15year FRM at 3.35% or a 30year FRM at 4.35%???
The payment on the 15year loan is a lot higher than the payment on the 30year FRM.
The interest saved over 15years 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 15year 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 30year FRM is paid off after 15 years.
The bottom line from the IRR analysis is that a 15year FRM is better project than the 30year FRM. However, a person with a higher cost of capital due to other debts can maximize net present value by taking the 30year FRM.
Summary Statistics Below:
30year FRM  15year 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

AfterTax 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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