## Wednesday, September 18, 2019

### Modeling House Equity Growth Over Multiple House Purchases

Abstract:   This post shows how to model house equity accumulation over a lifetime for different mortgage choices.   We consider a person who purchases two homes over 25 years, staying in the first home for 10 years and the second home for 15 years.  Two mortgage scenarios are considered.  The first scenario involves two 30-year mortgages.   The second scenario involves two 15-year mortgages.

Question:   How does the choice between a 30-year and 15-year mortgage impact house equity and lifetime debt payments for multiple house purchases?

The Specific Problem:   Our example involves a person purchasing two houses over twenty-five years.   The buyer stays in the first house for 10 years and the second house for 15 years.

The first house costs \$250,000 with the buyer taking out a 90 percent LTV loan.

The second house costs \$500,000 with the buyer placing all funds from the sale of the first house as a down payment on the second house.   The house appreciates at an average annual rate of 1 percent per year.   The seller of the first house pays a 6 percent commission.

The home buyer considers two financing options.   The first financing option involves two 30-year fixed rate mortgage at 3.8 percent.  The second option involves two 15-year fixed rate mortgages at 3.3 percent.   Typically, the interest rate on a 30-year FRM is higher than the interest rate on a 15-year FRM; although, rate levels and the differential between 30-year and 15-year mortgage rates can vary.  The interest rates used in this example are similar to rates currently available in the market.

How do the financing options impact monthly debt payments, lifetime debt payments and accumulated house equity?

Analysis:

The lifetime debt payment calculations and the accumulated mortgage calculations for the two financing scenarios are presented in the table below.

 Two Lifetime House Financing Scenarios Scenario One Two 30-year FRM Scenario Two Two 15-year  FRM House One Purchase Price \$250,000 \$250,000 LTV 0.9 0.9 Loan House One \$225,000 \$225,000 Interest Rate First House 0.038 0.033 Term 30 15 Payment (\$1,048) (\$1,586) Years in House 10 10 Total House Payments for first House (\$125,808) (\$190,377) Appreciation Rate for First Home 0.01 0.01 Value of First Home on Sale Date \$276,156 \$276,156 Mortgage Balance on Sale Date (\$176,056) (\$87,640) Sale Commission 0.06 0.06 House Equity from the Sale of First House \$83,530 \$171,947 Down Payment of Second Home \$83,530 \$171,947 Value of Second Home \$500,000 \$500,000 Mortgage on Second Home \$416,470 \$328,053 Interest Rate on. Second Home 0.038 0.033 Term (Years) 30 15 Payment (\$1,941) (\$2,313) Years in Home 15 15 Total Payments for Second Home (\$349,303) (\$416,360) Total Payment on Both Homes (\$475,112) (\$606,737) Appreciation Rate for Second Home 0.01 0.01 Value of Second Home at end of period \$580,484 \$580,484 Mortgage Balance on Second Home at end of period (\$265,939) \$0

Major Differences Between the Two Financing Scenarios:

·      The person who uses two 15-year FRM has a \$0 mortgage balance at the end of 25 years after staying in his second home for 15 years.   The person employing two 30-year fixed rate mortgages has 15 years of mortgage payments remaining and an outstanding mortgage balance of nearly \$266,000.

·      The person using the two-15-year FRM paid around \$132,000 more in mortgage payments over the 25-year period.  However, the person using 30-year mortgages must either sell the home or continue making payments.   The mortgage is not scheduled to be repaid for 15 more years.

·      The monthly payments on the two 15-year loans are higher than the monthly payments on the two 30-year loans.  The differential is 34 percent for the first home purchase compared to 16 percent for the second home purchase.   The smaller differential in monthly mortgage payments occurs because of the larger accumulation of equity and the larger down payment stemming from the use of the 15-year mortgage.

Comment on Pros and Cons for the Two Financial Scenarios:

Pros associated with use of two 15-year FRM:

·      The advantage of using the two 15-year FRMs is that a home is completely paid for after 25 years.  The person using this strategy can now increase his savings in financial assets if still employed.  The person does not have to disburse funds from a 401(k) plan to pay down a mortgage during retirement.

Cons Associated with use of two 15-year FRMs:

·      The person using two 15-year FRMs makes larger mortgage payments and will probably have to reduce investments in liquid assets to make the larger mortgage payments.

Pros of use of 30-year FRMs:

·      The lower mortgage payments allow this homebuyer to make larger investments in financial assets.

Cons of use of 30-year FRMS:

·      The person after 25 years still has a large mortgage payment.  This reduce future savings in financial assets if the person is still working

·      Additional payments from 401(k) plans to pay down the mortgage are fully taxed as ordinary income. Hence, the person who retires with a 401(k) balance because of the use of 30-year FRMs will have larger tax obligations.

Caveats on this Analysis  The potential gain from different mortgage arrangements depends on holding periods for each home, the number of homes purchased during a lifetime, and interest rates.  We look at two different mortgage arrangement for only one scenario.   Results presented for different assumptions on house purchases and interest rates will differ from the results presented here.

Final Question:   Is it better to increase house equity and totally eliminate mortgage debt or should one stay in 30-year mortgages and increase investment in financial assets?  This question is not addressed in this post.  The breakeven point for holding debt must account for taxes when assets are invested in a conventional 401(k) plan because all disbursements from 401(k) plans are taxed as ordinary income.  The desire to avoid financial risk would also favor the mortgage elimination option.

Certainly, if you are planning to stay in your home after you retire you are exposed to a lot of financial risk if you keep a large mortgage and a large share of your financial assets are equity tied up in a 401(k) plan.  The topic presented here is related to the issue of to what extent investors should prioritize 401(k) saving over other financial priorities.  Go here for a discussion of this topic.

Six Reasons 401(k) plans should not be your top priority