## Tuesday, June 11, 2019

### Mobility and lifetime house equity.

This post utilizes a housing equity calculator to estimate the impact of a move from one house to another on lifetime house equity.

Question   In this problem all houses are purchased with 15-year FRMs at an interest rate of 5.0%.  Also, all houses appreciate in value at a rate of 1.0% per year.    These assumptions can of course be altered in a spreadsheet.

At the beginning of a 15-year period two people purchase a \$300,000 house.   One person stays in the same house for all 15 years.   The other person buys a new house identical in value to the one he is currently living in after 7 years.

The sales commission on the first house is 6.0%.   In addition, closing costs on the new house are equal to 4.0% of the house price.

The second person lives in his second house for eight more years.

How much equity do the two people have after 15 years?

Answer:    The house equity calculation for the first homebuyer involves only one home.   The two-home house equity calculator used in the previous problem needs to be modified to include costs associated with sale of first home and purchase of the second home.

The results presented in the table below demonstrate the high cost of moving when all financing is done with 15-year mortgages.   The person who stays in the same house for 15 years has equity of \$348,291.    The person who moves to an identical house after 7 years has house equity of \$215,036.    The difference in house equity is \$133,255.

Note most of the difference in equity is due to the reduction in the payoff of the mortgage.  Only around 25% of the loss in house equity is due to the sales commission on the first house and the closing costs on the second house.  Nearly ¾ of the loss in house equity is due to a reduction in the pay off the mortgage.  (Mortgages pay off more rapidly near the end of their life.   Since Person B sells his first house he does not enter the rapid payoff period for his mortgage during the 15-year period.)

 The Potential Loss of House Equity From Moving Person A Lives in One Home for 15 Years Person B Lives in One Home for 7 Years and One Home for 8 Years Assumption Price of First House \$300,000 \$300,000 Assumption Mortgage LTV First House 0.90 0.90 Assumption Mortgage \$ First House \$270,000 \$270,000 Assumption Mortgage Term Years First House 15 15 Assumption Mortgage Interest Rate 0.05 0.05 Calculation Mortgage Payment First House -\$2,135 -\$2,135.14 Assumption Holding Period First Home 15 7 Calculation Mortgage At End of First Period Holding Period \$0 -\$168,653.73 Assumption Annual Appreciation First House 0.01 0.01 Calculation House Price At End of Holding Period First House \$348,291 \$321,641 Assumption Sales Commission on Old House and Closing Costs on New House 0.10 Calculation Loss of Equity due to Commission and Closing Costs 32,164.06 Calculation Available Equity First House \$120,823 Assumption Fraction Used for Down payment First House 1 Calculation Down payment Second House \$120,823 Assumption Price Second House \$321,641 Calculation Mortgage Second Home \$200,818 Assumption Mortgage Term Second Home 15 Assumption Mortgage Interest Rate Second Home 0.05 Calculation Mortgage Payment Second Home -\$1,588.06 Assumption Holding Period Second Home 8 Calculation Mortgage at End of Second Period Holding Period -\$112,357.98 Assumption Annual Appreciation Second House 0.01 Calculation House Price at End of Holding Period Second House \$348,291 Assumption Sales Commission 0.06 Calculation House Equity After 15 Years \$348,291 \$215,036

The loss in equity is smaller but still considerable when 30-year mortgages are used instead of 15-year mortgages.   This is so because equity accumulation under 30-year mortgage is very slow until the final years of the mortgage.

The decrease in the tax deduction of the mortgage interest for the person who entirely pays off their mortgage will offset part of the equity difference but the offset is relatively small.