## Thursday, May 16, 2013

### An exotic mortgage.

An exotic mortgage

This post was motivated by a paper on shared appreciation mortgages that I am scheduled to present at the 5-31-13 AREUEA meetings in Washington DC.

Situation:

You are purchasing a home worth \$200,000.  You are given two mortgage options.  Option one is a \$180,000 30-year fixed rate mortgage with a 5.0% interest rate.  Option two involves a smaller \$140,000 30-year fixed rate mortgage also with a 5.0% interest rate.  Under option two, the additional \$40,000 is raised from a third-party investor.  The private investor is promised the return of \$40,000 plus 40% of the capital gain on the home.

The house is sold after seven years.  The average annual growth rate in the house price over the seven-year period was 4.0%.

Questions:

• What are the monthly mortgage payments under the two options?
• What is the value of the home, the amount owed on the property, and house equity after seven years?
• The reduced mortgage payments obtained from selecting option two over option one are invested in the stock market.   What rate of return on stocks would result in an identical return for the two financing options?

• The payment on the mortgages is calculated with the PMT function in Excel. For the \$180,000 FRM we have PMT(0.05/12,360, \$180,000) -- \$966.  For the \$140,000 FRM we have PMT(0.05/12,360,\$140,000) or \$752.

• The house price after 7 years is \$200,000 x (1.03)7 or \$263,186.

• The amount owed from the \$180,000 mortgage on the first financing option is obtained from the FV value in Excel.   The future value of the mortgage is FV(0.05/12,84,\$966, \$180,000)=\$158,301.    There is no SAM so this is total housing debt.  The house equity is \$263,186-\$158,301 or \$104,885.

• The amount owed from the \$140,000 mortgage is \$123,123.  This is obtained from the FV function FV(0.05/12,84,\$752,\$140,000).  The amount owed on the SAM is \$65,275 (\$40,0000+.40 x (\$263,186-\$200,000))    The total owed from the mortgage and SAM is \$188,398.  House equity is \$74,789 (\$263,186-\$188,398)

 House Equity from Two Mortgage Arrangements Option 1 2 Interest rate 0.05 0.05 Term 360 360 Loan \$180,000 \$140,000 SAM \$0 \$40,000 Holding period (years) 7 7 Monthly Payment (\$966) (\$752) Value of Home \$263,186 \$263,186 Amount owed on mortgage (\$158,301) (\$123,123) Amount owed on SAM NA (\$65,275) Total Owed (\$158,301) (\$188,398) House Equity \$104,885 \$74,789

• The mortgage payment for the SAM/FRM combination is \$215 lower than the mortgage for the FRM.   House equity is \$30,097 higher under option 1, the standard FRM with no SAM.  In order for a person to invest \$215 per month and end up with \$30,097 the person must earn an average annual rate of 13.78%.  Observe that 12*RATE(84,-\$215,\$0,\$30097)=13.78

Check this answer by placing 13.78 into the FV function and getting a final value of \$30,096.

 Analysis of returns Monthly mortgage savings from SAMS \$215 Future value of annuity needed to bread even \$30,097 Return needed to break even 13.78% Check (\$30,096.54)

The primary focus of my paper is on how SAMS affect household wealth.  I find that the gains to borrowers are small when house prices are low.   The loss to homebuyers is large when house price increases are large.  Household savings is the second most important component of retirement saving.  The use of SAMS would erode wealth available for retirement.

My paper should be available on the AREUEA web site soon.  I will update this post when it is available.