## Wednesday, May 29, 2013

### NPV analysis of the shared appreciation mortgage contract

NPV analysis of the shared appreciation mortgage contract

My presentation on the shared appreciation mortgage is on Friday.  I will start writing on new topics soon.

Question:  A homebuyer gives an investor a share of the future capital gain on his property and receives a \$180 decrease per month in his mortgage payment.  The foregone capital gain from this transaction ranges from \$40,000 to \$240,000.   The homebuyer holds the property for 30 years and then sells.  On the basis of the net present value determine when it is best for the homebuyer to enter the gain-sharing contract with the investor.

When will this homebuyer choose to enter the contract with the investor if his cost of capital is 5.0%?  When will the homebuyer enter the contract with the investor if his cost of capital is 10.0%?

Comment on the limitations of the use of net present value analysis on the mortgage choice problem.

Analysis:  Solve the problem by taking the net present value of cash flows.  As stipulated, the savings in mortgage payments by entering the contract with the investor is \$180 per month.  The foregone capital gain depends on the house price after 30 years, which varies from \$40,000 to \$240,000.

(Note the NPV function in Excel treats the PMT variable as an outflow of cash.  In this problem \$180 is an inflow of cash.  You must use -\$180 as an input for PMT.)

The shared appreciation contract makes sense when house prices remain low.  The shared appreciation contract should be accepted over the conventional financing decision if the NPV is positive.

At a 5.0% capital gain the cutoff between positive and negative NPV is somewhere between \$120,000 and \$160,000.  The gain sharing arrangement should be accepted if housing prices remain lower than \$153,000 or so.

At a 10.0% cost of capital the present value of the cash flows is always positive.  This suggests that for the given range of inflows and outflows the gain sharing arrangement should always be accepted.

This result is unusual and counter-intuitive given that most people finance their homes with a conventional 30-year FRM with no gain sharing arrangement.

One problem with putting people in a gain sharing contract based on this analysis is that it is possible that their cost of capital can change.  They may be better off waiting a few years to purchase their home when their cost of capital is lower.

A second problem with this method is that it does not consider the investor’s entire portfolio.  An investor who give up a share of his house to outside investors may have to accept greater risk on other investments in order to recoup lost wealth.

There are also other problems with the gain sharing arrangement discussed in my presentation.   The gain sharing arrangement can result in large losses to homebuyers when house price increases are robust.  Also, mortgage contracts with a gain sharing arrangement are often difficult to refinance when interest rates fall.

 Cost of capital 5.0% Lower mortgage payment \$180 \$180 \$180 \$180 \$180 \$180 Decrease in house equity \$40,000 \$80,000 \$120,000 \$160,000 \$200,000 \$240,000 PV of cash flows \$24,578 \$15,625 \$6,671 (\$2,282) (\$11,235) (\$20,188) Cost of Capital 10.0% Lower mortgage payment \$180 \$180 \$180 \$180 \$180 \$180 Decrease in house equity \$40,000 \$80,000 \$120,000 \$160,000 \$200,000 \$240,000 PV of cash flows \$18,495 \$16,478 \$14,462 \$12,446 \$10,429 \$8,413