(This is Part 2 of a two-part series. Read Part 1, “Too much equity can deny homeowners loan mods.”)

The first article in this series pointed out that when a mortgage borrower is unable to make the required payments, the servicing agent has an obligation to the owner of the mortgage to resolve the problem in the way that is least costly to the owner. The usual method is foreclosure, but an alternative is to modify the loan contract to make the payment more affordable.

In making their decisions, loan servicers usually ignore an asset possessed by the borrower that could shift it from foreclosure to modification. This asset is the right to a share of the future appreciation in the value of the borrower’s house.

To make the decision process easier, I have designed a new calculator, numbered 7e on my Web site. The calculator compares the cost of a subsidy provided under a contract modification to the estimated value of a share of the appreciation, over any future period up to 10 years. Because costs are incurred monthly while appreciation is realized at the end of a period, all figures are translated into present values to make them comparable.

For example, in 2005, John Subprime took out a 2-year adjustable-rate mortgage for $100,000 at 5 percent. It was a 100 percent loan, but the balance had been paid down to $97,237. The initial payment of $537 was affordable, but lasts only two years.

The interest rate will be reset in two months to equal the value of the rate index, currently 5 percent, plus a margin of 3 percent. If the index stays where it is now, the rate will go to 8 percent, and the payment to $724. John cannot afford this payment.

Using the formula developed in the first article of this series, John convinces the servicer that he can afford no more than $580 a month for the next three years. The modification keeps the rate at 5 percent and adjusts the payment to $580. Over three years, the difference between the affordable payment and the scheduled payments with an 8 percent rate sums to $5,190, which at 6 percent has a present value of $4,337. This is the cost of the payment subsidy to the owner of the mortgage.

In addition to the payment subsidy, there is a balance subsidy because keeping the loan at 5 percent allows a more rapid pay-down of the balance. The subsidy is equal to the difference between what the balance would have been at the end of the contract period had there been no modification, and what it will be with the modification.

Over the three years, the balance subsidy amounts to $3,670 with a present value of $3,067. The present value of the payment and balance subsidies combined is $7,404. This is the cost of contract modification to the investor without an offset from appreciation.

The net cost of foreclosure to the investor is the estimated expense of foreclosure less the equity in the borrower’s house, which is available to offset foreclosure expenses. Equity is the difference between the estimated proceeds from a foreclosure sale and the mortgage balance.

If net foreclosure costs in my example are $5,000, this is lower than the $7,404 cost of modification, and the servicer will opt for foreclosure. But factoring a share of future appreciation into the equation can change the result.

Suppose the servicer estimates that John’s house may increase in value by 2 percent, 3 percent and 4 percent over the next three years. On these assumptions, the appreciation will be $9,262, with a present value of $7,740. Using this number, a 50 percent share of the appreciation would reduce the net cost of modification to $3,534, which is lower than the cost of foreclosure.

Borrowers with payment problems who have a lot of equity in their homes have the most to gain from pledging a share in future appreciation. Such borrowers are otherwise unlikely to qualify for a contract modification because foreclosure will be less costly to the investor.

Borrowers in trouble, however, can’t assume that the servicer will take the initiative in proposing any modification deal, let alone a more complex variety that includes a pledge of future appreciation. The culture of loan servicing discourages such initiatives because they raise costs and do not generate any additional revenue.

Troubled borrowers with the best chances of negotiating a contract modification are those who are persistent and who provide the information required to support their case. If they have significant equity in their home, this should include a proposal to share future appreciation with the investor, including reasonable estimates of what that might be worth. The more of the servicer’s job they do, the better their chances of success.

The writer is professor of finance emeritus at the Wharton School of the University of Pennsylvania. Comments and questions can be left at www.mtgprofessor.com.

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