The test is filled with secrets and uncertainties, but the grading is simple: You either pass or fail. Pass, and you are offered a mortgage modification. Fail, and you don’t get a loan modification. NPV, which stands for net present value, is a concept used in making financial choices. “It’s a way for financial people to express a decision in today’s dollars,” says Brent Lippman, CEO of Response Analytics, a financial modeling company.

Mortgage servicers use an NPV test to decide which action is more profitable (or less unprofitable) in the long run:

•Modifying the loan and accepting lower monthly payments.

•Not modifying the mortgage and possibly tipping the borrower into foreclosure.

For the homeowner, the decision seems like a no-brainer: Modify the mortgage so it’s affordable and the loan won’t go into foreclosure. But a lot of modified mortgages wind up in default again, despite the borrowers’ intentions. So the net present value formula includes an estimate for the likelihood that the mortgage will redefault — that is, that it will end up in foreclosure, anyway, even after a modification.

Besides the redefault rate, the NPV calculation makes guesses about several things:

•How many months are likely to pass, on average, before a redefault.

•How likely the borrower is to catch up on the payments if the loan isn’t modified (the “self-cure rate”).

•How much the home is worth now.

•How much the home will be worth a year from now.

•How much it would cost — from legal fees to utilities — to foreclose and take possession of the house.

•How much the house would fetch in a foreclosure sale, using a formula that the government calls the REO discount.

For two of those items — the home’s projected value in a year and the REO discount — the servicer must use formulas crafted by the federal agency that oversees Fannie Mae and Freddie Mac. The servicer assigns its own values and probabilities to the other items. (REO stands for real estate owned, which is how a property is identified after it goes back to a mortgage company.)

These numbers are secret. They’re unavailable to borrowers. If you want to know your home’s estimated value a year from now, or the odds that you’ll redefault, no one will tell you.