"NPV Test: Failed."

That was the red-lettered verdict on the computer screen of a CitiMortgage negotiator in June. The result: An 83-year-old widow in Illinois was denied a loan modification through the Obama administration’s Making Home Affordable program, even though the employee admitted in an e-mail, "I am unable to come up with a reason for the denial."

The Net Present Value test is a complex computer model used by loan servicers to determine whether a homeowner qualifies for the federal loan modification program.  The test compares two scenarios – modification and foreclosure – and determines which would be more profitable for the lender. If it’s foreclosure, the lender has no obligation to modify the loan. But the model is a black box. What goes in isn’t entirely clear, and what comes out isn’t always reliable.

The Treasury Department has refused to release the exact formula for the NPV model, bringing criticism from homeowner advocates and industry experts. Cloaking the NPV formula in secrecy makes it difficult to identify any potential flaws in the design of the program, which has generated fewer modifications than anticipated. There are assumptions built into the model, and they may not be the right ones, said Diane Thompson of the National Consumer Law Center. "Someone needs to be able to review it."

In congressional testimony last Wednesday, Michael Barr, assistant secretary for financial institutions, said that the Treasury Department was taking steps toward "greater disclosure of the NPV evaluation." Full disclosure would bring the department in line with the Federal Deposit Insurance Corp., which made public the NPV formula (PDF) developed for its loan modification program, on which Making Home Affordable is based. In the meantime, a Treasury spokeswoman responded to all questions by pointing to an overview of the model (PDF) available online.

In it, the department says that the NPV is an "objective test" that standardizes the process for evaluating mortgages under the program.

In testimony to the Senate Banking Committee in July, Thompson said that homeowners and advocates need access to the model to determine whether loan servicers have used the test accurately — or at all. Without it, she said, "homeowners are entirely reliant on the servicer’s good faith."

She said that she had heard many anecdotal reports about servicers entering inaccurate information into the model. Because the results give little indication of which variable is to blame, there’s little recourse to challenge a lender’s refusal to modify. Nor is there an opportunity for the homeowner to correct the problem.

An additional concern is whether servicers are even using the test for all candidates. Irwin Trauss, supervising attorney at Philadelphia Legal Assistance, told a House Judiciary Committee panel in July about a homeowner who was denied a modification by Wells Fargo, even though "there was no suggestion that the NPV test … was even done." When his organization brought the case to Fannie Mae, Wells Fargo was "embarrassed into" reversing its decision, according to Trauss. Wells Fargo did not respond to a request for comment.

The lack of transparency is also vexing because certain variables in the formula – like home value, the estimated time it will take to foreclose, the risk of default and estimated foreclosure costs – are subjective and could be improperly assessed, industry experts say.

"It’s more art than science," said Guy Cecala, publisher of Inside Mortgage Finance. "Who knows whether the borrower will default, what the value of the property is, what will happen to home values," he said. "I’m skeptical of all of it."

"The valuation of a house is a very variable thing," Trauss said. "A real estate agent drives by and gets a price, but it’s fairly worthless and subject to being overstated or understated depending on the lender."

Nathan Reynolds, a mortgage broker assisting the 83-year-old Illinois homeowner with her loan modification on a pro bono basis, was given the rare chance by a CitiMortgage negotiator to see the actual numbers plugged into the NPV — and Reynolds insists that the company used an inflated home value. "They just pulled some bogus appraised value out of the air," he said.

Mark Rodgers, a CitiMortgage spokesman, did not respond to questions about the house value, saying only, "We are pleased to have identified a solution for this borrower." That solution is a modification requiring monthly payments that are about $900 less than she is paying now, but roughly $200 more than they would have been under the Making Home Affordable plan.

The purpose of the NPV test is to indicate to lenders how to make the most money off of a particular borrower. Ironically, homeowners who have more equity in their home may be at a disadvantage.

A "huge driver" of the test, according to Thompson, is the relationship between the current value of the home and the unpaid portion of the loan. If a house is worth more than the remaining mortgage balance, "there’s a benefit to the investor from foreclosing. It will recover the entire value of the loan if it forecloses, not if it modifies," she said. The impact of this variable, however, can be offset by other considerations, like the amount of time it will take to foreclose or the likelihood of foreclosure.

If the NPV test ultimately churns out a "negative" result, meaning the lender will make more money by denying the modification, the homeowner won’t get a Making Home Affordable modification unless the lender agrees to take a loss.

"Even though the administration is promoting loan modifications, they’re still operating from the premise that ‘we don’t want you to make loan modifications that aren’t going to make more money than a foreclosure,’" Cecala said. "This is very different from what community groups see as the (program’s) purpose."