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Hotel heiress Leona Helmsley owns a 20,000-square-foot mountaintop mansion in Paradise Valley, Ariz., with an underwater sound system in the pool and a movie projector and screen that drop from the dining-room ceiling. The house is on the market for $25 million, but the county has valued it for property-tax purposes at less than a third of that.

Kim and Barbara Bullerdick live in the same county in a 1,900-square-foot tract house for which they paid $201,000. But the county has valued their house at two-thirds of their purchase price.

Across the country, people who live in mega-mansions are paying proportionately less in property taxes than people who live in more modest houses. That’s because trophy properties are appreciating at a much faster rate than tract houses in the current real-estate boom, and tax assessments simply aren’t keeping pace. Indeed, even if Helmsley’s house proves to be worth only half her asking price, she’s still getting a huge break on property taxes.

“I’m not surprised,” says Mrs. Bullerdick, a homemaker and former accountant. “People with money and power set things up for themselves.”

In fact, Helmsley, who was convicted of federal income-tax evasion and is credited with the remark that “only little people pay taxes,” didn’t have any personal role in setting her property-tax bill. Maricopa County assessors base their estimates on comparable sales in the area, and there’s never been a house close to the price of Helmsley’s even in tony Paradise Valley.

Olivia Quist, Helmsley’s real estate agent, isn’t surprised by the huge gap between her client’s asking price and the county’s valuation.

“Most properties here are assessed at so much less than they’re worth,” she says. “And the discrepancy becomes bigger the higher you go.”

Theoretically, at least, property-tax laws in most states treat all residents equally by estimating a property’s market value and then using a formula to determine the assessed value, which is used to calculate the tax.

This works well for mass-produced housing, where market value tends to be obvious, improvements limited and appreciation predictable. In many cases, assessors don’t even need to visit a tract home to come up with a fair valuation. They use computer models instead.

But if a home is unusually large or customized, the computer models don’t always work. In Helmsley’s case, assessors factored in her 1988 purchase price of $6 million, plus news reports and permits that indicated she put in just under $2 million in improvements, resulting in a current estimated market value of $7.6 million.

Glenn Bonner, an assistant manager in the Maricopa County Assessor’s Office, acknowledges that the house would fetch millions more in today’s overheated market but says assessors rarely boost their estimates without an actual sale.

“You might say she’s been getting a free ride,” Bonner concedes.

In fact, an analysis of 1997 property tax records for five of America’s wealthiest counties, prepared for the Wall Street Journal, shows how wide the discrepancy can be.

Experian, a research firm in Anaheim Hills, Calif., determined that the gap between actual 1997 market values and their most recent assessed values was consistently greater for mansions than for ordinary houses.

In ritzy Fairfax County, Va., for example, the sales prices of homes costing $1 million or more averaged 71 percent higher than their assessed values. But the sales prices of smaller Fairfax homes (those that sold for less than $250,000) averaged just 8 percent higher than their assessed values.

In King County, Wash., home of Bill Gates and other techno-tycoons, the sales prices of $1 million-plus homes on average were nearly triple (171 percent) their assessed values, while the sales prices in the smaller-home category were just 35 percent higher than their assessed values.

Assessors miss the boat on high-end homes for a variety of reasons, including lack of resources and statutory limitations.

In Maricopa County, one chief assessor and 39 deputies are responsible for 760,000 residential parcels. Last year, the parcels that had to be assessed included 32,500 new homes.

The assessors cope by relying on a computer model, but the county’s Bonner concedes, “There’s probably a fallacy in our computer model. It’s good for cookie-cutter houses, but not for custom homes.”

Even if there were enough people, performing an eyeball appraisal of a custom property can be costly.

Annie Aubrey, spokeswoman for the International Association of Assessing Officers in Chicago, says that single-property appraisals cost around $250 apiece.

“Multiply that by 100,000 homes and that’s more than most city budgets,” she notes. Jim Hogan, chief deputy tax collector for Maricopa County, adds that the revenue from reassessing luxury homes isn’t always worth the cost.

In some areas, assessors don’t have much flexibility anyway. While there are localities that reassess houses every year, in California a law known as Proposition 13 caps the increase on annual assessments at 2 percent.

Upon sale, houses are reassessed at the purchase price. In other areas, houses are assessed less frequently, and not necessarily upon sale. In such circumstances, even if numerous mansions are selling at whopping prices, the increase in value won’t be reflected in tax assessments for years.

In Greenwich, Conn., for instance, houses are valued for tax purposes every 10 years, as well as when they undergo major renovations.

The last time Greenwich valued its houses was in 1992, during an economic downturn. Now, the town is booming. Currently, the average home price is more than $1.1 million, and sales prices are 13.5 percent higher this year than last, according to the Greenwich Record of Real Estate Sales. But even if a Greenwich house sells for millions more than its assessed value, it could take years for the new owner’s property-tax bill to reflect that.

Ivana Trump owns a six-acre Greenwich estate with a nine-bedroom house, an elevator and yacht moorings. She bought it with her then-husband, developer Donald Trump, for $3.7 million in 1984 and acquired sole ownership as part of her divorce settlement.

According to Fairfield County property-tax records, the county estimated the house’s market value at $8.6 million in 1992.

Trump now has it on the market for $18 million, a price local brokers don’t consider outrageous. After all, three years ago, in a slower real estate market, the house next door, which was about the same size, was listed for $18.5 million and sold for $13.7 million.

Of course, some wealthy homeowners still think they are being taxed too heavily. Earlier this year, Microsoft Corp. Chairman Bill Gates hired a team of appraisers to reassess the value of his new, 40,000-square-foot home in Medina, Wash., after the King County assessor’s office valued it at $53.4 million (annual property-tax bill: $600,000).

Local real estate brokers speculated that the move meant he might try to challenge the county’s numbers and fight the assessment in court, but Microsoft spokesman John Pinette says Gates doesn’t plan to.

Then there is Dell Computer Corp. owner Michael Dell, who challenged the $600,000 property tax bill he got this year for his 33,000-square-foot mansion in Austin, Texas. The granite and stainless-steel house has eight bedrooms, 21 bathrooms, a home gym and an indoor lap pool, and it is more than twice the size of Travis County’s next largest dwelling.

County assessors, who were barred by guards from visiting the property, pegged its price at $22.5 million. Art Cory, the county’s chief appraiser, says he based his assessment on a “conservative” reading of newspaper reports that Dell spent between $40 million and $60 million on the property, plus photos taken by helicopter.

Dell’s own appraisers argued that the house was incomplete when the county assessed it, and should have been valued at between $5 million and $6.5 million, giving him a tax bill of about $160,000. He’s now suing in a county court to have the assessment reduced, and has agreed to let county appraisers tour the property after all.

Pete Winstead, Dell’s attorney, acknowledges that his client spent about $30 million on improvements, but says that’s beside the point.

“People who build high-end homes tend to build monuments to themselves,” Winstead says. “But a buyer won’t necessarily pay what the seller put into it.”

Cory, the appraiser, is willing to conduct another assessment, but for now he is sticking by his $22.5 million figure.

“If the house were on the market today, would he list it for less than $22 million?” Cory asks. “I don’t think so.”