Yet despite its sublime finishes, refined pedigree and nosebleed prices, the residential portion of that Manhattan building is officially valued by the city, for tax purposes, at only $332 per square foot. According to the Miller Samuel appraisal firm, the average price per square foot for apartments sold there over the past 18 months has been $7,813.

The remarkably low official figure is the result of a state law dating from decades ago that requires the city to calculate the value of condominiums and co-ops by using as comparable properties rental buildings, instead of apartment sales. At the tippy top of the market, populated by $20 million, $30 million, $40 million, even $88 million apartments, real estate experts say that truly comparable rental buildings essentially do not exist.

As a result, the owners of many of the highest-end apartments pay a far smaller percentage of their apartments’ sales value than other condo and co-op owners pay. So despite a boom in the sale of stratospherically expensive apartments in recent years, the city is unable to truly cash in.

“The highest-value ones are going to tend to be the hardest to line up,” said George Sweeting, deputy director of the city’s Independent Budget Office. Their resulting effective tax rates, he continued, “will be extremely low, even by the standards of the city.”

According to the Independent Budget Office, the overall city valuation for condos and co-ops is only about 20 percent of what it would be were the city allowed to use comparable sales. That is a striking discount, but one that shrivels in comparison with the market’s upper echelons, which means the percentage of the sales value that those apartments pay in taxes shrivels right along with it.

In a study of 2010 nationwide property tax rates, the average homeowner paid a median of 1.14 percent of home value that year, according to the Tax Foundation, a research group. In Manhattan, that figure was 0.78 percent. For the $88 million apartment at 15 Central Park West, 0.78 percent would be $686,000. But this year, the property taxes due on that penthouse were $59,000.

The relatively low tax bill was mainly due to its valuation, but the owners of that penthouse — the financier Sanford I. Weill sold it to a trust controlled by Ekaterina Rybolovleva, the daughter of a Russian billionaire — were also helped by a program called 421a, which gives developers big tax breaks for a certain number of years that they can pass along to condo buyers, in exchange for which the developers build or help finance affordable housing.

But even without the 421a abatement, the bill for the penthouse would have been only $145,000.

An apartment at the Plaza Hotel that sold for $48 million last year is valued by the city at $1.7 million. A condo at 80 Columbus Circle that sold for $30.55 million last summer is valued at $2 million. And the $88 million apartment is valued at $2.97 million, or just 3.4 percent. The impact on city revenue needs then ripples down.

“If a certain kind of property is systematically undervalued, another kind of property has to pick up the slack,” said Andrew Hayashi, a property tax expert at the Furman Center for Real Estate and Urban Policy at New York University.

The state law mandating the use of rental data has been on the books since the 1980s, when the market in the city was a very different place. Manhattan had more rent regulation, many fewer condos and lots of co-op conversions.

A 2006 city report said tying the value of co-ops and condos to rentals was expected to keep an apartment’s official value — and, thus, its property taxes — from rising too quickly, because rent regulation kept rental values relatively stable.

Today, to find a condo’s or co-op’s comparable rental cousin, the Finance Department looks at factors like age, location and size. Older buildings, even the grandest, often have a greater value discrepancy than new condos because older rentals are more likely to have at least some rent-stabilized unit; this means that the taxes on those properties are generally lower.

But for any truly lavish building, finding a comparable rental is a challenge. One of the rental buildings used to find the value of 15 Central Park West, for example, is 145 West 67th Street — a very tall, but otherwise unremarkable, building.

“We understand that the requirement by state law to ignore sales prices makes an already complex property tax system even more confusing for property owners, which raises questions of equity within the system,” Owen Stone, a spokesman for the Finance Department, said in an e-mail. “We are always looking for ways to make things more transparent.”

Property tax experts say that from time to time, some effort is made to rethink the way apartments are valued. But changes can be made only by the State Legislature, and the technical and political pressures tend to overwhelm the cause, which then is quietly put on a shelf.

“It’s not so easy to go and change one screw,” said Ana Champeny, a supervising analyst at the Independent Budget Office. “Potentially, you have to redo the whole system.”

These property taxes, of course, are not paid in a vacuum. The city does receive a transfer tax every time a property is sold, as well as a mortgage recording tax — though many high-priced homes are bought with cash. And while the property taxes on mansions in the sky may be a relatively low percentage of sales value, they are still substantial.

A spokeswoman for Extell, which is developing the luxury market’s hottest ticket of the moment, One57, where two apartments are under contract for at least $90 million, said the project would contribute over 1,000 construction jobs and hundreds of permanent jobs to the city.

As it happens, Extell has also applied for 421a tax abatements for One57.

But if the property taxes on these luxury apartments were to rise, would it even make a difference in sales to the superrich?

“I think you’d choke off that market,” said Jonathan Miller, president of Miller Samuel.

Mr. Miller said that in some instances, exceptionally high carrying costs had tugged down prices and slowed the pace of sales, even in apartments that cost tens of millions of dollars.

“The logic was that the high end of the market doesn’t really care if the monthly charges are high; it’s more readily absorbed than on the lower end, and that turned out not to be true,” Mr. Miller said. “The conventional wisdom was, ‘Ah, the wealthy don’t care!’ But of course they do.”

It happens all the time. Sue hears that a friend of a friend, Bob, is looking to buy a place. Turns out, Sue is looking to sell her home. Or a guest in someone’s one-of-a-kind home tells the owners they’d love to buy the property, should the homeowners ever decide to sell.

And so begins the discussion between the would-be buyer and seller of a home that’s not even on the real estate market. How do they do the transaction? What steps are involved? What are the risks?

There are pros and cons for both parties and major considerations before either signs on the bottom line. But too often, these sellers and buyers get ahead of themselves and don’t think through the logistics and details. Here are seven questions to ask yourself about selling or buying a home that’s off the market.

Are both parties serious?

Buyers and sellers like the idea of making a deal off the market. But when it comes down to it, are both parties really on the same page? Has the buyer been in the market for a while? Are they truly ready to buy? Is the seller really ready to sell? Are their numbers in the same range, or is one way off?

Often, an unrealistic seller will throw out a number that’s way higher than what the market supports. They do this because they’re either uninformed or they feel they should get more because they’re risking selling off the market. On the opposite side, an uneducated buyer will throw out a lowball offer if they haven’t been in the game long enough to know the value.

How to decide on price?

Both parties have a serious commitment and are ready to do a deal. Great; now they need to agree on how to make it work.

Among other things, a price needs to be established. If they’re in the same price range but can’t agree on a number, there are a few options. One would be to have two independent appraisers come out and do formal appraisals of the property. The buyer and the seller can average the two. However, many argue that the appraised value (the number the appraiser comes up with) is always lower than the market value (the amount an able and willing buyer/seller would pay on the open market). In this case, a real estate agent may be called in; more on that in a minute.

Are there savings on the real estate commission?

Many sellers see the opportunity to sell off the market as a chance to save the agent’s standard 6 percent commission. But this can be short-sighted. First, both parties often bring a real estate agent into the transaction at some point. Second, the buyer might want the 6 percent commission deducted from the purchase price, but the seller doesn’t see it that way. For example, the seller might want $500,000. The buyer offers $470,000 ($500,000 minus the 6 percent commission). If they split the difference and the home sells for $485,000, they both win.

What ultimately happens is that the market decides the purchase price. If inventory is low and the buyer wants to make the deal work, they may pass the savings on to the seller. Or if it’s a slow market and there’s too much inventory, the seller may pass on the savings to the buyer. Many times, however, the seller and buyer agree on a number in the middle of the 6 percent, so each party benefits.

What are the risks?

The buyer and seller will likely have that little voice inside saying, “What would this sell for if it were on the market?” Buyers may wonder if they’re paying too much, while sellers might worry they could get more money on the open market. This is the risk both parties take in an off-market deal. Both the buyer and seller need to feel comfortable before they sign the contract. This is why a real estate agent is often consulted.

What is the role of the real estate agent?

With so much at stake financially and emotionally, most buyers and sellers ultimately don’t want to go it totally alone. The fear or uncertainty will outweigh any potential savings. An active buyer may have been working closely with an agent for months. A serious seller could be on the verge of signing a listing agreement. One or both may want the feedback or advice of their agents on price.

Some real estate agents will provide an opinion of value for a nominal fee or for free. Another good option is to ask the agent, in addition to providing the opinion of value, to take on the back-end parts of the deal at a discounted rate. In this case the agent might be responsible for inspections, disclosure review, title search and the contract, but not any marketing, open houses or showings. How this is negotiated is up to both parties. And be aware that some agents won’t feel it’s appropriate to reduce their fee at all.

Should you hire an attorney or escrow company?

There are some situations in which the buyer has a specific home they want to buy and a fair price is obvious to both parties. Maybe there is a one-of-a-kind home they’ve been eyeing in their neighborhood for years, and they know the value because they live nearby. Or the buyer may find a home on Zillow with a “Make Me Move” price in line with their budget. If the prices are right for both parties, and there aren’t any complications in the disclosures or inspections, they may hire an attorney or an escrow company to facilitate the deal for a flat or hourly rate.

How to cover all the bases?

If you decide not to go the formal listing and sales route, be sure to cover your bases and protect yourself legally and financially. Always go with your gut. If something doesn’t seem right or you’re uncertain, bring in the professionals. Going it alone may have its upsides, but the downsides could outweigh them in a heartbeat. Don’t be afraid to ask your real estate agent for advice. A good agent will recognize that, while a full commission would be great, two potential future referrals may be worth the time and effort.