The first time I attended a timeshare presentation, my daughter, who is wise beyond her years, wouldn't let me take my checkbook. If I had, I would be the owner of an annual Hawaiian vacation. But I would have bought it based on fuzzy math.

Thanks to Samantha, the timeshare salesman's mathematical sleight-of-hand occurred to me as I walked the half mile back to my hotel room to get my checkbook. I didn't go back.

I have since attended enough presentations--including one earlier this week--to know that the fuzzy math delivered at the first presentation was not the exception, but the rule. I have nothing against buying timeshares. But I do think you should understand what they cost before you sign on the dotted line.

For the benefit of those who don't have a wise teenager, I'm going to run through timeshare math, both fuzzy and real, to explain how you determine the real cost and why that's so hard to figure out in the presentation room.

First, the real math
There are two components to the cost of a timeshare.

• There's the amount it takes to purchase your "deed" which gives you the right to a week (or two) in one or more locations offered by the timeshare promoter. This purchase price is usually a lump sum that amounts to tens of thousands of dollars.
• The second component is the annual maintenance fee.
Your annual cost of ownership is the sum of the annual maintenance fee, plus an "opportunity" cost on the money you invested in this purchase. If, for example, the purchase price is \$30,000 and the annual maintenance fee is \$1,500, your annual cost equates to about \$3,000.

How'd I get that? I multiplied the \$30,000 investment by a 5% return. That's my estimate of what I could earn on that money if it was invested elsewhere. I added the resulting \$1,500 in opportunity costs to the \$1,500 maintenance cost. Voila.

Assuming that this \$3,000 gets you the right to one week a year in a timeshare resort, your accommodations cost you roughly \$429 a night. Whether that's a bargain or a bust depends on what you would pay for accommodations of similar quality in a similar location. This real math is pretty simple.

But that's not what they're going to lead you to believe in the presentation room.

There they will throw dozens of numbers at you, many of which are meaningless. But the meaningless numbers make it appear that the timeshare is the bargain of the century, even when that's far from the truth. Let's take a look, based on my most recent experience, to show how it works.

The pitch
Anna, a lovely and charming saleswoman, meets our group of three in the lobby of the Westin Ka'anapali Ocean Resort, where we're offered coffee and donuts before being led through this stunning oceanfront property. Because this property is owned by Westin, she also introduces us to the company's properties around the world by leading us through a hall filled with a series of poster-sized glamour shots of hotels in Venice, Italy; Whistler, Canada, Spain, Greece, etc.. Why the world tour? If you buy, you can trade nights in your timeshare for "points" that will allow you to stay in the chain's other hotels and resorts. (Marriott, where I attended a previous presentation. offers virtually the same deal. I understand this is also true with many of the other hotel chains that also offer timeshares.) Good so far.

While leading us through the property, Anna asks questions about how we like to vacation; how important vacations are to us; whether we travel with children, with friends, or alone. That information will be used in the sales pitch later. Once we're star-struck by the fabulous possibilities, we're led back to Anna's office to run through the numbers.

Now comes the fuzzy math
"You say you vacation at least two weeks--14 days--a year? What do you think you spend on each hotel night?" she asks.

My brother-in-law answers that his family spends \$300 a night, or about \$4,200 annually on hotels. Now Anna wants to know what he spends on rental cars and flights. She plugs his responses into a computer program before asking, "How many more years do you plan to vacation this way? Twenty-five?"

That, and a modest 3% inflation rate, are added into the program. My sister and brother-in-law will spend almost a quarter of a million--\$249,746 to be precise--vacationing this way over the next 25 years, it says. This figure, which would have been twice as much if Brian had aceeded to Anna's suggested 7% to 11% inflation rate, is supposed to draw gasps.

"When you are done with those vacations, what do you have?" Anna asks rhetorically before providing the right answer: "Nothing. You don't own anything. The vacation just goes away."

A better choice, Anna suggests, is ownership.

Now that you have that \$250,000 rolling around in your head, another sales person comes in to give the timeshare pricing and you find that all this (with a whole bunch of asterisks) can be yours for a mere \$94,900.

Fuzzy Math #1
The implication, which they carefully don't say outright, is that you get 25 years of vacations for less than half the cost. But, of course, you don't. The recently calculated \$250,000 adds in the cost of flights and rental cars that are not included in your time share.

Fuzzy Math #2
The previous example also accounted for inflation, which they have specifically not breathed a word about with relation to the timeshare. But the timeshare has an annual maintenance fee ranging from \$2,200 to \$2,600, that can rise every year, too.

If you turn around and use their math and assumptions on their investment, adding in the cost of the maintenance fees, rental cars, flights and inflation, the timeshare vacation costs \$400,000 over 25 years vs. your existing \$250,000.

Fuzzy Math #3
This timeshare gives you a week--not two weeks--of vacation time. However, they explain that the two-bedroom unit that you're considering can be split into two, one-bedroom units, which will give you the two weeks you're accustomed to.

Fuzzy Math #4
If you balk at the \$94,900 price, you're told that you can buy a week every-other year for half the price. Or you can buy a smaller unit; or one with a lesser-view. But this is the equivalent of car dealer making monthly payments more affordable by stretching them out over a longer period of time. The price isn't better. You're just paying less to get less.

Fuzzy Math #5
Your unit could appreciate, they tell you. So even though it sounds expensive, it's an investment.

Quick reality check: At this price, this two-bedroom high-rise condo is selling for the equivalent of \$4.9 million, plus \$125,000 in annual maintenance. (That's your cost multipled by the 52 weeks in the year, since you're only getting a week out of this.) That's no bargain, even in the highest priced real estate markets in the world.

Another reality check: Drive a few miles north into Lahaina town and you'll walk by a half dozen timeshare resellers. The same unit that's being peddled for \$94,900 in the presentation room has got a \$44,000 asking price in Lahaina. Or you can look up timeshare resales on line, which offer much the same units, but without the ability to trade your units for system points. (The point system is only available to those who buy direct at retail prices.)

This deal's real math
At 5% interest, your annual opportunity cost on that \$94,900 amounts to \$4,745. Add \$2,400 in annual maintenance fees for a total outlay of \$7,145. If the buyer uses both bedrooms, that suite costs him \$1,020 a night. If he splits it (getting two weeks from the purchase), the one-bedroom costs \$510 a night.

If that sounds like a good deal for the accommodations you're getting--and you don't have any trouble affording the price now and in the future because timeshares are not at all easy to resell--by all means buy. But don't be confused. This is a way to prepay for a luxury vacation, not a screaming bargain.

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