"I don't believe you're really an economist," snarled the time share salesman for Spinnaker Resort of Hilton Head Island, S.C., as my family and I left without buying. Having just drawn for us a trash can to illustrate where our vacation rental payments were going, he no doubt felt deserving of the Nobel Prize.

Meanwhile, I had determined that the deal was a loser, based on his figures and an economic formula for the profitability of buying vs. renting.

profitability = rental rate + appreciation rate - interest cost

When people go to the beach for a week, they typically rent the place where they stay. People who spend a lot of time at the beach might choose to buy a place. The idea of time-sharing is that instead of buying or renting a beach condo, you buy a week at a beach condo. Every year, you can go to the beach and stay in the condo for the week that you own it.

Isn't it always better to buy than to rent? After all, if you buy, you "own" something, while if you rent, you do not. Well, if you have to pay $500,000 to buy something, and you could rent it for a nickel a year, would you still buy it? No. In fact, the decision to rent or buy depends on prices, rents, and other factors that go into the profitability formula.

A major advantage of owning something is that when you are finished using it, you have something of value. The value of a piece of property will depend on the rate at which the price appreciates. That is why the appreciation rate is in the formula.

When you own the place where you are staying, you do not have to pay rent. Therefore, you can add in the rental rate (the ratio of the rent to the purchase price) to the profitability calculation.

The main disadvantage of buying is that you have to tie up cash (or borrow funds). The interest cost on these funds has to be subtracted in the profitability calculation.

Here is how I used the salesman's figures in the formula.

1. For the rental rate, I noted that the rent for our vacation was $1200 for that week. His time share cost $11,900 to buy--call this $12,000. Simply dividing one by the other would have given a 10 percent rental rate, which would have been very nice.

   However, it is important to adjust this calculation for fees. The timeshare charged a maintenance fee of $433.25 per year, a membership fee of $200 per year, a publication subscription fee of $67 per year, and another fee of $93 per year, which I believe was a processing fee of some sort (I cannot be entirely sure that I have this straight, because when I tried to take the piece of paper on which I had written this down, the salesman tore it out of my hand).

   The fees add up to $793, so every year instead of saving $1200 in rent, we would save $1200 - $793, or $407. This is the net rental value of the timeshare. Dividing $407 by the price of the time share, $11,900, gives 3.4 percent for the rental rate, which is the first figure required by the formula.

2. When he was giving his pitch, he used the classic timeshare salesman assumption that rent and prices will go up by 10 percent per year, so I used that for the appreciation rate.

3. He said that the financing rate for us would be 17.9 percent, so I used that for the interest cost.

When I put all of these figures into the formula, the net result was:

profitability = 3.4 + 10.0 - 17.9 = - 4.5%

The negative number means that compared with renting, buying this time share would cost 4.5 percent more per year. To illustrate the economic value of this timeshare, you should draw an even bigger trash can.

This quick calculation has some flaws. For example, I have assumed implicitly that the fees will go up at the same rate as rents. They could go up by more, or by less.

Also, our rental condo and his timeshare were not exactly identical. They were very close in terms of square footage and furnishings, but there were some differences:

• "I would never stay on a public beach," the salesman said, pointing out the value of the 24-hour security at the timeshare. "Anybody with a machine gun can go in there." Mercy! We thought: not only were we staying at the public beach, but we were letting our children swim without flak jackets!

• Offsetting the value of the security guard was the fact that our rental was closer to the beach. We were right on the beach, while the timeshare was, according to the salesman, "A 4-minute walk to the beach." We later measured the distance as 7/10 of a mile, which takes 10-15 minutes to walk.

• While perhaps a case can be made that beachfront rents will go up because such land is limited, I don't see that degree of scarcity in property 7/10 of a mile away. So, I don't think the 10 percent annual appreciation is something I would bank on.

• Finally, I need to mention one thing. We were vacationing in August, when children are out of school. The timeshare price of $11,900 was for mid-May, when I imagine you could rent an equivalent place for less than the cost of the annual fees. The price for August? $17,900.

Another way to see what a bad deal this was would be to add up the price of all 52 weeks and compare it to the price of a condo. The total price for all the weeks came to about $600,000. My guess is that the condo did not cost more than $200,000. And on top of that $400,000 in profit for the timeshare company come all those lovely annual fees.

I don't want to generalize and say that all timeshare salesman are sleazebags, only the ones that I've met. Nor do I mean to criticize people who buy timeshares. I'm sure there are some happy owners. However, the economics are very unfavorable for the buyer.

The formula is something that an economist might use to determine the value of a capital asset. A capital asset is something that will last for a long time, such as a house, a factory, or a truck. A textbook example of a capital asset is a fruit-bearing tree (most economists love fruit-bearing trees, but I'm allergic to the ones near where I live).

An asset will yield "rents" (the fruit from the tree) and will enjoy price appreciation (I may be able to sell the tree for more than the original price I paid). The formula for determining whether or not it is profitable to buy the fruit tree is

profitability = rental rate + appreciation rate - interest cost

What I mean by profitability is the expected annual profit, expressed as a percent of the price of the asset. The asset could be a house, some shares of stock or of a mutual fund, or our fruit tree.

If a house costs $100,000 and the profitability is 1.5 percent, this means that every year I save 1.5 percent of $100,000, or $1500, by buying the house rather than renting. If the profitability is -1.0 percent per year, then I could save $1000 per year by renting rather than buying. If profitability is close to 0, this would say that buying and renting are economically equivalent.

The rental rate is the ratio of the first year rent to the purchase price. The first-year rent for a house would be the rent on an equivalent house. The "rent" from shares of common stock would be the dividends from the stock. The rent from the fruit tree is the proceeds from selling the fruit.

The appreciation rate is the rate at which the price increases, expressed as an annual percentage rate. Much of this price increase could be due to general inflation. In the late 1970's, inflation in the U.S. reached 10 percent per year and over. More recently, inflation has been closer to 2.5 percent per year.

Some of the price increase may be specific to the particular market. In housing, over long periods of time prices go up at the same rates as rents in an area. However, over short periods of time, housing prices can run up quickly or go into decline.

The interest cost is the cost of financing the asset purchase. With housing, most people think of this as the mortgage interest rate. With stocks or mutual funds, many individuals do not borrow. However, they could have put their money in CD's or bonds and earned interest, and it is this foregone interest (or "opportunity cost") that should be used as interest cost. Whether we borrow to buy the tree or finance the tree with our own funds, there is an interest cost to tying up our money in the tree.

Here is a way to look at the cash flows involved in buying $100,000 fruit tree, and then selling the tree after three years. The assumptions are:

1. We borrow the entire $100,000 to pay for the tree.
2. The interest rate is 12 percent per year.
3. The first year, the fruit from the tree is worth $7000. This is the "rent."
4. Each year, the rent and the price of a fruit tree go up by 6 percent per year.

The business has a negative cash flow. The "rent" from the fruit trees is less than the interest cost. Thus, the business gets more in debt each year, so that the interest cost keeps rising. However, if you include the increase in the value of the fruit tree as income, the business has a profit.

Incidentally, a major league baseball franchise is like this fruit tree. The "rent" is equal to revenues minus operating expenses, which is not enough to cover interest costs. So the baseball owner's cash flow is negative, but nonetheless the franchise appreciates in value. As long as the value appreciates by more than the negative cash flow, the business is worth owning.

Review

Suppose that we are considering buying a baseball team for $100 million. We will have to borrow money at a 10 percent interest rate. Annual revenues are $70 million, and annual expenses are $65 million.

1. Assume that revenues and expenses go up at a rate of 3 percent per year. The price of a franchise also goes up at 3 percent per year. Is this a worthwhile investment?
2. Assume that revenues, expenses, and the price of a franchise go up at a rate of 6 percent per year. Is this a worthwhile investment?
3. At what rate should revenues, expenses, and the price of a franchise go up to make this a break-even investment?