According to a __ news story from Reuters __ , a recent Tufts University study (available __ here __ ) says that “if nothing is done to combat global warming,” then, by the year 2100, “two of Florida’s nuclear power plants, three of its prisons and 1,362 hotels, motels and inns will be under water” because of rising sea levels—all of which could cost Florida $345 billion a year. The study says that “the sort of mitigation efforts needed to restrict sea level rises to 7 inches or less would cost a U.S. state like Florida between 1 percent and 2 percent of GDP.” Hence, “doing something may seem expensive, but doing nothing will be more expensive.”

I don’t have the scientific training to make informed judgments about global warming, but I do know a little about economics, and this last claim seems to me to be utter nonsense. According to __ this report __ from the Commerce Department’s Bureau of Economic Analysis, the GDP of Florida in 2006 (in chained 2000 dollars) was about $610 billion. One percent of that figure is $6.1 billion. The authors of the study thus argue that it’s a bargain to spend $6.1 billion to avoid a cost of $345 billion—which it would be, if we were talking about spending $6.1 billion * today * to avoid spending $345 billion * today * . The question, however, is whether we should spend $6.1 billion today to avoid spending $345 billion * ninety-three years from now * in 2100.

It makes a big difference—indeed a huge one—because money in the future is worth less than money in the present. If I asked you, for example, which you would prefer—$1,000 today or $1,000 ten years from now—you would of course take the money today. Why? Maybe because you don’t want to defer consumption, or maybe because you’re worried you’ll never get the future payment. At the very least, if you take the money today, you can invest it for ten years and have more than $1,000 ten years from now. For instance, if you invested $1,000 today at 5 perent, in ten years you’ll have $1,629.

This last point provides the key insight in contemporary finance theory: The present value of a future payment is the amount you have to invest today at a given interest rate in order to generate the amount of the future payment at the time the future payment is due. For instance, if you can invest today at 5 percent, the present value of $1,000 payable ten years from now is only about $614, for if you invest $614 today at 5 percent, in ten years you’ll have $1,000. Thus the * present value * of a * future payment * is always less than the amount of that payment.

More generally, if * FV * is the future payment, * PV * the present value you need to invest today, * r * the interest rate, and * T * the number of years in the future the payment is due, then * FV = PV * (1 + r) ^ T * , or, rearranging the terms in this formula, we find that the present value of a future payment is * PV = FV / (1 + r) ^ T * . The crucial number in this calculation is * r * , the interest rate, which is usually called a * discount * * rate * in such contexts. The present value of a future payment is thus some lesser amount obtained by * discounting * the future payment using the appropriate discount rate.

In general, the discount rate should include about 2 percent for the time-value of money (that is, compensation for delaying consumption), another 2 percent to 3 percent to cover inflation, and a risk premium, which reflects the fact that the future payment is uncertain. Economists estimate the rate for the time-value of money and for inflation by observing actual financial markets. The risk premium varies with the uncertainty of the future payment: The more uncertain it is, the higher the discount rate must be. That’s why borrowers who are likely to default pay higher interest rates than borrowers who are likely to repay.

So, when the Tufts study tells us that global warming could cost Florida $345 billion per year—but only in 2100—how much is that today? In other words, what’s the present value of $345 billion ninety-three years in the future? The study purports to account for inflation, so we need worry only about the time-value of money and a risk premium. Allowing 2 percent for the former and, say, 8 percent for the latter, we might use a discount rate of 10 percent. By comparison, the risk premium on large-cap stocks is about 9 percent; an 8 percent risk premium for estimates stretching out nearly a century surely underestimates the uncertainty and so exaggerates the present value of the future payment. Assuming this total 10 percent discount rate is correct, the present value of $345 billion payable ninety-three years from now is—brace yourself—about $49 million. (If you’re shocked at how low that number is, __ read this article on compound interest __ at the Motley Fool.)

The authors of our study are thus telling us it’s a bargain to spend 1 percent of Florida’s current GDP, or about $6.1 billion, to save only $49 million. In other words, we should spend about $124 dollars to save $1. That’s obviously irrational.

In reality, of course, no one can predict with reasonable certainty costs to be incurred a century hence. Any estimates of such future costs are highly uncertain, and so the discount rates to be applied to them should be very high. The table below shows the present value of $345 billion in 2100 using various discount rates at 5 percent intervals.

Present Value of $345 Billion in 2100Discount Rate Present Value

5% $3,691,596,977

10% $48,786,468

15% $781,484

20% $14,927

25% $335

30% $9

If forced to decide, I’d say the right discount rate in this case has to be at least 15 percent, that is, about the rate one might use for very risky, long-term investments. The correct rate may well be very much higher. Using a 15 percent discount rate, it makes sense to spend no more than $781,000 today to avoid a cost of $345 billion in 2100. I worry that the Tufts study alone cost more than that. Even at a ludicrously low discount rate of 5 percent—which is lower than the rate on long-term, low-risk corporate bonds—we’d still be spending $6.1 billion to avoid a cost of $3.7 billion. By any reasonable estimate, it can’t be economically rational to spend $6.1 billion today to avoid the costs that the Tufts study identifies.

As I said above, I don’t know anything about the science of global warming, and I express no opinion on scientific matters. But even taking the direst of scientific forecasts about global warming as correct, many of the policies advocated by global warming alarmists are clearly irrational from an economic point of view—so irrational, in fact, that they call into question everything such alarmists might say about global warming. Whenever I read about Al Gore in the newspaper, I find this a comforting and beautiful thought.

* Robert T. Miller is an assistant professor at the Villanova University School of Law. *