Low interest rates generally lead to inflation, which is bad for everybody. But if inflation were really low, then low interest rates would tend to follow, and in that situation, low interest rates just might save the world.

Present value

This article is really about present value. (It's about saving the world, too, but first it's about present value.) Present value is the way economists think about the value today of something that you're going to get in the future. Money that you're not going to get for a while is worth less for a whole list of reasons:

• You can't spend it now
• Inflation might make it worth less before you get it
• There's some risk that whoever is supposed to give it to you won't
• If you had the money now, you could invest it and earn some return

So, how do you calculate the value today for some money that you're supposed to get in the future? You calculate the present value of the money.

The calculation is rather complex. That's not a big deal--any financial calculator and many web sites include a present value calculator--but it's worth understanding the basics of the formula. The gist of it is in that last bullet item there--if you had the money now, you could invest it and earn some return. The formula essentially figures out how much money you'd need to have now in order to be able to invest it and get whatever you've got coming to you later.

Let's say some rich uncle died and the lawyers tell you that you can expect to receive $1000 once the estate settles in six months. Further, let's say you could get 5% on the money in your internet savings account. Plug those numbers into a present value calculator (6 months, 5%, and a future value of $1000) and it will tell you that the present value is $975.36. (That interest rate, by the way, is called the discount rate, because it's used to figure the discount of the present value to the future value.) An economist would tell you that you should sell your right to receive that money if anyone would offer you $976 for it. Likewise, if whoever is inheriting the money offers to let that economist have the inheritance in exchange for $975 today, the economist would no doubt jump at the chance to pick up a free 36-cent profit.

In the real world, of course, the second-to-last bullet point also comes into play. The 5% that you could earn on the money is all well and good if you've got great confidence in the lawyers, the estate is large, and the will clearly gives you $1000 off the top. But oftentimes things aren't so very clear. Maybe the estate is overly invested in subprime mortgages. Maybe there's an illegitimate son out there with a claim to the whole thing. Anything that adds uncertainty to the payment increases the discount rate.

Economists, of course, don't like to dirty their hands with figuring out what the discount rate actually needs to be to account for the fact that there might be another heir out there. Instead, they just tell you to use the "appropriate" discount rate.

Decision-making and present value

To an economist, not having to pay money is the same thing as getting money, so the present value formula lets you answer all sorts of questions about paying money now to save money later.

If you can buy a cheap widget today for $100 and have it last 10 years, or you could buy an expensive one for $200 and have it last 20 years, which would you pick? It's not even a toss-up: buy the cheap widget. The cost of the replacement widget ($100, 10 years from now, 5% discount rate) has a present value of only $61.39. If you had the $200 you could buy the cheap widget, invest the $61.39 (which would be worth $100 when the time came to replace your widget), and have the $38.61 to spend or invest in some other way. On the other hand, if the longer-lasting widget only cost $160, that would be the way to go.

Of course there's a lot of issues that need to be handwaved away for this to work out so simply: the risk that the cheap widget will fail at a critical time, the risk that the replacement widget might not be so cheap, the value of your time spent widget shopping twice instead of just once, and so on. But the principle is sound.

People make these sorts of calculations all the time. Why do roads need to be repaved every 3 years instead of being made to last 20? Because the present value of repaving an extra six times is less than the present value of making a road to last.

Choosing a discount rate

As I said, economists just tell you to choose an appropriate discount rate and leave the dirty work to you. It's a big deal, though, because which rate you chose has huge implications for what makes sense and what doesn't.

Suppose the appropriate discount rate were only 2% in the widget example. All of a sudden the right amount to pay for the better widget is $182. On the other hand, if the appropriate rate were 9%, you it wouldn't make sense to buy the better widget unless you could get it for just $142.

The main things that factor into the discount rate are the general level of interest rates in the economy (because you could invest whatever money you don't spend now--or alternatively, have to borrow whatever extra you need, which is the same thing to an economist) and any unique risk factors related to this particular transaction (such as the risk that they might not even make widgets ten years from now).

High discount rates in action

Ever see somebody who makes seemly irrational financial decisions, such as borrowing from payday lenders or skipping routine car maintenance that ensures much higher repair bills later? Without speculating on what is actually in the mind of such a person (feeding their family, perhaps), you can model their behavior by treating it as indicating a very high discount rate.

When would it make sense to borrow $100 today and have to pay back $115 in two weeks? It makes sense if your discount rate is over 365%. If it is, then $100 today is worth more than $115 in two weeks. Note that it doesn't matter if the borrower is actually making such a calculation--surely almost none of them are. But they're acting as if they were.

The effect of high discount rates is to make future results insignificant compared to the present. And the reverse is also true: If the future is insignificant (such as, for example, if you're dying of a terminal illness), then making decisions as if the appropriate discount rate were very high makes a certain kind of sense. So what if spending $30 on your car today could save you a $1400 repair bill next year if the car is sure to be repossessed long before then?

Roofing beams

Now we get to the saving the world part.

Here's a story I've heard more than once. Sometimes it's about Cambridge, sometimes it's about Oxford, but either way it goes like this:

The facilities guy comes to the head of the college and says, "The huge oak beams that hold up the roof in the great hall are almost 400 years old. They're wearing out and need to be replaced. I don't know where we're going to find replacements, and if we do find them, they're going to cost a fortune."

The head of the college gets advice from various people and eventually finds himself talking to the college forester. (Old colleges have odd positions like college forester.) He explains how the oak beams are wearing out and that they're trying to figure out what they can use as a replacement.

The college forester, of course, says, "No problem. When they built the great hall 400 years ago, my predecessor planted a grove of oak trees. They should be just about ready."

Now, this is a wonderful store about planning ahead and about the value of continuity--only a really long-lived institution, such as a college, could make such a thing work. It's also about sustainability. It just makes sense to do things this way

But think about this story in terms of the discount rate. Suppose 400 years ago beams for the roof cost a total of 1500 pounds sterling (back when a pound was really worth something). Someone doing the net present value calculation at the time, trying to figure out whether to devote the land necessary to grow a whole grove of oak trees to provide replacements, would have found that (at a 5% discount rate) the future value of 1500 pounds in 400 years would only be worth 0.00001 of a pound. In other words, you couldn't even justify the cost of the acorns, let alone the cost of tying up the land for 400 years. If the discount rate were only 2%, the present value of the oak beams 400 years later would be 0.54 of a pound--easily enough to pay for the acorns, anyway. If the discount rate were 1.1%, then the present value would be nearly 20 pounds--very possibly enough to make it worth tying up the land (especially since other trees can be grown alongside oak trees).

In other words, sustainable behavior makes economic sense if the discount rate is low enough.

How to get low rates

The government manipulates interest rates all the time. In the US the Federal Reserve raises rates to head off inflation and then cuts them again to protect the financial system from the harm done by high rates.

Setting the rates too low produces inflation--and leaving the rates low after inflation has begun to rise makes savings grind to a stop. (If your money is worth less every day, why hold onto more than you need just to transact daily business?)

The only way to get lasting low rates is to have very low inflation. During periods when people had great confidence in their money, such as in England and the United States during the gold standard, people made just the sort of long-term decisions I'm talking about. Planting oak trees to be harvested after 400 years is an extreme (and probably apocryphal) example, but there were plenty of real-world examples of investments made and stewardship undertaken that only made economic sense if the discount rate were 2% or less.

A few years ago the inflation rate got down close to zero and the Fed panicked. They're much happier with an inflation rate that runs between 1% and 2%, because they worry that they don't have the tools to stop deflation once it starts. The problem with not driving inflation down to zero, though, is that long-term sustainable behaviour will never make sense when interest rates are high.

If you're going to get $100 after 50 years it doesn't make sense to invest even $9 today, if the discount rate is 5%. If the discount rate is 2% then you might invest $37, and if the discount rate is 1% then you might invest nearly $61.

To make sensible sustainable activity also make economic sense, you need to have very low interest rates. And the only way to get very low interest rates is to have very low inflation.