### Discounting

Discounting is an important topic in economics. Any economic prediction looking more than a year or two into the future is completely dependent on it.

It’s nothing to do with discounts offered by traders trying to persuade you to buy something!

The idea is that costs in the future are less important than costs today, and that benefits in the future are worth less than benefits today. The logic is that if I can delay some spending for a few years, I can earn interest on the money for a few years – or avoid paying out interest for a few years, if I’m borrowing the money. Likewise, if I’m not going to get the benefits for a few years, they’re worth less than benefits today – if I can sell the benefits, I can get interest on their value for a few years more. Even if I’m not selling the benefits, I can put a value on them based on what I’d get if I sold them, so the effect is the same.

How much one discounts future values (positive and negative) like this is basically down to interest rates. If the interest rate is 5%, then £100 today would grow to £105 in a year, £110.25 in two years, £115.76 in three years, and so on. Correspondingly, £100 next year (whether a cost or a benefit) is only worth £95.24 this year, £100 in two years time is only worth £90.70 this year, and so on.

The flaw in this may already be apparent to many people, given today’s economic climate. When I first raised the issue as an engineering student in the late 1960s, people thought I was crazy.

This is somewhat oversimplified even for an economist’s mind. You’ve got to take account of inflation. Basically, what you have to do is subtract the rate of inflation from the interest rate, and use the difference as your discount rate.

So far, so logical. You can’t fault the logic or the maths.

Now let’s apply it to a real problem. Let’s compare the costs and benefits of a hypothetical nuclear power station project and a hypothetical coal-fired power station project.

Nuclear power stations have a high up-front (capital) cost, but low fuel costs. Coal-fired power stations have a lower capital cost, but higher fuel costs. Fuel costs recur every year.

This is all hypothetical, so we’re not using real numbers. Let’s say the nuclear station costs £150 million to build and £1 million a year for fuel, and the coal-fired station costs £50 million to build but needs £5 million a year for fuel.

We’ll assume a 30-year life for each.

We’ll use a discount rate of 4% – that might be 5% interest, 1% inflation, or it might be 8% interest, 4% inflation, or whatever. This calculation is insensitive to changes like that.

None of these are real numbers at all, they’re just to illustrate a point.

If you don’t use discounting, the total cost of the nuclear station over its lifetime will be £150 million + 30 x £1 million = £180 million, and the coal-fired station will cost £50 million + 30 x £5 million = £200 million. Nuclear wins comfortably.

Use discounting, and things look different. Now the nuclear station’s cost is, in £millions:

150 + 1 + .962 + .924 + ... + .321 = 167.98 – not a lot less than if you don’t use discounting, because most of the cost is up front.

But the coal-fired station’s cost is:

50 + 5 + 4.808 + 4.623 + ... + 1.603 = 139.92. Coal wins comfortably, because most of the cost is in the future, and discounted.

You can’t fault the logic or the maths.

But you can fault the inputs. Will interest minus inflation really be 4% every year for the next thirty years? It doesn’t matter if interest and inflation go up and down in step, always 4% different; it doesn’t even matter if the difference varies a bit from year to year, as long as it doesn’t stray far, and isn’t consistently higher or lower. But even a small variation that’s consistently in the same direction changes the picture, and it doesn’t take a very big variation to change it out of all recognition.

Look at the history of interest rates and inflation, and you’ll see that the chance of getting nothing more than small variations over a thirty year period is practically zero. So to make any sort of useful prediction, an economist has to guess the future of interest rates and inflation.

Actually, it’s even worse than this. For the example above, it’s really future inflation in the price of coal (and to a lesser extent, uranium) that’s relevant, not general inflation. The future price of any one particular commodity is even less predictable than general inflation.

In the late 1960s interest rates were around 6.75%, and inflation was around 4.75% – difference 2%. Do the same calculation with a discount rate of 2% and the discounted costs are 172.84 (nuclear) and 164.22 (coal). Coal still wins, but it’s close.

But in the 1970s, inflation averaged 13.25% while interest rates averaged 9%, giving a discount rate of *minus* 4.25%. If we’d guessed that in the late 1960s and used that rate, the discounted costs would have been 210.38 (nuclear) and 351.88 (coal)!

Economists don’t like negative discount rates – it looks very silly when you weigh future values higher than current values, and progressively higher the further into the future you look, but that’s the implication of inflation being higher than interest rates. But economists don’t like it, and always base their estimates on the assumption that such situations are short term. This is not necessarily true!

We’ve recently entered such a period again. How long it will last, who knows?

What economists like is a high interest rate and low inflation. That way you can discount the future beyond the first few years almost completely, the sums are nice and predictable, and a short-term view of the future is all you need. This is really the reason why things like power stations have projected lifespans of thirty years or so – the economists in the planning process want to discount any value too far into the future, but don’t dare to say that such a big investment is any shorter term than that. *I’ll be retired by then* is really what they’re thinking.

The real killer, to my mind, is this: the *real* reason that nuclear enthusiasts like economists and their wonderful discounting trick is that it makes costs a hundred years or more in the future disappear completely. It lets them completely off the hook for the cost of looking after radioactive waste for the next few hundred years, or more to the point, for the cost of all the damage it will do when no-one has the faintest idea *how* to look after it all. Isn’t economics wonderful?

Economists’ discounting? Not giving a damn about your descendants – or anyone else’s.

Economists’ predictions? Pah. You might as well ask a fairground fortune teller.

*In fact, you’d be better off asking a fairground fortune teller – the answer would probably be random, rather than deliberately skewed in favour of some vested interest or other.*

_{If you would actually like to look at the history of interest rates and inflation, here they are: }