The old saying, “time is money” is a reminder not to waste your hours when you could be getting on with making profits. However, it also could be interpreted in an almost literal sense. Money invested in a project or merely left alone in a bank account does, one hopes, grow with the passage of time, so in that sense, time generates money. I remember my delight as an eight-year-old at the amazing realisation that the bank would actually give me money for nothing, it seemed, if I let them look after my few dollars of cash. Almost too good to be true it seemed, notwithstanding the pitiful rate of interest they paid. It was safer than leaving the money at home anyway, given the risks of Mum being short of petrol money one day, or little brother deciding to bury it in the sandpit.

A question that manages to confuse many people is, how should time be accounted for when comparing different projects that involve different costs and benefits at different times? The only thing that is really obvious is that you can’t ignore the issue. You can’t just pretend that a dollar now is equivalent to a dollar in ten years time, because the dollar now can at least earn interest in a bank account, if not higher rates of return in an alternative investment.

This insight actually points the way to part of the solution. The first thing you need to know (or decide or guess) is what you would do with the money, and what the benefits of that use would be, if you did not put it into this new investment you are considering – let us call it investment X. The strategy that you would have pursued provides a benchmark for comparison. Economists call the benchmark the “opportunity cost”, since it is an opportunity you have to give up in order to pursue investment X.

The new option, investment X, has to be “better” than what you were already planning to do. Presumably, you weren’t planning to leave the money in a cardboard box under your bed, which is the sort of thing you would have to do to break the link between time and money. The choice of a realistic benchmark already implicitly includes some aspects of time, because the benchmark use of your money would have involved some growth of the asset over time.

The second thing you need to decide is what “better” means at the start of that last paragraph. What rule will you use for judging it? In economics and finance, the universally-used rule is: the better option is the one that generates the greater accumulated benefits by the end of the time period. We imagine that the investment, whatever it is, is like a bank account that starts with a zero balance, and that all costs and benefits are taken out of or put into that account. If the current balance is positive, you earn interest, and if negative you pay interest. The final balance is a combination of benefits, costs and interest.

Now, while this rule has a lot of intuitive appeal, it has to be admitted that this is not the only conceivable rule you could use. Nevertheless, it is the standard approach, and we’ll stick to it for purposes of this explanation. It is a rule that gets us into some difficulties when we get to really long-term investments, but we’ll worry about that (and some other complexities) another time.

That is pretty much the essence of the solution. Things do get more complex when you try to put it into practice, but understanding the essential idea is not that hard. Assets compound in value over time to some final value. Which investment option grows to the largest final value? The benchmark investment that you were going to do, or the new option, investment X?

Unfortunately, economists then confuse matters mightily by turning around the direction of time, and talking about asset values as if they shrink as time passes backwards!! I kid you not, they really do.

This kind of negative growth is the idea behind “discounting”, with the notional interest rate (the average rate of compound growth) reinterpreted as a “discount rate”. We “discount” future benefits and costs back to the present (giving us their “present value”) and then we can compare them validly because we have factored time and interest out – the opposite of what we did above, which was factoring time and interest in.

Discounting to calculate a “present value” is exactly equivalent to the “largest final value” approach that involves compounding benefits and costs through to the end of the planning period and comparing them at that point in time. If you do them both properly, they will always give the same ranking of the options.

In fact it doesn’t matter which point in time you choose to make the comparison. It could be somewhere in the middle of the time period if you wish, requiring discounting of later values, and compounding up of earlier values. It will work out, as long as you choose a single point in time and use it to compare all of the benefits and costs. Economists always choose the present, but this is arbitrary.

Note that this discussion is not about inflation. The usual approach is to factor inflation out of all the costs and benefits before you start the above calculations, expressing them in “real” terms. Of course you then have to factor inflation out of the discount rate used as well. So we are talking about growth of benefits and costs beyond the inflation rate, due to the opportunity cost of money: its value in generating real benefits over time.

Some people get really worried about the use of discounting. It just doesn’t feel right, somehow. Part of the problem is that it has such dire implications about the present value of benefits in the future. Some people find it objectionable that a dollar of benefits in 30 years time should only be considered to be worth about 5 cents in the present. It seems almost immoral! If you are one of those people, think about it as being effectively the same as choosing the “largest final value”, and perhaps you will feel more comfortable about it. The dollar in 30 years’ time will then still count as a dollar, but the dollar earned in year one will have accumulated enough interest to be worth say $20. Same effective result, but maybe it feels more reasonable.

One colleague working in biological science once objected to me that we are assuming that the money earned will actually be reinvested at the going rate and will continue to accumulate interest until the end of the period. What if this doesn’t actually happen? What if the investor did not reinvest the proceeds, but took some of them part way through the period and used them to pay for CDs or hold a big party?

He had in mind that this should reduce the discount rate used, so that future benefits would not be so diminished in the present. However, the logical implication is quite the opposite.

If I buy CDs, rather than leave money in the bank (which is pretty much how I actually behave, mostly), it is because I am judging the overall benefits to me of having the CDs to play is greater than the benefits of letting the money accumulate interest in the bank. In effect, the benchmark for me is a better option than using the bank, so the effective rate of inflation of benefits over time is higher! Or equivalently, the rate of deflation of future benefits to the present (the discount rate) should also be higher.

David Pannell, The University of Western Australia

Further reading

Pannell, D.J. (2004). Avoiding simplistic assumptions in discounting cash flows for private decisions, In: D. Pannell and S. Schilizzi (eds.), Discounting and Discount Rates in Theory and Practice, Edward Elgar, (forthcoming). full paper (45K)