The time value of money

One of the odd things about this blog is that though I work in finance, I rarely write about it. Partly this is to keep my blogging life and my work life separate, but perhaps that separation is greater than it need be. Shortly, I plan on publishing my review of Karl Marx’s Capital. In writing that review, it became necessary to critique Marx’s dismissal of the notion of the time value of money. However, I recognise that not all of you are necessarily chartered accountants or have A-levels in economics. So you may not have heard the term before. If you have, and are aware of it, you may happily go about and read something else unless you want to pick my analysis apart. For those for whom the term does not mean something precise, then I hope this will sharpen up the concept in your mind, though I apologise if this comes across as patronising.

The concept of the time value of money should be one that you find fairly instinctive. I’ll demonstrate this with a few examples. Firstly, I offer to you a sum of money, let’s say £100. You can have that today, no strings attached. Or I could ask you to wait a week and then I would give you £110. Which is more valuable to you?

You have a choice between a smaller value or a greater value in the future. Can you wait for a week or is your need for the cash flow so great that you would settle for a smaller sum, effectively forfeiting £10?

Another trade-off would be if I offer you £100 now or £101 in ten years’ time. Which is more valuable to you?

I would hope that in the first case, waiting is the better option for you and that in the second case it is better to take the guaranteed sum now. Yet all this hinges on a level of subjectivity. It can vary from person to person or from business to business. The trick is to try to find an equivalent rate whereby the current value is equal to some future value. For example, if our choice was between £100 now and £105 in a year’s time, then would you “um” and “ah”, being unable to work out which is more valuable to you. If you put the money in a bank would you get a net rate of interest of 5%? If you could get more, then it’d more rational to put the £100 in the bank and get more interest, so at the end of it you have more than the £105 you might have had. If the net interest rate is lower, is there another way by which you could get a greater return in one year? If not, then your best bet is the £105 in a year’s time.

So the time value of money is expressed as an interest rate, being the rate that you would consider reasonable for a rate of return if given the opportunity to have a different sum at a future point in time.

One of the consequences of this is that higher interest rates are associated with higher levels of risk. You may have heard the phrase, “high risk, high return”, particularly if you’ve looked at choices for pension investments or if you think back to the global financial crisis of 2008, particularly with regards to the critique that the high risk aspect was ignored by the bankers whose actions played a significant part in precipitating the financial meltdown.

In my view, a part of the reason for this was that the fundamental subjectivity of the notion of the time value of money was forgotten by the systematic use of the Black-Scholes formula for options trading. That attempted to turn finance into a science which is a category error. Risk cannot be accurately quantified and it is a mistake to try to do so. Measures such as interest rates are indicative, so one looking at bonds can tell that a rate of 7% is riskier than one offering 2%. I know this personally quite well as I had considered changing my ISA some years ago and found the best rates of interest available to UK investors were to be found in Iceland. I even got so far as to the have an application form on my living room table. But I was suspicious about the high interest rates and, coupled with the relative devaluing of the Icelandic Krona against the Pound, I hesitated. Two months later those Icelandic banks collapsed. They were offering a high return because they were high risk investments.

The other aspect to think about is inflation. This is another reason why I stated at the top that the time value of money should be fairly instinctive, even if the term is new to some. Inflation is the creeping rise of prices of various goods, services and assets. If you have a fixed sum of money then it’s value decreases over time. In my childhood, £1 could buy you four packets of sweets with change left over. Years later, £1 might leave the shopkeeper asking for the rest of the money if you try to buy a single packet. So looking at cash as the arbiter of value is inherently flawed. What we can do is ask about what is known as present value.

What this does is look at future (generally fixed) payments and ask how much is the sum of those payments worth at today’s values. For example, the rent on my one bed, mouse-infested and rather cold flat is £11,700 per year. Let’s say that that rent doesn’t change for 10 years. Is the present value £117,000? No, because in 10 years’ time £11,700 will not be worth the same as £11,700 is today. I need to employ my subjective interest rate, my measure of risk, to do a calculation. Yet even that calculation will be assuming a constant rate of risk, but who knows what the future may bring?

If anything, that’s the point. The world of finance and of economics in general contain a great many unknowns. Those who would profess to declare with confidence exactly what will happen in the future are generally false prophets. Look out for this in the economic arguments in the general election. There, politicians from party Y will declare unanimously that if party X is elected then the economy is doomed whilst at the same time asserting with equally misplaced confidence that if they are placed in stewardship of the economy (though I doubt they have the humility to use the term stewardship) then all will be well. This will be on top of party X and party Y making promises on the other’s behalf.

I wouldn’t trust either who take such an approach to finance, but I would also warn against placing trust in finance in the first place. Believe me, I’m an accountant!

Advertisements

One response to “The time value of money

  1. Pingback: Book Review: Capital (Das Kapital) by Karl Marx | The Alethiophile