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Understanding investment in 50 objects Part 4: time and money studies

Understanding investment in 50 objects Part 4: time and money studies
May 27, 2016
Understanding investment in 50 objects Part 4: time and money studies

It says much about the enduring popularity of the novels of Charles Dickens that first-edition copies of his work are still widely available. Here’s one – specifically, it’s a first edition of Bleak House, Dickens’s sprawling and complex satire on the English legal system, and this particular copy was recently offered for sale on the ABE web-based market place for second-hand book sellers.

True, like most of Dickens’ novels, Bleak House was first published in magazine format; specifically, in 20 parts spread over March 1852 to September 1853, the final two parts being printed in a bumper double issue. Also like most of the great man’s novels, the parts were then collected together and, with added illustrations, sold as a book. In book form – and with extra illustrations by H. K. Browne, who worked with Dickens for over 20 years – Bleak House was published by Bradbury and Evans in 1853 for 25 shillings – £1.25 in decimal money.

Because we know precisely the original price of the first edition, when it was published and because there is an active market in trading first-edition copies today, then Bleak House provides a really good way to show the wonder of compound interest. And – in some ways – a wonder it is. Not for nothing did Albert Einstein rank compound interest as the eighth wonder of the world.

Let’s explain why. First, we need to define ‘compound interest’. It is the interest that’s added to a deposit so that in future the interest as well as the capital earns interest. So a savings account offering a rate of 1.5 per cent per year, and with a deposit of £10,000, will generate £150 of interest in its first full year. If that interest is then added to the capital – so that it becomes capital, too – then at the end of the second year the interest added would be £152.25 – 1.5 per cent of £10,150. At the end of the third year £154.53 of interest would be added, and so on.

At this stage, those differences don’t seem to matter much. Who cares if, at the end of year three, the account holder picks up £154.53 of interest instead of £150? But that’s to underestimate the remorseless power of compounding as it stacks up over the years. By the end of year 20 the annual interest on the principal that has been swollen by all those years of accumulated interest would be virtually £200 and the aggregate amount of accumulated interest would be approaching £3,500.

It’s to do with the way that the maths of compounding works. The effect of adding the interest to the capital is that, in a way, the interest rate gets higher for each succeeding year that the deposit is maintained. That’s because each year the capital sum is multiplied by a bigger number, which is driven by an exponent that rises in line with the number of years (or, to be precise, with the number of compounding periods).

So, in compounding, time plays a crucial role and this is best illustrated if we compare the long-term outcomes of what seem like small differences in interest rates.

Imagine that, while one savings account offered interest at 1.5 per cent, simultaneously another offered 3 per cent. Obviously in the first year the interest paid – and added back – would be twice the amount of the less generous account – for a deposit of £10,000, £300 compared with £150. But because the compounding rate was higher then the interest paid by the 3 per cent account would accelerate away from the 1.5 per cent account. In year two, interest would be £309 compared with £152.25. By year 20, the respective amounts would be £526 and £199 and the interest accrued over the full years would be £8,061 versus £3,469. Put simply, with compounding over long periods small differences in interest rates have big consequences.

Okay, so let’s relate this to Dickens’ Bleak House. Say your great, great grandfather bought a first edition back in 1853 and paid the sum of 25 shillings (£1.25). Today, depending on its condition, the book could sell for anything from £3,000 to £9,000. But the one we’re focusing on was offered by an American bookseller (most copies seem to be in the USA) for £4,267.27.

Two questions arise: first, at what rate – measured by its annual compound interest rate – has the book’s value risen? Second, how does that compare with the most familiar benchmark, retail price inflation?

The answer to the first is 5.12 per cent a year. That’s the interest rate, when compounded annually, that takes £1.25 to £4,267 over a period of 163 years. Second, it compares well with estimates for rates of inflation, whether that’s the rate for the US – 2.1 per cent – or for the UK, which is 3.01 per cent.

But if the interest rate differential between that for Bleak House and that for basket-of-goods inflation doesn’t sound very great, then consider this: back in 1853 your great, great grandfather spent £1.25 to buy a nice, new, leather-bound copy of Bleak House and today that slightly worn copy is worth £4,267. If instead he had put the same amount of money into something that endured but whose value had just happened to rise at exactly the same rate as the UK’s inflation rate then what would it be worth today? All of £157.13. In other words, £4,267 plays £157. Now that’s the power of compounding.

7: An HP-12C calculator

The investment lesson: discounted cash flow

This isn’t just any old calculator. This is the HP-12C – almost certainly the world’s best-selling calculator, though its maker no longer knows how many it has sold. What is known is that the 12C has been in continuous production since 1981 with very little in the way of improvements to its hardware or its software. For a machine that’s basically a micro computer, that defies belief. After all, the umpteen iterations of Moore’s Law since 1981 mean that today’s average computer is about 60,000 times more powerful than its 1981 counterpart. Yet the 12C just keeps chugging along.

It’s still widely available. Buy one direct from its maker, HP – the computer-making spin off from Hewlett-Packard – but that will set you back £79. Get the same machine from Amazon’s market place and you’ll pay just under £50. There is a more powerful version of the 12C available, the 12C Platinum. It’s cheaper, yet it does not sell so well. Somehow, it lacks the iconic status of the basic 12C.

Probably what’s so special about the 12C is that generations of financial analysts have been brought up on it. The 12C is the original tailor-made financial calculator. Its software is designed to do those tasks that financial analysts perform by the bucket load – working out bond pricing, yield to maturity, annuity rates. Today it remains the analysts’ tool of choice for the back-of-the-envelope calculations needed in the hurly-burly of financial markets. When it was a new product, however, it was a revelation. Effortlessly it performed big calculations that previously had analysts spitting blood. In particular, it made a doddle of the most basic, the most tedious, but the most important calculation of all – working out the time value of money.

It’s hardly an exaggeration to say that the time value of money is at the core of all capitalism. It alone dictates whether it’s right to spend or to save. It drives financial markets because they are simply mechanisms by which people trade between spending money today (the sellers) or spending it in the future (the buyers).

And what dictates the decision whether to spend/sell or save/invest – or, say, the decision whether or not a company goes ahead with a new project – is whether the money that’s likely to be received in the future will be greater than the outlays when all the cash flows are adjusted for the time value of money. What’s crucial about time value is that it acknowledges – and adjusts for – the fact that £1 received in the future is less valuable than £1 received today. In an investment decision, the question is how much less valuable will those future £s be and will there be enough of them to compensate for that loss of value caused by time?

To decide that, a discounted cash flow calculation is needed, which is what we have in the table. All the ingredients are there. First, the nominal value of the cash flows, starting with a £12m outlay upfront and ending with an £8.5m cash profit at the end of year 6.

Net Present Value The cash flows of a project (£m)Year 
Nominal valuePresent valueCumulative present value0
-12-12-121
-2.5-2.3-14.32
1.51.27-13.033
3.52.74-10.294
4.53.25-7.045
53.33-3.726
8.55.211.49 
Net present value:1.49  
Cost of capital:8.50%  
Internal rate of return:11.00% 

Next, there is a cost of capital – 8.5 per cent – which is the interest rate demanded for new investments. That means the future cash flows from the project are ‘discounted’ by the cost of capital. A discount rate is simply an interest rate worked backwards. Applying it tells us, for example, that the £3.5m to be received at the end of year 3 would have a present value of £2.74m, so it’s the same as investing £2.74m today and earning interest at 8.5 per cent for three years.

Then there is an internal rate of return (IRR), which is the discount rate that sums all those nominal cash flows to zero. If IRR is greater than the cost of capital then the project will be profitable. In this case, that profit – the net present value – is £1.49m. In other words, the forecast says that all the cash flows from the project will be the same as receiving £1.49m in cash today.

Does that make this particular project a winner? Not necessarily. In assessing any investment proposition – whether it’s for a company to do a project or for an investor to buy a company’s shares – what really matters is the amount of net present value (NPV). After all, which would you prefer (and assuming the same cost of capital for both) – a super-duper project that earns a big fat IRR but which will only ever be small-scale so its NPV is just £1m, or a project whose IRR is only modestly more than the cost of capital but whose scope is large enough for the NPV to be £10m? It’s obvious, isn’t it?

And there is another problem with IRR calculations. Projects that have alternating years of positive and negative cash flows will have more than one IRR, which is bound to confuse; mathematicians know this from ‘Descartes’ rule of signs’. Yet there will only ever be one figure for NPV.

The beauty of the HP-12C is that it can do all this almost in a trice. Sure, it huffs and puffs a bit if you input too many numbers, but it gets there. If the calculation is really complex, then there is little doubting that a computer spread sheet will do a better job. But that takes time to construct. For your quick-and-dirty, back-of-the-envelope calculations that give a feel for whether an investment proposition is sensible or stupid, still nothing beats the HP-12c.