Chapter 1
Time Value of Money

Which is worth more: one dollar today, or one dollar tomorrow?

The Standard Theory

The standard theory of the time value of money states that a dollar in your hand today is worth more than the same dollar in your hand in the future. This is true even if there is no inflation.

Here's one example. Would you rather have $100 today, or $100,000,000 in a million years? Even if you were absolutely certain that the $100,000,000 would be "yours" in a million years, it would be worth nothing to you, because you would not expect to be around to enjoy it. Further, even if your great, great, great, etc., grandchildren could be assured of receiving it, it would probably mean little to you.

But what about more realistic waiting periods? For example, suppose you have the choice between $100 now, and $100 in a year from now. The standard theory says that the rational person will always choose the $100 now, because you could do everything with $100 now that you could do with it in a year from now, and you could invest it to earn interest between now and then.

This standard theory is right, but it has a few important assumptions buried in it. The most important of these assumptions is that you can save money at no cost and at no risk between now and the future. In thinking about the standard theory, or any economic theory, it is important to remember the assumption of "all other things equal" (from the Latin, ceteris paribus).

Assumption: You Can Save Money at No Cost

The assumption that you can save money at no cost means that if you have a certain amount of money today, you can save that money for any period at no cost. No cost means that you don't have to pay any storage charges, or insurance charges, or handling charges, or taxes, or charges of any kind.

In the last hundred years or so, citizens in developed economies have gotten used to the idea that they can save money, in a bank for example, and not have to pay for the service. We will not be surprised if financial historians of the future look back and see this as a sort of financial magical thinking, which has indirectly had catastrophic costs by making the entire banking system unstable.

In general, if you want to store any valuable commodity, you would have to do it yourself - perhaps in your home, in a rented vault, or perhaps even burying it in the ground. You would not expect that you can store it securely for free.

In principle, money is no different. But the way banking has developed over the past several hundred years, bankers, with the willing cooperation of their depositors, have purported to "save" money for free for their depositors. Of course, nothing is free. The bankers have been willing to offer this service for free so that they could get their hands on the money. Do they "save" it for you? Absolutely not. They lend it out. This lending puts your money at risk, and generates income for the bank, provided that the bank doesn't suffer too many loan losses. If the bank suffers too many loan losses, they may not even be able to pay you back the money that you deposited.1

Despite the inherent instability of this practice, it has become so entrenched in the modern banking system that it seems like a permanent feature. We don't think history will prove it so, but for the time being (and perhaps for the foreseeable future), it is.

Assumption: You Can Save Money at No Risk

The assumption that you can save money at no risk of not getting it back (in other words, that you can save money with the guarantee that you'll receive 100% of it back) is easy to understand in principle. It is a bit surprising that so many people believe it to be literally true. There is no truly riskless proposition in the material world. It may be the case that some things carry extremely low risk, but in our world, that risk is never actually zero.

Nevertheless, most people in the developed world behave as though they can put money in the bank, and have no risk of not getting it back in the future.

As long as you can put money in the bank and expect to receive it back in the future, and the bank doesn't charge you for the service, a dollar now is worth more than a dollar in the future, because you can turn it into a dollar in the future by storing it. Anything you can do with a dollar in a year, you could do with a dollar now because you could just wait. But you can do things with the dollar now, such as spend it now, that you cannot do with a dollar in a year. So the dollar now is worth at least as much as the dollar in the future.2

Time Value of Money and Compound Growth

Economists, financial professionals, and talking heads often conflate the time value of money with the phenomenon of compound growth. You don't need to worry about the finer points of theory as discussed earlier, but you do need to understand the math of exponential or compound growth.

Perhaps the easiest way to understand compound growth is to think in terms of "interest on interest." Suppose you have $100 and you can earn 10% per year. (For the purpose of illustration, we assume that the 10% earnings are risk-free, but remember the real world is never risk-free.) Table 1.1 shows how your money would grow if you get paid interest at the end of every year, and reinvest the interest.

Tabelle 1.1 Compound Growth Assuming Interest Payments Are Reinvested

In the first year, you earn $10 of interest, which is 10% of your $100. But in the second year, you earn $11, because you earned your 10% on your original $100, but you also earned 10% on your $10 of interest. That "interest on interest" earned you $1 in year two. You earned a total of $11, which could be thought of as $10 on your original $100, plus $1 on the interest you earned the first year.

Each year, you still earn the $10 on your original $100, but the "interest on interest" gets bigger every year. By the ninth year, you are earning more "interest on interest" than on your original $100!

This compound growth is the phenomenon that people get so excited about. Almost everyone who has ever amassed significant wealth legitimately (i.e. other than by stealing it) has done it, at least in part, by putting compound interest, or exponential growth (another term for the same phenomenon), to work. Just in case you're not convinced, here is a bit of argumentum ad verecundiam (just a fancy sounding way of saying argument from authority).

"Compounding is the magic of investing."

-Jim Rogers

"The effects of compounding even moderate returns over many years are compelling, if not downright mind...