TL;DR
The time value of money (TVM) is a concept that states it's better to receive a sum of money now than the same sum in the future. This is because you could invest the money, giving you a return. The concept can be taken further to look at a future sum's present value and a present sum's future value.
TVM can be mathematically represented with a selection of equations. Compounding can also be added, and inflation is also commonly considered when making TVM decisions.
Introduction
How much we each value money is an interesting concept. It may seem that some people value it less than others. Others are willing to work harder for it too. While these concepts are pretty abstract, when it comes to valuing money over time, there is, in fact, a well-established framework. If you're wondering whether to wait for a larger end-of-year raise or get a smaller one now, the time value of money is a great principle to learn.
Introducing the Time Value of Money
The time value of money (TVM) is an economic/financial concept that states it's preferable to receive a sum of money now than an equal amount in the future. Within this decision is the idea of opportunity cost. By choosing to receive the money later, you miss the opportunity to invest it in the meantime or use the money for some other valuable activity.
Let's look at an example. You loaned your friend $1,000 a while back, and they've now got in touch to return it. They offer to give you the $1,000 today if you pick it up, but tomorrow they're going on a round-the-world trip for one year. However, they would give you the $1,000 once they're back in 12 months.
If you're feeling particularly lazy, you may wait 12 months. But the TVM means you'd be better off picking it up today. Within those 12 months, you could put it in a high-interest savings account. You could even wisely invest it and make some profit. Inflation would also mean that your money is worth less 12 months into the future, so you're actually being paid less in real terms.
An interesting question to consider is what would your friend have to pay you in 12 months to make it worth the wait? For one thing, your friend would at least need to offset the potential earnings you could make in the 12 months waiting period.
What Is Present Value and Future Value?
We can summarize this whole conversation neatly in a succinct formula known as the TVM Formula. But before we jump into that, we need to get some other calculations out of the way first: the present value of money and the future value of money.Â
The present value of money lets you know the current value of a future sum of cash, discounted at the market rate. Looking at our example, you might want to know what the $1,000 from your friend in one year is actually worth today.
The future value is the opposite. It looks at a sum of money today and calculates what its worth will be in the future at a given market rate. So, the future value of $1,000 in a year would include a year's worth of interest.
Calculating the Future Value of Money
The future value (FV) of money is simple to calculate. Let's return to our previous sample, and we'll use the interest rate (2%) as the possible investment opportunity at hand. The future value in one year of the $1,000 you receive today invested would be:
FV = $1,000 * 1.02 = $1,020
Imagine your friend now says their trip will be two years. The future value of your $1,000 would then be:
FV = $1,000 * 1.02^2 = $1,040.40
Note that in both these cases, we've assumed compounding interest. We can generalize our future value formula as:
FV = I * (1 + r)^n
 I=Initial Investment, r=interest rate, and n=number of time periods
Note that we can also substitute I for the present value of money that we'll cover later. So why might we want to know the future value? Well, it helps us plan and know what invested money today may be worth in the future. It also helps us with our previous example, where a decision needs to be made to take some amount of money now or another sum later.
Calculating the Present Value of Money
Calculating money's present value (PV) is similar to our future value calculation. All we're doing is trying to estimate what an amount in the future would be worth today. To do this, we reverse the calculation for future value.
Imagine that your friend tells you that after a year, they'll give you $1,030 instead of the original $1,000. However, you need to figure out whether that's a good deal or not. We can do this by calculating the PV (assuming the same 2% interest rate).
PV = $1,030 / 1.02 = 1,009.80
Here, your friend is actually offering you a good deal. The present value is $9.80 more than what you would get from your friend today. In this case, you'd be better off waiting one year.
Let's look at the general formula for calculating PV:
PV = FV / (1 + r)^n
As you can see, FV can be rearranged for PV and vice versa, giving us our TVM formula.
The Effects of Compounding and Inflation on the Time Value of Money
Our PV and FV formulas provide a great framework for discussing TVM. We already introduced the concept of compounding, but let's expand it further and see how inflation can also affect our calculations.
Compounding effect
Compounding has a snowballing effect over the years. What starts as a small amount of money can become much larger than an amount with only simple interest. In our established model, we looked at compounding once a year. However, you may compound more regularly than that, say every quarter per year.
To build this in, we can adjust our model slightly.Â
FV = PV * (1 + r/t)^n*t
PV=Present Value, r=interest rate, t=number of compounding period per year
Let's plug in our 2% per annum compounded interest rate given once per year on $1,000.
FV = $1,000 * (1 + 0.02/1)^1*1 = $1,020
This is, of course, the same as what we calculated earlier. If, however, you have the chance to compound your earnings four times a year, the result is greater.
FV = $1,000 * (1 + 0.02/4)^1*4 = $1020.15
An increase of 15 cents may not look much, but with larger sums and over longer time periods, the difference can become large.
Inflation effect
As of yet, we've not factored inflation into our calculations. What good is a 2% per annum interest rate when inflation is running at 3%? In periods of high inflation, you may be better off plugging in the inflation rate rather than the market interest rate. Wage negotiations are one place where this is commonly done.
However, inflation is a much trickier thing to measure. For one, there are different indexes to choose from that calculate the increase in the price of goods and services. They commonly provide different figures. Inflation is also fairly hard to predict, unlike market interest rates.Â
In short, there isn't much we can do about inflation. We can build into our model a discounting aspect for inflation, but as mentioned, inflation can be wildly unpredictable when it comes to the future.
How Does the Time Value of Money Apply to Crypto
There are multiple opportunities in crypto where you can choose between a sum of crypto now and a different sum in the future. Locked staking is one example. You may have to make a choice between keeping your one ether (ETH) now or locking and getting it back in six months with an interest rate of 2%. You may, in fact, find another staking opportunity that offers a better return. Some simple TVM calculations can help you find the best product.
More abstractly, you might be wondering when you should buy bitcoin (BTC). Although BTC is commonly called a deflationary currency, its supply actually increases slowly until a certain point. This, by definition, means it currently has an inflationary supply. Should you then purchase $50 of BTC today or wait for your next paycheck and buy $50 next month? TVM would recommend the former, but the actual situation is more complex due to the fluctuating price of BTC.
Closing Thoughts
Although we've defined TVM formally, you've likely already been using the concept intuitively. Interest rates, yield, and inflation are common in our daily economic lives. The formalized versions we worked on today come in great use to large companies, investors, and lenders. For them, even a fraction of a percent can make a huge difference to their profits and bottom line. For us, as crypto investors, it's still a concept worth keeping in mind when deciding on how and where to invest your money for the best returns.