Summary
The time value of money (TVM) is a concept that states that it is better to receive a sum of money now than the same sum of money in the future, because by receiving it now, you could invest the money, which would give you a return . The concept can be taken further and analyze the present value of a future sum and the future value of a current sum.
The TVM can be represented mathematically with a series of equations. When making decisions based on the TVM, compounding can also be added and inflation is usually considered as well.
Introduction
How much each person values money is an interesting concept. It may seem like some people value it less than others. Others are also willing to work hard to earn it. Although these concepts are quite abstract, when it comes to valuing money over time, there is, in fact, an established framework. If you're wondering whether to wait for a bigger raise at the end of the year or get a smaller one now, the time value of money is a principle you should know.
Introduction of the Time Value of Money
The time value of money (TVM) is an economic-financial concept that states that it is preferable to receive a sum of money now than the same sum of money in the future. This decision includes the idea of opportunity cost. By choosing to receive the money later, you lose the opportunity to invest it or use it for some other valuable activity.
Let's look at an example. A while ago, you lent a friend $1,000 and now he or she has contacted you to pay you back. He offers to give you $1,000 today if you can pick him up, because the next day he's leaving to travel the world for a year. However, he proposes that when he returns in 12 months he would give you the $1,000 without you having to go get it.
If you're too lazy to go, you could wait 12 months, but the TVM means you'd be better off picking them up today. During those 12 months, you could deposit the money over time with high interest. You could even invest wisely and make some profits. Inflation could also make your money worth less in 12 months, so in real terms you would be getting less money back.
An interesting question to consider is: what would your friend have to pay in 12 months to make it worth the wait? On the one hand, your friend should at least make up for any potential gains you could make during the 12-month waiting period.
What is the present value and the future value?
We can summarize this entire conversation in a short formula known as the TVM formula. But before we get to that, we need to clear up other calculations: the present value of money and the future value of money.
The present value of money allows you to know the current value of a future sum of cash, discounted at the market rate. Going back to our example, you might want to know what the current value of the $1,000 your friend will give you in one year is.
Future value is the opposite. You take a sum of money today and calculate its value in the future at a given market rate. So the future value of $1,000 in one year would include one year's interest.
Calculate the future value of money
Calculating the future value (FV) of money is simple. Let's go back to our example. We will use the interest rate (2%) as a possible investment opportunity available. The future value in one year of the $1,000 you receive invested today would be:
FV = $1,000 * 1.02 = $1,020
Suppose your friend now says that his trip will be two years. The future value of your $1,000 would then be:
FV = $1,000 * 1.02^2 = $1,040.40
Keep in mind that in both cases we assume compound interest. We can generalize our future value formula as follows:
FV = I * (1 + r)^n
I = initial investment, r = interest rate and n = number of time periods
Note that we can also replace I with the present value of money, which we will see later. So why might we want to know the future value? It helps us plan and know how much the money you invest today may be worth in the future. It also helps us with our previous example, in which we must make the decision to accept one amount of money now or another later.
Calculate the present value of money
Calculating the present value of money (PV) is similar to that of the future value, we are only trying to estimate how much a future amount would be worth today. To do this, we reverse the calculation for the future value.
Imagine your friend tells you that after a year he will give you $1,030 instead of $1,000. However, you need to find out if 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
Your friend is offering you a good deal. The present value of the money you will receive in the future is $9.80 more than you would receive if he gave you the money today. In this case, you might want to wait a year.
Let's look at the general formula to calculate PV:
PV = FV ÷ (1 + r)^n
As you can see, the FV can be rearranged for the PV and vice versa, giving us our TVM formula.
The Effects of Composition and Inflation on the Time Value of Money
The PV and FV formulas provide a great framework for analyzing TVM. We already introduced the concept of compounding, but let's expand on it and see how inflation can also affect our calculations.
Composition effect
Over the years, the composition has a snowball effect. What starts out as a small amount of money can turn into a much larger amount just because of the interest. In our established model, compounding is observed once a year, but you can apply compounding on a more regular basis, such as quarterly.
To build this, we can slightly adjust our model.
FV = PV * (1 + r/t)^n*t
PV = present value, r = interest rate, t = number of compounding periods per year
Let's add the given compound annual interest rate of 2% per year on the $1,000.
FV = $1,000 * (1 + 0.02/1)^1*1 = $1,020
Clearly, this is the same as we calculated before, but if you have the opportunity to apply compounding to your earnings four times a year, the result is greater.
FV = $1,000 * (1 + 0.02÷4)^1*4 = $1020.15
A 15 cent increase may not seem like much, but with larger amounts and over longer periods of time, the difference can be big.
Inflation effect
Until now, we did not include the inflation factor in the calculations. What good is a 2% annual interest rate if inflation is 3%? In periods of high inflation, it may be better to add the inflation rate instead of the market interest rate. This is commonly applied in salary negotiations.
However, inflation is a much more difficult factor to measure. On the one hand, you can choose between different indices that calculate the increase in the price of goods and services. They usually provide different figures. Inflation is also quite difficult to predict, unlike market interest rates.
In short, we can do very little about inflation. We can include an inflation discounting aspect in our model, but as we mentioned, inflation can be very unpredictable when it comes to its future situation.
How the Time Value of Money Applies to Cryptocurrencies
In the crypto space, there are many opportunities where you can choose between one sum of money now and a different sum in the future. Locked staking is an example. You may have to choose between holding your own ether (ETH) now or locking it up and getting it back in six months with a 2% interest rate. In fact, you can find another staking opportunity that offers a better return. Some simple TVM calculations can help you find the best product.
From a more abstract point of view, you might be wondering when you should buy bitcoin (BTC). Although BTC is known as a deflationary currency, its supply is actually slowly increasing to a certain point. This, by definition, means that you currently have an inflationary supply. So should you buy $50 of BTC today or wait for your next paycheck and buy $50 next month? The TVM would recommend you do the former, but the real situation is more complex due to the fluctuation of the BTC price.
Conclusions
Although what we have just done is define TVM formally, you have probably already been using this concept intuitively. Interest rates, yields, and inflation are common in our everyday economic lives. The formalized versions we work on today are very useful for large companies, investors and lenders. For them, even a fraction of a percentage can make a big difference in profits and bottom lines. For us as crypto investors, it is still a concept worth keeping in mind when deciding how and where to invest your money for the best returns.
Further reading
What is money?
How to calculate Return on Investment (ROI)
APY vs. APR: what's the difference?
