Summary
The concept of time value of money (TVM) means that it is more advantageous to receive the same amount of money now than in the future because you can invest the money and earn a return. This concept can be further applied to the study of the present value of future amounts and the future value of current amounts.
TVM can be expressed using a series of mathematical equations. When making TVM decisions, compound interest and inflation factors are often considered.
Introduction
The amount that each person values money is an interesting concept. Some people seem to value money less than others, while others are willing to work harder to earn it. While these concepts are fairly abstract, there is in fact a well-established framework when it comes to valuing money over the long term. If you're wondering whether you should wait for a big raise at the end of the year or get a smaller raise right away, it's important to understand the important principle of the time value of money.
Introduction to the Time Value of Money
The time value of money (TVM) is an economic/financial concept that refers to the fact that receiving the same amount of money now is more beneficial than receiving it in the future. This decision involves the concept of opportunity cost. If you choose to receive the money later, you will not be able to invest or use the money for other valuable activities in the meantime.
Here's an example: A while ago, you lent your friend $1,000, and now they've contacted you to ask for a refund. If you pick it up today, they'll give you the $1,000 back, but tomorrow they're leaving on a year-long trip around the world. If you don't pick it up today, they'll give you the $1,000 back after a year of traveling.
If you're too lazy to do it, you can wait a year. But TVM means you'd better go get your money today. During the year, you can put the money in a high-interest savings account. You can even invest it wisely to earn a profit. Inflation also means that the money will lose value in the coming year, so the actual value you get will be lower.
So let's think about it, how much money does your friend have to pay you back after one year to make it worth waiting for so long? First of all, the money paid back must at least cover the income you may get during the one-year waiting period.
What is present value and future value?
We can use a concise TVM formula to simply summarize the entire conversation above. But before that, we need to understand how to calculate the present value of funds and the terminal value of funds.
The present value of money is the present value of a future cash payment discounted at market prices. In the previous example, the present value is the actual value today of the $1,000 that your friend will return in one year.
The future value, on the other hand, is the future value of a sum of money today at a given market interest rate. So a future value of $1,000 in one year would include the value of the interest you've earned over that year.
Calculate the final value of funds
The future value (FV) of funds is easy to calculate. Going back to the previous example, we will use a 2% interest rate as the possible investment opportunity at hand. If you invest the $1,000 you receive today, the future value in one year will be:
FV = $1,000 * 1.02 = $1,020
If your friend says his trip will extend to two years, the future value of the $1,000 is:
FV = $1,000 * 1.02^2 = $1,040.40
Note that in both cases, we have taken into account the effect of compound interest. In summary, we can summarize the formula for calculating the terminal value as follows:
FV = I * (1 + r)^n
I represents the initial investment, r represents the interest rate, and n represents the number of periods.
Note that we can also use I instead of the present value of money, which we will introduce later. We need to know the future value of money because, on the one hand, it can help us plan and understand how much money invested today may be worth in the future. On the other hand, it also helps us choose whether to receive a sum of money now or wait until later to receive a different amount of money, as mentioned in the previous example.
Calculate the present value of money
The present value (PV) of money is calculated similarly to the future value of money. All we are doing is trying to estimate how much a future sum of money is worth today. To do this, we need to reverse the way the future value is calculated.
Suppose your friend tells you that after one year, they will pay you back $1,030 instead of the original $1,000. However, you need to figure out if this is a good deal. We can do this by calculating the PV (assuming the same 2% interest rate).
PV = $1,030 / 1.02 = 1,009.80
This result shows that the present value of $1,030 is $9.80 higher than the $1,000 you could get from your friend today. Therefore, this is a good deal. In this case, it is worth waiting a year.
The calculation formula of PV can be summarized as:
PV = FV / (1 + r)^n
As you can see, from FV we can calculate PV and vice versa, which gives us the TVM formula.
The impact of compound interest and inflation on the time value of money
Our PV and FV formulas provide a good framework for discussing TVM. We have already introduced the concept of compound interest, and we will expand on this later to explore how inflation affects our calculations.
Compounding Effect
Compounding creates a snowball effect over time. A small amount of money that you start with can grow much more over time than if you used simple interest alone. Our model only takes into account the effect of compounding annually. However, you may compound more frequently, such as quarterly.
To take into account more frequent compounding, we can fine-tune the model:
FV = PV * (1 + r/t)^n*t
PV stands for present value, r stands for interest rate, and t stands for the number of annual compounding periods.
We plug the present value of $1,000, the 2% compounding rate, and the number of annual compounding periods into the above formula:
FV = $1,000 * (1 + 0.02/1)^1*1 = $1,020
Of course, this is the same result as our previous calculation. However, if you had the opportunity to compound interest four times per year, the result would be higher:
FV = $1,000 * (1 + 0.02/4)^1*4 = $1020.15
An increase of 15 cents may not seem like much, but if the amount is larger and the term is longer, the difference between simple and compound interest can be more significant.
Inflationary Effect
So far, we have not taken inflation into account in our calculations. What good is a 2% annual interest rate when inflation is 3%? In times of high inflation, you are better off considering the inflation rate rather than the market interest rate. This is often the case when negotiating wages.
However, measuring inflation is a very tricky business. First, there are different indices to choose from to calculate the increase in the prices of goods and services. These indices are often not exactly the same. Also, unlike market interest rates, inflation is difficult to predict.
In short, there is nothing we can do about inflation. We can factor inflation discounting into our models, but as mentioned earlier, predicting future inflation rates is extremely difficult.
How to Apply the Time Value of Money to Cryptocurrency
The cryptocurrency space contains a variety of opportunities where you can choose between receiving one cryptocurrency payment now and another cryptocurrency payment in the future. Locked staking is one example. You may have to choose between keeping your Ether (ETH) now, or staking it and getting it back in six months at a 2% interest rate. In fact, you may find another staking opportunity with a higher return. Doing some simple TVM calculations can help you identify the best products.
More abstractly, you might be wondering when is the best time to buy Bitcoin (BTC). While BTC is often referred to as a deflationary currency, the fact is that its supply has been slowly increasing until a certain point in time. This means that BTC's current supply is inflationary, by definition. So should you buy $50 of BTC today, or should you wait until next month to buy $50 of BTC? TVM would recommend the former, but the reality is more complicated due to BTC's wild price fluctuations.
Conclusion
While this article formally defines TVM, you’ve most likely already used the concept intuitively. Concepts like interest rates, yields, and inflation rates are common in our daily economic lives. The formal definition of TVM presented in this article today will be of great benefit to large companies, investors, and lenders. For them, even a difference of a few tenths of a percent can have a huge impact on their profits and earnings. For cryptocurrency investors, TVM is also a concept worth keeping in mind when deciding what products to invest in and how to invest in order to get the best returns.
Further reading
What is currency?
How to Calculate Return on Investment (ROI)
What is the difference between APY and APR?
