What is the time value of money?

The Time Value of Money(TVM) concept refers to the idea that for the same amount of funds, receiving money now is more advantageous than receiving it in the future. The reason is that you can invest the funds to earn returns. This concept can be further used to study 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, factors such as compound interest and inflation are often considered.

Introduction

Everyone’s valuation of money is an interesting concept. Some people seem to value money less than others, while some are willing to put in more effort to obtain it. Although these concepts are quite abstract, there is a mature framework when it comes to long-term valuation of money. If you want to know whether it’s more cost-effective to wait until the end of the year for a large salary increase or to accept a smaller immediate raise, understanding the important principle of the time value of money is necessary.

Introduction to the Time Value of Money

The(TVM) concept is an economic/financial idea that indicates that for the same amount of funds, receiving money now is more advantageous than receiving it in the future. This decision involves the concept of opportunity cost. If you choose to receive the funds later, you cannot invest or use the money for other valuable activities during that period.

For example: Not long ago, you lent your friend $1,000. Now they have contacted you and plan to repay the money. If you go to collect today, they will return $1,000, but starting tomorrow, they will embark on a one-year global trip. If you do not go to collect today, they will return the $1,000 after a year when they come back from their trip.

If you are too lazy to go now, you can wait a year. But the meaning of TVM is that it’s better to collect the debt today. During this year, you could deposit the money into a high-interest savings account. You could even wisely invest it to earn profits. Inflation also means that this money will depreciate over the next year, reducing its real value.

So, we can think about how much your friend should repay you after a year to make it worth your wait. First, the amount repaid should at least cover the income you could have earned during that year.

What are Present Value and Future Value?

We can use a simple TVM formula to briefly summarize the above discussion. But before that, we need to understand how to calculate present value and future value of funds.

Present value refers to the current worth of a future sum of cash discounted at the market rate. In the example above, the present value is the actual value today of the $1,000 your friend will repay after one year.

Future value, on the other hand, is the opposite; it refers to the value of a sum of money today calculated at a given market interest rate. Therefore, the future value of $1,000 after one year will include the interest earned during that year.

Calculating Future Value of Funds

The(FV) of funds is easy to calculate. Returning to the previous example, we will use a 2% interest rate as the potential investment opportunity. If you invest the $1,000 you receive today, the future value after one year will be:

FV = $1,000 * 1.02 = $1,020

If your friend says their trip will extend to two years, then the future value of that $1,000 will be:

FV = $1,000 * 1.02^2 = $1,040.40

Note that in both cases, we consider the effect of compound interest. In summary, the future value calculation formula can be summarized as:

FV = I * (1 + r)^n

I represents the initial investment, r is the interest rate, n is the number of periods.

Please note that we can also use I to replace the present value we will introduce later. We need to know the future value because, on one hand, it helps us plan and understand how much the invested funds might be worth in the future. On the other hand, it also helps us decide whether to receive a sum of money now or wait for a different amount later, as mentioned in the previous example.

Calculating Present Value of Funds

The calculation of present value(PV) is similar to that of future value. We are simply estimating how much a future sum of money is worth today. To do this, we invert the future value calculation.

Suppose your friend tells you that after one year, they will repay you $1,030 instead of the original $1,000. But you need to figure out whether this deal is worthwhile. We can do this by calculating PV (assuming the same 2% interest rate):

PV = $1,030 / 1.02 = 1,009.80

This result indicates that the present value of $1,030 is higher than the $1,000 you could get from your friend today by $9.80. Therefore, this deal is more favorable. In this case, it’s worth waiting a year.

The PV formula can be summarized as:

PV = FV / (1 + r)^n

As you can see, PV can be calculated from FV, and vice versa. Based on this, we can derive 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. The previous text introduced the concept of compound interest, and further exploration will examine how inflation affects our calculations.

Compound Interest Effect

Compound interest creates a snowball effect over time. A small amount of money initially can grow significantly over time, far exceeding what simple interest would produce. Our existing model only considers annual compounding. However, your compounding frequency might be higher, such as quarterly.

To account for more frequent compounding, we can adjust the model:

FV = PV * (1 + r/t)^n*t

PV represents present value, r is the interest rate, t is the number of compounding periods per year.

For example, substituting $1,000, a 2% interest rate, and 1 compounding period per year:

FV = $1,000 * (1 + 0.02/1)^1*1 = $1,020

This matches our previous calculation. But if you have the opportunity to compound quarterly (4 times a year):

FV = $1,000 * (1 + 0.02/4)^1*4 = $1020.15

An extra 15 cents may seem small, but with larger amounts and longer periods, the difference between simple and compound interest can become more significant.

Inflation Effect

So far, we haven’t considered inflation in our calculations. What is the use of a 2% annual interest rate when inflation is 3%? During high inflation periods, it’s better to consider the inflation rate rather than the market interest rate. When discussing wages, inflation is often a key factor.

However, measuring inflation is quite tricky. Different indices are used to track price increases for goods and services, and these indices often differ. Moreover, unlike market interest rates, inflation rates are difficult to predict.

In short, we are powerless against inflation. We can incorporate inflation discount factors into our models, but as mentioned earlier, predicting future inflation rates is extremely challenging.

How to Apply the Time Value of Money to Cryptocurrency

The cryptocurrency space offers various opportunities where you can choose between receiving crypto funds now or in the future. Staking is one example. You might have to choose between holding your Ethereum(ETH) now or staking it to earn a 2% interest rate over six months. In fact, you might find another staking opportunity with a higher return. Simple TVM calculations can help you identify the best product.

More abstractly, you might wonder about the best time to buy Bitcoin(BTC). Although BTC is often called a deflationary currency, its supply has been slowly increasing until a certain point. By definition, this means BTC is currently in a state of inflation. So, should you buy $50 worth of BTC today or wait until next month to buy another $50? TVM would recommend the former, but due to BTC’s price volatility, the actual situation is more complex.

Conclusion

Although this article has formally defined TVM, you have likely used this concept intuitively. Concepts like interest rates, yields, and inflation are very common in our daily economic life. The formal definition of TVM introduced here is highly beneficial for large companies, investors, and lenders. For them, even a tiny percentage difference can significantly impact profits and returns. For cryptocurrency investors, TVM is also a crucial concept to remember when deciding which products to invest in and how to invest to maximize returns. **$HNT **$BTT **$LPT **