The Time Value of Money: A Fundamental Concept for Cryptocurrency Investors

What is the time value of money?

The time value of money (TVM) constitutes a fundamental financial principle that states that a given amount of money is worth more today than that same amount in the future. This concept is based on the potential for investment: money available now can be invested to generate returns over time. The TVM allows for the systematic evaluation of the present value of future amounts and the future value of current sums.

To accurately determine these values, the TVM is calculated using specific mathematical equations. Additionally, it is possible to incorporate inflation adjustments into these calculations to make more precise financial decisions.

Fundamentals of the Time Value of Money

The value of money represents a fascinating concept. While some people do not attach much importance to it, others are willing to work hard to earn income. Although these approaches may seem abstract, when we analyze the value of money over specific periods, we refer to concrete and quantifiable indicators. This concept is particularly useful for evaluating situations such as deciding between accepting a smaller salary increase now or waiting until the end of the year for a larger one.

The time value of money establishes that receiving money today is preferable to receiving it in the future. At the core of this concept lies the opportunity cost: when you choose to receive money later, you lose the chance to invest it or use it productively during that interval.

Let's consider a practical example: some time ago you lent $1000 to a friend who now wants to return it. This friend would like to give you the $1000 today, as he will be leaving for a trip around the world for a year tomorrow. You can get your money back today or wait 12 months.

If you can't meet with him today, you will have to wait a whole year. According to the TVM, it is more advantageous to receive the money now. During those 12 months, you could deposit that capital in a high-yield account or make investments that generate profits. You should also consider the impact of inflation: in a year, your money will have less purchasing power, meaning you will recover less real value than what you originally lent.

An equally relevant question would be: how much should your friend pay you in 12 months for the wait to be justifiable? At a minimum, it should compensate for the potential returns you would have earned during that year.

Present and Future Value of Money: Essential Concepts

This reasoning can be expressed through formulas to calculate the TVM. First, let's analyze how the present and future value of money are calculated.

The present value allows estimating the current value of a specific amount that will be received in the future, considering the prevailing market rates. In our example, it would be useful to calculate what the true present value of the $1000 you will receive in a year is.

The future value represents the opposite concept: it estimates how much a current amount will be worth in the future, applying a certain market rate. Therefore, the future value of $1000 in one year will include the corresponding annual interest rate.

Calculation of Future Value

The future value (FV) is calculated relatively simply. Referring back to our example and using an interest rate of 2% as an investment opportunity, the future value of the $1000 received and invested today would be:

FV = $1000 * 1.02 = $1020

Now let's assume your friend indicates that his trip will last two years. The future value of $1000 would be:

FV = $1000 * 1.02² = $1040.40

Note that we are analyzing compound interest in both cases. The general formula for calculating the future value is:

FV = I * (1 + r)^n

Where:

• I = initial investment
• r = interest rate
• n = number of time periods

Keep in mind that we can replace I with the present value of money, a concept that we will examine next. The calculation of future value is fundamental for planning and determining how much an investment made today will be worth in the future. This information is also crucial when you need to decide between receiving an amount now or another amount later.

Present Value Calculation

Calculating the present value (PV) is similar to calculating the future value. In this case, we estimate how much a future amount would be worth today. For this, we use the future value equation.

Let's assume that instead of $1000, your friend promises to return $1030 within a year. To evaluate how convenient this offer is, we calculate the PV (using the same interest rate of 2%):

PV = $1030 / 1.02 = $1009.80

It turns out that your friend is offering a good deal: the present value of the future debt exceeds what you would receive today by $9.80. In this scenario, it is more advantageous to wait a year.

The formula for calculating the present value is:

PV = FV / (1 + r)^n

As you can see, PV and FV are interchangeable in the formulas, forming the basis of the TVM concept.

Effects of capitalization and inflation on the time value of money

The PV and FV formulas form the basis for calculating TVM. We have already mentioned capitalization, but let's expand on this concept and examine how inflation impacts our calculations.

Capitalization effect

In prolonged periods, capitalization produces an exponential effect. Initially, small amounts can exceed amounts with simple interest accumulated. In our model, we consider annual capitalization, but it can be performed more frequently, such as quarterly.

Considering this, we can slightly adjust our model:

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

Where:

• PV = present value
• r = interest rate
• t = number of compounding periods per year
• n = number of years

Applying a compound interest rate of 2% per year, calculated annually on $1000:

FV = $1000 * (1 + 0.02/1)^(11) = $1020*

This result matches our previous calculations. However, if we capitalize quarterly, the profits increase:

FV = $1000 * (1 + 0.02/4)^(14) = $1020.15*

Although 15 additional cents may seem insignificant, with larger amounts and longer terms, the difference becomes considerable.

Effect of inflation

So far, we have not considered inflation in our calculations. What is the point of obtaining a 2% annual return if inflation reaches 3%? During periods of high inflation, it is advisable to use the inflation rate instead of the market interest rate, especially when analyzing wages.

However, measuring inflation is complex. There are various indexes that calculate price increases in goods and services, generally yielding different figures. Moreover, inflation is difficult to predict, unlike market interest rates.

Consequently, the possibilities for action against this phenomenon are limited. We can incorporate inflation adjustments into our model, but as we mentioned, inflation is highly unpredictable in the long term.

Application of the time value of money in cryptocurrencies

In the cryptocurrency ecosystem, situations frequently arise where we must choose between receiving funds now or in the future. Staking is a clear example: participants must decide whether to keep their Ether (ETH) available now or lock it for six months at a rate of 2%. However, there are numerous staking alternatives that offer higher returns. TVM calculations are essential for selecting the most profitable product.

This concept can also guide decisions on when to acquire Bitcoin (BTC). Although BTC is commonly described as a deflationary currency, its supply gradually increases until it reaches a set limit, which technically makes it inflationary. Should you buy $50 in BTC today or wait until your next payment to buy $50 the following month? According to the principle of TVM, it is preferable to buy today, although in practice the situation is complicated due to the price volatility of BTC.

Practical Conclusions

Although we have presented formal definitions of the TVM, you probably already intuitively understand this concept. Interest rates, yields, and inflation are fundamental elements of our everyday economic life. The formulas and calculations analyzed in this article are particularly useful for large companies, investors, and lenders, where even small fractional percentages can create significant differences in financial outcomes.

For cryptocurrency investors, considering the time value of money is essential when determining how and where to invest to maximize returns. Systematically applying these principles can make the difference between mediocre and optimal investment strategies, especially in markets characterized by their volatility and variable return opportunities.