What Does Time Value Of Money Mean In Crypto?

At its core, the time value of money (TVM) is a fundamental concept that demonstrates why receiving a sum of money in the present is more valuable than the same amount of money in the future. By investing the money now, one can earn a return, leading to greater value over time.

The concept of TVM extends to examining the present value of future sums and the future value of present sums, both of which are crucial in financial decision-making.

TVM is not merely a theoretical concept, but can be precisely calculated using a variety of mathematical equations. Additionally, factors like compounding and inflation play a significant role in the practical application of TVM, making it an indispensable tool for investors and businesses alike.

Introduction

Everyone has a different opinion about money. Some people may seem like they value it less than others while some people work really hard to get more of it. Although these differing opinions might be hard to understand, there is a framework to figure out how much money is worth over time: this is called the time value of money. For example, if you're trying to decide whether to wait for a bigger raise at the end of the year or take a smaller raise now, the time value of money can help you decide.

The time value of money (TVM) is an economic concept that states it’s likely better to receive money now than to get an equal amount in the future. When a person decides to choose to receive the money later, the person takes on opportunity cost, which is missing the opportunity to invest it or use the money for something else.

For example, imagine your friend borrowed $5,000 from you to pay off his debt, and after a year the time for him to return it has come. He offers to pay it in full today if you drive over to his place, but explains that he’s going on a 1 year trip tomorrow. So if you want the money now, you have to drive over today, otherwise you will have to wait for a year.

You might feel like you don’t need the money now, and decide to wait for a year. But the TVM dictates that you are better off picking up the money today. Within the year, you could have invested the money, placed it in a high-interest savings account or even use it as capital in your business. Taking inflation into consideration, your money now will not be worth the same as a year into the future, so you’re actually getting less than what you should receive!

A question to consider is what would your friend have to pay in a year to make it worth the wait? Your friend will need to add a certain amount to the original principal to make up for the opportunity cost of you not receiving your money earlier.

What Is Present Value And Future Value?

Before we touch on the TVM Formula, we first need to understand how to calculate for the present value of money and the future value of money.

The present value of money lets you know the current value of money that will be given in the future, discounted at the market rate. For example, if your friend promises to return the $5,000 in 1 year, the present value is how much that money is actually worth today.

The future value is the opposite, and pertains to the future value of the money, with interest. The future value of $5,000 in 1 year would include 1 year worth of interest.

Calculating The Future Value Of Money

We’ll start with the simpler equation of the two: the future value of money. Let’s go back to our previous example, and we’ll use the interest rate of 5% as the opportunity cost. The future value of $5,000 would be:

FV = 5,000 * 1.05 = $5,250

Now, let’s say your friend extends their trip and will be staying for two years. The future value will now be:

FV = $5,000 * 1.02^2 = $5,512.5

Note that in both cases, we’ve accounted for simple compounding interest. We can now generalize FV using the formula:

FV = I * (1 + r)^n

I=Initial Investment, r=interest rate, and n=number of time periods

Note that I (initial investment) can be substituted for the PV which we'll cover next. So why do we want to know the FV? Knowing the future value helps us plan and make decisions about what to do with our money. For example, we can use it to understand how much money invested today will be worth in the future, and helps us decide whether to take a certain amount of money now or wait for a larger sum in the future.

Calculating The Present Value Of Money

Calculating for the present value (PV) of money is similar to the FV calculation. Instead of estimating what the money would be worth in the future, we now look at the current value of a sum of money that is to be given in the future. To do this we take the FV formula and reverse it.

Now your friend tells you that after a year, they’ll give you $5,500 instead of the original $5,000. You can use PV to determine if it’s a good deal or not. You can use the following formula (assuming the same 2% interest rate):

PV = $5,500 / 1.02 = 5,392.15

Based on the results, your friend is making you a good deal. The present value is $392.15 more than what you would get from your friend in today’s current value, so you are better off waiting for one year.

Let's look at the general formula for PV:

PV = FV / (1 + r)^n

As you can see, FV can be substituted for PV and vice versa, resulting to the TVM formula.

The Effects Of Compounding And Inflation On The Time Value Of Money

As you can see, PV and FV formulas provide a great framework for discussing TVM. However, it is also important to understand the concepts of compounding and inflation and see how they can affect our calculations.

Compounding Effect

What is compounding? Think of compounding as the snowballing of your money over the years by adding the interest that you made for that time period to your principal. In this way your principal continues to grow and what started as a small amount of money may eventually “snowball” and become larger. In our examples above, we only looked at compounding once year, but in reality it can be compounded more regularly.

To include compounding effect we now use the following formula:

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

PV=Present Value, r=interest rate, t=number of compounding periods per year

Let’s input the 5% per annum compounded interest rate given annually on $5,000.

FV = $5,000 * (1 + 0.05/1)^11 = $5,250*

This of course is the same amount we came to with our computations in the previous example. Let’s compare it to an investment that is compounded quarterly or four times in a year:

FV = $5,000 * (1 + 0.05/4)^14 = $5,254.73*

Compared to annual compounding, quarterly compounding resulted to an increase of $4.73, which may not seem like a huge amount. But when you think about using larger sums of money and a longer time period, compounding stands to increase your returns significantly.

Inflation Effect

As this point, we have not taken inflation into consideration to our calculations. How is a 5% per annual interest rate better for an investor if the inflation rate is at 7%? In periods of high inflation, investors often use the inflation rate rather than the market interest rate to make decisions whether or not to invest.

However, inflation is much more trickier to measure. There are many indexes that attempt to compute for inflation by measuring increases in the price of goods and services. Oftentimes, they have different results making interest rate hard to compute and predict, unlike market interest rates.

To summarize, there are limited actions we can take to address inflation. We may incorporate inflation discounting in our model, but as previously noted, forecasting inflation for the future can be highly erratic.

How Does The Time Value Of Money Apply To Crypto

There are different ways to earn cryptocurrency, such as staking, where you can choose to receive a sum of cryptocurrency now or a different sum in the future. For example, you might decide to lock your Ether (ETH) for six months and receive it back with an interest rate of 5%. You can use some simple TVM calculations to find the best staking opportunity that offers the highest return.

If you're thinking of buying Bitcoin, you might wonder when the best time is to buy it. Even though Bitcoin is called a deflationary currency, its supply actually increases slowly until a certain point, which means it currently has an inflationary supply. Say you have $100 to spend and are wondering if buying Bitcoin now or a month down the road is the best idea - while the TVM calculation would recommend buying it now, the actual situation is more complex due to the fluctuating price of Bitcoin.

This may have been your first time formally defining TVM, but chances are you might have already been using the concept without even realizing it. Things such as interest rates, yield and inflation are all part of our every day financial lives. Formalizing TVM can be especially helpful for big companies, investors, and lenders, as even a small change in percentage can significantly impact their profits. As crypto investors, we can also benefit from keeping TVM in mind when deciding where and how to invest our money for the best returns.

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