Carefully! Lots of text.
The time value of money (TVM) is the concept that it is preferable to receive a certain amount now than the same amount in the future. The fact is that during this period money can be invested and made a profit. This concept can be taken further to consider the present value of a future amount and the future value of a current amount.
IRR is calculated mathematically using a series of equations. In addition, inflation-adjusted compounding can be used when making IRR decisions.
Introduction
The value of money is an interesting concept. Some people do not attach much importance to money, while others are willing to work hard to earn an income. Although these concepts are quite abstract, when we talk about assessing the value of money over a certain period of time, we mean specific indicators. So, if you're wondering whether to wait until the end of the year for a larger raise or get a smaller one now, the concept of the time value of money may be useful to you.
Time Value of Money Basics
The time value of money (TVM) is an economic concept that states that receiving money now is preferable to receiving money in the future. At the heart of this concept is the idea of missed opportunities. When you decide to receive money later, you cannot invest it or use the funds for other tasks in that particular period of time.
Let's look at an example. Some time ago you lent a friend $1000, and now he wants to pay you back. A friend would like to give $1000 today because tomorrow he will be traveling around the world for a year. You can withdraw your money today or in 12 months.
If you are unable to meet him on this day, you can wait 12 months, but under the VSD it is better to receive the money today. During these 12 months, you can put the funds into a high-interest savings account or invest them and earn a profit. It's also worth considering inflation and the fact that in a year your money will be worth less - meaning you'll get back less in real terms than you borrowed.
An equally interesting question is how much would your friend have to give you in 12 months to make it worth the wait? At a minimum, it would have to offset the potential earnings you could have earned during that year.
What is the current and future value of money
Our reasoning can be expressed by a short formula for calculating IRR. However, first let's understand the calculation of the current and future value of money.
The current value of money allows you to estimate the value of a specific amount of money at the market rate at the moment. Returning to our example, it might be helpful to calculate what the present real value of the $1,000 you will receive in a year is.
Future value is the opposite concept. With its help, the current amount of money and its value in the future are estimated at a given market rate. Thus, the future value of $1,000 in one year will include the annual interest rate.
Calculating the future value of money
The future value (FV from English Future Value) of money is calculated very simply. Let's go back to our example and use the interest rate (2%) as a potential investment opportunity. The future value of the $1,000 you received and invested today will be:
FV = $1000 * 1,02 = $1020
Suppose a friend says the trip will last two years. Then the future value of $1000 will be:
FV = $1000 * 1,02^2 = $1040,40
Please note that in both cases we were looking at compound interest. The formula for calculating future value is 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 current value of money, which we'll look at next. Why do we need to calculate future value? First of all, it helps to plan and know how much money invested today will be worth in the future. This will also be useful in the previous example, where you need to make a decision: take some amount now or another amount later.
Calculation of the current value of money
Calculating the current value of money (PV from English Present Value) is similar to calculating future value. In this case, we are trying to estimate how much this or that amount would cost today in the future. To do this, we use future value calculation.
Let's say that instead of $1000, a friend promises to return you $1030. However, you need to understand how good this deal is. To do this we will have to calculate the PV (with the same interest rate of 2%).
PV = $1030 / 1,02 = 1009,80
It turns out that the friend is indeed offering a good deal. The present value of the debt from the future is $9.80 more than what you would receive today. In this case, it is better to wait one year.
Let's look at the formula for calculating PV:
PV = FV / (1 + r)^n
As you can see, PV can be substituted for FV and vice versa, and we get the VSD formula.
The Effect of Compounding and Inflation on the Time Value of Money
The PV and FV formulas are a good basis for calculating IRR. We've already mentioned the concept of compounding, but let's expand on it and see how inflation affects our calculations.
Compounding effect
In the context of a long period of time, compounding has a snowball effect. Initially, a small amount of money may exceed the amount with simple interest accrued. In our model, we considered compounding once a year, but it can be done regularly, such as every quarter.
Taking this into account, we can slightly adjust the model.
FV = PV * (1 + r/t)^n*t
PV=present value, r=interest rate, t=number of compounding periods per year
We will also introduce a compound interest rate of 2% per annum, calculated once a year on $1000.
FV = $1000 * (1 + 0,02/1)^1*1 = $1020
The result, of course, coincides with our previous calculations. However, if you have the ability to compound your income four times a year, the profits will be higher.
FV = $1000 * (1 + 0,02/4)^1*4 = $1020,15
A profit of 15 cents may not seem like much, but with larger amounts and over longer periods the difference will be significant.
Inflation effect
Up to this point, we have not taken inflation into account in our calculations. What's the point of a 2% annual rate if inflation is 3%? During periods of high inflation, it is better to use the inflation rate rather than the market interest rate. In particular, this indicator is often important when discussing salary.
However, measuring inflation is much more difficult. There are various indices that calculate price increases for goods and services and usually provide different figures. Inflation is also quite difficult to predict, unlike market interest rates.
In other words, there is not much that can be done about this phenomenon. We can build inflation discounting into our model, but as mentioned above, inflation is highly unpredictable over the long term.
Application of the time value of money in the field of cryptocurrencies
In the cryptocurrency space, there are many situations where you have to choose between receiving funds now or in the future. One such example is staking. Stakers have to choose between holding one ether (ETH) now or staking it for a six-month period at an interest rate of 2%. That being said, there are many alternative staking opportunities that will provide higher returns. IRR calculations will be useful in choosing the most profitable product.
In other words, this calculation can tell you when to buy Bitcoin (BTC). Although BTC is commonly called a deflationary currency, its supply gradually increases to a certain volume. This means that the supply of BTC is inflationary. Should you buy $50 BTC today or wait until your next payday and buy $50 next month? Within the framework of the VSD, it is better to buy today, but in reality everything is more complicated due to fluctuations in the price of BTC.
In conclusion
Although we have given a formal definition of VSD, you most likely already intuitively understand the essence of this concept. Interest rates, yields and inflation are integral parts of our daily economic lives. The formulas and calculations that we have discussed in this article will be useful for large companies, investors and lenders. For large sums, even a fraction of a percent will make a huge difference to profits and the bottom line. It is also useful for crypto investors to consider this concept when deciding how and where to invest for the best returns.
Recommended reading
What is money
How to Calculate Return on Investment (ROI)
APY and APR: what's the difference?