What does the time mean when we talk about the present value or future value of money?
Time is money, you must have heard that term before. But how much is it worth? This is shown by present value and future value.
Maybe I’m not saying something new by saying that if someone offers you a certain amount today, you’re going to do more than if you only get the same amount next time. On the one hand, you can invest the amount you have received, and on the other hand, make sure that it is not affected (so much) by inflation.
Notations when calculating present and future values
PV: present value. The present value of money is the amount you already have, or how much the money you receive later is worth. It is even referred to as C as capital.
FV: future value. The future value of money. The amount of money you will receive after a certain amount of time.
r: growth rate. It is usually given annually, which is how much the value of your money changes over 1 year. If the question is not a comparison of investments, but only which of the two amounts of money available to you at different times is worth more, then r is the inflation rate.
n: number of periods. The number of years your money works.
Why is present value and future value calculation necessary?
We have already clarified that the 100 forints received today are more valuable than the 100 forints received tomorrow, as the value of money changes over time. Because of this, you can’t just add up the money that arrives at different times.
This is, of course, regardless of whether you get the money from the same place or not, i.e. if you keep getting money from one of your investments, say, every year, then the same amounts you get each year will represent different values. Because of this, if you are curious about its actual value, you cannot sum up the money received without calculating present value or future value.
While if you got money from two different investments on the same day, obviously their value will also be clear at that time, so you can do operations with them without any problems.
What do you need to do to compare two amounts coming in at different times?
In order to be able to compare two amounts of money coming at different times, and at the same time be able to tell which investment you are doing better, it is necessary to bring them to a “common denominator”. The easiest way to do this is to either convert any future incoming amounts to how much they would be worth today, or you can set an arbitrary date and determine the value of those amounts at that time.
The first is the present value calculation, the second is the future value calculation.
Where do you use it to calculate present and future values?
Investment comparison
There are good investment offers and there are some that just sound good. By calculating present value and future value, you will be able to distinguish between the two and tell which one is best for you.
Compare loans
There can also be large differences between credit and credit, whether in interest rates or other conditions. This may be true for both small and large volume loans. If you are able to compare not only marketing but also actual offers, you can also make a larger investment on credit and as planned.
In the case of a floating rate loan, the loan interest rate may change at the end of the interest period. By using the present value and the future value, you will be able to tell what it means to you specifically numerically.
If you also use the prepayment option, you will see when and what the prepaid fee means to you.
Investment planning
When you need to be able to decide whether to invest a certain amount somewhere or just buy some product or service you need on it, you will be able to tell which one you are doing better. You will also be able to calculate the extent to which you are better off with one or the other solution.
Present Value Calculation
The present value calculation is called discounting.
Then we look at how much the future cash flow would be worth today at a given yield level
PV = FV / ( 1+r )n
This formula reduces the amount promised for later by the rate of expected growth, i.e., discounts the future value.
When comparing two investments, pay attention to what you are curious about:
- when you get more returns: then the one with a higher present value will be preferred.
- which one is cheaper for you in case of several deposits (ie which one requires less money for the same increase): then choose the one where the present value is lower
Example of present value calculation
Suppose there are 2 investment opportunities for you, each of you would invest 1 million forints for 5 years. One option gives you 5% a year, ie you get 50.000 forints a year, the other gives you 260.000 forints at the very end. The question is which one do you do better.
Many people can point out that HUF 260.000 is more than HUF 5 × 50.000, but the money arriving at different times cannot be compared.
Since the question here is which solution will give you more growth, it will benefit you where the present value will be higher.
Solving the present value calculation example
Here the future value is known, because it was stated that you will receive 260.000 forints.
FV = 260.000 HUF
The time frame is also given because you will get it in 5 years, so
n = 5
The r as a growth rate is not available to you here, but there is a solution.
If you really want to strive for simplicity, you can also use 5%, assuming you could only invest that money in the other investment. You can also see this calculation in the video.
Or, as an option B, you can calculate your own interest factor for this investment based on the interest calculation article. Let’s do it now, we get that in this case
r = 4.73%.
Perhaps even from the interest rate, it turns out that even though the 260.000 forints are more numerically, you still don’t get better with it. If we also calculate its present value, we get that
PV = 260.000 / (1+0,0473)5 = 206.349,21 Ft
The present value of the 50.000 forints is longer only in the inscription, the methodology is the same. The exponent (i.e., the value of n) will depend on how many years later you get that amount.
PV = 50.000 / (1+0,05)1 + 50.000 / (1+0,05)2 + 50.000 / (1+0,05)3 + 50.000 / (1+0,05)4 +50.000 / (1+0,05)5 = 216.473,8 Ft
If you follow the calculation shown in the video and apply the 5% interest rate, there will be a slightly bigger difference, but you will also get that you are 5 × 50.000 forints better in terms of present value.
The Future Value Calculation
The future value calculation is nothing more than a compound interest calculation. Then we look at how much a given amount of money will be worth at a later date.
Comparing the example above with future value calculation, we also get that you are not doing well if you choose the higher amount you received later.
Example and solution of future value calculation
You don’t need a calculator for the future value of 260.000 forints, you don’t get a penny here before, so there is no amount whose present value would increase until then.
The question is whether the future value of HUF 50.000 is more or less than this. That is, which one will pay you more in 5 years.
FV = PV * (1+r)n
Here at the exponent, pay attention to the time intervals. When calculating future value, the question is not in how many years you will receive it, but how many more years that amount can work until the date in question.
The first HUF 50.000 received can work for another 4 years, so when calculating future value, the exponent will be 4. The last HUF 50.000 paid as interest can no longer work for any year until maturity, so its exponent will be 0. (The value of power 0 is 1, so you can calculate the future value of this item in your head)
FV = 50.000*(1+0,05)0 + 50.000*(1+0,05)1 + 50.000*(1+0,05)2 + 50.000*(1+0,05)3 + 50.000*(1+0,05)4 = 276.281,6 Ft
You can see that here too it came out that the future value of the numerically lower amount is higher than the higher value paid later.
Questions:
- How do you compare different investments?
- What do you think: in comparison, is it necessary to reduce the applied interest rate with inflation? (That is, use real growth)
- What rate would you use for a comparison other than inflation if the only question is which of the two amounts available to you at different times is worth more?
Contact us with your questions so we can help you.