Valuation Principles: Time Value of Money
If I offered you $500 now or $500 in a year, which option would you take? You might be thinking it’s a trick question and you probably will pick the correct answer intuitively (hint: it’s to take the money now!), but a proper canalization of the options can help better understand a crucial principle in financial valuation: Time Value of Money.
So, let’s examine what the concept is all about and the theoretical reason for going with Option A.
THE CORE CONCEPT OF TIME VALUE OF MONEY
The concept of Time Value Money (TVM) is a useful concept for everyone to understand. Aside from being known as TVM, the theory is sometimes referred to the present discount value. The concept is one of the many theories of financial management and it can help you understand the value of things more comprehensively.
Instead of just knowing what the value of something is at the current moment, you should also be aware of the value in the future or indeed in the past. So, what does TVM imply? The core principle of TVM states that money at the present value is worth more than the same amount of money in the future. The statement sounds simple, but that is the beauty of TVM: the core concept shouldn’t be that difficult to grasp. If you get $500 now, the value of it will be higher than if you get $500 in a year.
The explanation is also simple. If you are scratching your head thinking how can the same amount of money be more valuable now than in six months, the answer is: it has more earning potential. You are essentially able to increase the value of your $500 from the present more than the value of the $500 you get in a year. The money you receive sooner will have more time to increase in value, through interest, than the money you receive later – even when the actual amount is the same in value.
This idea is one of the core principles of finance and if you think about it, it’s rather obvious, isn’t it? Your money can earn more interest the quicker you get it. If you want to look at what you have in a year, the $500 you get today will have more time to gain interest than the $500 you get in next year.
AN EXAMPLE OF TVM
Check the introductory video of an example of the above information:
You can also consider through the question I posed at the start. If you are given the option to take $500 today or $500 next year, which option would you take? Now the answer rather intuitively would be to say, ‘I’ll take the$500 now, thank you very much’. After all, why would you wait a year to get your hands on the money?
In this instance, your intuition is quite right, too. But it’s not just about accepting the money sooner and thus being able to go shopping straight away that makes accepting the money now better. The $500 you take today will have higher value to the $500 you’d receive in a year.
Although most people would choose the first option straight away, many would make the mistake of stating the value is the same in both occasions. But the earning potential of the $500 you accept today is higher than the earning potential of next year’s $500. It is this earning potential, which increases the value of your $500.
The reason the first option is more valuable is down to a few reasons, which you need to understand about the TVM. Your today’s $500 is more valuable because:
- The risk associated with the value is non-existent. You simply don’t have any risk in getting back money, which you already have.
- The purchasing power of the money you receive now will be higher. This is down to inflation, which can reduce the value of your $500 in a year. For instance, the $500 you receive today would have bought a lot more things 20 years ago.
- By taking the money later, you would face an opportunity cost. As mentioned, the money you receive now will be able earn interest longer than the money you receive in the future. The lost opportunity to earn the interest creates the opportunity cost.
What does the example here tell us about TVM? It highlights the two fundamental principles of the concept: more is better than less and sooner is better than later.
Let’s put the above information down into a graph format, as it can help understand the example of TVM even better. So, you’ll have two options:
|Option A: Take $500 now
|$500 – interest
|Option B: Take $500 in six months
WHAT TO FIND OUT WITH TVM
OK, so TVM tells us the rather obvious principle that you should accept the offer if someone wants to hand out money for you now, rather than wait a few years to get it. But is there anything more to the time value of money? Why should we understand things like earning potentials and value of money?
TVM can help you understand a basic, yet crucial concept of finance, which is that the net value of money at different points in time is different. If you need to deal with money and investments, you should be able to understand the concept. Whether you are an investor, a business owner or just a savvy saver, the concept will be valuable in figuring out the real value of the money you receive, either true investments, savings or cash flow or income. TVM essentially helps you to understand:
- Investments – Can answer questions, such as, ‘What happens to your investment depending on the timeline of your investments?’ It’s also often used by investors to calculate the risk free rate of return, i.e. the value of a guaranteed future payment in today’s money to figure whether an investment today is worth it.
- Cash flow – Helps you figure out why the cash flow changes depending on when you receive the money.
- Savings – Useful in calculating the differences between different investment scenarios.
- Earnings – Shows the changes in your earning potential based on when you receive the income.
The TVM concept is useful in understanding the true, present value of a sum, together with the possible future value of a sum. With the help of the formula, you can be fully aware of what that $5 is actually worth at this moment, as well as the earning potential it has in the future. To put it in the simplest terms, the TVM formula can help you calculate:
- The present value of something. The calculation could be about the present value of things like annuities and perpetuities. This can help you evaluate whether a specific cash flow is currently an earning or an obligation to the organization, for example.
- The future value of something. Again, this might be in regards of the future value of an annuity. If you are taking out a retirement annuity, you can use the formula to count how much more you could make by starting it right now, against starting in five years, for example. Similarly, you can figure out what changes occur if you change the sum, you are putting in and so on.
With the concept, you are essentially able to understand the different value money has depending on how much you have it and when you put it to use – whether it is through investments or savings.
THE TVM FORMULA
So, how can you calculate the time value of money? The formula requires you to examine the following variables:
- A balance – In the example, the balance would be $500.
- A periodic rate of interest – The interest you gain during a specific period. For example, it could be 2% each month.
- The number of periods – The number of periods of interests you’ll have. In the example, if you gain 2% each month, the number of periods would be 12 months.
- A series of cash flow/monetary intake–Refers to any additional money intake that might take place during the time. This is especially important when dealing with savings accounts or cash flow predictions.
Let’s look at the components in another way and explore the actual formula you would use to calculate future value with TVM. The formula looks like this:
|Future Value of Money. The equation is to solve what the future value of your amount will be. In our example, it would be about finding the value of the $500 in a year’s time.
|Present Value of Money. The amount of money you are examining, which in the example would be $500.
|Interest Rate. This is the amount you’re gaining in interest during a specific period of time. It could be 2% annual gain or a monthly interest payment.
|Number of compounding periods per year. This refers to how often the money gains interest during a year. If in our example, the interest is paid monthly, the number of compounding periods per year would be 12. If the interest was only paid once a year, it would be 1 and so on.
|Number of years. You might have more than one year of interest payments in your situation. In my question I only asked for a one year period, but in most actual TVM calculations you would be looking at a longer time period, such as five years or ten years.
If we take the above information and calculate our little thought experiment, the calculation would look like this:
After you do the math, the answer would be:
The above formula is the most fundamental TVM formula that you can use. From it, you can quickly draw up the other formulas to count things like Present Value or Future Value of Annuity. For example, using the fundamental formula, the way you would calculate the Present Value of something – for instance, the value of an investment gain you are promised – using the below formula:
If you were offered $10,000 in two years, what would the present value of the amount be? Using the above formula, you would be able to understand what kind of investment you are talking about in current value. This is essential to understand when considering an investment, for example.
While our example of ‘take $500 now or in a year’ is a rather simplistic one, the above formula and the concept of TVM is highly useful if you are presented with the choice of two different sums. What if I had offered you to either take $500 now or $800 next year, which would you have accepted? Knowing the ‘right’ answer is easier when you understand and can calculate the TVM, as you’ll be able to know:
- What is the future value of the $500?
- What is the present value of the $800?
Essentially, you are only going to need to know four of the five components to figure out the fifth. This makes the formula easy to use and to understand.
COMPOUNDING AND DISCOUNTING
The final pieces of the puzzle you need to understand with TVM are the two crucial techniques of compounding and discounting. Each one of your TVM calculations will deal with either of these techniques.
Compounding is essentially about the money moving forwards in time. It’s the process, which determines the future value of your money, such as an investment. The idea of compound growth tells you that if you have $500 today and it earns an annual interest of 2%, then your initial money will grow into something bigger in the future.
Furthermore, compounding shows the future value in instances where the interest continues to add as the value goes up. What does this mean? Well if you originally invest $500 and your investment earns 2% every year, with your investment lasting five years. On the first year, you gain interest on the original $500, but after that you gain interest on the $500 + the interest from previous years. This would mean:
Starting investment: $500
Year One: $500 + 2% interest = $510
Year Two: ($500 + 2% interest) + 2% interest = $520.20
And so on. The initial amount is compounding because it gains interest on the initial amount, but also because it earns interest on the interest payments.
Compounding can be used to solve three major themes of issues in regards to understanding a future value of money. These are:
- The future value of a single sum. If I get $500, what will it be worth in 5 years with a determined annual interest?
- The future value of a series of payments. If I get $500 every year, what will it be worth in 5 years with a determined annual interest?
- The payments needed to make in order to achieve a future value. If I want to have $10,000 in five years and I know the determined interest, how much do I need to have at the moment or invest annually to achieve this?
As you might have guessed, discounting is the opposite of compounding. In discounting, money is moving backwards in time. The process determines what the present value of a known value in the future is. In discounting, the current value is determined by applying the opportunity cost to the value expected to be received in the future. So, if you were told to receive $500 in five years, you could determine the present value of this money with the technique of discounting. Discounting is essentially the inverse of growing.
Discounting can be useful to solve three specific issues of TVM. These are:
- The present value of a single sum. If I’m told to have $500 in five years, with the interest standing at 2% annually what is the value today?
- The present value of a series of payments. If I have an annuity that pays $1,000 every month for next ten years, how much shall I pay for it, in order to gain 2% each year?
- The amount needed to amortize a present value. How much do I need to pay on a 10-year loan of $20,000 if the annual compound rate is 3.5%?
THE BOTTOM LINE
Time Value of Money is an essential concept of financial theory you should be aware of. It quite literally, shows that time is money. The same amount of money today is different in value to the same amount in five years. The $500 today is not the same as the $500 in a year because you have more earning potential with the money you receive earlier.
But as the above has shown, the TVM formula is not just good at determining the obvious – that you should accept an offer of money today, instead of getting the same sum later – but it helps solve a lot of investment and savings related problems. With the help of the formula, you can find out what the future and the present value of money is and make better spending, savings and investment calls based on this knowledge.
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