The time value of money (TVM) is a fundamental concept in finance that explains why a dollar today is worth more than a dollar tomorrow. Whether you’re saving for retirement, considering a loan, or just thinking about your future, understanding TVM can help you make smarter financial decisions. It also helps you compare different financial options, such as choosing between a lump sum payment today or receiving smaller payments over time.
Consider a scenario where you win the lottery and are given a choice: Collect a lump payment of $8,000 now or receive $1,000 every year for the next 10 years. Which is better? By understanding TVM, you can figure out which option is worth more in today’s dollars. First, however, let’s delve into what TVM really means.
What is TVM?
Imagine someone offers you $100 right now or $100 one year from now. Which would you choose? Most people would take the $100 today. Why is that?
The reason is simple. If you have the money now, you can spend it, save it, or invest it, and it could grow into something more by next year. This is the key idea behind TVM: Money today is worth more than the same amount of money in the future because it has the potential to grow.
How does interest play a role?
Interest is the extra money you earn when you invest or save or the extra money you have to pay when you borrow. Let’s say you deposit $100 in a savings account with a 5% interest rate. In one year, you’ll have $105. That extra $5 is the interest you earned, and it shows how money grows over time.
On the flip side, if you borrow $100 today and have to pay it back in one year with 5% interest, you will owe $105. Lenders charge interest because they are letting you use their money instead of using it themselves.
Present value vs. future value
To understand TVM better, you need to be familiar with two key terms: present value and future value.
- Present value (PV): This is the value of money right now. For example, if you have $100 today, that’s its PV.
- Future value (FV): This is the value of money at a specific point in the future, considering interest or investment growth. If you invest $100 at 5% interest, the FV in one year will be $105.
If you want to know how much today’s money will be worth in the future, you calculate the FV. Conversely, if you know how much money you’ll have in the future and want to know its value today, you calculate the PV.
Which option is better?
Let’s go back to our lottery example. You have two choices:
- Option A: Receive $8,000 now.
- Option B: Receive $1,000 every year for the next 10 years.
We already know the present value of Option A—it’s $8,000 because you get that money right now. To compare it to Option B, we need to figure out how much each of those future payments is worth in today’s dollars.
For each $1,000 payment, we adjust its value downward because receiving the money in the future is not the same as having it today. For example, if you were to receive $1,000 in one year, its value today would be less than $1,000 because you could have invested that money and earned interest.
Assuming a 5% interest rate, the total PV of the 10 yearly payments is $7,721.73. Since that’s less than the $8,000 you would get today, Option A (the lump sum) is the better choice. The table below shows how this analysis could be done in a spreadsheet.
What if the interest rate changes?
The interest rate in our example was 5%, but interest rates can vary. Let’s say we use a lower one, like 3.50%.
At this rate, the present value of the 10 annual payments becomes $8,316.61. Now Option B (the yearly payments) is worth more than the lump sum, so you should choose that instead.
Interest rates help us decide how much future payments are worth today. The higher the interest rate, the less future money is worth today. The lower the interest rate, the more future payments are worth when compared to taking a lump sum.
Conclusion
TVM teaches us that having money today is more valuable than having the same amount in the future because of the potential for it to grow. By understanding this concept, you can make better choices about saving, investing, or borrowing. Whether you’re trying to decide how to invest, whether to take out a loan, or even what to do with a lottery prize, remember: A dollar today is worth more than a dollar tomorrow!
