Is the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity?

Robinhood Learn

Democratize finance for all. Our writers’ work has appeared in The Wall Street Journal, Forbes, the Chicago Tribune, Quartz, the San Francisco Chronicle, and more.

Definition:

The time value of money refers to the fact that money received in the present is worth more than the same amount received in the future, due to the earning power of the money.

Takeaway

The time value of money is like your money getting older…

There are things you can do in your 20s that hurt when you are in your 40s. Just try hiking that mountain. Even though the mountain hasn’t changed, it requires a different amount of effort, pain, and dedication to get to the top. The same hundred-dollar bill in 20 years from now is a lot weaker than that hundred-dollar bill in your pocket today — due both to inflation and the interest you could earn on it in the meantime.

Why is the time value of money important?

When considering an investment, the time value of money is a critical component of your decision. Without consideration of time value, it would be very difficult to compare opportunities.

Take this simple example:

You have the opportunity to purchase a $1,000 bond from a reputable corporation. They offer you the choice between receiving $1,100 in one year or getting $1,200 in two years. Without considering the time value of money, the second option is clearly offering a better return on your money ($200 rather than $100).

However, you might notice that you are getting $100 per year in either case. By waiting an extra year, you increase your return by $100. But, if you purchased that one year bond, you could take the $1,100 at maturity, purchase another $1,000 one-year bond the next year, and get that same $100 return on the second year while having $100 in your pocket. That’s clearly better.

How do you account for the time value of money?

The time value of money is the amount of money that you could earn between today and the time of a future payment. For example, if you were going to loan your brother $2,500 for three years, you aren’t just reducing your bank account by $2,500 until you get the money back. There is also a time value to your money that you are forgoing.

In order to account for the lost earning power, you need to have three pieces of information.

1. The amount of money that you will be giving up. This is the size of your investment or whatever amount of money that you won’t have access to for a while.
2. How long you are giving the money up for. Because of compound interest, the time value of money grows exponentially over time. If the reference period is several years, the time value of money is likely extremely high.
3. A reasonable return your investment would yield. If there is an alternative investment with similar risk, the rate of return on that investment is a good discount rate to use. If there is comparable risk to an equity investment, the average return of the stock market might be a reasonable return. If the investment is less risky, the return on U.S. Treasury bonds might be a good comparison. Whatever that alternative investment with a comparable risk level is, that’s the money you are not earning while your money is tied up. So, its potential interest rate is a good benchmark for figuring out time value.

To calculate for the time value of your money, you would use this formula:

Future value = Current value x (1+ annual interest rate) ^ number of years

Let’s assume your money would earn you a 5% return if it stayed in your account. Plugging in the values from this example, we can calculate the time value of your money.

Future value = $2,500 x (1.05)^3 = $2,894

In other words, your $2,500 would turn into $2,894 in the three years of the loan. So, if you only get your $2,500 back, you’ve lost the time value of that money. In this case, that is $394 ($2,894 – $2,500).

How do you calculate the present value?

Sometimes, you will want to compare payments you will receive at different points in the future. Or, you might be interested in understanding how much a future payment is worth today. To do so, you need to do the reverse of the future value of money calculation.

That is, rather than figuring out how much interest you would earn on an investment today, you will need to figure out how much you would need to invest today in order to match that future payment.

The formula for doing this is:

Present value = Future value / (1+ annual interest rate) ^ number of years

For example, if you were scheduled to receive a bond maturity payment of $500 in two years, and you had a discount rate of 5%, you could use the present value formula as follows.

Present value = $500 / (1.05)^2 = $453.51

In other words, getting $500 in two years is equivalent to putting $453 in the bank today at 5% interest. If the best you could earn is that 5% interest, then buying the right to that future payment for anything less than $453 would earn you more money.

What is the difference between annually and continuously compounding interest?

The frequency with which an investment earns interest will influence how quickly the interest will accumulate. One frequently used method is to calculate interest once per year. At the end of the year, the interest rate is applied to the balance. As you hold the account open for another year, you earn interest on the original deposit, but also on the interest that is still in the account.

Sometimes, you might have the interest apply every six months, every quarter, every month, or even every day. With more frequent applications of interest, the amount of earnings grows more quickly. The formula for calculating these more frequent compounding periods is:

Future Value = Present value * (1 + (annual interest rate / number of periods in the year)) ^ (number of years * number of periods in the year)

Compare the following table of a 12% simple interest rate, computed with annual and quarterly compounding. Note that the quarterly interest payments are 3% each (12% / 4 quarters).

| | Annual | Quarterly | | ---------- | ---------- | ---------- | | 1Q 2020 | $100.00 | $100.00 | | 2Q 2020 | $100.00 | $103.00 | | 3Q 2020 | $100.00 | $106.09 | | 4Q 2020 | $100.00 | $109.27 | | 1Q 2021 | $112.00 | $112.55 | | 2Q 2021 | $112.00 | $115.93 | | 3Q 2021 | $112.00 | $119.41 | | 4Q 2021 | $112.00 | $122.99 | | 1Q 2022 | $125.44 | $126.68 | | 2Q 2022 | $125.44 | $130.48 | | 3Q 2022 | $125.44 | $134.39 | | 4Q 2022 | $125.44 | $138.42 | | 1Q 2023 | $131.71 | $142.58 |

The most extreme compounding formula is called continuously compounding interest. In that case, the time value of money formula is slightly different.

NEED FORMULA HERE

Where:

P = Present value e = Euler’s constant r = Annual interest rate t = Time (number of years)

Calculating the value of that $100 investment over three years using continuous compounding would lead to the following:

Future value = 100e^(.12*3) = $143.33

What does net present value mean?

The net present value (NPV) is the sum of money that a future stream of payments is worth in the present, after accounting for the time value of money. It is also the amount of money that you would need to invest today, at a given interest rate, to receive the same stream of payments in the future.

NPV is an important calculation when attempting to compare revenue streams of different sizes and timelines. By converting both prospective investments into a common metric, they can be directly compared.

Take these two payment series for example:

| | Option 1 | Option 2 | | ---------- | ---------- | ---------- | | Year 1 | $100 | $500 | | Year 2 | $200 | $400 | | Year 3 | $300 | $300 | | Year 4 | $400 | $200 | | Year 5 | $500 | $100 | | Total | $1,500 | $1,500 |

Both options provide the same amount of money over the same period of time. But, they are not of equal value. We can reveal the difference by calculating the NPV, which highlights the time value of money. To do so, calculate the present value of each payment, then sum them up. We used a 5% discount rate here.

| | Option 1 (present values) | Option 2 (present values) | | ---------- | ---------- | ---------- | | Year 1 | $100 | $500 | | Year 2 | $190 | $381 | | Year 3 | $272 | $272 | | Year 4 | $346 | $173 | | Year 5 | $411 | $82 | | NPV | $1,319 | __$1,408 __ |

Because of the larger payments earlier in the series, option 2 is more valuable than option 1. It allows you to earn a larger return if you reinvested those payments.

Put another way, the NPV is the amount of money you would need today to if you wanted to make the string of payments in the table. By paying the $500 payment in year 2, you have less time to earn a return on an initial balance. Therefore, you need to start with more money in order to pay those larger early payments.

The NPV is notionally the maximum amount of money someone should be willing to pay for the revenue stream in question. When the revenue stream is the future cash flow from a business, it is commonly known as the discounted cash flow (DCF).

How do you pick the correct discount rate?

The time value of money is directly linked to the amount of earning power that money has and how the purchasing power of money is changing over time. Therefore, the best discount rate to use is the opportunity cost of that money, which is the interest rate of the next best alternative investment.

In the case of borrowing money to make an investment, the proper discount rate is the weighted average cost of capital (WACC). That is, you should use the borrowing cost as the time value of money, as that is what you are paying for the use of the money over that period of time.

In simple analyses, it is common to use round numbers such as 10%. It is also common to use the prime rate, the average stock rate of return, or the current U.S. Treasury yield as the discount rate.

In other cases, a corporation might have a standard discount rate it uses to compare prospective investments. It is important to use the same discount rate when comparing alternative uses of funds.

In public finance, it is often more difficult to determine a proper discount rate. Because governments endure, they tend not to put as much weight on the present as private corporations or individuals do. A social discount rate tends to be very low, or even zero.

Individuals tend to have very high personal discount rates. The preference for the present leads to trade-offs that would imply discount rates much higher than any investment could be expected to yield.

For example, a person might prefer receiving a payment of $100 today over $200 in one year. That would mean that such a person has a personal discount rate of over 100%. There are many reasons this may be true. Most notable is the desire to meet current needs may be greater than almost any interest rate could offset.

Ultimately, there is no correct answer in which discount rate to use. That number is dependent on the person doing the analysis and their unique circumstances.