Understanding the Time Value of Money With Formulas and Examples Several factors play into making investments. One key? The time value of money. Read on for more information, formulas and examples.
In corporate finance and valuation, experts and self-taught learners rely upon various guiding principles. One of those core principles is the time value of money.
Whether you're a professional in the finance industry, an entrepreneur breaking ground on a new business venture or simply wanting to educate yourself on personal finance, understanding the time value of money is critical.
What is the time value of money?
The time value of money is the concept that the value of money today is worth more than the value of that same lump sum in the future, assuming you put today's money to good use. Three reasons make this principle reliable.
1. Opportunity cost
Opportunity cost, also known as implicit cost, compares the value of money today versus a future financial payment. In other words, the money you have today can be invested and increase in value over time.
On the other hand, if you wait for a future payment, that money will not have the same amount of time to accrue interest as the money you receive and invest today. Today's cash provides immediate purchasing power, so put that money to good use.
Inflation has been a hot topic as of late. Inflation is the measure of the rise in the personal consumption expenditures price index, which indicates the expenses of goods and services over a certain period.
With inflation being a real and present obstacle in a post-pandemic world, this factor is more relevant than ever.
The money you have today may not go as far in the future. Inflation may erode the purchasing power your money has over time, so the amount of money you have today is worth more than that amount may be worth in the future.
For example, if you have ten dollars in your pocket today, you can see a movie in the theater. However, that same ten dollars in your pocket might not cover the cost of a ticket two years down the line.
Therefore, if you're looking for a way to spend that ten dollars, you should go to the movie theater today.
In 2022, inflation rates were up to 8.8%. And while economists expect that number to decline to 6.5% in 2023 and 4.1% in 2024, history shows slowed deflation speed when rates exceed 8%, as they did in September 2022.
In addition, if you plan to invest the amount of money you have today, inflation must be factored in to calculate your actual return on investment (ROI). To calculate that factor, take the percentage return your money earns and subtract the inflation rate.
The money you have in your hands now is worth more than the hypothetical money you might receive in the future. Until you have the money, it is not yours. You can only make investments or plans with the money you have.
The uncertainty factor is a reminder that anything can happen, so sometimes, it is better to plan for the future instead of planning in the future.
Time value of money
There are two critical factors in the equation to solve for the time value of money: the present value of money and the future value of money.
The future value is based on the idea that you will invest the present-day sum of money; it predicts how much a set sum will be worth at a set date. The present value formula calculates a future amount using a present-day amount.
The future value formula is:
- FV = PV x [ 1 + (i / n) ] (n x t)
The variables included in TVM formulas include:
- FV = Future value.
- PV = Present value.
- i = Interest rate or rate of return that can be earned.
- n = Number of compounding periods of interest per year.
- t = Number of years.
Example of how to apply the future value formula by hand
To provide a simple example, let's say a piece of real estate you've been looking to sell has caught the interest of a buyer. The potential buyer offers you $20,000 to purchase it today but also offers to pay you $500 more if they can buy the same property in two years.
Even though a higher payment sounds better, based on the time value of money principle, $20,000 today is worth more than $20,500 in two years.
You decide to stick to this principle and make today's money work for you. You take the $20,000 the real estate buyer offered you today and deposit the lump sum into a savings account with a 2% compound interest rate each year.
To calculate how much money your investment can make you, plug in the correct variables and use the future value formula.
- FV = 20,000 x [ 1 + (.02 / 1) ] (1 x 2)
- FV = 20,808
By this logic, the $20,000 the real estate buyer pays you today will be worth $20,808 in two years if you invest it according to plan.
However, if you take the two-year offer of $20,500, you will lose out on $308 of interest from your savings account. Again, just because the future offer sounds like more does not mean it will end up being more.
Example of how to apply the future value formula by a data processor
If by-hand calculations aren't something you look forward to, you can also find future values using tools like Microsoft Excel and Google Sheets.
To calculate via data processor, use:
In this formula, the variables are:
- Rate: Equates to the "i" in the manual formula — the period's rate of interest or discount rate.
- Nper: Equates to the "t" in the manual formula — the number of periods in which payment occurs for a given cash flow.
- Pmt or FV: Equates to the "FV" in the manual formula — the payment or cash flow to be discounted. It's not necessary to include values for both pmt and FV.
- Type: Time period when the payment is received — use one for the beginning of the period, use 0 for the end.
The time value of money and net present value
A closely related factor you might come across as you calculate the time value of money and how it pertains to investment opportunities is the net present value. When you decide to invest, the hope is that you will receive an ROI.
In addition, a solid ROI not only exceeds the amount of your investment but can also make up for any potential losses due to the TVM.
The net present value is an equation that predicts future investment growth to today's dollars. Net present value accounts for the time value of money and the declining value of future money in order to show the ultimate value of your investment.
The time value of money and annuities
An annuity is the dollar amount you can receive in a lump sum or at a fixed monthly amount. Annuity generally comes into play in real estate, retirement and pensions. A standard financial calculator can provide the answer to these formulas.
The formula for annuity varies based on whether you're trying to calculate:
- Ordinary annuities: Payment made at the end of the recurring period.
- Annuities due: Payment made at the beginning of the recurring period.
- Perpetuities: Annuities that last indefinitely.
When it comes time to figure out how you'd like to handle annuities, the formulas function similarly to the time value of money formula to ensure you're making the best financial decision.
What the time value of money can mean for you
The time value of money is an important concept, as it can help you make future financial decisions. It can also aid in calculations and considerations in other areas of finances, like annuities.
As you continue to grow your investment portfolio, remember: Money in your hand today is worth more than that same lump sum in the future. Why? Opportunity cost, inflation and uncertainty.