When I take the time to truly consider the financial decisions that I make, I like to ask myself a certain question: Is the money that I receive today worth the same as money that I receive in the future? The best way to go about answering this question is by learning how to calculate present value. Knowing how to calculate the worth of future money helps me make better financial decisions regarding my investments and my retirement. It also helps me determine opportunities in the financial world that would be more valuable to me.
I believe thinking about money in terms of time is a great way of thinking about present value. Having a sum of money available to you today is a lot more valuable than money that you will receive in the future. Money that is available to you today can be invested, and it can also just be used to cover an expense that may occur in the future. With the time value of money and a discount rate in mind, I can just about determine what a future value is worth today.
With a basic understanding of how to work the formula and a simple Excel spreadsheet, calculating the present value is not too difficult. Calculating the present value of money may seem difficult, but all it takes is understanding some simple concepts and the basic principles behind how money works. I have included some examples that show how Excel can be used to perform present value calculations for you.
What Is Present Value?
Present value (PV) is the amount of money expected in the future, expressed in terms of today’s value. It is based on the concept of the time value of money, which is the idea that money today is worth more than money in the future, because money today can earn a return.
For example, if I’m given the choice to receive $1,000 today or in three years, and I decide to take the money today, I have the opportunity to earn a return on my money. If I take the money in three years, I miss the opportunity to earn a return for those three years.
Of course, there are other factors, like risk, taxes, inflation, and personal circumstances, that could affect the decision. Present value gives me a uniform way to compare money I’ll receive at different times. It can also be useful when evaluating investments and other financial decisions.
What Is the Present Value Formula?
The standard formula for calculating the present value of a single future payment is:
PV=FV(1+r)n
Here is what each symbol means:
- PV: Present value, or the estimated value today.
- FV: Future value, or the amount expected later.
- r: Discount rate per period, expressed as a decimal.
- n: Number of periods until the payment arrives.
The discount rate is the rate at which future money is converted to its present value. The appropriate rate is determined by the purpose for which the calculation is being made and the risk and opportunity associated with the alternatives available.
A 5% annual discount rate is written as 0.05 in a formula. If I am expecting to receive $1,000 in 3 years, I convert the future value of $1,000 to present value by dividing by (1.053)
The basic concept of present value isthat iff we hold all factors constant (discount rate, time value and other factors), present value will always be less than the future value.
How to Calculate Present Value
Present value is calculated using the following components: the future value, the discount rate and the time value. The components determine the value used in the formula.
Step 1: Future value is the expected amount to be received in the future. If we expect to receive $5,000 in 4 years, the future value is $5,000 and is represented by FV.
Step 2: Discount rate: If the interest rate is 9%, the discount rate is 0.09.
Step 3: The time value is the length of time we must wait to receive the future value. Since we expect to receive the future value in 4 years, the time value is 4 and is denoted by n.
Step 4: Once we know the future value, discount rate and time value, we can plug the figures into the formula.
PV=2000(1+0.06)4
PV=20001.26247696
Step 5: Interpret the result. The present value is approximately $1,584.19.
With a 6% annual discount rate, $2,000 received four years from now is equivalent to roughly $1,584.19 today. The rate and time period need to be consistent; otherwise, even a correctly entered formula can create a misleading answer.
Present Value Calculation Examples
Let’s make the calculation more practical. Perhaps I’m comparing two financial opportunities, and for either of them, I want to know the value of a future payment in present terms.
Example 1: Future Payment Calculation
For the sake of example, let’s say I will receive $5,000 in five years. With a 4% annual discount rate, what is the present value? The calculation would look like this:
PV=5000(1+0.04)5
PV=50001.216653
The result is approximately $4,109.64.
In other words, at a 4% annual discount rate, $5,000 received five years from now is equivalent to roughly $4,109.64 today.
Example 2: Comparing Different Discount Rates
Suppose that the future payment is still $5,000 and arrives in five years, but in one calculation, I use a 4% discount rate and an 8% rate in another calculation.
| Annual discount rate | Present value |
| 4% | $4,109.64 |
| 8% | $3,402.92 |
The payment amount hasn’t changed. The only difference is the discount rate.
This illustrates the importance of choosing the correct discount rate. The higher the discount rate, the lower the present value, so I can not just pick a discount rate that gives me a result I prefer.
How to Calculate Present Value in Excel
I can use Excel to perform a calculation or compare a series of calculations to see how different financial scenarios play out. If I have a single future payment to make, I can use a simple equation rather than perform all the necessary calculations manually.
I will assume cell A1 has a future payment of $1000, cell A2 has an annual discount rate of 5%, and cell A3 is equal to 3 (the number of years).
I can enter the following equation to get Excel to perform the calculation for me.
=A1/(1+A2)^A3
Excel returns $863.84.
I can also use Excel’s PV function. In a situation like this, where we have a single future payment with no recurring payments, we can enter the following
=PV(5%,3,0,-1000)
Excel returns $863.84 using cash-flow sign convention. A negative future amount means a payment is received, and is therefore the inverse of the cash-flow sign convention. For calculations like these, we always check whether payments are made at the beginning or end of the period, and if the rate used is the same as the payment frequency.
What Is the Effect of a Discount Rate on Present Value?
The effect of changes in the discount rate on present value is also important to understand because the discount rate reflects the rate to convert future money to present money. Learning how to find present value means understanding the effect the discount rate has on it.
Suppose I expect to receive $10,000 in 5 years. If the discount rate is 3%, the present value is about $8,626.09. If the discount rate is 7%, the present value is about $7,129.86. Why is this the case? A higher discount rate means future money is discounted more. The longer the time to receive the money, the more future money is discounted.
However, a higher discount rate doesn’t always mean the correct discount rate for analysis. It should be appropriate for the analysis and reflect factors such as risk and relevant alternative returns. Inflation may impact the buying power of money depending on whether cash flows and discount rates are stated in nominal or real terms.
Present Value, Future Value, and Net Present Value
These three financial terms are easily confused because they sound similar. Knowing the difference allows me to determine which to use based on the question I want answered.
- Present value (PV): What is a future payment worth today?
- Future value (FV): How much could money invested today be worth later?
- Net present value (NPV): After discounting expected future cash flows, how much value remains after accounting for the relevant initial investment or costs?
For example, I may invest $1,000 and expect it to grow at 5% annually for 3 years. Using the future value calculator, the ending value of my investment would be $1,157.63. Present value works in the opposite direction. It determines what an investment is worth today by factoring in expected returns or rate of growth.
NPV is most beneficial when a business project or investment is analyzed to have multiple cash inflows and outflows. It is used to decide whether the discounted benefits meet or exceed the costs associated with the project or investment under consideration.
Remembering the phrase “present value looks back from future payment to today”, “future value looks forward from today to a future date” and ” NPV looks at the overall value of cash flows” makes calculating cash flow value easier.
When is Present Value Used?
Present value aids in comparing financial amounts that are expected to occur in the future. Looking at future financial obligations or expected returns in today’s money becomes easier to analyze with the use of present value.
Common applications include:
- Investment decisions: Estimating the current value of expected future cash flows.
- Retirement planning: Evaluating the value today of future retirement income.
- Business valuation: Assessing projected cash flows when estimating what a business or project may be worth.
- Loan analysis: Understanding the relationship between a loan’s amount, payment schedule, and interest rate.
- Personal financial planning: Comparing a lump-sum payment with money received over time.
Let’s consider a simple personal finance situation. I am given a choice between receiving $3,000 today or $3,500 in two years. Traditionally, I would take the $3,500 in two years, but by calculating the present value of the delayed payment, I can determine the true value of the payment in two years and compare the result to $3,000.
Now that I understand how to calculate present value, I can apply the method to other payment schedules to compare payment options, keeping in mind taxes, risks, and the reliability of payment.
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Mistakes when Calculating Present Value
Often, when calculating present value, the results come out to be incorrect because of user error. Below, I have outlined the main errors I have made in the past:
- Using the wrong discount rate: The rate should reflect the purpose of the valuation and the risk of the cash flow.
- Mixing time periods: An annual rate should generally be paired with annual periods. Monthly calculations require a compatible monthly rate and number of months.
- Entering the wrong number of periods: A payment due in three years is not the same as one due in three months.
- Confusing present value with future value: Present value discounts money; future value estimates how money grows.
- Ignoring cash-flow timing: A payment received at the beginning of a period differs from one received at the end.
- Overlooking assumptions: A calculated result depends on the chosen discount rate and expected payment actually being reasonable.
My advice is to write down the future value, rate, and time period before plugging anything into a calculator. It takes only a few seconds and can prevent making a careless mistake.
Frequently Asked Questions
1. What is the Easiest Way to Calculate Present Value?
The easiest way is to use the standard formula PV=FV/(1+r)n. Enter the future value, the discount rate as a decimal, and the number of periods. A financial calculator or spreadsheet can do the arithmetic for you.
2. How Can I Manually Calculate Present Value?
I can do it manually by adding 1 to the discount rate, raising it to the power of the number of periods, and dividing the future value by that number. About $1,000 due in 2 years at 5% per year is presently worth about $907.03.
3. What Happens to Present Value if Discount Rate Increases?
If nothing changes in the future payment and timing, a larger discount rate means a lower present value. A higher discount rate means you expect to receive the money further in the future.
4. Can I Calculate Present Value in Excel?
Yes. To calculate the present value of a future payment using Excel, you’ll use the following formula: =FV/(1+rate)^periods
In the case that you’re dealing with a loan or multiple future payments, Excel’s PV function would be better suited.
5. What Is the Difference Between Present Value and Net Present Value?
Present value is the amount of money that a future payment or cash flow is worth today. Present value depends on the discount rate. Net present value (NPV) is the present value of all of the relevant cash flows (and/or payments). NPV is typically used to evaluate potential investments and projects to determine if the investment or project is profitable.
Final Thoughts
Understanding present value provides me the ability to estimate when cash flows and payments will occur. Discount rates, future values, and time periods are the few variables that I need to make the calculation, and if reasonable estimates are made and the inputs are double-checked, then I can use the calculation to provide a financial estimate rather than a definite answer. Excel can also perform the calculation for me.
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