If you won the lottery, what would you do? I’m not talking about buying jet skis or a new mansion; I mean would you take an immediate lump sum or choose to take a series of payments over an extended period of time?

For most of us, this is just a fanciful daydream, but how you go about the process could have implications for real-life investment decisions.

Let’s go back to the daydream. How do you go about deciding between the lump sum or the long-term series of payments? What factors go into your decision-making process?

Sure, for some of you, it will be a choice of personal preference. Maybe you have some immediate ideas for spending that money or perhaps you realize having a stream of income can help with budgeting and make it easier to stretch that money over the rest of your life.

After all, you’ve heard of MC Hammer and all the lottery winners and professional athletes who’ve gone bankrupt, and you’d like to avoid a similar fate by steering clear of the temptation to overspend.

What if you’re just interested in the total amount of money? You have faith in your self-discipline and budgeting skills but you have no immediate need for a large sum of money—you just want to take whichever option will give you the most cash.

Can’t you just add up the total of the series of payments and compare that to the immediate payment? No—if they offer you $20,000,000 today or $1,000,000 a year for 20 years, you might get the same amount but you’d objectively be better off taking the $20,000,000 today.

Why is this? The reason is a concept referred to as the present value of money that says a dollar today is worth more than a dollar in the future. In this case, the immediate $20,000,000 is worth more than the same amount being paid in the future.

Simply knowing this concept makes the decision in our hypothetical lottery easy since the amounts are the same. However, we can also use this principle to decide whether to take a lesser amount today or a greater amount to be paid at some future date.

In this article, we will examine the principle of the present value of money, how to calculate the present value of money, and the benefits and limitations of these analyses.

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## What is the Present Value of Money?

**The present value of money is the current worth of a future sum of money or streams of income given at a specified rate of return. **

In other words, it allows you to know how much the guarantee of future money is worth to you at this moment.

In the lottery example, you know the $20,000,000 lump sum is worth $20,000,000—you can use the idea of the present value of money and the formula we’ll introduce shortly to calculate how much that $20,000,000 spread over 20 years is worth today. This allows an easy comparison of the two.

## Why Does Present Value Exist?

Before getting into the math, let’s examine why money today is worth more than the same amount paid in the future. There are three reasons for this—opportunity cost, inflation, and uncertainty.

The opportunity cost is the lost opportunity to invest the money and earn a rate of return. If you had the money today, you could invest and earn interest.

That $20,000,000 lump sum could be put into an account that would earn compound interest or a U.S. Treasury bond that would pay interest. At the end of twenty years, you would have both the $20,000,000 principal and the interest it earned.

By accepting smaller payments spread over time, you would be giving up the opportunity to immediately invest it and earn interest. This is referred to as the **opportunity cost**.

Secondly, there is **inflation**. You’ve all heard the trope about how everything used to cost a nickel, right? What can you get for a nickel today?

The same principle applies to large sums of money. That $1,000,000 you’ll receive in twenty years as the final payment in your series of payments will not buy as much as it would if you had it in your pocket (or bank account) today.

Finally, there is **uncertainty**. The money in your bank account is, well, money in the bank. The series of payments is a promise to pay. A lot can happen in the course of a year, and a lot can also happen in the course of twenty years.

You could die before ever receiving the money, or the entity running the lottery could go bankrupt. In either scenario, you’ll never receive the full amount. Taking the money right now guarantees that the payment actually comes to fruition.

## Formula

How do we know how much those future payments are worth in present terms? We use this formula:

PV = FV/(1+r)^{n }

PV = present value

FV = future value

r = rate of return

n = number of periods

So, to calculate the present value of the $1,000,000 lottery payment in a year, you’d simply plug in the numbers as such:

PV = $1,000,000/(1+r)^{1 }

and do the math. To find the total value of the series of payments, you’d simply do this for each payment and add the total. The calculation would look like this:

PV = [$1,000,000/(1+r)^{1}] + [$1,000,000/(1+r)^{2}] … + [$1,000,000/(1+r)^{20}]

If you don’t like doing the math yourself, the internet is once again here to help. There are a number of present-value calculators online where all you have to do is enter the numbers and let the calculator do the work.

## Determining the Discount Rate

You may have noticed something missing from our calculations; specifically, what is r, or the rate of return?

**The rate of return that is applied to a present value calculation is known as the discount rate. It measures the opportunity cost of the rate of return foregone by agreeing to accept the money in the future. **

In other words, it’s the rate of return you could have gotten by taking the money today and investing it rather than waiting until a future date.

Determining the rate of return is highly subjective since, until the money has been invested, you don’t know what that rate of return will be.

For example, stocks can yield higher returns than bonds, but there is also an increased risk of underperformance or even losing money. This increased risk is often compensated by a higher rate of return, but what should you use in your calculation?

Again, there is some subjectivity, as, depending on your options, your estimates of the rate of return you can earn will vary.

However, a good rule of thumb often followed in these calculations is to use a risk-free rate of return, that is, the interest rate paid by an instrument such as a U.S. Treasury bond with an almost nonexistent risk of default.

This is often known as a hurdle rate, since any riskier investment must pay a greater rate to justify the risk, and is often used in these calculations since it forms a good baseline of what can be achieved through investments.

Additionally, if you are mostly concerned with inflation, the inflation rate can be used. This will tell you how much the payment you’ll receive in the future is worth in terms of today’s money. This will account for inflation, but not the opportunity cost.

## Benefits of Present Value Calculations

Present value is an important consideration in a number of financial calculations such as pension obligations or bond yields.

On a personal level, learning how to use present value calculations can help decide whether to accept offers such as cash rebates, 0% financing on a car, or pay points on a mortgage.

It is also critical in investment decisions. Using present value can provide valuable insight into whether or not to make a certain investment, or in choosing one investment over another.

Companies and individuals use it to determine whether an investment’s future value and rate of return are enough to make it worth pursuing.

This ability to compare future dollar amounts to present dollar amounts makes the present value of money a key comparison tool during the investment process, and can also help clarify decisions such as taking a lesser sum now as opposed to a larger sum paid out in the future or over a period of time.

This can help determine the value of potential future bonuses or in assessing the value of long-term contracts.

Finally, understanding present value can shed light on the economic impact of the changing value of money during periods of high inflation.

## Limitations

However, there are limitations to the usefulness of present value calculations.

First, they involve **assumptions** about the discount rate, as we’ve already discussed. An overly optimistic or pessimistic assumption about the rate of return you can hope to earn can lead to poor decision-making.

It also allows those with a bias towards or against one investment or the other to get the results they want by changing their assumptions about the discount rate to justify their biases.

Even with the best of intentions, the rates of returns are still **estimates of future earnings**. Since they haven’t happened yet, exact numbers are impossible. As with all investments, they aren’t guaranteed, and inflation can erode the spending value of these earnings.

## Conclusion

Despite these limitations, present value calculations are an important tool to use in comparing future values to their present value.

To learn about more, related topics, check out our articles on the time value of money and the future value of money.

As always, we hope you enjoyed this article, that you will be able to use what you’ve learned in your own financial decisions, and that you will subscribe to join us for more articles on other interesting financial topics.