# The Time Value Of Money

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If you’ve ever worked most jobs, you probably know about tax withholdings. Every pay cycle, your employer takes a certain amount of your salary out of your paycheck and pays it directly to the government based on their estimates of what you will owe in taxes.

At the end of the year, you file your taxes and, if the government took too much, you get a refund. All is well, right? After all, you received the same amount you would have without the withholdings—it just took a little longer to get it. Why should this matter?

Well, it turns out that a dollar paid today is worth more than a dollar paid in the future. In other words, you’d rather have the money today than receive the same amount in the future.

Reasons for this include the opportunity cost of losing the chance to invest the money (thus, earning interest) and inflation. In this article, we’ll take a look at the time value of money, how to calculate it, and why it matters.

Contents

## Time Value of Money

Simply put, the time value of money refers to the concept that money paid today is more valuable than the same amount paid in the future. This is because the money can be put to use immediately, including being invested and earning interest.

For example, if you have \$1,000 today and can earn 10% interest annually, you will have \$1,100 in a year. This is clearly more than if you received \$1,000 in a year.

Additionally, inflation may diminish the purchasing power of the money received in the future—although the dollar amount might be the same, it will buy less than it would today.

The time value of money is also sometimes referred to as either the present discounted value or the net present value of money.

## Formulae

This is all fine and good, but how can you apply it in practice? Sure, if somebody offers you \$1,000 today or \$1,000 a year from now, the choice is simple enough, but how likely is it to be this simple?

What if, instead, somebody offers you \$1,000 today or \$1,100 a year from now? How can you compare the two?

This is where math comes in. There is a formula you can use to compare a future value to its present value and vice versa. It is:

FV = PV[1+(i/n)](n x t)  or PV=FV/[1+(i/n)](n x t)

FV = Future Value of money

PV = Present Value of money

i = interest rate

n = number of compounding periods per year

t = number of years

Using this formula allows us to compare a present amount to its corresponding value in the future, and vice versa.

To demonstrate, assume you are trying to decide between the \$1,000 today and the \$1,100 a year from now. If you can earn 10% interest compounded annually, then: i = 0.1

n = 1

t = 1

Thus, the future value of that \$1,000 is:

FV= \$1,000[1+(0.1/1)]1 x 1 = \$1,000(1.1) = \$1,100

Thus, the two values are equal. As you can see, the most important variable is the rate of interest that you can earn.

A simpler formula (though failing to account for things such as compound interest) is:

FV = PV(1+r) or PV = FV/(1+r)

where r = rate of return

Using this formula, you can see that if you could only receive a 9% rate of return, the future value would be:

FV = \$1,000(1+.09) = \$1,000(1.09) = \$1,090

Likewise, at an 11% rate of return, the future value equals:

FV= \$1,000(1+.11) = \$1,000(1.11) = \$1,110

We can use these formulae to compare present amounts with the promise of greater amounts in the future.

## Factors Influencing Time Value of Money

We’ve established the principle that a dollar today is worth more than a dollar in the future. We’ve also looked at how to calculate the future value of money so that you can compare the future promise of money with an amount paid immediately.

However, why is this? What makes a dollar today worth more than a dollar in the future?

It turns out that there are three reasons:

1. Opportunity Costs
2. Inflation
3. Uncertainty

We will now take a look at each of these and how they each impact the future value of money.

### 1) Opportunity Cost

If you have the money today, you can invest it today. It will earn a return, and at the end of the year, you will have both the amount and the return it’s earned.

For example, if you get \$1,000 and can get a 10% return, in a year you will have the \$1,000 plus another \$100. This is what the formulae we discussed previously are intended to help calculate.

If you don’t get the money until a year from now, you have forgone the opportunity to invest it—this is what is referred to as an opportunity cost.

However, while the formulae we’ve mentioned help calculate the monetary economic costs, there is another type of opportunity cost worth mentioning.

In addition to investing the money, you could spend it. If instead of investing the \$1,000, you would have bought a PlayStation, then you’ve foregone a year of playing PlayStation by delaying the payment for a year.

If there’s an event such as a concert or sporting event that you need that \$1,000 to attend, by accepting the future \$1,100, you’ve foregone the opportunity to attend that event forever.

Though these opportunity costs might not impact your economic bottom line, they will impact your utility—the satisfaction you get from the goods and services you exchange the money for.

If you’ve missed seeing your team play in the Super Bowl because you accepted the delayed payment, nothing you can buy with the extra money will make up for that. It’s gone forever.

This is something worth considering in your decision-making process, even if it can’t necessarily be quantified or measured in dollars and cents.

### 2) Inflation

Another important consideration is inflation. After all, the purpose of money is to buy stuff with it. What’s the point in foregoing payment for a greater, future payment if that future payment can’t buy as much?

For example, if you forego a \$1,000 payment today for a 10% higher payment a year from now, but inflation was 20%, you’d actually be losing on the deal. The \$1,000 today could buy more than the \$1,100 you’d receive a year from now.

Note that the formulae used to calculate the future present value of money do not include the inflation rate. This means that they’ll give you the nominal amount but not tell you what it means in terms of real dollars—dollars that have been controlled for inflation.

In other words, that \$1,100 you’ll receive a year from now might only buy as much as \$900 would today.

However, although the formulae do not explicitly account for inflation, the interest rate often does—the higher the inflation, the higher the interest rate is likely to be.

Nevertheless, it is important to keep in mind that the future value you’ve calculated might have less buying power than it would today.

### 3) Uncertainty

As the old saying goes, “A bird in the hand is worth two in the bush.” Money today is money in your hand or bank account; the promise of a future payment is just a promise.

There is always the risk that you’ll never receive the future payment. This can occur because the promisor goes bankrupt, breaks the agreement, or some other unforeseen circumstance.

When deciding whether to forgo money in your pocket today for a future payment, this is something that you must take into consideration—how likely is the payment to actually materialize?

The promise of a payment from someone you just met should be valued considerably less than the promise of a payment from a trustworthy institution like a bank or the US government. Likewise, the returns from investing in a well-established company are more likely to materialize than investments in a startup.

Like inflation, the formula does not explicitly take this into account. However, depending on the investment you are considering, it may be incorporated into the interest rate.

This is why US Treasury bonds pay a lower interest rate than junk bonds—they are less risky. Because the uncertainty, or risk of default, with junk bonds is higher, those issuing these bonds must pay a higher rate of interest to entice investors to take the risk.

Since the US Treasury is extremely unlikely to default, there is less uncertainty; thus, the lower interest rate.

When considering investments and the time value of money, you must also take into account the possibility of receiving no payment in the future.

## Conclusion

Knowing the time value of money is important because it can help guide financial decisions such as investments and payouts.

In this article, we’ve discussed the formulae used to calculate the time value of money as well as the impact that inflation and uncertainty should have in guiding these decisions.