# Time Value of Money and Opportunity Cost

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Could the phrase “time is money” actually be right and not just a commonly used quote? One of the most critical concepts to understand in the realm of personal finance is the time value of money. A solid understanding of this concept can change your view of many financial decisions, and in the end, save you a lot of money.

## What is the Time Value of Money?

The time value of money (TVM) concept is used to compare two or more financial outcomes. The basic idea is that a dollar today is worth more than the same dollar in the future.

A dollar today is worth more than the same dollar at some point in the future

If I offered you \$1,000 today, or \$1,000 a year from now, which would you choose? The logical person would, of course, select the \$1,000 today because you wouldn’t have to wait.

But what if I offered you \$1,000 today or \$1,050 in a year?

The decision becomes more difficult. If you took \$1,000 today, you would need to earn (using basic math) a 5% interest rate on the money to end up with \$1,050 in 12 months. If you thought you could make a higher return, then you would take the money now. If you didn’t think that was realistic, then waiting 12 months for the money might make more sense.

### Future Value and Present Value

One way to compare the two options is to use the financial formulas of future value and present value. If you took the money today, you would use the future value formula to determine the future value of the money you had today. Likewise, you could determine the actual value in today’s dollars of the money you would receive in the future.

As noted above, if the interest rate assumptions are the same, then the money is worth the same today as it is in the future. But if the values are different, you need to compare the two to see which is best.

If you had the option of \$1,000 today or \$1,200 in three years, assuming a 2% interest rate if you saved the money today, which is the best choice?

The Future Value equation is

FV = Principal * ((1 + interest rate)^number of periods)

In our example:

• Principal is \$1,000
• Interest Rate is 2% or 0.02
• Number of Periods is 3

The future value of \$1,000 is

FV = \$1,000 x (1+0.02)^3 = \$1000 x 1.061 = \$1,061.21.

The Present Value equation is

PV = FV ÷ ((1 + interest rate)^number of periods)

In our example, the present value of \$1,200 in three years is

PV = \$1,200 ÷ 1.061 = \$1,131.

If your interest rate assumption for the 3 years is accurate, you would be better off waiting for the \$1,200 payment in the future rather than taking \$1,000 today.

## Inflation and Opportunity Cost

The time value of money is a basic principle to compare two known scenarios: a payment today or the value of a payment in the future. But TVM also connects with inflation and opportunity cost.

Inflation itself will devalue the money you receive today. You need to be considering what the future value of the money sitting in your bank account is. Any money you have today that isn’t earning interest (as is the case with most major banks’ accounts) is slowly going down in value. You need to make some return to keep up with inflation.

Another important concept connected with the time value of money is opportunity cost. Even if you get more money by wait three years, you still might be better off by taking the payment now. You could take \$1,000 today and pay off some credit card debt, build your emergency fund, or invest in a side business. Those decisions might better your financial situation immediately rather than waiting three years for \$200 more.

Speaking of credit card debt, when you carry a balance on a credit card, you are making a time value of money calculation. You are determining that whatever you are buying is more valuable than a larger amount of future dollars due to the interest you will pay. You’ll put \$1,000 on a credit card today, but end up spending a total of \$1,600 over the next several years paying off the balance. Is the item really worth those extra payments? Understanding the time value of money can help you make better financial decisions.

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12 years ago

Thanks! I’ll add these formulas to my budget spreadsheet so I can make better decisions when balancing money decisions 😉

Joe
12 years ago

Yes, ALWAYS consider opportunity cost. I can’t stand when financial writers say “I bought a \$600 bike, but it’s only \$10 a month over its useful life!” Well, what if you had invested that amount of money? Suddenly a \$600 bike gets more expensive, the more time over which you divide the expense calculation. An honest opportunity cost assessment would save many students from becoming debt-indentured slaves to get useless degrees.

WR
12 years ago

Great article. Well done.

Sometimes this analysis is easy, as in the case of prepaying a MRC such as Vonage. (not a plug for Vonage but a good example. Will probably drop V in the next few months. Having a ‘home phone’ is becoming less of a necessity)

Anyhoo, They offer a 10% discount if you pay for a year (rather than monthly)

There are no guaranteed 10% returns out there anywhere. I am always looking for prepays that pay. (You have to make sure that you actually want/use the thing you are saving money on though)

-WR

LMR
12 years ago

I’ll take the money now no matter how the formula comes out since the world is going to end December 21st anyway. Party on! 😀

12 years ago

It’s not that easy to decide between 1000 USD today versus 1050 USD in 12 months (except in the model world of wealth maximising agents). Utility maximising can lead an agent to take 1000 USD now rather than 1200 USD in 12 months depending on the personal time preference.

For example, if I strongly prefer consumption today to consumption in a year, I take the money now.

A textbook example: If you can choose between a chocolate bar now or two chocolate bars after a year, which one would you choose?

David Sneen
12 years ago

Well said. It becomes so much simpler when you write the numbers down and analyze them. But, how many of us actually think of the opportunity costs down the road when we purchase that reclining chair for the den? So much of our spending comes from a “gotta have it” mode.

A question one might ask before making a purchase is, “Would I want to work __ extra hours to buy this? The answer might be different after a tough day on the job.

## Time Value of Money and Opportunity Cost

by Kevin Mulligan time to read: 3 min
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