What Is the Time Value of Money?

With shelter-in-place orders in effect, we figured now might be a great time to learn the core financial concepts that underpin our money and our economy. We’ll start with the basics and build up our knowledge over time. Here are the major themes we’ll get to: 

• The theory behind investing.
• What determines how valuable a stock or bond is?
• What makes a market?
• Asset classes and what they’re for.
• Account types and how you can get the most out of your money.
• How to build and stick to a savings plan.
  

And we promise to keep it light, approachable, and hopefully practical.

With that out of the way, let’s dive into our first topic: what is the time value of money?

Money now, money later

At its core, finance is concerned with the value of money now versus what it could be worth in the future. You might be thinking, that money is the same today as it will be tomorrow. In everyday life, this is true. You can buy something for say $100 today and return it for $100 tomorrow without thinking about whether there’s a difference between the amount you paid today and the amount you’ll get back tomorrow. 

But what about over longer time periods? 

Here’s a thought experiment: would you rather I pay you $100 now or wait 10 years for me to pay you $100 then? Most people would answer now. We humans have an innate sense that money now is worth more than the promise of money in the distant future, but why is that?

Why is a dollar worth more today?

There are actually a few reasons why you’d prefer money today over money tomorrow:

• If you have $100 now, you can spend it now and satisfy some desire sooner rather than later.
• If you have $100 now, you can invest it, and earn some return on it before that 10 year mark hits. That means your $100 now will amount to more than $100 in 10 years.
• There’s a risk that you might not ever receive that $100 in the future. Maybe I won’t pay. Maybe the US monetary system collapses. Or maybe the value of that $100 is eaten away by rampant inflation. Who knows? A lot can change in 10 years.
  

So, a dollar received today is worth more than a dollar received tomorrow. But how much more?

In a perfectly predictable world, if you know some information like the interest rate you’ll receive on your money by investing it and how often it will be compounded over what time period, you can use a formula to understand how valuable that $100 would be in the future. 

Conversely, you can use the same data points to discount the value of a future $100 to its present value. Either way, with those numbers in hand and a formula at the ready, you can convert back and forth between the value of your money today and its value in the future.

How much more valuable should you expect that $100 to be in the future? Another way of asking that question is how much would your $100 grow to between now and then? To figure that out, consider how much you would expect in interest if you loaned your money to an extremely trustworthy person that would pay you back on time.

What is a risk-free return?

The interest rate used for such a person is called the risk-free rate. Usually, the return on 3-month US Treasury bills is used as a stand-in for the risk-free rate because of how safe and predictable lending to the government over short periods of time is. Compensation for the opportunity cost of missing out on the risk-free return is ultimately where the time value of money comes from in our perfectly predictable world.

But what if the world isn’t perfectly predictable. What if you have to worry about things like inflation, trust in institutions, or unpredictable returns? That’s where things get tricky, but it all comes down to risk. We’ll tackle risk in our next post.