Understanding Present Value, Part 1

Chalkboard with Formulas

It occurred to me that I haven’t done a proper intro to the concept of present value for readers who didn’t major in finance.  The following is the first post in a series about present value and how you can use it to make better financial decisions.

What is Present Value?

Unlike a lot of financial concepts, this one is pretty straightforward and means exactly what it says:

Present Value is how much something is worth (value) as of today (i.e. the present)

That something can really be anything, but in this case it’s best to think of it as a stream of future cash flows.  They can be positive or negative, recurring or irregular, or even the difference between different cash flows.  The point is that by understanding present value, you can get a much better handle on your finances and, at the same time, more effectively make financial decisions.

A Simple Example

How much would you be willing to pay me today, for me to give you $100 a year from now?  Something less than $100, right, because you want to make a return on your investment in exchange for giving up your money.  Let’s say you’d like to make a 5% annual return, so whatever you’d give me today * 105% would need to equal $100.  Dusting off a bit of algebra from 7th grade tell us $100 / 105% = $95.24.  So you’d be willing to part with $95.24 on the condition that I return $100 to you a year from now.

All of this supports a simple equivalency: at 5% interest, $95.24 today = $100 one year from today.  In this simple example, those two things are worth exactly the same and you should be indifferent between which one you have.  Using the lingo of present value, you’d say that $100 in a year has a present value of $95.24 when discounted at 5%.

Why do we say “discounted” when talking about the interest rate?  It’s because the value today is at a discount to the value in the future.  If you’re familiar with time value of money, it’s the exact same concept, just looking at it from a different angle.

How Does Time Impact Present Value?

Let’s revisit the simple example from before, but now assume I’ll give you $100 five years from now.  In this case you’d still want your 5% return, but now for 5 years.  105% * 105% * 105% * 105% * 105% = (1.05)^5 = 127.6%.  In other words, you’d need to get a total 27.6% return over 5 years.  Using the same math as above, $100 / 127.6% = $78.35.  This logically makes sense, you’d be willing to give me less than before, since it’s going to take you longer to get it back.

This leads to a simple take-away: the further out in the future money is to be received, the less it is worth to you today.  The sooner money is to be received, the more it is worth to you today.  The same logic applied to when you’re paying out money, but in reverse.  Delaying payment into the future is worth more to you today, while accelerating payment is worth less.

Here’s a simple chart illustrating this concept, showing the present value of $100 (discounted 5%) for a range of different time horizons.  As you can see, if you have to wait 10 years then the value has a nearly 40% discount in total.  In fifty years, that discount grows to more than 90%.  This is effectively the impact of inflation that makes things in the future worth less in present value terms.  That’s incredibly important when thinking about potential resources or obligations way out in the future.

Present Value of $100 by Time

How Does Discount Rate Impact Present Value?

As I said above, the discount rate is the mechanism by which we can move between present and future values.  If the rate is 0%, there is no discount and therefore no difference between money now or later.  The greater the discount rate, the greater the difference between the undiscounted value in the future and the present value today.

Here is another simple chart illustrating the concept, showing the value of $100 to be received 5 years from now at different discount rates.

Present Value of $100 by Discount Rate

So why would you pick one discount rate over another?  Risk.

Discount Rate = Risk

This concept should make intuitive sense as well.  If you want to put money in a more risky investment, you’ll demand a higher return to compensate.  Likewise, a riskier future cash flow demands a higher discount rate so that it is worth less today (to compensate for the risk).

Let’s say I approach you with two investment opportunities, one high risk and one low risk, that will both return $100 five years from now.  How much would you be willing to pay to buy into each investment?  The more risky one would obviously be less since it’s riskier.  Using the numbers above, you might be willing to buy into the low risk investment for $82.19 (and earn a 4% return), but only $62.09 for the high risk one (and earn a 10% return).

Applying Concepts of Present Value

You can apply these concepts of present value when making financial decisions a couple of different ways:

  • Putting investments with different levels and timing of payouts on a common (present value) basis to determine which is more valuable.
  • Comparing relative riskiness of investments by calculating their implied discount rates.
  • Exploring the value of accelerating or decelerating payment or receipt of cash flow.

I will explore these concepts in greater detail and provide examples for each in a future post.

Summary

Present value can be a little difficult to wrap your head around at first, but once you do it vastly expands your options to think about your financial world.  It helps take some of the guesswork out of financial decision making, which only can lead to better decisions.  Let me know in the comments if there is any additional explanation I can provide.

John started Present Value Finance in 2017 to share his experiences and insights on personal finance to help people make better decisions and take control of their financial lives.  

He achieved financial independence in 2016 by walking away from the high stress world of corporate finance to focus on his family. He’s a husband, father, family CFO, and all around finance geek.

Leave a Reply

Your email address will not be published. Required fields are marked *