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## Time Value of Money Part VII

### Loving the Present Value Equation at Lollapalooza

In this small business financial management lesson, we’ll talk about how we can tie in the present value equation with a rock concert. Between the junior and senior years of my undergraduate Chemical Engineering degree, I took an internship in Chicago. Since I love going to concerts and everything to do with music, living in Chicago was awesome in the summer since they have live music anywhere you go. One of their big music events is Lollapalooza, which is a three day music festival with all types of artists. I had always wanted to go so I found some friends and headed over to Grant Park to rock out.

Let’s say that once I got there with my friends, one of them told me that they didn’t have any money to spend on the ticket. Since it will be a couple of years until they are done with college, they promise that they’ll give me $100 for the day pass in three years if I buy them the ticket today. Since I understood the concept of the time value of money and knew that $100 in three years was worth less than $100 today, I wanted to see what it was actually worth today. At the time, we’ll say that I could get 3% in my savings account.

Remember that fancy future value formula that we discussed in the previous post? For a refresher I’ll show it again:

Future Value = Present Value x ( 1 + Interest Rate ) ^ Number of Years

So in the last post we used the formula to calculate how much we’d have in the future (the future value) if we invested some money at a certain interest rate for a period of time. Let’s take a look at this problem and see what information we have. Overall, we know that we’ll be getting $100 in 3 years. The $100 that we’ll be getting is the future value in the formula above and the 3 years what we can put in as the number of years. We also know that we can save at 3% so that is our interest rate. Since we have three of the values needed, we can solve for the fourth which is the present value. By using a little fancy algebra, we can change the formula above into the present value equation:

Present Value = Future Value / ( 1 + Interest Rate ) ^ Number of Years

Let’s solve for the present value which is just a different way of saying what the $100 three years from now is worth to us today.

$100 / (1 + 3%)^3 = $100 / (1.03)^3 = $100 / 1.09273 = $91.51

So, if my friend gives me the $100 in three years, it’s the same as if they gave me $91.51 today. While it wouldn’t really matter since I’d be a good guy and help out my friend get into the concert, we’ve shown that we can use the present value equation to calculate the present value as long as we know the future value, interest rate and number of years in the future.

### One More Shot at Using the Present Value Equation

I still become amazed that some companies still offer mail in rebates on their products. Let’s say that we just bought a gaming console and the mail in rebate that we’ll get back is $25. Since these take forever to process, let’s say that it will take 4 years to actually get our rebate (yep, I’m being a bit dramatic but we’ll go with it). Currently, we could invest in a savings account at 4% and want to figure out what this rebate is actually worth to us now.

To solve for the present value (what it’s worth to us today), we put what we know into the present value equation above:

$25 / (1 + 4%)^4 = $25 / (1.04)^4 = $25 / 1.1699 = $21.37

Although the rebate is for $25, it’s really only worth $21.37 to us today since it takes so long to get it back. From this you can see why companies have an incentive to take their time in processing rebates.

**Key Takeaway:** We can use the same formula as in the last lesson to find the present value equation after a little rearranging. Overall, to find the present value for any situation, we just need to know the future value, the time period and the interest rate. After we get that information we can just plug it into the present value equation and solve:

Present Value = Future Value / ( 1 + Interest Rate ) ^ Number of Years

In the next small business financial management lesson, we’ll talk about things called annuities and how the time value of money plays into them.

Test Your Knowledge: Present Value Equation

**To Next Lesson: What Are Annuities?**

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