In the last chapter, we learn that when there are more than one cash flows, we can't directly add them up unless they come at the same time point.
Here we are going to learn how to add the values of cash flows, when they come at different time points. This task may sounds daunting, but you will probably not believe how easy it can be after I show you the "how to's".
All right. Let's cut the corners. The trick is actually very, very short: when we run into multiple cash flows coming at different time points, just remember, all we need to do is to find the present value (PV) of each of them, and then add these PV's up. Case closed.
Don't worry too much for now. Let's go through an example and it will pretty much explain itself.
Your boss is very happy with your performance in the past year 2020. In return, he offer you a bonus plan, which will pay you 110 bitcoins by the end of 2021, 121 by the end of 2022, and 133.1 by the end of 2023. Suppose today is January 1st, 2021, how much does your total bonus plan worth today? The interest rate in the market is 10%. (We ignore the difference between Dec. 31st and Jan. 1st since it is too short compared with one year).
Analysis: this question talks about 3 CF's (cash flows) coming at different time (the end of 2021, 2022, and 2023). We need to figure out what is the PV (present value) of each of them first and then add these PV's up. So it goes like this:
Below is an animation which breaks down the above calculation piece by piece. Click the "next" button to get started!
Believe or not, this trick (converting CF's to their PV's and adding PV's up) is the general solution for all cash flow problems we run into in this course, and pretty much most cases of your daily life. This is how simple finance can be — easy peasy lemon squeezy!
If you were suffered the by long and tedious terms your mortgage manager try to "explain" to you, then this is a good start to figure out and handle it yourself.
Before we bring the game to the next level of the specific patterns of cash flows, I have a little bit more twists for our general rule here in the next section. I do this to this to make sure we are indeed in a good shape before we run into the battles.