The Only Rate That Will Fly!
In Mrs. Pritchard’s second-grade classroom, one of the favorite lessons is the butterfly lesson. This is the one where students get to see the little caterpillar grow before forming a chrysalis and then turning into a monarch butterfly that will fly away.
The second part to this lesson is the finance version. In my book Would Your Boomerang Return? I write about matching the hatch, a concept that comes from fly fishing, to describe the requirement to correspond or match the time span in between periods or payments (on the timeline) and the time span of the true investment yield. Without the match there’s no way to discount or compound. For those who have read the book or followed this blog, this is TVM Rule #2.
The best way I’ve found to teach students how to manipulate the investment yield starts with the building block True Investment Yield equation and then gets them to call the individual yields or rates by name. Let’s take a look at this building block Time Value of Money equation:
Illustration by Scott Alberts. Copyright 2022 Brent Pritchard. All rights reserved.
Ignoring the boomerang for a moment, use your imagination to see a caterpillar in the “s,” which is a simple investment yield that doesn’t consider the effects of compounding. This is what I refer to as the “caterpillar rate.” Let’s assume our caterpillar rate was a 1.50% simple quarterly investment yield. We’ve called it by name just like we can name a caterpillar.
Here’s where most people stop calling the investment yield by name, which is the main reason why I think people struggle manipulating investment yields. Keep that in mind as you calculate the “chrysalis rate.” I can see the shape of a chrysalis in the parentheses around “s” divided by “c.” Can you? If the 1.50% simple quarterly investment yield compounded monthly, there are 3 compounding periods within the time span of the simple investment yield. So, you would divide .015 by 3. But that’s not all. Let’s call this simple investment yield by name. The chrysalis rate is a 0.50% simple monthly investment yield.
We’re left with the “butterfly rate,” which is the only investment yield that will fly when it comes to applying the Time Value of Money. Let’s assume the time span in between periods or payments (on the timeline) is one year. The only rate that will fly is a true annual investment yield. Since our chrysalis rate is stated in monthly terms, how many months are in a year? That’s the value you need for “n.” And after subtracting one we call it by name. The butterfly rate is a 6.1678% true annual investment yield.
And there are times when a caterpillar is on a fish’s menu…. You can’t make this stuff up.
How do you feel about your ability to manipulate the investment yield? (Without it you can’t apply the Mathematics of Finance.)
Brent Pritchard is an author and college finance lecturer with over two decades of industry experience and cofounder of Boxholm Press, LLC, a family-owned-and-operated publishing company providing educational content, products, and services. He pioneers an innovative and approachable new way of learning and teaching the Time Value of Money as well as thought leadership in other business topics. His most recent book is Would Your Boomerang Return? You can contact him on his website here.