Stay in Your Own Lane.

By Brent Pritchard

Lots of people, when asked about their ability to operate a vehicle, will likely tell you that they consider themselves to be an above-average driver. But that’s impossible based on the law of averages!

International driving may just be the great equalizer. For example, you wouldn’t want to miss a Do Not Enter sign:

Photo by Brent Pritchard.

Here’s an excerpt from my book Would Your Boomerang Return? What Birds, Hurdlers, and Boomerangs Can Teach Us About the Time Value of Money (2023):

For questions involving multiple streams of cash flows, you can think bigger than the information provided in the question. For example, if you are asked to determine the amount of a savings account balance at a certain point in the future, you can extend the future value of deposits and even the future value of withdrawals to that point in time. You’re keeping the different payment types in their own lane so that you can get to a point in time where you can add or subtract or compare money. When you wrap your head around this point, it opens things up and makes thinking about Time Value of Money questions more manageable. Remember that you possess the Flux Capacitor of Finance, (1 + i)^N, which allows time travel in the context of the Time Value of Money by way of “indifferent lines.”

And speaking of streams: 

Photo by Brent Pritchard.

(It’s not uncommon for runners to maintain an ever-changing mental list of “Top 5 Runs.” Today’s made the list!)  

Where are you in your journey of acquiring the skills necessary to apply the Mathematics of Finance? 

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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.

Learn to Count Your Days.

By Brent Pritchard

Prior to when teaching and a desire to expand my influence outside of Corporate America won the day, I worked as a commercial mortgage loan officer for the real estate arm of a global life insurance company. One of my favorite mortgage bankers and someone I’m proud to call a friend to this day is Peter Dailey. (In case you’re wondering, this isn’t his real name.) Speaking of days, let’s discuss day-count conventions.

Here’s an excerpt from my book Would Your Boomerang Return? What Birds, Hurdlers, and Boomerangs Can Teach Us About the Time Value of Money (2023):

The most common day-count conventions are 30/360, Actual/360, 30/365, Actual/365, and Actual/Actual. For each day-count convention, the last number or word represents the agreed-upon number of days in a given year, and the first number or word represents the assumed number of days in a given month. The day-count convention 30/360 is also known as the “banker’s year.”

The “banker’s year” assumes that there are 360 days in a year and 30 days in each month. The 30/360 day-count convention makes the math easy. Not all mortgage “bankers” are as good with math as Peter and need some help!

A mortgage loan is an example of a negotiated agreement, and the borrower and lender agree that for the purpose of calculating the simple daily interest rate, the assumption will be that there are 360 days in a year, and that for the purpose of calculating the simple accrued interest, it will be assumed that there are 30 days in each month.

In the inc shorthand for most mortgage loans, “c” would be 12 and the “n” would be 1. But this is really a 30/360 “banker’s year” day-count convention in disguise, since you could divide the simple annual interest rate by 360 (/360) and then multiply by 30 to ultimately get the true monthly interest rate: the “c” isn’t 360 because the loan document doesn’t call for daily compounding or 360 compounding periods within the time span of the simple interest rate.

Now let’s run the numbers using the inc shorthand “0.005, 1, 12.” If this were a mortgage loan that required monthly debt service payments with interest calculated and accrued based on a 30/360 day-count convention, you could back into the simple annual interest rate of 6% in an unconventional way using the day-count convention:

Illustrations by Scott Alberts. Copyright 2022 Brent Pritchard. All rights reserved.

You’ve been working with a “banker’s year” day-count convention all along, even if you didn’t realize it.

Today’s the day to learn more about day-count conventions, if you don’t have a handle on them already, because a finance professional who doesn’t know about day-count conventions is a finance professional whose days in the industry may be numbered.

Who is the first person to educate you on this topic of day-count conventions? (If not your finance instructor, then what’s up with that?!)

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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.

The Only Rate That Will Fly!

By Brent Pritchard

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.)

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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.