## Biweekly Payment Magic

A while back, I did some foundational work for a leading biweekly payment service.  That is, the math part, which I will reprise here.  Biweekly works best in a climate of high interest rates and, unfortunately, soon after this project, the Federal Reserve dropped their reference rate to zero.  The Fed has not been persistently above 2% until recently, and biweekly is once again looking good.

The featured chart shows a scenario first constructed by my erstwhile partner Phil Battista.  I call it the “magic trick” because the customer in this scenario has financed an extra \$3,250 with no change to the term, APR, or payment.  Before presenting the trick, here are some basics about biweekly.

## Biweekly Payment Plan Basics

In Canada, the banks offer loans with native biweekly payment schedules, and dealers feature them in their advertising.  Here in the States, you have to use a service.  The service collects payments biweekly via direct debit and manages the lender to accelerate the amortization.

Here is an example.  According to recent Cox data, the average price of a new car is now above \$49,500 with an APR of 7.0% and a 72-month term.  By the way, this survey does not include luxury brands, and some people are financing up to 84 months.

Below, I have modeled this “average” loan showing monthly versus biweekly payment schedules.  This is showing the amortization only, omitting whatever fees the biweekly service may charge.  You can see that the loan is paid off seven months early.

If you’re using longer terms to fit customers into payments, biweekly will shorten the trade cycle a bit.  Also, credit-challenged buyers may be better off with direct debit synched to their paychecks.

Nostalgia Alert: coding for the U.S. Equity project was originally done in C# by my son, Paul, who would have been around fourteen at the time.  We were making an OO model to include all loan and lease instruments as subclasses.  Coding for this article was done by me, in Python, which is 10X easier.

## The Magic Trick

If you compare the two charts above, you can see graphically how Phil’s trick works.  Instead of starting your biweekly loan at the same amount and having it end earlier, you start it higher and aim to end on the same date.

The trick works because half the monthly payment is higher than a native biweekly payment would be – by \$33 in this example.  The customer makes the equivalent of thirteen monthly payments per year, and the bank loses a little bit of interest income.  Here are the steps:

1. Increase the amount financed, which will increase the monthly payment.
2. Increase the term until the monthly payment comes back down to where it was.
3. Use the biweekly program to bring the term back down to where it was.

Congratulations, you can now finance more product with the same monthly payment.  I covered the concept for menu systems in Six Month Term Bump.  To do goal seeking, as I’ve shown here, you will need some Python (or a precocious teenager).

## Moving to Powersports

Back in 2020, I contacted all the leading F&I administrators, pitching my plan for AI-priced service contracts.  As soon as the conversation touched on VIN decoding, they would invariably stop and ask me if I could get VIN data for powersports.  This turned out to be a trend.

Having been in automotive for many years, I was a little sniffy about powersports – although I had worked with Ducati, Harley, and RumbleOn during my tenure at Safe-Guard.  What I knew then was that powersports had only one DMS (Lightspeed), one menu system (Maxim), and no – there was no good VIN service.

When you’re in the powersports industry, you’re selling fun.

At \$34 billion, powersports is dwarfed by the mighty auto market, but it has higher margins and better growth.  According to published financials, gross profit is around 20% for auto retail and 30% for powersports.  I expect that the 3% CAGR will perk up as the ecosystem improves, which is the topic of today’s post.

In automotive, we have a rich software ecosystem.  In powersports, not so much.  The ecosystem is complicated by a wide array of vehicles, from jet skis to snowmobiles, with the attendant challenges in standard process and vehicle ID.

## The Powersports Market

There are roughly 17,000 car dealers in America, compared to 7,000 motorcycle dealers.  From a dealer’s perspective, powersports means less competition and higher margins, according to Mercer Capital – and it is terra nova for software vendors, as well.  Public auto group Sonic took Mercer’s advice, recently acquiring 13 powersports dealerships.

Here is another explainer, this one from SEMA, on the market structure of ATVs, UTVs, and motorcycles.  I am including it basically for this great quote from dealer consultant Rob Greenwald.  “When you’re in the powersports industry, you’re selling fun,” he said. “We sell lifestyle.”

Unlike buying a car, a powersports purchase is discretionary.  This means it’s more susceptible to economic downturns, but it’s also more fun.  People enjoy visiting the dealership, and that changes the technology model.

Digital retail, for example, is still important – but not to reduce time in the dealership.  It’s so that we don’t have to pull you out of that RZR to sign papers.

## Crossover Software Vendors

A few of the website providers I wrote about are also active in powersports, like Dealer Inspire and Fox.  However, neither of these seems to have their digital retail solution in play.  One DR vendor that I recognize from auto is Joydrive, which made a strong entrance by partnering with Polaris and Octane.

Octane is the leading finance source in powersports, but there is a new entrant from the auto space, RouteOne founder Toyota Financial.  TFS is now the private label consumer and wholesale finance source for Bass Pro.

Another crossover vendor is Darwin which, after dominating the auto space, moved first into motorcycles – challenging Maxim’s lock on Harley-Davidson – and now into other powersports.  Speaking of menu selling, F&I providers here are Galt, Safe-Guard, and Protective.

## Movement Toward Powersports

What I encountered in 2020 seems to have been a general movement toward powersports.  Lured by big groups like Bass Pro with its 170 locations, Marine Max (125), and RumbleOn (60), software vendors are extending into powersports.

There sure are a lot of motorcycles at this car show.

They will go where the dealers are and, as I walked the NADA show in Dallas, I had to smile at the untapped demand.  “Drop your business card and win this Harley,” offered one vendor.

“There sure are a lot of motorcycles at this car show,” I remarked.  And then there was the Kawasaki booth, enlisting car dealers looking to diversify – for fun and profit.

Readers with up-to-date Twitter skills will recognize the classic Willem Defoe meme.  I have been doing web apps for a long time, and it seems everybody is an expert in UI and UX – both!  They have, as Jamie puts it, a “flair” for web design.  Genius-level stuff, like green CTA buttons because green means go.

What will it look like? I don’t care.

On a recent gig, the first thing I did was replace hi-fi mockups with Balsamiq.  The product team had been killing themselves to do mocks in Figma, and failing, and then wrangling with the UI developers well into each sprint.  There’s a good reason why Balsamiq uses scratchy lines and a comic font, which the crew understood instantly.

Is this what it’s going to look like?  No!  What will it look like?  I don’t care!  Well, I do care, but I studiously avoid having an opinion about web design because I respect the professional competence of my UI/UX team.  I have a habit of saying “I don’t care,” when what I really mean is: I don’t want to interfere in a decision better made by actual experts.

We know exactly what the page will do, from business analysis and functional design.  We also know roughly what it will look like, from the style guide.  But, what will it look like, exactly?  I am content to wait and see, and BTW we’re agile and we’re AB testing – so it will change, anyway.

Everybody thinks they’re an expert because UI/UX is the presentation layer.  It’s (seemingly) just visual.  People think, hey, my socks match my pants, so I can play too.  Oddly, no one ever offers advice on how to do the data layer, or what message bus to use.

I recently saw this chart (below) from PNAS.  It’s one of those popular psych studies that asks “does having more money make people happier?”  They discovered that higher annual income does indeed make people happier, but in a logarithmic relationship.  This reinforces something I wrote in Sensitivity Testing Model Assumptions, namely: know your time series.

In today’s post, I’ll explain about log scales using an example from stock trading, and then circle back to the happiness data.  I’ll wind up with an example from my own experience, contrasting exponential versus polynomial functions.  You may also want to check out my earlier posts on seasonal adjustment, and Bayesian probability.

“When interpreting these results, it bears repeating that well-being rose approximately linearly with log(income), not raw income”

Reported “life satisfaction” and “well-being” increase linearly with log income, not straight income.  That is, the next notch up in happiness requires an order of magnitude more money.  Previous studies had found a plateau around \$75,000, with little or no increase in happiness after that.

So, this is a new finding – or is it?  Take another look at that income scale.  If that were a straight scale, the chart would show diminishing returns from additional income.  To enjoy steadily increasing happiness, you have to earn exponentially increasing income.

## Log Scaling for Stock Charts

Here is a chart of Carvana during 2018, when the stock was rising rapidly.  Comparing the tiny candles in March with the longer ones in June and beyond, you might conclude that the stock had become more volatile.  The average daily trading range increased from one dollar to three over the period.

But a dollar when the stock is at \$20 is not the same as a dollar when the stock is at \$60.  To have the candles represent percentage change, you must set the price scale to logarithmic.  See, in the chart below, how the price intervals get closer together as they proceed up the scale.

Whenever a stock chart covers a wide price range, you’re better off using a logarithmic scale.  You may recall from school that adding logs is the same as multiplying the numbers.  So, a linear scale shows additive change, and a log scale shows relative change.

log ab = log a + log b

Take another look at the first Carvana chart above.  Stock traders call that “going parabolic.”  Parabolic growth, also known as “quadratic,” is another rapid growth trend, easily confused with exponential growth.  I did a quick regression analysis, and both models fit the Carvana data pretty well.

Pro tip: Never use “exponential” to describe something that’s not a time series.  Some people seem to think it just means “big,” as in “last month was exponential!”

The point to “know your time series” is to understand the mechanisms underlying your data.  Exponential growth comes from compounding, like if you increase sales by ten percent, and then you increase the new, higher, base by another ten percent – and you keep doing that.

I’ll provide an example of quadratic growth later, but first let’s finish up the PNAS chart.  I think of this as a time series because I picture someone earning steadily more income over their career (the data is actually different people at different income levels).

When I say “steadily more income,” I mean exponentially.  Note that each tick mark on the PNAS income scale doubles the value.  This is a log scale, like the Carvana price scale, above.

Many real-world metrics are based on log scales, like decibels and the Richter scale.  An earthquake of magnitude 6.0 on the Richter scale is ten times as powerful as a 5.0.

The chart below shows what this blessed career looks like.  If you start making \$15,000 at age 18 and double your salary every six years or so, then you will experience steadily increasing “well-being.”  My red line is the same red line as in the PNAS chart.

I think showing the data as someone’s career is a good way to tell the story.  Income and well-being are shown together, with straight scales, and mediated by the hypothetical age.  On the other hand, the correlation has disappeared.  To show that, we must apply a log scale to the income series:

This is why the authors make clear that, to enjoy steadily increasing (linear) happiness, you must earn steadily increasing (exponential) income.  To put it another way, if you only earn increasing (linear) income, then you will have only increasing (log) happiness.

Many real-world metrics are based on log scales, like decibels and the Richter scale.  An earthquake of magnitude 6.0 on the Richter scale is ten times as powerful as a 5.0.

## Polynomial versus Exponential Functions

Once upon a time, way back when databases had size constraints, I observed that parabolic growth in BMW Financial lease transactions would pose a danger to the database.  I ran a regression analysis, calculated when the database would fail, and sent a memo to my boss.

I also worked out a mitigation strategy, but let’s stick with, “the database will blow up on April 21,” for dramatic effect.  Instantly my office filled up with expensive auditors and consultants.

“No, it’s not a malfunction.”

“No, it’s not growing exponentially.”

Lease transactions were growing quadratically, which is why I chose this example.  If new leases are steady at 1,200 per month, that’s a flat line.  Total rows in the lease table will thus increase by 1,200 per month.  That’s a sloping line.

Now, if each lease generates roughly two transactions per month, then total transactions will be a parabola.  Readers with a little calculus will recognize this as integrating, twice, from the constant rate of new leases to the second-order rate of transactions.

This is the essence of “know your time series.”  The regression analysis showed quadratic growth, unequivocally, and it was also supported by how we expected the data to behave.

The auditors milled around for a while, charged us about a million bucks, and decided I was panicking over nothing because the database wasn’t really going to blow up until April 29.  Not to mention my mitigation strategy.

## Big O Notation

In the example above, I showed that a linear function of a linear function is a parabola, also known as a “quadratic” or second-order polynomial.  Compose another linear function on top of that, and it’s a third-order polynomial.

Excel has a handy feature, shown below, for fitting polynomial functions of different order.  This is a little dangerous, because you can easily find a fit without thinking about it.  It’s not enough to get a good R-Square (fit) value.  You must understand why the data behaves as it does.

This “order” thing is sufficiently important to data analysts that they have a notation for it, called “Big O.”  The quadratic example we just worked through would be O(n2) or “order n-squared.”  I notice that Excel will also fit a Power Law, or “Pareto” series.  That will have to wait for a later post.