Auto Finance – Page 2 – Virag Consulting

Life (Credit Life) without Recursion

I was chatting with Tim Gill the other day about auto finance math, and the topic of recursion came up. Tim is one of the few vendors in this space with his own “calculations engine.” Otherwise, there are not many people who will talk to me about esoteric math problems. That’s why I write a blog.

People commonly describe Credit Life as a recursive calculation or, more properly, an iterative one. This is because the premium must cover the amount financed, and the premium is itself financed. So, if we write the premium as CLP, a function of the amount financed, A, then:

This is generally how people solve it. They run a few iterations, and CLP converges quickly. This is a preference, however, not a requirement. Assuming that the premium calculation is distributive over addition, which it is, we can just as easily set the problem up as:

… which can be solved analytically. This approach will work for most of your popular recursive calculations, like GAP insurance. For an example, let’s take a typical “cost per thousand” insurance calculation, where f works out to ten percent. You could go the infinite series route, which looks like this:

Or, you could simply work the algebra problem:

Now, I know what you’re thinking. You’re thinking that credit life calculations are far too complicated for this approach. You may also be thinking that the premium is based on the monthly payment, M, not A. In fact, these complaints are related. The payment is directly related to the amount financed, through the PV annuity factor, which combines the term and the APR into this handy relation:

So, when you see a payment formula like this one:

The insurance carrier is actually helping you, by combining the calculations for premium and monthly payment. By the way, the last time I checked, C# did not have the payment and related methods from VB and Excel. You are much better off coding your own PV annuity factor, and using it as described here.

Now, if you are designing a calculations engine, you may still prefer to use iteration, for the same reason that you may not want to algebraically reverse all your tax and fee calculations. It is better, though, to use your algebra and know your options, than to rely blindly on iteration.

Automotive News Corrigendum

Regular readers know that, from FMCC to Spartefinanz Abteilung, I am a captive finance booster. See here, for example. So, I was disappointed to see this omission from the BMW Centenary coverage in Automotive News.

I was employee number six behind, if memory serves, Kevin Westfall, David Paul, Mark Mundahl, Bob Devine, and John Dick. David is quoted in this ancient interview. Take a bow, gentlemen. Kudos also to the professional staff supplied by Bank One.

It’s worth noting the structure of this partnership. BMW had hired PWC to administer an RFP. Of many strong entries, Bank One was the only partner willing to use our computer systems. They were aware of our intention ultimately to bring the enterprise in-house, and control of the systems was key. This planned migration from a service provider to insourcing is the same structure Kevin employed for AutoNation Financial Services, and one I would still recommend today.

Biweekly Leasing

Last month, I wrote that Canada offered a better variety of financing plans, and this is a great example. The picture below is from a print advertisement for Oakville Honda. Back when we were setting up U.S. Equity, a dealer told me that the key to using biweekly was to highlight the low payment in his local Saturday newspaper. In the States, he could only do this by using a service such as ours.

Here, the dealer avails himself of a program from Honda Finance Canada, which takes an already subvented APR and spreads it over 104 biweekly payments. It makes a great ad, and they’re running it on TV, too.

GMAC 2.0

AmeriCredit is the new GMAC, only five years since divestment of the old GMAC. I am a strong believer in captive finance, and I never thought it made sense for GM to sell its lending arm. Of course, in 2006, GM was already under financial pressure.

In 2008, as the situation worsened, I had lunch with a friend in the online credit business. He remarked that GMAC had just about stopped making car loans. The new owner, Cerberus, was taking measures to protect its capital – sensible for them, but not what a dealer wants to hear.

GM concluded that it needed a captive lending arm after all: in October it bought AmeriCredit.

I observed that GM would have to develop a new captive, to take care of its dealers. GMAC 2.0, I said. I might have added, after Chapter 11.

What followed was a mad rush to certify GMAC as a bank holding company and obtain TARP funds. My DMS integration project was cancelled, and many of my friends at GMAC were laid off. Last year, the new GMAC bank signed up with Dealer Track. Of Route One’s exclusive captives, this left only Ford and Toyota.

When GM bought AmeriCredit, that seemed to validate my observation. Oddly, GM was denying it as recently as January of this year. That’s why this week’s announcement is important. Adding floorplan proves that AmeriCredit, now GM Financial, is the new GMAC.