## Saturday, 17 August 2013

### MAT: Credit Beats Cash

Buying on credit is cheaper than using cash. At least in Canada, where we don't physically spend pennies any more - we round off to the nickel. Yet cents are still tracked on credit. In other words, if your total is \$5.99, your credit total is the same, but with cash, you'll pay \$6.00!
 Of course, I'm assuming you're paying off your balance...

Conversely, if your total is \$5.92, your credit total is the same, but with cash you'll pay only \$5.90. The idea is that it balances out. You have to pay a bit more at .99, .98 but a bit less at .97, .96... so if it balances, why am I making the claim that credit is, in fact, cheaper?

Well, I could be wrong. But I think there's an argument to be made regarding pricing, and the number of items you typically buy.

#### CUTTING TAXES

First, let's face it, any individual item is going to end with a 9. There's been studies done on this... psychologically, people are more likely to buy something worth \$19.99 than something worth \$20. It "feels cheaper", or as noted in one of those articles, feels "less expensive" when compared to something worth \$24.99. The exception to the 9s being anything you purchase by weight, which varies too much for me to want to consider.

This means that if you buy two items, the total will end in .-8, three will end in .-7, and so on. Before we cash out though, a brief word on taxes. I'm going to illustrate with 13%, which is the total rate in Ontario and some Atlantic provinces. (Whoa, looks like Alberta has no provincial tax? I thought that was only true in the far north! Only 5% Goods & Services Tax? Huh. Anyway.)

We're looking at (price)*1.13 = (new price). Going to make a quick chart here. The decimal termination pattern obviously repeats after \$10, but if you look closely, you'll see the savings pattern actually repeats every \$5.

Of course, that assumes you just ran in to buy one item. Let's adjust the chart slightly for the case where you buy two.

Same pattern - it's simply moved. Moreover, within the \$5 repeat, your savings and your excesses do cancel out. In other words, if your two item total is \$17.98 today, so you actually SAVE two cents, next time it could be \$14.98, causing you to pay two cents MORE.

Thus, given the impossibility of knowing what it is you're actually buying, I'm going to assume that (on balance), the taxes themselves aren't going to be a major player from this point on. If you would like to make a case for why YOUR total is more likely to trend to \$14.98, enjoy yourself. If you could like to make a case for why anyone's total in GENERAL is more likely to trend to \$14.98, that might be interesting.

By the way, I also ran a check using the Alberta 1.05 tax system, aka GST. Taxes aren't a factor there either, but it's because the rounding doesn't change after taxes.

#### BACK TO TOTALS

So at this point, we assume that your receipt ending in 0.99 is going to lose you money - on balance. Meanwhile, your receipt ending in 0.97 is going to save you money - on balance. We're also assuming that a total of 0.97 means you bought three items (aka the number of pennies to take you up to a dollar).

So, at what item amounts do you lose money?

You lose out if you buy 1, 2, 6, or 7 items. (And 11, 12, et cetera.) I now claim that you are more likely to buy at those numbers. Because barring those big shopping trips on the weekend, you're probably just running in to buy one or two things. Or you're buying a few - but stopping at six, so that you can get into that "six items or less" lane! (In some stores that's "ten items or less" but at ten you're back at par, so the method of checkout wouldn't matter.)

Conclusion? If you pay cash, you are more likely losing money over time, rather than not. Barring any sort of credit transaction fees.

If you think I've screwed something up here, please let me know in the comments. Finally, why was I even thinking about this? Because I saw the following sale on chocolate milk:
 Lots of 2L left by the way. Few 1L.

The 1L is listed for \$1.99, the 2L for \$3.99. My brain quickly clicked in, and I realized I could buy two of the 1L for equivalent volume, and pay only \$3.98. Yet even as I went to do that, I realized... if I pay cash, it doesn't matter. It's \$4.00 in both cases. Well, damn. Worse, the store is actually gaining TWO CENTS from me on the 1L deal instead of ONE CENT. Is that clever, or merely a fluke?

On top of that, I call shenanigans. The 2L milk is regularly \$5.19. I'll now leave you with this last question: What percentage discount was necessary on the larger milk, to create the "equivalent" savings on the smaller?