When computer programmers dabble in economics: Buying prepaid lunch vouchers

Several years ago, the Microsoft cafeterias phased out their prepaid lunch voucher system. Under the new system, you "load up" your security badge with money (either by paying cash at any register or by having the amount deducted from your paycheck) and then swipe your badge at card readers installed at each register. But in the old days, the system operated manually.

Under the old system, you paid \$25 cash for a voucher which, when folded in half, was about the size of a business card. On the card were boxes with various denominations (\$1, 25¢, 10¢, 5¢), and when you bought something with your voucher card, the person at the register used a pen to X out the various boxes to void them. For example, if you bought something for \$3.50, the person at the register would cross off three \$1 boxes and two 25¢ boxes. (And since I know people will ask even though it's totally irrelevant to the story: Yes, there were provisions for "making change", for example, if you had four 25¢ boxes remaining and you bought something for 90¢, but they were rarely needed.)

Yes, this system was easily hacked, but nobody did. Partly because the fact that it was so easy to hack removed the challenge, but mostly because we try not to hire dishonest people.

When you bought one of these voucher cards, you receive \$27 in credit for your \$25 prepayment. The security badge payment system doesn't have this "cash bonus" feature, and when the cafeteria people announced that voucher card system was being phased out, one of my colleagues sat down and, making various assumptions on the time value of money, how much money a typical lunch cost, and possibly even the current price of energy on the spot market for all I know, calculated the optimum number of voucher cards to purchase in order to maximize the benefit from the cash bonus.

As I recall, the calculations determined that seventeen voucher cards was the optimum.

[Raymond is currently away; this message was pre-recorded.]

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1. mikeb says:

Given what’s going on in the financial arena these days, I think I should have put all my investments into prepaid lunch vouchers.  That makes my optimal number of vouchers about 23.

2. Spire says:

Time is an illusion. Lunchtime doubly so.

3. Arthur Dent says:

@J. Edward Sanchez:

Oh, very witty. You should send that in to Reader’s Digest. They have a special page for people like you.

4. pne says:

I find it rather quaint that the card had values corresponding to US coins rather than, say, typical lunch costs or ease of "making change" with comparatively few boxes.

(I presume the perceived benefit is that people are used to figuring out how to break prices down into those denominations but not so much with unusual-for-coins ones such as 50 cents, let alone Fibonacci sequences or other such games.)

5. Ens says:

Well, that and typical lunch costs are themselves not necessarily easily divided.  Also, tax laws can change independently of the cafeteria prices.

It only really works if you have a very small variety of choices in all cafeterias, or you limit the pricing scheme very carefully to correspond to the tick-boxes.  Microsoft however has a very large campus and the cafeterias in the different buildings are not totally standard in their offerings (I think the prices within offerings are standard, though), and some of the cafeterias have quite a large variety, and some include random outside vendors.

Still, yes, I agree it could benefit from skipping some coins like 1¢ 5¢ 25¢ \$1 or perhaps going the other way and introducing intermediates, eg. 1¢ 5¢ 10¢ 25¢ 50¢.

That said, maybe it did.  We’re getting a story related by a guy presumably disinterested in this aspect, from cards that ceased to be sold “a few years ago”.

[Exactly. The detail is irrelevant to the story and I therefore put no effort into verifying its accuracy. -Raymond]
6. Peter says:

pne: I see what you mean, but for someone who doesn’t live in the States, it’s strange to hear 50c described as unusual for coins.

The question I feel I have to ask is why the need for this voucher system in the first place, when there are these quaint things called “coins” that fulfill the same purpose? Is it supposed to be faster to process the vouchers or something?

[It’s faster, more convenient, and you don’t have to wash your hands after using it. -Raymond]
7. mikeb says:

Holy crap – it looks like nitpicking has reached some sort of new level.  I’m just not exactly sure what that level is.

8. Umesh says:

calculated the optimum number of voucher cards to purchase in order to maximize the benefit from the cash bonus.

Now we all know what the real finance whiz’s would have done here – they would have bought up all the lunch vouchers before they stopped selling them, securitized them and started trading derivatives on them.

9. Daniel says:

I have a friend who used to do something similar with supermarket Christmas saving vouchers.

The scheme went something like – pay a reduced price now for a voucher which you can redeem at Christmas time for full price. The reduced price was based on a sliding scale depending on how far away it was from Christmas. For example you could buy a \$5 face value voucher in August for \$4 but it was wasn’t redeemable until the month of December (once it got close enough to Christmas vouchers only sold for the full face value)

He calculated that the best time to buy was on the 31st October as vouchers could be purchased for \$4 and the rate would change on the 1st November. He would then redeem these on 1 December for gift vouchers – the gift vouchers would earn the buyer loyalty card points which could be saved and redeemed later. He would then calculate how much breakfast cereal he ate each morning, and the typical expiry date of a box of breakfast cereal (to calculate the theoretical maximum purchase amount), then factor in storage costs for storing a bulk amount of cereal, and then calculate the optimum amount of cereal to buy (he also did the same with frozen chicken, peanut butter, sugar and tuna). Most of these products were bound to be discounted from full price in December, so he would wait until the right time and then the purchase would then be made with the gift vouchers (and presenting the loyalty card earned extra points redemmable for discounts in the future).

I don’t know how much money he actually saved by doing this, but it was comical when visiting his house to see a stockpile of cereal in his garage.

He now works for the tax department…

Was the \$34 saving even worth his time?

11. Richard Swift says:

I do just the same calcs each time I hear that Sydney pre-paid ten-trip bus ticket prices are due to increase!

12. Stephen Mok says:

Richard, and how exactly do you calculate what’s best and what conclusion do you reach? (Just out of curiosity as a fellow Sydneysider… :)

13. David Walker says:

@Daniel: Unless you REALLY enjoy spending the time that it takes to calculate stuff like this, I personally think it’s never worth it.  I would much rather spend the time reading a book, and spend the extra \$20 at the store.

Reminds me of the urban legend that says that if some random billionaire drops a \$100 bill on the ground, it would not be worth his or her time to stop and pick it up (since his/her income is more than \$100 in the time it takes to stop and pick it up).

Which is stupid, because the person doesn’t stop earning while picking up the dropped currency.  If they stop to pick it up, they would be \$100 richer (or, at least, not \$100 poorer), and if they didn’t stop to pick it up, they have lost the \$100.

My Mom once stopped to pick up a bunch of nails off the floor that some remodelers had dropped while they were adding a room.  It wasn’t worth THEIR time to stop and pick them up, but my Mom, whose per-hour income was much larger than theirs, didn’t lose anything by picking them up.  And our household gained some nails that could be used later.

Calculations that involve the cost of your time can be problematic…

14. John Muller says:

I still have \$12.75 on my last voucher…

15. pcooper says:

Do your coworkers do something similar with the Forever stamp when stamp price changes are announced?