Wine by the Case – Amazing Math

Welcome to my “daily comment.” The ground rules Ceres and I have agreed to are simple. I can write whatever I want, ranging from a sentence to an epic, and nothing is off limits. I can even say things like, “Don’t trade stocks yourself — for most people, it’s smarter to invest through no-load mutual funds.” Which it is.

This example has sort of evolved. The first time I used it was in 1978, on The Tonight Show. Say you bought a $10 bottle of wine for dinner every Saturday night, but could instead get a 10% discount buying by the case. You’d “make” 10% on the extra money you tied up. And you’d “make” it in just 12 weeks — a bottle a week for 12 weeks equals one case of wine — which works out, I explained, to “better than a 40% annual return.”

I didn’t explain how much better. I figured 40% was dramatic enough. Where else can you earn 40% tax-free? (Uncle Sam doesn’t tax you for smart shopping.)

As the years passed, I found people were having trouble understanding this little shtick of mine. Why is it 40% if I just got a 10% discount?

So I tried explaining it in a little more detail. What actually happens, I explained, is that instead of going to the store and laying out $10 for one bottle, you are laying out $108 for 12 bottles — $120 less the 10% discount. Which means you are laying out $98 more than you otherwise would have. That extra $98 is your “investment.” By keeping at most that much extra tied up all year, you save $1 a week on wine — $52 a year. And “earning” $52 a year by tying up $98 is earning 53%.

So now I was up to 53%, an even better tax-free return.

This confused people even more. That first $98 is gone, they would tell me, and now you have to come up with a new $98 to buy your next case of wine.

But think about it. If you were someone who planned to spend $10 every week on wine — $520 a year — and who would have LOVED to save 10% buying by the case but just couldn’t scrape up enough money all at once to do it, how much financing would you need?

Would you have to go to a bank and ask for a $400 line of credit in order to be able to change your buying habits?

No, you would need only a $98 credit line — and you would only fully draw it down that very first week. After that, you would replenish it by $10 a week (the $10 you used to spend on wine by the bottle), which means that after 12 weeks, when you needed to buy the next case, you would not only have replenished the full $98, you’d actually have an extra $12 to work with (the money you saved buying by the case). So now you’d have to draw down only $86 of your $98 credit line.

In other words, to finance this change in habits you’d need a maximum credit line of $98. But you’d only actually draw down that much the very first week. Within 10 weeks you’d have paid the balance down to zero; then run it back up to $86 in the 13th week to buy your next case of wine; then paid that off in 9 weeks; then run it back up to $74 to buy your next case — and so on. On average, over the course of the year, you’re using far less than the full $98 to finance this change in buying habits.

So the return on your decision to tie up that $98 at first, and then gradually less, is actually much greater than 40% or 53%.

If my friend Less Antman has keyed all this into his Hewlett Packard financial calculator right — and I’ve never known him to err — it works out to an annualized 177% rate of return (though try explaining THAT in 40 seconds on The Tonight Show).

It’s still only $52 you’re earning — $1 a week by getting the 10% discount. But you’re earning it NOT on that first $98, which is the MOST you ever have to set aside to change your buying habits, but on an average “investment” throughout the year that’s much lower.

Next step: find a vintage you like equally well that’s $8 a bottle.

Tomorrow: Potpourri