Monday, September 19, 2011

Back of the Envelope Calculation: Is It Worth It?

I am probably the only person in the Greater Madison area who purposefully drove to the east side of town to "experience" the construction on Willy Street. Ah, the things a mother will do to please her 3 year old son who is obsessed with construction. While taking in the cement mixer pouring a new sidewalk, we found ourselves in front of the Willy Street Co-op. Having two little ones (ages 3 and 1) it is almost always "snack time". On that day I decided to check out the co-op; they've opened a west side location not too far from our home. My main objective was to note their price on milk and eggs. The price was a good deal higher than either Woodmans or Target. We did pick up an apple and some amazing bulk "energy chunks" for a snack.

At the checkout we were asked for our member number. "We don't have one" I responded. The clerk asked if we belonged to any other food cooperative in town. "No" I replied. To which he asked, "would you like to join, it is $10/year for an individual, otherwise there will be a 5% surcharge on your purchase". I paused. $10 -- that isn't much money, but how often will I actually shop here? I told him I'd pass for today and keep it in mind for next time. I paid my $4.87 and we enjoyed our snack on their outdoor terrace.

Later that evening I recounted the event to my husband. He muttered to himself a bit, as most engineers are inclined to do when calculating something in their head. A moment latter he said, "you'd have to spend $200 a year there to break even". These moments should not stun me as they still do, but I thought, goodness, how I wish I could be a human calculator at times. My gut told me the $10 wasn't worth it, this confirmed it. I doubt I'd spend $200 a year at the co-op. Primarily because they do not have carts set up for two kids in diapers. It's amazing how much of a pull those mega-carts have on a mom with a 3 and 1 year old. If, like me, you are wondering how he reached that number, here is his back of the envelope calculation:

  • X*0.05 = 10
  • x=10/0.05
  • x=200
That translates into dividing $10 by the 5 cent surcharge, which comes out to $200/year. With this number I can make an accurate estimate of how likely I am to benefit from the $10 expense. I'd have to spend $200 in year in order to benefit from the $10 membership. This tool can be applied over and over again as you make educated purchases!


  1. Now how might we do the math on Amazon Prime? $3.99 for next-day delivery. Free two-day delivery. Plus netflix-style movie streaming? For $75/year? I can't imagine how I might work that out—but I'm not giving up my prime membership! :)

  2. I didn't realize Amazon Prime provided access to all those movies. I typically pay around $4 for shipping from Amazon.
    So here are the condition under which I would use it:
    Amazon Prime Yearly Membership Fee < $4 * num of shipments not eligible for free Amazon Saver shipping + 0.9 * amt spent purchasing on-demand video.
    Be sure to follow order of precedence, i.e. work multiplication first, then add.
    Suppose you pay shipping twice and order three $10 videos:
    $4*2 + 0.9*$10*3 = $8 + $27 = $35 --> Does not justify Prime membership b/c $75 > $35.

    The 0.9 is a fudge factor to account for the fact that you have to keep the membership in the future to keep viewing the movie. If you buy the on-demand content, you get to keep it as long as Amazon supports the system. This is analogous to buying physical media like a video cassette; you get to keep using it until the medium goes obsolete.