Levelized cost of wear

I consider this post a work-in-progress. If there’s any real merit to this concept, I’ll need to come back and clean up the post so that it’s coherent to someone who isn’t already familiar with all the ideas I use to build up the concept.

There’s an idea related to clothes shopping called “cost per wear.” It’s a simple idea for quantifying the cost of different items of clothing that’s (arguably) more useful than their sticker price. To find an item’s cost per wear, you simply divide its cost by the number of times you expect to wear it before getting rid of it:

CPW = \frac{cost}{times\ worn}

You can find plenty of articles about cost per wear (some good, and some which grossly misinterpret it), but in this post I’ll propose an extension to the idea. But before proposing the extension, I’ll recount how I ended up with it. I was first introduced to the idea of cost per wear by my undergraduate research advisor, who claimed that you should never spend less than $2000 on a suit (he always dressed very sharp). The reason he gave was cost per wear: if you buy a cheap suit, you’ll never want to wear it, and you’ll only get a few uses out of it before throwing it away. If you buy a nice suit, you’ll use it as much as you can (for dates, interviews, any vaguely formal event, etc.), and in the long run it will be cheaper – at least in terms of cost per wear. Putting numbers to this, there seems to be some wisdom in his claim. If I buy a cheapo suit for $120, it might last me two years, and I’ll only wear it when I absolutely need to wear a suit (maybe three times a year). This yields:

CPW_{cheapo\ suit} = \frac{\$120}{2 years* 3 wears/year}=\$20/wear

If I buy a primo suit for $2000, it could last me closer to ten years, and I’d want to wear it whenever I had the chance (maybe once a month). Therefore:

CPW_{primo\ suit} = \frac{\$2000}{10 years* 12 wears/year}=\$16.67/wear

Since the nice suit has a lower cost per wear, the argument goes, it’s actually the thriftier purchase. Somehow this idea came up in a discussion with a fellow grad student, and from our perspective it didn’t seem to paint an accurate picture of our situation if we were in the market for a new suit. A point that cost per wear misses is that a dollar in my pocket today is not the same as a dollar in my pocket ten years from now (something that grad students are acutely aware of, as in ten years we imagine our salaries will be at least triple what they are today).

There is another idea, called levelized cost of energy, or LCOE, which is used to calculate the effective cost of electricity from different sources – specifically as a way to compare renewable sources like wind and solar that are “free” once they are installed to conventional sources that required burning fuel which you have to pay for. The piece that’s relevant here is that even if you had a maintenance free solar panel that lasted forever, if you have to pay for the panel initially it’s LCOE would not be zero (i.e., the electricity it generates is not free). This is because even though you get infinite electricity from that panel, it’s spread out over infinite time. And when you consider inflation, the electricity that the panel generates in one or two hundred years has almost no value to you today.

I’m sure this explanation is insufficient for anyone not already familiar with LCOE, but in any case, that’s the idea I borrowed from to come up with “levelized cost of wear” or LCOW, an extension to cost per wear. LCOW is calculated as follows:

LCOW=\frac{cost}{\sum\limits_{t=1}^n \frac{wears/year}{(1+r)^t}}

where n is the number of years you expect the item to last and r is your “personal inflation rate” – nominally we can say that it’s how much you expect your salary to increase annually. LCOW takes into account how the value of money might change over time for an individual, whereas CPW does not. We can revisit the cheap vs. expensive suit using LCOW, using an r of 12% (this would be very high for most individuals, but for the PhD student example, it corresponds to about triple the salary in 10 years):

LCOW_{cheapo\ suit}=\frac{\$100}{\sum\limits_{t=1}^2 \frac{3}{(1.12)^t}}=\$23.67

LCOW_{primo\ suit}=\frac{\$2000}{\sum\limits_{t=1}^10 \frac{12}{(1.12)^t}}=\$29.49

When considering LCOW, the cheap suit is the thriftier purchase. Intuitively this makes sense – my friend and I will have plenty of time to go shopping for nice suits once we have real jobs. In the meantime, it’s a better use of our money to buy the cheapest suit that can get us through graduation.

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