Optimal Purchasing Under Technological Disinflation

"But next year it will be twice as fast and cost half as much!"

© 2007, Martin Rinehart
MartinRinehart at gmail dot com

The rate of inflation in many high-tech fields is negative. It's typical for computer equipment costs to drop by half in eighteen months (approximately 37% deflation per year). Nothing you buy this year looks like a good buy next year. It is generally agreed that a buyer must accept this fact and go ahead and buy what is needed as it is needed.

This is not correct, however. It is possible to optimize purchasing under technological price deflation. Let me back up a few years.

The Search for an Answer

I was in charge of the Quantitative Analysis Group at a major American investment bank when I first began searching for the answer to this question. I would tell management, "This could really boost productivity. The cost is trivial compared to the benefits."

And I would then be asked, "Won't the price drop 50% if we wait a year?" (It would, of course.) I wanted to move, but I couldn't make a cogent, productivity maximizing/price minimizing analysis. To make a long story short, my search for the answer was fruitless.

The problem was that I was trained to compute costs and benefits. That approach would not solve this problem, as I and many others found. I stumbled onto the answer quite accidentally, some years later.

The Search for Ski Equipment

I would find the answer in the ski equipment field. Much less dramatic than computer prices, skis are improved every year yet ski prices remain resonably constant. If you have a fixed sum to spend on skis, put it in the bank and wait for next year. You'll get better skis and a bit of interest, too.

My skiing had improved to the point where my intermediate-quality skis were holding me back. Coincidentally, my wife had taken lessons the previous year, decided that she liked the sport and wanted to get her own intermediate-quality equipment. (We're not the same size, so hand-me-down was not an option.)

That left me with perhaps $1,200 dollars to spend on my equipment and half that for my wife. Those expenditures wiped out most of the ski budget. Cash would be needed for necessary extras, such as lift tickets. So with loosely defined budget constraints (every dollar saved was another dollar for lift tickets) I started searching for good buys.

What I found was this: if I was willing to buy last year's leftovers, prices dropped dramatically. The prices were (and still are) roughly $700 list for expert-quality skis, generally available discounted to $500. Last year's top-of-the-line could be had for $300. I eventualy stumbled on a shop with some two-year-old leftovers for just $100.

Similar searching for still-new but older technology in boots and bindings, and my $1,200 expense was down to $300. My wife's gear, a year behind the state-of-the-art, was purchased for about $300. Savings: $1,200. Enough for 30 days' lift tickets!

Bargain Skis Become a Strategy

That I was exploring optimal purchasing strategies under conditions of technological deflation had not yet occured to me, although you can see the relationship: last year's gear, being less capable, costs less. Those price drops— $500 for this year's gear, $300 for last year's gear, $100 if it's two-year-old gear—are a lot like computer pricing.

I wondered what I would do next year. Buy no equipment because we already had what we needed? Look for the area of most rapid improvement and steadily upgrade with a moderate portion of the ski budget? Slowly I began to see what I wanted to optimize: I wanted to minimize my years behind the current state-of-the-art.

Note that there is no economic benefit from ski equipment for recreational skiers. Better gear makes for better skiing. It's more fun. We expect bigger smiles at the end of a day on the slopes. (And as a corollary, fitter hearts, lungs and thighs, since we'll be making more runs.) We are not expecting economic benefit. If ski purchasing can be optimized, it suggests that the analysis of economic benefit for high-tech purchases might have been an unnecessary impediment in that analysis.

Indeed, it didn't prove hard to optimize ski purchases. Assume that one's budget is $100/year for skis and that one's capability is able to benefit from top-of-the-line skis. Here are three strategies:

  • Buy new, once every five years, $500.
  • Buy year-old, once every three years, $300.
  • Buy two-year-old, every year, $100.

(You don't need to be an MBA to see that $500 up front is actually more expensive than $100 per year, but we'll not need that sort of fine-tuned computation to illustrate the main point.)

Buying new, you are zero years behind the state of the art the first year, one year behind the second year, and so on. The total years-behind is ten years and the average is two years behind over the five years.

Buying one-year old gear you are one year behind in the first year, two years behind in the second and three in the third. That's six years total, and it also averages two-years behind the state of the art.

Buying two-year old gear every year means you are always two-years behind, which of course averages two years behind.

Filling Out the Analysis

Note that there are a lot of other considerations. I've already mentioned the time-value of money, but that's a small one. Skis, unlike computers, physically deteriorate with use. Buying two-year olds and upgrading annually, your skis are, on average, half a season old. Buying one-year olds and upgrading every three years means your skis have .5, 1.5 and 2.5 seasons wear in years one, two and three, respectively. That's 1.5 seasons old, on average. The average for the skis you buy new and trade every five years is 2.5 years of actual wear, on average.

Residual value is important. You may be able to get value from hand-me-down within the family. You can sell your old skis at a swap-meet. ($50 for the skis you bought two-years old; maybe $40 for the skis you bought one-year old that will be four-years old when you sell them; less for the new skis that will be five-years old when you sell them.) And you can go to less trouble and still get psychic income from donating your used skis to charity.

From these factors you can readily see that purchasing two-year old skis every year is overwhelmingly the best choice for the budget. It keeps you as close to your ideal (state-of-the-art) as does the buy-new-every-five-years strategy. It let's you ski on brand new equipment every year and it realizes the most residual value. The time-value of money is also there, although its a minor factor compared to the others.

We have, for a given budget and a given price curve, optimized our ski purchasing decision. We also have a technique that can answer other questions: how much do I need to budget if I want to be within two years of state-of-the-art? How much will it take to stay within one year of state-of-the-art? (Buy brand-new every other year costs $250 per year. Buying one-year-old every year costs $300 per year. Brand-new is optimal and $250 is the answer to the question.)

Extending the Analysis to Business Decisions

The most basic price curve in computers is still Moore's Law, that chips double in speed every eighteen months. (See Note 1.) A bit more study of historical trends can yield a deflation curve for any other class of equipment. (Equipment classes just invented will need best-guess estimates.)

Physical depreciation is seldom an issue. Our computers are generally hopelessly obsolete before they fail physically.

Then we have tax savings from depreciation to subtract from the cash flows. From here, it becomes a straightforward analysis, although there is a tradeoff between budget and months behind state-of-the-art. For X budget, how can we get closest to the state-of-the-art? If we want to average no more than Y months behind the state-of-the-art, what will we need to budget?

As always, analysis is no substitute for business judgment. How far behind the state-of-the-art can we afford to be? Where will our competitors be relative to the state-of-the-art? What technologies are so compelling that we have to act now? What technologies are not really important to us?

There are no one-size-fits all answers, but it is still possible for an enterprise to optimize its purchasing decisions under technological deflation. You optimize for distance from the state-of-the-art within your budget. This is possible when you realize that it's great to have state-of-the-art systems, but that the smart enterprise decides that an appropriate lag will add to its bottom line, just as I added to my days on the slopes.

Note 1. (See Wikipedia for more details.) Gordon Moore, cofounder of Intel, observed in 1965 that transistor density of computer chips was doubling every 24 months. In 1970 Carver Mead christened this observation "Moore's Law." Over time 24 was shortened to 18, though Moore says he did not change.

Moore's Law became the assumption and therefore the fact, within the semiconductor industry. (What decisions would you make for your own operation if you assumed your competitors would improve by a factor of two every eighteen months?)

There is no possibility that this rate will continue indefinitely. No sober observer in 1970 would have suggested that this would still be a useful rule of thumb in the 21st century.

P.S. January, 2018. No sober observer in 1970 would have been correct. Anyone who predicted Moore's Law would still apply in 2018 would have been laughed at. Written off as insane.

And completely vindicated. 2015 marked the 50th anniversary of Moore's Law.