Big things

It's interesting how the Pyramids are considered a monument to Egyptian civilization but the Ryugyong Hotel is considered an embarrassment to North Korea.

The true price of software?

Robert Lefkowitz has written an interesting analysis of the true value of computer products, by breaking down those products into their components, much as an economist breaks down financial instruments into their components, or a theoretical physicist breaks down particles into their elementary primitives. He identifies several services: repairs, maintenance, and the option to upgrade to future versions, that in his view constitute a large percentage of the value of the product, and concludes that, in the case of software, the underlying software itself has essentially very little value compared to the rights to support and upgrades.

I believe his analysis is seriously flawed, and not simply because I dispute his assumptions as to the volatility of future support/upgrade pricing. Let's go through some of his examples:

A 17-inch iMac was $1,499 at the Apple store the last time I checked. You can purchase an extended warranty, AppleCare, for $169. That warranty is for years two and three; year one is included. AppleCare also includes extended telephone support, but I'm going to ignore that for now to simplify things.

After a quick trip to Wikipedia's page on failure rates (leavened with anecdotal rumors), it is not unreasonable to suppose that computers experience more failures in their first year than in the subsequent two years. The overall failure rate for computers runs about 15 percent--Macs do better than average. Still, it is not unreasonable to suggest that the curve looks roughly something like 8 percent failure in the first year, 4 percent in the second, and 2 percent in the third. That means the first-year warranty is worth about $225. So really, that 17-inch iMac costs $1,274 for the computer and $225 for the first-year warranty.

He apparently derives this $225 figure for the value of year one of the warranty by multiplying 15% times the cost of the iMac, but there are two problems with that. First, and trivially, he assumes the iMac's failure rate in the first year is only 8%, so the value of AppleCare during that time should be 8% of the value of the underlying hardware, not 15%. But second, even if the first-year failure rate is 15%, it should be 15% of the value of the hardware, not 15% of the value of the hardware plus the value of the AppleCare. In other words:

AppleCare + Hardware = $1,499
AppleCare = 0.15 x Hardware
Hardware = $1,499 / 1.15 = 0.87 x $1,499
AppleCare = 0.13 x $1,499 = $196

Not too far off from his value of $225 (assuming 15%, not 8%, failure), but this has exposed a basic flaw in his reasoning which will become much more relevant when we get into the discussion of software. Namely, he bases his reasoning on the very assumptions which his reasoning disproves. In this case, he fails to price the value of the AppleCare relative to his logic's implied value of the hardware — rather, he values the AppleCare relative to the same naïve valuation of hardware that he has just shown is faulty.

Now, let's move onto software. Here's his thought experiment:

Let's normalize the values to a $100 software license and say that a one-year option has a $20 underlying price; a year of maintenance is 20 percent of the license, so we'll assume it's worth $20 today. The strike price (what you can buy it for in a year) is also $20--a 5 percent risk-free rate. With all of those inputs, the value of that option is about $2.85. That is to say, for $2.85 you can lock in the price of the maintenance contract so that one year from now, you'll have the right to buy it for $20.

The right to buy the same maintenance for $20 two years from now is about $4.25; three years is $5.35; four years is $6.35. That takes us five years out. Assuming that you've locked in the maintenance over the five years to 20 percent of the purchase price, that set of options is worth $2.85 + $4.25 + $5.35 + $6.35 = $18.80. Five years is not an unreasonable horizon for enterprise software.

But wait, there's more.

Another option included in the license price is the option to upgrade to future versions at some price that will be less than the regular price. Right? That's clearly an option. The same informal poll of enterprise software users asked what they would pay for software when they didn't have the option to upgrade to the next release. The strike price is less standard than regular maintenance. (If you think about it, new versions perform "maintenance" by adding features as opposed to fixing bugs.) Now we're buying an option to upgrade in five years as part of this license.

The underlying price--the price you'd have to pay if you didn't have an option--we'll leave at $100. The next version will be priced the same as this one. Because you're upgrading, you have an option with a strike price of, let's say, $50. That is, you'll be able to upgrade to the new version for only $50. A five-year option for a $100 underlying price with a strike price of $50 and a volatility of 30 percent (with a 5 percent risk-free rate) is about $62.50.

Of course, most software offers new releases more frequently than once every five years--but enterprises don't like to upgrade very often and usually plan on skipping every other release in order to avoid upgrading too often. Then it would be two options. Much like adding additional planetary bodies to a problem in gravitational dynamics, the complexity mounts rapidly. I'm trying to keep it simple. (I suggest follow-up research problems for interested students.)

At this point, the astute reader will have noticed that the sum of the value of the option for the upgrades plus the options for the maintenance is $18.80 + $62.50 = $81.30. That is to say, our $100 software license consists of $18.70 for the value of the actual software and $81.30 for options on future maintenance and enhancements.

But wait a minute! If the right to upgrade is already included in the first purchase, then what is the upgrade itself getting you? Only the software plus a new maintenance contract, which is worth just $37.50! Sure, you now have the right to upgrade to future versions, but you already had that right. So if his conclusion is correct, and the underlying software+support is only worth $37.50, then in fact the right to upgrade at $50 is worth almost nothing — it's a call option that is way out of the money!

Lefkowitz's approach has been exposed as an accidental pyramid scheme, and the foundation has just come crashing down!

Now, I am not saying the right to upgrade is worth almost nothing. That would be making the same fallacy that Lefkowitz makes. I am saying that his logic is self-contradictory, and that a proper analysis will find an equilibrium price for both the right to upgrade and the immediate product, rather than consisting of one "iteration" of analysis on assumptions that the very analysis has shown to be wrong.

There's another, more abstract problem with his reasoning: he's attempting to seperate inherently complementary products, and arguing that the value of one is virtually nil without the other. But that process works in reverse, too. What's the right to maintenance worth without the actual software? What's a car with no steering wheel good for?

The answer is, a car with no steering wheel is good for making a car, once you've got the steering wheel. But this doesn't mean the steering wheel is the majority of the value of the car. It means the car is worth X, and the individual components are worth whatever the supply and demand situation says they're worth. That calculation is substantially more complex than just subtracting the utility of a car with no steering wheel from X. You must consider factors such as the consumer's desperation, the cost to the supplier, and the level of competition and commoditization in the marketplace.

It may be that a good business model can be built on cheap or free software, but Lefkowitz's argument is surely not why.