No. of Recommendations: 11
Have you ever heard a bull on tech funds speak? Listen closely. The sermon will be on the limitless possibilities the internet and new technology will have on our lives. Our children will have a job whose profiles don't exist today. My fridge will be able to order milk as I finish it or as it goes sour. My TV will give me access to my bank account, and allow me to pay my subscription to Soldier of Fortune (metaphorically, I assure you). The opportunities are truly infinite.

Are investors buying an infinite concept? If they are, what would one pay for a limitless concept, how is it measured? If the concept is limitless, then balance sheets and income statements could theoretically transform an infinite concept into a finite one.

Consider the following. A good friend of mine had recently listed an internet venture on the Australian stock exchange. His profits have assured us that he will pay for the next 3,276 rounds at the local pub. Just before listing, however, he happily informed his investment bankers that the new contract would mean that his firm would make a modest profit this year. Hurrah, or so he thought. The bankers needed their nappies. "Quick," said the investment banker, "spend the profit now. Go into loss. You can't possibly list with the company making a profit!!!" What the banker meant, if you make a profit you give yourself a lightening rod to which you can be measured. The infinite (un-measurable) becomes finite (measurable).

This concept of valuing the un-measurable is not mine to take. The paradox actually goes back to the early 1700s, where a Swiss mathematician first proposed the theory of marginal utility.

In 1731 Daniel Bernoulli presented before the Imperial Academy of Sciences in Petersburg. Bernoulli's paper discusses the following paradox: "Peter tosses a coin and continues to do so until it lands "heads". He agrees to pay Paul, his cousin, one ducat if he gets "heads" on the very first throw, two ducats if he gets it on the second, four ducats in on the third, eight if on the fourth, sixteen on the fifth, and so on, so that with each additional throw the number of ducats Peter must pay Paul is doubled. What should Paul pay Peter to play such a game?"

It must be remembered that the probability of obtaining a "heads" from a coin toss is always 50%, as each toss is independent of the other. The probability is always fixed at 50%, regardless of the number of times the coin is tossed. The potential winnings from such a game is infinite. Hence, the principles of mathematical expectation imply that Paul should be willing to pay Peter an infinite price to enter this game. Common sense, however, tells us that the game cannot be infinite. As Peter and Paul are only mortal, the game would have to cease when one dies. Peter's solvency would also have to limit the gains. Bill Gates himself, the richest man in the world, would have to limit the game to only 32 times. If Paul were lucky enough to strike "heads" 42 times, he could conceivably buy every listed stock in the world! With this progression, the sky is literally the limit. This game reward's are truly limitless. Even if Paul were to agree to stop after 100 times, the stake, though finite, would stagger the imagination.

If instead of tossing coins, Peter were to list his game on the NASDAQ, and add a "dot com" to his game, what should Paul pay for this share? The changes that the new economy will have are limitless and perceived to be infinite. Like the coin toss game, the assumption is of limitless gains. As dot coms have an infinite growth rate (as we're so often reminded), how can one conceivably discount a fair value price?

The mathematicians amongst you will state that eventually the marginal utility (the additional utility received from the consumption of an additional unit) will restrain the price. But as we have been reminded by today's new economy investors, "So what?!" The gains from the "new economy" shares are limitless and infinite. As they point out, the question is not what is the game worth, but what is it worth not to play the game (or not to invest in tech shares for that matter)?

In many ways this paradox helps explain why investors are willing to pour their life savings with little if any regard to balance sheet analysis. As we have argued for some time, the CONCEPT of new economy is limitless. Our lives, and that of our children, will no doubt be hugely affected by the changes going on from technology innovations. Such changes will no doubt continue indefinitely. If this is so, how then can we place a finite price on a concept which in itself is infinite?

The old world accountant in me tells us that something has to give. As pragmatists, we know that we cannot toss the coins indefinitely into the future, nor could we afford to pay the winnings after just 15 tosses, the game nonetheless can nonetheless yield an infinite gain. Investing in a concept which is in itself infinite, one wonders, might similarly yield infinite rewards. Hence, how can one place a finite price to play such a game?

To date the Petersburg paradox has yet to be resolved undisputedly. The very fact that the worlds leading intellectuals and mathematicians have been unable to solve this paradox suggest that the new economy paradigm offers no great hope towards a satisfactory answer. Mere consultants, like ourselves, can only hope that others can answer this paradigm before we're caught short. We certainly concerned at the current prices paid for tech.
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