#### What Knowledge is Useful? > Companies and Functions

Charles Christensen on NPV

## Transcript

Well, Bob asked me if I knew anything about present value. And it happened I knew a little bit about it, partly because I had taken—because of my interest in Wall Street, I had taken the second-year course in management by George Bates. And George Bates periodically would write on the blackboard a long, present-value formula for how to get the value of a stock given future dividend stream. And the reason George Bates was familiar with it, is that there was a fellow named John Burr Williams who had been a Business School classmate of Bates, who had come back after a number of years and who had done a Ph.D. in economics.

And his thesis was essentially applying the present value concept of valuing stocks. This is before Modigliani and Miller and other people all brought up this idea that the value of the stock was the present value of its future dividends. . . .

I was intrigued, so I read up on it a little bit. And so, Anthony, when he found out that I knew something about it, he gave me some assignments in connection with the consulting project. But he also said that he wanted to introduce the concept of present value for evaluating investment decisions into the first year course. And one of the problems was that the published present value tables were mostly designed for valuing bonds, mortgages and so forth. And typically didn’t go above 8 percent, as far as the interest rates are concerned.

And Anthony’s position, of course, was that the appropriate rate was much higher than that. So he asked me to look into how to prepare tables that would go up to higher interest rates. So I worked out the mathematics of it. Anthony, also at the same time, had a research project going on business computing, data processing. Had a classmate of my named Pete McInerny working on that project, who was involved with some of Aiken’s people.

So I asked Pete if—In fact, I think I had probably gone over to see the Computation Lab over there with Peter, at some point. And I knew that the Mark I, which is a relay machine, flip-flop thing, was essentially used all the time to calculate mathematical tables. So I asked Peter if it might be possible to get some time on the Mark I to calculate these tables. And he introduced me to one of Aiken’s graduate students, Tony Ottinger. And we talked a bit, and Tony thought it would be better to do this on the Mark IV, which was the first electronic computer.

So, I sat looking over Tony’s shoulder while he programmed the machine. This was at a time when there was no such thing as even assembly language, or certainly not the higher-level languages like Basic or Fortran and so forth. So you had to do it in binary. And I remember he was having very great difficulty in figuring the best way to do certain things, but because of my knowledge of the underlying mathematics, I was able to make some suggestions that simplified that.

So we ended up producing tables that went up to 100 percent, I think. And the successor tables to that, I guess Bob still has as the appendix in his management accounting book.