Steve, you're making some errors in your analysis.
The the value of a perpetuity is A/i where i is the appropriate discount rate and A is the cash flow received at the end of each period. The hypothetical was phrased as a certainty, so you could think of this in terms of a bank account which pays a fixed interest at i% per year. There is nothing magic about this -- this is a standard financial calculation. In fact,
A/(1+i) + A(1+i)^2 + A/(1+i)^3 + ... + A/(1+i)^n = A/i
That's why a bank account paying out $1 per year is worth $10 regardless of whether I remove the money at the end of the year, or let it compound. For example, 1 year from now the bank account will have $11 in it. I may remove the dollar, in which case I will have received a cash flow of $1 plus the present value of the future cash flows. But the value of the account in today's dollars is still $10 regardless of whether I intend to do with the cash.
Secondly, my model was intended to mimic a residual dividend policy. Simply stated, that policy says that you pay out dividends to shareholders only to the extent that you cannot invest those funds at some rate greater than some hurdle rate. I use free cash flow as a surrogate for the potential dividend that might conceivably be paid. So, in my "model" I assumed that all of the free cash flow would be invested in projects that earn 50% per annum. Once free cash flow is is made available to investors (either through dividends or stock repurchases) it becomes part of the discounted stream.
You go on to say The value of the company producing all this cash is the total of all the cash, the sum of the present values of the cash dribbling in year by year.
My point is that the value of the company is the present value of the cash flow made available to shareholders, either directly through dividends, or indirectly through share repurchase (which is a surrogate for a dividend). The cash coming into the company is not what is valued. It is the cash or potential cash going to shareholders that is the source of the company's value.
Hope this helps,
TTFN,
CTC
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