[Thorrez]

I don't understand your reasoning for why the price increases. To use your equation with my original example:

Initially:

market cap = $100

book value = $20

discounted future cash flows = $80

share price = $1

number of outstanding shares = 100

After the buyback:

market cap = $99

book value = $19

discounted future cash flows = $80

share price = $1

number of outstanding shares = 99

So the market cap didn't change.

I agree it's effectively the same as dividends (although I think buybacks are slightly better for the taxes of stockholders).