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Re:“Buy and Hold” No More: The Resurgence of Active Trading by Thorrez on Sunday April 11, 2021 @09:56PM (#26775443)
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).

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