Open Question: DRIP tax considerations?

I'm a little confused on how taxes work for a DRIP. I've done a lot of online research but it's still a little vague but here's my interpretation so far... I invest in a company for say 10 years. Each year, I report how much money I received in dividends (all of which I have chosen to reinvest), and I pay taxes on that amount. Then I go to sell the shares at the 10 year mark. (Final sale amount) - (initial investment + initial commission + (each dividend times their respective share prices) + final commission to sale the shares) = capital gains that I pay taxes on. Is this correct or did I misinterpret what I've been reading?

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