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There's a lot of bad info in this thread. I'll reply to each one individually, so this might get a bit long. Sorry about that. Here goes.

Can't I just keep a "cost-average" and then use that number to determine my gain or loss when I buy or sell?

No, you can't. You need to track each DRIP purchase as a separate purchase. You can only use average cost basis with mutual funds.

What you'll need to do is set up a spreadsheet - manual or computerized - with the following columns: date, number of shares, dollars. With the initial purchase and each reinvestment, record a line with the appropriate info. You'll note that nowhere do I have a price per share. That's because you'll be tempted to do all sorts of wrong things with it if it's there. When we need a price per share, we'll do the division to get it. Most of the time you won't need it. (Unless you want it to track the investment performance, but that's a different issue.)

When you sell, you'll add some more columns to the spreadsheet. Namely: date sold, number of shares, dollars. Once again, note the lack of a per share column. You don't need it. To fill out the sale columns, you'll need to prorate your sale proceeds to your purchases, starting with your oldest purchase. When you get to the end, you'll probably need to split up a purchase to match up with the last bit of the sale.

Lastly, you can add a final column to calculate the gain or loss on each separate line. Just subtract the cost from the sale proceeds.

In theory, you'd then report each line of your spreadsheet on your schedule D. In practice, it's fine to summarize, as long as you're careful to watch short-term vs. long-term items.

But you will need to compute each line separately for another reason. If any lines show a loss, you'll need to watch out for wash sales. With a typical stock dividend, you will have roughly one month out of every three where a sale will be outside a wash sale window.

And now, for advanced students, you can use specific identification instead of the FIFO method I've described, providing you can get the DRIP broker to give you written confirmation of your instructions to sell specific lots.

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