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If you do reinvest it, you need to add 1k to your cost basis.

Actually, it becomes a purchase of a new lot of shares (or fractional shares), with the cost basis of that new lot being the amount of that distribution. Likewise, the determination of whether this is long term or short term for purposes of capital gains (losses) is when those shares where purchased by the reinvesting of the distribution vs. when they were sold: if the holding period is over 1 year, it is long-term gains (losses), but if holding period was 1 year or less, it is short-term gains (losses).

So, typically one would receive a 1099-DIV on distributions (whether the distributions were reinvested or not), and a 1099-B on the sale of the shares (no matter whether they were original purchase, purchased with additional investment funds, or purchased by reinvesting distributions).

Even if one uses average cost basis, one will have to calculate this unless the fund broker is tracking the average basis and has accounted for the first sale of the most expensive shares. In any case, one would have to compute the number of shares that are "short term" and the number of shares that are "long term".

A few months ago I sold my taxable investments to replace them with Vanguard funds, and it took a good afternoon to calculate the gains/losses for the funds, with the bond funds producing the most activity by the fractional shares purchased every month by reinvesting distributions for five years. (I needed this information for tax planning purposes before the fund family I was leaving would cut its 1099-DIV and 1099-B so that I could increase my W-4 withholding. Fortunately (?) it ended up that I didn't have to worry about gains--I realized almost $21,000 of capital losses and, at the advise of my tax adviser, changed my W-4 for more allowances.)
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