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<<I got a cash in lieu payment after the GM-Hughes-Raytheon transaction....Can I just document the basis as the original price of the GM, and ignore the fact that I've been gradually buying a share or two here and there for the past 15 years at higher prices?>>

DNK if TMF Taxes or KAT in Chicagoland have addressed this issue, but my take on it would be that your "sale" of .8 Raytheon would be FIFO anyway, so the basis of your .8 share would be from the Raytheon lot derived from the "original" GM shares.

Here's a tangential question I'll toss out reagrding DRIP's and (non-taxable) spin-offs, that would have an effect if one sold most of the stock received in the spin-off.
Technically, each quarter's DRIP purchase is a new lot. In other words, you'd have something like (I hope these columns work):

date purch shares cost
4-19-67 400 18,000 (first lot)
6-30-67 3 147 (qtrly DRIP purch)
9-30-67 3 162 (qtrly DRIP purch)
12-31-67 4 201 (qtrly DRIP purch)

and so on. Your Raytheon shares would get allocated from each lot (.06377 * each lot), and cost as well (.0529), and of course you tack the holding periods.

Theoretically this is correct, but does anyone actually do this, other than the serious number-cruncher/tax people? (We do this where I work, but the accounts are so huge that what they call a "dividend reinvestment" is what most people call "the value of my entire portfolio"). Isn't it a bit unwieldy to have 30+ lots of .23 or so shares of Raytheon? What is the cut-off for materiality so that the IRS won't jump on you? Most people (unlike me) have real lives, and aren't going to keep THAT MUCH detail of their holdings.

I apologize in advance if this issue has been addressed previously.

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