YOUR GRANDMOTHER gave you 500 shares of General Electric. Excellent. Now you can pay off that crushing credit card debt. Of course you'll owe capital gains taxes when you sell the shares. But how much? Granny has no records, though she vaguely remembers buying the shares back in the early 1940s.

Or perhaps your father just discovered some long-forgotten American Motors share certificates he inherited from an uncle. And he's decided to give them to you. Again, you've got a dilemma. How will these things be taxed? Let's start with the simple stuff.

Shares Received by Inheritance

If your granny left you that GE stock in her will, you're in luck. The tax basis of shares received as an inheritance is generally stepped up to their current market value on the date the original owner dies. So worst case, you have to make a trip to the library to check the stock prices. Take the average of the high and low prices on the date of death, and that's your basis. Your holding period is automatically deemed to be more than one year, so you qualify for the long-term capital gains tax rate on any gain from a sale even if you sell immediately after getting your hands on the shares.

Don't wait around to establish your basis. Subsequent splits and takeovers can make the chore more difficult. And, if your granny was due any stock or cash dividends, claim them now because they could wind up being classified as unclaimed property by the state.

Shares Received by Gift

In this case, your tax basis is the same as the donor's, unless the market value on the date of gift was lower. In that case, your basis is the lower figure. Usually the same-as-the-donor rule applies, which isn't very helpful when that person has no records.

If the shares were kept in your benefactor's brokerage account, you may be able to reconstruct their basis by asking the broker to reproduce transaction statements as far back as possible. If that doesn't work and you have a reasonable estimate of the acquisition date but can t find what you need online, another visit to the library microfilm room is in order. Again, take the high and low prices for the estimated acquisition date and average the two. That per-share price is close enough to the donor's original basis for IRS purposes.

So far, so good. But you still don't know the basis of the shares in your hands unless there have been no stock splits, stock dividends, spin-offs or returns of capital involving the company from the date the shares were purchased by the donor through now. If any of these corporate transactions referred to as capital changes occurred in the interim, you have to adjust the basis of the shares you now own.

For example, if your best guess is that the donor paid $80 per share when he acquired his original holding, but the company had three 2-for-1 splits between then and now, the basis of each share in your hands is only $10 (1/2 x 1/2 x 1/2 of the amount for each original share).

The same sort of basis adjustment is required if there were tax-free stock dividends. In this case, some of the original basis is allocated to the dividend shares, with the rest remaining with the original shares.

In a tax-free spin-off, the basis of the original shares is allocated between the parent-company stock and the shares of the spun-off company. So a calculation is needed if you wind up with shares in either outfit. Less likely are return-of-capital cash distributions, which require you to reduce the basis of the shares by the amount of the distribution.

In other words, knowing the per-share basis of the original batch of stock is just the starting point. You must then find out if there have been intervening capital changes affecting that initial per-share basis number. Fortunately, this is not an impossible task.

Capital Changes Reporter to the Rescue

It is also available on CD-ROM and via subscriptions to CCH s parent company Web site, www.wolterskluwerfs.com You can look up the company in question and trace all the capital changes over the years.

So where can you find the Reporter? Not at Barnes & Noble. This is a highly specialized (and expensive) publication. However, you should be able to track down a copy at public libraries in big cities and good law-school libraries. Offices of the big national and regional CPA firms should also have one for their tax staff. If you grovel pitifully, you will probably be invited in to use their Reporter free of charge.

Full-service brokers should also subscribe, often via fax or the Internet. But good luck getting your broker to do the research, unless you are an important (and very insistent) customer. So if you live outside a big city, a road trip may be necessary.

Shares You Acquired Yourself

If you have lost the basis records for shares you yourself purchased, shame on you! However, you are obviously not alone. If you were, the Capital Changes Reporter would not exist. Just follow the same procedure explained above for shares received by gift.

Old Share Certificates

Now let's say you find or inherit some dusty, old stock certificates. If the company is still publicly traded, follow the steps outlined earlier, including a check of the Capital Changes Reporter. You could discover you are theoretically entitled to some additional shares, because of splits or spinoffs. However, the state may become the owner of unclaimed assets after a period of time. Contact the company's investor relations department and ask what your rights are.

If the shares are in a now-defunct corporation, you could still be in luck. It may have merged with another still-standing publicly traded company. Again, you can find out by checking the Capital Changes Reporter. For example, if you look up American Motors, you'll see it merged into Chrysler in 1987. American Motors shareholders received Chrysler stock in the deal. Of course, Chrysler has since merged with Daimler-Benz. You may be entitled to stock in the new company.

The Reporter also lists worthless securities going back forever. If your funky old shares fall into this category, the owner should have taken a worthless stock deduction (treated as a capital loss) in the year the company went belly up. If that owner was you, the loss is equal to your basis in the worthless shares. The good news: If you failed to take a deduction in the year of worthlessness, you have seven years from the due date for that year's return to claim a refund by filing an amended return. If the seven years are up, you are out of luck. Sorry about that.

Shares in an IRA

If your shares are held in an IRA or qualified retirement account, you don't need to go searching through the Capital Changes Reporter. The only relevant number is your basis in the account from any nondeductible contributions. For traditional IRAs, you can find this amount on your latest Form 8606 (if you've been filing correctly). For company plans, your basis should appear on your statement. All your withdrawals beyond your basis are taxed as income (except for Roth IRA payouts).