there is no right answer in your situation. I don't know how much is involved. Before going through what I suggest after completing your return except for this issue I would then drop in the sales price and use a zero cost basis to see what using zero will cost you. for some taxpayers, the gain can be taxed at 0% which means doing all the work suggested won't produce any or only minimal benefits.
If audited and using a non-zero amount, the agent might have a prove it or lose it attitude. You could then go to appeals or court which are usually reasonable but it's costly. Some agents are more reasonable. I would take the market value on 1/1/79 and 12/31/ 79 and then divide the sum by 2. then do the same for each year for 1980 through 2018 for 2019 I would take the average of the 1/1 and sales date value. total all these averages and then divide by the number of years. when doing this you have to take into account any stock splits. this average would then be multiplied by the number of shares for which you have no cost data. maybe your broker will help gather this info. one thing I would do is contact the trustee of the dividend reinvestment program to see what history they can provide and use that for those shares. I would also compare the average cost basis for those shares you can obtain to what you developed from the average of all those years for purposes of reasonableness.
