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Basis is generally the amount of your investment in a property for tax purposes.
The basis of property you buy is usually its cost - the amount you pay for it in cash, debt obligations, and other property or services.
If you receive property as a result of an involuntary conversion, you can figure the basis of the replacement property you receive using the basis of the converted property.
Assuming that you did not report a capital gain/loss on conversion as not taxable transaction - generally - the replacement property's basis is the old property's basis on the date of the conversion.
see for reference - the IRS publication 551 page 7 - http://www.irs.gov/pub/irs-pdf/p551.pdf
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Yes - that is correct.
In case that were two separate transactions:
-- the disposition of the seat on the NY Board of trade - the capital gain would be = (the fair market value of shares of Intercontinental Exchange) - (the basis - what you originally paid for the seat)
-- then - the fair market value of shares of Intercontinental Exchange on that day would establish the basis of that property.
For involuntary conversion - the disposition of the seat on the NY Board of trade is not reported as taxable transaction and the basis of shares of Intercontinental Exchange would be - what you originally paid for the seat.