Final answer:
Calculating the capital gain for Roger's stock redemption involves subtracting the adjusted basis of the sold shares from the amount received. The claim of a $100,000 gain is false; the correct capital gain is $580,000, as the adjusted basis for the redeemed shares is $320,000.
Step-by-step explanation:
The statement that Roger's recognized gain is $100,000 from the stock redemption is false. When determining the capital gain from selling shares, one must consider the adjusted basis of the remaining investment post-redemption against the amount received.
If Roger owns 40% of Gold Inc., with an adjusted basis of $800,000, and Silver redeems 60% of his shares for $900,000, we calculate the remaining shares' adjusted basis. Initially, Roger's entire stake would have an adjusted basis of $800,000. The redemption of 60% would then leave Roger with an adjusted basis of 40% of the $800,000, which is $320,000 (40% of 800,000). Since the redemption is treated as return of capital, the $900,000 he received is compared against the $320,000 adjusted basis of the sold shares, and the capital gain would be calculated as $900,000 - $320,000, resulting in a gain of $580,000, not $100,000.