he Shield Corporation has two shareholders, Peg and Nick. The basis of Peg$$s $600$ shares, which she acquired in $2011,$ is $$70,000.$ The basis of Nick$$s $400$ shares, which he acquired in $2013,$ is $$75,000.$ Peg and Nick are unrelated.

The Shield Corporation has owned and operated two businesses since $2010.$ Its accumulated earnings and profits as of January $1,2024$ were $$227,000.$ In $2024,$ the two businesses earned taxable income of $$80,000$ and current earnings and profits $($before federal income tax$)$ of $$85,500.$ On December $31,2024,$ the corporation sold one of its businesses for $$250,000,$ resulting in a $$50,000$ gain that is not included in the taxable income or earnings and profits amounts shown above. It retained the other business, the net assets of which had a fair market value of $$150,000.$ The corporation used the $$250,000$ proceeds from the sale to redeem some stock of Peg and Nick. It paid $$150,000$ to Peg for $375$ of her shares and $$100,000$ to Nick for $250$ of his shares. a$.$ Compute the Shield Corporation$$s taxable income for the year ended December $31,2024.$

b$.$ Compute the corporate income tax of Shield Corporation for the year ended December $31,2024.$

c$.$ Compute the Shield Corporation$$s current earnings and profits for the year ended December $31,2024.$

d$.$ Determine the amount of the income recognized by Peg as a result of the redemption.