Please show detailed calculations and explanations. Answers without showing calculations$/$explanations$,$ will not receive credit.

a$)$ Pure Action Cycles Incorporated, a bicycle manufacturer, has a net capital loss in $2022$ of $$(67,000).$ It had net capital gains of $$21,350$ in $2021,$$$46,500$ in $2020,$$$10,300$ in $2019($but suffered a net operating loss in $2019),$ and $$8,300$ of net capital gain in $2018.$ What is the net capital gain in $2021$ after the carryback is applied?

b$)$ Imperial Construction Incorporated $($IC$)$ issued $100,000$ incentive stock options $($ISOs$)$ to its employees on January $1,2021,$ with an estimated value of $$5\mathrm{.}50$ per option. The options vest $($accrue$)$ at $25$ percent per year for four years $($beginning in $2022).$ Each option allows the holder to purchase one share of stock at $$8.$ On January $1,2023,$ employees exercised $12,500$ options as IC's stock price reached $$14\mathrm{.}72.$ What is the amount of the book$-$tax difference in $2023$ associated with the incentive stock options? Is it favorable or unfavorable? Is it temporary or permanent?