On January $1,2019,$ Pierce Company establishes a performance$-$based share option plan for its $80$ top executives. The terms of the plan are that each executive is granted a maximum of $200$ options after completing a $3-$year service period. The exact number of options granted, however, depends on the percentage increase in sales over the $3-$year period. The terms are: $(1)$ if sales increase between $0\%$ and $3\%,$ each executive is granted $90$ options; $(2)$ if sales increase between $4\%$ and $6\%,$ each executive is granted $140$ options; and $(3)$ if sales increase at least $7\%,$ each executive is granted the maximum number of options. Each option entitles the executive to acquire one share of the company$$s $$10$ par common stock at a price of $$45.$ The options expire at the end of $4$ years.

On the grant date, Pierce uses an option pricing model to estimate that the fair value of each share option is $$15\mathrm{.}50.$ Pierce$$s employee turnover rate is expected to be $16\%$ over the service period. At the end of $2020,$ because of lower turnover, Pierce revises its estimated turnover rate to $14\%$ for the service period. At the end of $2021,$ options vest for $68$ executives. On February $3,2022,50$ executives exercise their options when the market price of the company$$s common stock is $$62$ per share. During the remainder of the year, the market price declines so that at the end of $2022$ the other $18$ executives allow their options to expire.

Based on a projection of past trends, on the grant date Pierce estimates that its sales will increase about $5\%$ by the end of $2021.$ This estimate appears accurate through $2020.$ However, in the last half of $2021,$ sales increase so much that at the end of $2021$ Pierce determines that its total sales have increased by $7\%$ over the $3-$year service period. All inventory is shipped by Pierce to its customers under FOB destination terms.

Required:

$1.$ Prepare a schedule of Pierce$$s compensation computations for its compensatory share option plan for $2019$ through $2021.$

$2.$ Prepare Pierce$$s memorandum and journal entries for $2019$ through $2022$ in regard to this plan.

$3.$ Show how the account$($s$)$ related to the plan is $($are$)$ reported in the shareholders$$ equity section of Pierce$$s December $31,2020,$ balance sheet.