$($a$)$ Inventory:

$(1)$ Compute Richardson$$s inventory for the balance sheet, based upon the dollar$-$value LIFO cost method, as of each December $31,2020$ through $2024(5$ years total$).$

$(2)$ Prepare the FIFO$-$to$-$LIFO conversion entry Richardson must make at December $31,2020.$ Assume the company made a reversing entry dated January $1,2020$ to reverse the effects of the December $31,2019$ FIFO$-$to$-$LIFO conversion entry.

$(3)$ Prepare the FIFO$-$to$-$LIFO conversion entry Richardson must make at December $31,2021.$ Assume the company made a reversing entry dated January $1,2021$ to reverse the effects of the December $31,2020$ FIFO$-$to$-$LIFO conversion entry.

$(4)$ Prepare the FIFO$-$to$-$LIFO conversion entry Richardson must make at December $31,2022.$ Assume the company made a reversing entry dated January $1,2022$ to reverse the effects of the December $31,2021$ FIFO$-$to$-$LIFO conversion entry.

$($b$)$ Inventory $$ data analytics:

$(1)$ Compute the year$-$end $2022$ LIFO inventory as a percentage of the year$-$end $2022$ FIFO inventory $($i$.$e$.,$ LIFO $/$ FIFO$)$ for each of the three public companies. Prepare a clustered column chart to compare the year$-$end $2022$ percentages for the three companies. Which company shows the lowest year$-$end $2022$ percentage? In one sentence, what causes this percentage to be less than $100\%?$

$(2)$ Compute the estimated year$-$end $2022$ Cumulative tax savings from using LIFO as a percentage of the year$-$end $2022$ Stockholders$$ equity $($i$.$e$.,$ savings $/$ equity$)$ for each of the three public companies. For purposes of this question, assume an income tax rate of $30\%.$ Prepare a clustered column chart to compare the year$-$end $2022$ percentages for the three companies. Which company shows the highest year$-$end $2022$ percentage? In one sentence, what does this percentage mean for the company?