Problem $8-38$ Variable Costing and Absorption Costing Income Statements; Reconciling Reported Operating Income $($LO $8-2,8-3,8-4)$

Chataqua Can Company manufactures metal cans used in the food$-$processing industry. A case of cans sells for $$25.$ The variable costs of production for one case of cans are as follows:

Direct material

Direct labor

Variable manufacturing overhead

Total variable manufacturing cost per case

Variable selling and administrative costs amount to $$0\mathrm{.}70$ per case. Budgeted fixed manufacturing overhead is $$492,000$ per year, and fixed selling and administrative cost is $$41,500$ per year. The following data pertain to the company's first three years of operation.

$\backslash$table$[[,$Year $1,$Year,Year $3],[$Planned production $($in units$),82,000,82,000,82,000],[$Finished$-$goods inventory $($in units$),$ January $1,0,24,600,],[$Actual production $($in units$),82,000,82,000,82,000],[$Sales $($in units$),82,000,58,000,94,000],[$Finished$-$goods inventory $($in units$),$ December $31,0,24,000,12,000]]$

Actual costs were the same as the budgeted costs.

Required:

Prepare operating income statements for Chataqua Can Company for its first three years of operations using:

a$.$ Absorption costing.

b$.$ Variable costing.

Reconcile Chataqua Can Company's operating income reported under absorption and variable costing for each of its first three years of operation. Use the shortcut method.

Suppose that during Chataqua's fourth year of operation actual production equals planned production, actual costs are as expected, and the company ends the year with no inventory on hand.

a$.$ What will be the difference between absorption$-$costing income and variable$-$costing income in year $4?$

b$.$ What will be the relationship between total operating income for the four$-$year period as reported under absorption and variable costing?