Replacing the component with a higher priced component will add $2 to variable costs. The new variable cost will be $24 per unit and the new contribution margin will be $60 ? $24, or $36. Acquiring the packing machine will add $18,000 in new depreciation expense to fixed costs ($180,000 ÷ 10 years life), so the new fixed cost will be $522,000. In order to earn after-tax income of $172,800, pre-tax income needs to be $288,000 ($172,800 ÷ (1 - 40%). Fixed costs of $522,000 + desired pre-tax income of $288,000 divided by the unit contribution margin of $36 = 22,500 units the company needs to sell to earn the desired after-tax net income of $172,800.
This answer results from using the after-tax desired profit as part of the numerator in the calculation of the number of units of sales required. The after-tax desired profit needs to be converted to before-tax profit before using it in the calculation.
This answer results from adding the full cost of the new machine and the desired after-tax net income to the present fixed costs to calculate the numerator of the calculation of the number of units to be sold. The full cost of the new machine should not be used, only one year of depreciation expense on it should be used. And the after-tax net income needs to be converted to before-tax net income before using it in the calculation.
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Management plans to improve the quality of its sole product by (1) replacing a component that costs $3.50 with a higher-grade unit that costs $5.50, and (2) acquiring a $180,000 packing machine. Austin will depreciate the machine over a 10-year life with no estimated salvage value by the straight-line method of depreciation. If the company wants to earn after-tax income of $172,800 in the upcoming period, it must sell