Austin Manufacturing, which is subject to a 40% income tax rate, had the following operating data for the period just ended:

Selling price per unit $60

Variable cost per unit $22

Fixed costs 504,000

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

Answer (C) is correct. The units to be sold equal fixed costs plus the desired pretax profit, divided by the unit contribution margin. In the preceding year, the unit contribution margin is $38 ($60 selling price – $22 unit variable cost). That amount will decrease by $2 to $36 in the upcoming year because of use of a higher-grade component. Fixed costs will increase from $504,000 to $522,000 as a result of the $18,000 ($180,000 ÷ 10 years) increase in fixed costs attributable to depreciation on the new machine. Dividing the $172,800 of desired after-tax income by 60% (the complement of the tax rate) produces a desired before-tax income of $288,000. Hence, the breakeven point in units is 22,500 [($522,000 + $288,000) ÷ $36].