Target units = (Fixed costs + Before-tax profit goal) ÷ Contribution margin per unit.

Before-tax profit goal = After-tax goal ÷ (1 – tax rate)

= $100 000 ÷ (1 – 0.25) = $133 333.

Contribution margin per unit = Selling price – Variable cost = $50 – $30 = $20.

Units = ($120 000 + $133 333) ÷ $20 ≈ 12 666.7.

Because only whole units may be produced, the firm must round up to the next feasible sales batch shown, 12 800 units. This quantity produces exactly (12 800 × $20) – $120 000 = $256 000 – $120 000 = $136 000 pretax, or $102 000 after tax, meeting (and slightly exceeding) the $100 000 after-tax target.

B. 14 800 units yield an after-tax profit of roughly $133 500—far more than the $100 000 goal, so unnecessary.

C. 15 360 units give ≈$140 400 after tax, again overshooting the required profit.

D. 16 000 units create ≈$150 000 after tax, well above the target and thus inefficient.

1. OpenStax, Managerial Accounting (2022), Ch. 6 “Cost–Volume–Profit Analysis,” section “Computing Target Income Including Income Taxes,” Example 6.3, pp. 235-236.

2. Garrison, Noreen & Brewer, Managerial Accounting, 17e, McGraw-Hill, Ch. 6, pp. 248-249: formula for units needed to attain a target after-tax profit.

3. MIT Sloan OCW, 15.514 Financial & Managerial Accounting, Lecture 15 slides, “CVP with Income Taxes,” slide 13 (demonstrates the same calculation).