A firm is considering a new project with estimated depreciation of $1,000, fixed costs of $3,600, and total sales of $8,146 at the accounting break-even level.

The variable costs per unit are estimated at $5.61.

What is the accounting break-even level of production?

Question

A firm is considering a new project with estimated depreciation of $1,000, fixed costs of $3,600, and total sales of $8,146 at the accounting break-even level.

The variable costs per unit are estimated at $5.61.

What is the accounting break-even level of production?

BlackTom AI · Accepted Answer

1) Relevant knowledge points and concepts
Accounting break-even is the output level where accounting profit equals zero. That means total sales minus total variable costs minus fixed costs minus depreciation = 0. Equivalently, contribution margin per unit (price − variable cost) times quantity = fixed costs + depreciation.

2) Complete reasoning process step by step
Let Q be the accounting break-even units. Total sales at the accounting break-even level are given as $8,146, so Sales = Price × Q = 8,146. Variable cost per unit v = $5.61. Fixed costs FC = $3,600 and Depreciation Dep = $1,000, so FC + Dep = $4,600. At break-even:
Sales − (v × Q) − (FC + Dep) = 0 → Sales − vQ = FC + Dep.

3) Calculations with intermediate steps
Plug the known Sales and FC + Dep:
8,146 − 5.61·Q = 4,600
Rearrange:
8,146 − 4,600 = 5.61·Q
3,546 = 5.61·Q
Q = 3,546 / 5.61
Compute Q:
5.61 × 632 = 5.61 × (630 + 2) = 3,534.3 + 11.22 = 3,545.52 ≈ 3,546
So Q ≈ 3,546 / 5.61 ≈ 631.88 → round to 632 units.

Check (optional): Price per unit = 8,146 / 632 ≈ $12.89. Contribution per unit = 12.89 − 5.61 = $7.28. Contribution × Q = 7.28 × 632 ≈ $4,600 = FC + Dep, so accounting profit = 0.

4) Why the correct answer is correct
The algebra identifies a unique Q that makes accounting profit zero given the provided total sales at break-even, variable cost per unit, fixed costs and depreciation. The computed Q (≈631.88) satisfies the break-even equality, so 632 units is the correct accounting break-even quantity.

5) Why the other options are incorrect
For each other option, 8,146 − 5.61·Q does not equal 4,600:
- 771: 8,146 − 5.61·771 = 3,820.69 ≠ 4,600
- 357: 8,146 − 5.61·357 = 6,143.23 ≠ 4,600
- 493: 8,146 − 5.61·493 = 5,380.27 ≠ 4,600
- 810: 8,146 − 5.61·810 = 3,601.90 ≠ 4,600
Thus none of these satisfy the break-even equation.

6) Conclusion
The accounting break-even level of production is 632 units, which matches the provided answer.

A firm is considering a new project with estimated depreciation of $1,000, fixed costs of $3,600, and total sales of $8,146 at the accounting break-even level. The variable costs per unit are estimated at $5.61. What is the accounting break-even level of production?单项选择题

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