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

We start by laying out what the problem provides and what must hold at the accounting break-even point:
- Depreciation = 1000
- Fixed costs = 3600
- Variable cost per unit = 5.61
- Total sales at accounting break-even = 8146
At break-even (profit = 0) we have Sales = Variable Costs + Fixed Costs + Depreciation.
Let Q be the quantity produced/sold at break-even and let P be the price per unit. Then:
1) Sales = P * Q = 8146
2) Variable Costs = 5.61 * Q
3) Break-even condition: 8146 = 5.61 Q + 3600 + 1000 = 5.61 Q + 4600
From (3): 5.61 Q = 8146 - 4600 = 3546, so Q = 3546 / 5.61 ≈ 632 units.
Now, evaluate each answer choice:
Option 1: 632 units — This matches the calculated Q from the break-even condition and the given sales figure. It is consistent with (1) and (3), so this is a correct result.
Option 2: 771 units — If Q were 771, then Variable Costs would be 5.61 * 771 ≈ 4328.31, and total costs would be 4328.31 + 4600 ≈ 8928.31, which exceeds Sales (8146). This would imply a loss, not break-even, so this cannot be correct.
Option 3: 357 units — 5.61 * 357 ≈ 2001. ; Adding fixed and depreciation 4600 gives ≈ 6601, which is well below Sales 8146. This would imply profit, contradicting break-even. So this is not correct.
Option 4: 493 units — 5.61 * 493 ≈ 2764.33; total costs ≈ 2764.33 + 4600 ≈ 7364.33, which is less than Sales 8146, implying a profit, not break-even. Hence incorrect.
Option 5: 810 units — 5.61 * 810 ≈ 4544.1; total costs ≈ 4544.1 + 4600 ≈ 9144.1, which exceeds Sales 8146, implying a loss. Therefore not correct.
In summary, only 632 units satisfies the break-even condition given the provided sales level and cost structure; all other quantities fail to balance Sales with Total Costs at the break-even point.

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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