Math Problem Statement

A firm made a capital investment of $2.2 million, depreciated straight line over 6 years to zero. The fixed costs excluding depreciation is $531,000. The sales price per unit of product is $1.80. The variable cost per unit is $1.40. What is the firm’s accounting break-even sales level in terms of the units of product sold? Question 5 Answer a. 3.0 million b. 2.2 million c. 1.7 million d. 4.3 million e. 1.1 million

Solution

To find the firm’s accounting break-even sales level in terms of units sold, we need to determine the point at which the firm’s revenue covers all of its fixed and variable costs, including depreciation.

Here's the step-by-step solution:

1. Calculate Annual Depreciation Expense

Since the initial capital investment of $2.2 million is depreciated straight-line over 6 years, the annual depreciation expense is: Annual Depreciation=2,200,0006=366,666.67\text{Annual Depreciation} = \frac{2,200,000}{6} = 366,666.67

2. Determine Total Fixed Costs (Including Depreciation)

The fixed costs excluding depreciation are $531,000. Including depreciation, the total fixed costs are: Total Fixed Costs=531,000+366,666.67=897,666.67\text{Total Fixed Costs} = 531,000 + 366,666.67 = 897,666.67

3. Contribution Margin per Unit

The contribution margin per unit is the difference between the sales price per unit and the variable cost per unit: Contribution Margin=1.801.40=0.40\text{Contribution Margin} = 1.80 - 1.40 = 0.40

4. Calculate Break-Even Sales Level in Units

The break-even point in units is calculated by dividing the total fixed costs by the contribution margin per unit: Break-Even Sales Level (units)=Total Fixed CostsContribution Margin=897,666.670.40=2,244,167 units\text{Break-Even Sales Level (units)} = \frac{\text{Total Fixed Costs}}{\text{Contribution Margin}} = \frac{897,666.67}{0.40} = 2,244,167 \text{ units}

Answer

Rounding to the nearest option, the correct answer is: b. 2.2 million

Would you like more details on any step or have further questions?


Here are some related questions that might expand your understanding:

  1. How would the break-even level change if the depreciation method changed?
  2. What impact does a higher sales price have on the break-even point?
  3. How would changes in variable costs affect the break-even units?
  4. How do fixed costs affect the break-even point in other scenarios?
  5. What are other methods to calculate depreciation and their impact on accounting?

Tip: Always remember, break-even analysis focuses on covering all fixed and variable costs. For accounting break-even, depreciation counts as a part of fixed costs.

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Math Problem Analysis

Mathematical Concepts

Break-Even Analysis
Depreciation
Contribution Margin

Formulas

Annual Depreciation = Capital Investment / Depreciation Period
Total Fixed Costs = Fixed Costs (Excluding Depreciation) + Depreciation
Contribution Margin = Sales Price per Unit - Variable Cost per Unit
Break-Even Sales Level (Units) = Total Fixed Costs / Contribution Margin

Theorems

Break-Even Point in Accounting

Suitable Grade Level

Undergraduate Finance or Accounting