Math Problem Statement

What is the company's total fixed cost amount?

Group of answer choices

$463,750

$265,825

$197,925

$196,875

What is the company's total fixed cost amount?

Solution

To find the total fixed costs, we use the formula for the break-even point in units:

Break-even point (units)=Fixed CostsPrice per unitVariable Cost per unit\text{Break-even point (units)} = \frac{\text{Fixed Costs}}{\text{Price per unit} - \text{Variable Cost per unit}}

Values from the image:

  • Break-even point (units): 17,50017,500
  • Product price per unit: 26.5026.50
  • Variable cost per unit: 15.2515.25

Substitute these values into the formula and solve for Fixed Costs:

17,500=Fixed Costs26.5015.2517,500 = \frac{\text{Fixed Costs}}{26.50 - 15.25}

Step-by-step Calculation:

  1. Calculate the contribution margin (price per unit - variable cost per unit): 26.5015.25=11.2526.50 - 15.25 = 11.25

  2. Rearrange the equation to solve for Fixed Costs: Fixed Costs=17,500×11.25\text{Fixed Costs} = 17,500 \times 11.25

  3. Multiply: Fixed Costs=196,875\text{Fixed Costs} = 196,875

Final Answer:

The company's total fixed cost amount is $196,875.

Group of answer choices:

  • Correct answer: $196,875

Would you like further details or explanations on this calculation?

Related Questions:

  1. How is the contribution margin ratio calculated and interpreted?
  2. What happens to the break-even point if fixed costs increase?
  3. How can changes in variable costs affect the break-even point?
  4. How would the fixed costs be distributed if multiple products are involved?
  5. How is the margin of safety calculated and used in decision-making?

Tip:

Always verify your contribution margin calculation when solving break-even analysis problems—it plays a critical role in ensuring the accuracy of your result!

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Math Problem Analysis

Mathematical Concepts

Break-even Analysis
Linear Equations
Contribution Margin

Formulas

Break-even point (units) = Fixed Costs / (Price per unit - Variable Cost per unit)
Fixed Costs = Break-even point × Contribution Margin

Theorems

Break-even Analysis Formula

Suitable Grade Level

Grades 9-12