Math Problem Statement

Calculate Contribution margin ratio given the sales price per unit, variable manufacturing and marketing expenses per unit, fixed expenses, and units sold.

Solution

To calculate the Contribution Margin Ratio, we first need to determine the contribution margin per unit and then express it as a percentage of the sales price per unit.

Given Data:

  • Sales price per unit = $500
  • Variable manufacturing expense per unit = $50
  • Variable marketing expense per unit = $50
  • Fixed expenses = $100,000 (not directly relevant for calculating contribution margin ratio)
  • Units sold = 5,000 (not directly relevant for calculating contribution margin ratio)

Steps:

  1. Calculate Total Variable Cost per Unit: Total Variable Cost per Unit=Variable Manufacturing Expense+Variable Marketing Expense\text{Total Variable Cost per Unit} = \text{Variable Manufacturing Expense} + \text{Variable Marketing Expense} =50+50=100= 50 + 50 = 100

  2. Calculate Contribution Margin per Unit: Contribution Margin per Unit=Sales Price per UnitTotal Variable Cost per Unit\text{Contribution Margin per Unit} = \text{Sales Price per Unit} - \text{Total Variable Cost per Unit} =500100=400= 500 - 100 = 400

  3. Calculate Contribution Margin Ratio: Contribution Margin Ratio=Contribution Margin per UnitSales Price per Unit×100%\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin per Unit}}{\text{Sales Price per Unit}} \times 100\% =400500×100%=80%= \frac{400}{500} \times 100\% = 80\%

Answer:

The Contribution Margin Ratio is 80%.

Would you like further details or have any questions?


Related Questions:

  1. How would changes in variable costs affect the contribution margin ratio?
  2. What impact does an increase in fixed expenses have on the break-even point?
  3. How can the contribution margin ratio be used to make pricing decisions?
  4. What is the significance of a high contribution margin ratio for a company?
  5. How does the contribution margin ratio relate to profitability?

Tip:

A higher contribution margin ratio indicates that a larger portion of sales revenue contributes to covering fixed costs and generating profit.

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Math Problem Analysis

Mathematical Concepts

Contribution Margin Ratio
Cost Analysis
Profitability Analysis

Formulas

Total Variable Cost per Unit = Variable Manufacturing Expense + Variable Marketing Expense
Contribution Margin per Unit = Sales Price per Unit - Total Variable Cost per Unit
Contribution Margin Ratio = (Contribution Margin per Unit / Sales Price per Unit) × 100%

Theorems

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Suitable Grade Level

Undergraduate (Business/Finance)