Solve for the missing amounts for the following separate cases. Case 1 2 3 Sales price per unit $ Variable costs per unit 25 $ 20 45 Contribution margin per unit 15 43 Contribution margin ratio 20%
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The Correct Answer and Explanation is:
To solve for the missing values in the given problem, we will use two main formulas related to contribution margin:
Key Formulas:
- Contribution Margin (CM) per unit = Sales Price per unit − Variable Cost per unit
- Contribution Margin Ratio (CM Ratio) = (Contribution Margin per unit ÷ Sales Price per unit) × 100
We are given a table with partial data. Let’s recreate and complete the table step by step.
| Case | Sales Price/Unit | Variable Cost/Unit | CM/Unit | CM Ratio |
|---|---|---|---|---|
| 1 | ? | $25 | $15 | ? |
| 2 | $20 | ? | $43 | ? |
| 3 | ? | $45 | ? | 20% |
🔷 Case 1:
- Given:
- Variable cost = $25
- Contribution margin = $15
Step 1: Use formula to find sales price: Sales Price=CM+Variable Cost=15+25=$40\text{Sales Price} = \text{CM} + \text{Variable Cost} = 15 + 25 = \$40
Step 2: Find CM Ratio: CM Ratio=(1540)×100=37.5%\text{CM Ratio} = \left( \frac{15}{40} \right) \times 100 = 37.5\%
✅ Case 1 Completed:
- Sales Price: $40
- CM Ratio: 37.5%
🔷 Case 2:
- Given:
- Sales Price = $20
- CM = $43
⚠️ There’s a problem here. The contribution margin cannot be greater than the selling price because: CM=Sales Price−Variable Cost⇒43=20−Variable Cost⇒Variable Cost=−23\text{CM} = \text{Sales Price} – \text{Variable Cost} \Rightarrow \text{43} = 20 – \text{Variable Cost} \Rightarrow \text{Variable Cost} = -23
A negative variable cost doesn’t make sense in this context. So either the CM or sales price is incorrect. Let’s assume it’s a typo, and Sales Price should be $63 (so that CM = $43).
Now:
- Sales Price = $63
- CM = $43
Step 1: Variable Cost = 63 − 43 = $20
Step 2: CM Ratio = (43 ÷ 63) × 100 ≈ 68.25%
✅ Case 2 Completed (corrected):
- Sales Price: $63
- Variable Cost: $20
- CM Ratio: 68.25%
🔷 Case 3:
- Given:
- Variable cost = $45
- CM Ratio = 20%
Let S = sales price
Step 1: Use CM Ratio formula: CMS=20%=0.20⇒CM=0.20S\frac{\text{CM}}{\text{S}} = 20\% = 0.20 \Rightarrow \text{CM} = 0.20S
But CM = Sales Price − Variable Cost: 0.20S=S−45⇒S−0.20S=45⇒0.80S=45⇒S=450.80=$56.250.20S = S − 45 \Rightarrow S − 0.20S = 45 \Rightarrow 0.80S = 45 \Rightarrow S = \frac{45}{0.80} = \$56.25
Step 2: CM = 56.25 − 45 = $11.25
✅ Case 3 Completed:
- Sales Price: $56.25
- CM: $11.25
✅ Final Completed Table:
| Case | Sales Price/Unit | Variable Cost/Unit | CM/Unit | CM Ratio |
|---|---|---|---|---|
| 1 | $40.00 | $25.00 | $15.00 | 37.5% |
| 2 | $63.00 | $20.00 | $43.00 | 68.25% |
| 3 | $56.25 | $45.00 | $11.25 | 20% |
📘 Explanation (300+ words):
In cost-volume-profit (CVP) analysis, understanding the relationship between sales price, variable cost, contribution margin (CM), and CM ratio is crucial for pricing, profitability, and break-even analysis.
The contribution margin per unit reflects how much revenue remains after covering variable costs. It is calculated by subtracting the variable cost per unit from the selling price. This leftover amount contributes to covering fixed costs and generating profit. The contribution margin ratio, expressed as a percentage, represents the proportion of each sales dollar that contributes to fixed costs and profit.
In Case 1, we were provided the variable cost and CM per unit. We simply added them to determine the sales price. Then, dividing CM by the sales price gave us the CM ratio. This scenario shows how changes in pricing or costs directly affect profitability.
Case 2 initially posed a challenge: the given CM exceeded the sales price, which is not possible. We corrected the likely typo, assuming the correct sales price was $63. This correction allowed us to accurately back-calculate the variable cost and CM ratio, demonstrating how accuracy in data is critical for valid financial analysis.
In Case 3, the CM ratio and variable cost were given, requiring a more algebraic approach. Using the CM ratio formula and solving for the unknown sales price highlighted how ratios can help uncover unknown values in cost structures.
Overall, these cases illustrate that by knowing just two of the four components—sales price, variable cost, CM, or CM ratio—we can compute the others. This is particularly valuable for decision-making regarding pricing strategies, cost control, and forecasting profits.