Wiser Group sells a single product for $30 per unit. The variable costs for each unit are $7.50, while the total fixed costs are $4,500. If a 10% sales commission is introduced what is the new Contribution Margin Ratio:
A) 72.5%.
B) 65%.
C) 75%
D) No Change
The correct answer and explanation is :
To calculate the new Contribution Margin Ratio after introducing a 10% sales commission, we first need to understand how the sales commission affects the cost structure. The Contribution Margin (CM) ratio is defined as:
[
\text{Contribution Margin Ratio} = \frac{\text{Selling Price per Unit} – \text{Variable Costs per Unit}}{\text{Selling Price per Unit}}
]
Step 1: Calculate the Original Contribution Margin (CM) Ratio without the sales commission.
- Selling Price per Unit = $30
- Variable Costs per Unit (before commission) = $7.50
[
\text{CM} = 30 – 7.50 = 22.50
]
[
\text{Contribution Margin Ratio (Original)} = \frac{22.50}{30} = 0.75 \text{ or } 75\%
]
So, the original contribution margin ratio is 75%.
Step 2: Adjust for the new sales commission.
The introduction of a 10% sales commission affects the variable costs. The commission is 10% of the selling price, so the commission per unit is:
[
\text{Sales Commission per Unit} = 10\% \times 30 = 3
]
Thus, the total variable cost per unit now becomes:
[
\text{New Variable Cost per Unit} = 7.50 + 3 = 10.50
]
Step 3: Calculate the new Contribution Margin Ratio.
The new contribution margin is now calculated as:
[
\text{New CM} = 30 – 10.50 = 19.50
]
The new contribution margin ratio is:
[
\text{Contribution Margin Ratio (New)} = \frac{19.50}{30} = 0.65 \text{ or } 65\%
]
Conclusion:
The new contribution margin ratio, after accounting for the 10% sales commission, is 65%.
The correct answer is B) 65%.
Explanation:
The addition of the 10% sales commission increases the variable costs per unit (from $7.50 to $10.50), which in turn decreases the contribution margin and, consequently, the contribution margin ratio. Initially, without the sales commission, the contribution margin ratio was 75%, but after the commission is introduced, it drops to 65%. Therefore, the new contribution margin ratio is lower, reflecting the increased costs due to the commission.