Answer :
The correct weighted average contribution margin to determine the total sales BPC must attain in order to reach a target profit of $90,000 is calculated by considering the contribution margin of each product and its proportion of total sales.
To calculate the weighted average contribution margin, follow these steps:
1. Determine the contribution margin for each product, which is the selling price per unit minus the variable cost per unit.
2. Calculate the proportion of total sales each product represents.
3. Multiply each product's contribution margin by its respective sales proportion.
4. Sum these products to find the weighted average contribution margin.
Let's assume we have the following sales mix and contribution margin data:
- Product A: Selling price per unit = $100, Variable cost per unit = $60, Contribution margin per unit = $40
- Product B: Selling price per unit = $150, Variable cost per unit = $100, Contribution margin per unit = $50
- Product C: Selling price per unit = $200, Variable cost per unit = $120, Contribution margin per unit = $80
Assuming the sales mix is 30% for Product A, 20% for Product B, and 50% for Product C, we calculate the weighted average contribution margin as follows:
Weighted average contribution margin (WACM) = (Contribution margin of A × Proportion of A) + (Contribution margin of B × Proportion of B) + (Contribution margin of C × Proportion of C)
WACM = ($40 × 0.30) + ($50 × 0.20) + ($80 × 0.50)
WACM = $12 + $10 + $40
WACM = $62
Now, to find the total sales BPC must attain to reach a target profit of $90,000, we need to consider the fixed costs. However, the fixed costs are not provided in the conversation. Assuming we know the fixed costs, we would use the following formula:
Total sales = Target profit + Fixed costs
To find the total sales in terms of contribution margin, we would divide the target profit plus fixed costs by the weighted average contribution margin ratio (WACMR), which is the WACM divided by the selling price per unit.
Total sales in units = (Target profit + Fixed costs) / WACMR
Without the fixed costs, we cannot complete the calculation for total sales. Once the fixed costs are known, the formula above can be used to determine the total sales required to achieve the target profit.
Final answer:
To calculate the weighted average contribution margin, subtract the variable cost per unit from the selling price per unit. Multiply the sum of fixed costs and target profit by the unit contribution margin to determine the total units needed to reach the target profit. Without the specific sales mix, an exact number can't be provided.
Explanation:
To calculate the weighted average contribution margin and determine the total sales Business Process Company (BPC) must attain to reach a target profit of $90,000, we first need to understand what contribution margin is. The contribution margin is defined as the selling price per unit minus the variable cost per unit. In the provided scenarios, if we take a unit with a sales price of $1.50 and subtract the variable cost of $0.30, we get a unit contribution margin of $1.20.
We can calculate the total number of units needed to reach the target profit by adding the fixed costs (FC) to the target profit and then dividing by the unit contribution margin. However, the information provided lacks the actual sales mix, but we can use the generic formula: Total Sales = (Fixed Costs + Target Profit) / Unit Contribution Margin. If we assume fixed costs (FC) are $40,000 as mentioned in one of the examples, the calculation would be Total Sales = ($40,000 + $90,000) / $1.20 per unit. The resulting figure from this equation will give us the total units needed to sell to achieve the $90,000 target profit.
However, without the specific sales mix, we cannot apply this calculation directly to BPC’s scenario. Also, it should be noted that to determine the total sales in dollars, you would further multiply the total units by the unit selling price.
