Final answer:
To achieve the desired profit using the contribution margin ratio approach, Stuart Company must generate $398,375 in sales and sell 11,382 units.
Step-by-step explanation:
The student's question pertains to determining the sales volume in dollars and units required to achieve a desired profit using the contribution margin ratio approach. To find these values, we first calculate the contribution margin per unit, which is obtained by subtracting the variable cost per unit from the sales price per unit. Next, we calculate the contribution margin ratio by dividing the contribution margin per unit by the sales price per unit.
Once we have the contribution margin ratio, we can use the following formula to determine the sales volume needed in dollars: (Fixed Costs + Desired Profit) / Contribution Margin Ratio. After finding the sales volume in dollars, we can find the number of units by dividing the required sales volume in dollars by the price per unit.
To solve the given problem:
- Contribution Margin per Unit = Sales Price per Unit - Variable Cost per Unit
- Contribution Margin Ratio = Contribution Margin per Unit / Sales Price per Unit
- Sales Volume in Dollars = (Fixed Costs + Desired Profit) / Contribution Margin Ratio
- Sales Volume in Units = Sales Volume in Dollars / Sales Price per Unit
Putting the values into the formulas, we have:
- Contribution Margin per Unit = $35.00 - $23.80 = $11.20
- Contribution Margin Ratio = $11.20 / $35.00 = 0.32
- Sales Volume in Dollars = ($67,680 + $60,000) / 0.32 = $398,375
- Sales Volume in Units = $398,375 / $35.00 = 11,382 units (rounded to the nearest unit)
Therefore, Stuart Company must generate $398,375 in sales and sell 11,382 units to achieve the desired annual profit of $60,000.