Marshalls Retailing now carries the Fabletics yoga pants line of athletic wear. Marshalls needs to ensure that the new line contributes no less to their profit than other clothing lines it carries. The Fabletics line needs to provide a 48.5\% gross profit margin percentage. Marshalls buys the Fabletics yoga pants at a cost of $12 per pair. At what price should Marshalls sell the Fabletics Yoga pants?
The correct answer and explanation is:
To ensure a 48.5% gross profit margin, Marshalls needs to sell the Fabletics yoga pants at a price that gives them that margin over the cost of $12 per pair.
Step-by-step Calculation:
Let the selling price be S.
The gross profit margin (GPM) is given by: GPM=S−CS\text{GPM} = \frac{S – C}{S}
Where:
- SS = selling price
- CC = cost = $12
- GPM\text{GPM} = 48.5% = 0.485
0.485=S−12S0.485 = \frac{S – 12}{S}
Multiply both sides by SS: 0.485S=S−120.485S = S – 12
Now, solve for SS: 0.485S−S=−12⇒−0.515S=−12⇒S=120.515≈23.300.485S – S = -12 \Rightarrow -0.515S = -12 \Rightarrow S = \frac{12}{0.515} \approx 23.30
Correct Answer: $23.30
Explanation (300 words):
Retailers like Marshalls use gross profit margin to evaluate how much money they make on the sale of merchandise after accounting for the cost of goods sold. The gross profit margin is a ratio that shows what portion of the selling price is profit. It is calculated as the difference between the selling price and the cost, divided by the selling price.
In this case, Marshalls buys each pair of Fabletics yoga pants for $12. To maintain profitability consistent with their expectations, they require a gross profit margin of 48.5 percent. This means that for every dollar of the final selling price, 48.5 cents must be profit. The remaining 51.5 cents covers the cost of the product.
To find the appropriate selling price that guarantees this margin, we set up the gross margin formula. Substituting the known values into the equation, we solve for the selling price. After completing the algebraic steps, we find that Marshalls must sell the pants for approximately $23.30 to meet their desired margin.
Selling the pants at this price ensures that Marshalls is not undermining its overall profitability by introducing a new product line. If Marshalls sold the pants for less than $23.30, their gross margin would fall below 48.5 percent, which could affect their overall financial goals. Pricing it at $23.30 allows Marshalls to offer a competitive product while protecting its profit targets.