SM.63 A small company has $6,750,000 in (annual) revenue, spends 42% of its revenues on purchases, and has a net profit margin of 12.75%. They would like to increase their profits and they are looking at focusing in one of two directions. First, they think they can save 2.65% on their purchase expenses. Or second, they can focus on increasing sales.

By what percentage would they have to increase sales in order to equal a 2.65% savings to purchasing expenses? (Write your answer as a percentage, and display your answer to two decimal places.)
  
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To find the percentage increase in sales that would equal a 2.65% savings on purchase expenses, we can follow these steps:

1. **Calculate the current purchase expenses**:
   \[
   \text{Purchase Expenses} = \text{Revenue} \times \text{Percentage of Revenue spent on Purchases}
   \]
   \[
   \text{Purchase Expenses} = 6,750,000 \times 0.42 = 2,835,000
   \]

2. **Calculate the savings from the purchase expenses**:
   \[
   \text{Savings} = \text{Purchase Expenses} \times \text{Savings Percentage}
   \]
   \[
   \text{Savings} = 2,835,000 \times 0.0265 = 75,097.50
   \]

3. **Determine the additional revenue required to match this savings in profit**:
   Since the net profit margin is 12.75%, we can find the amount of sales needed to achieve the same profit increase:
   \[
   \text{Required Increase in Revenue} = \frac{\text{Savings}}{\text{Net Profit Margin}}
   \]
   \[
   \text{Required Increase in Revenue} = \frac{75,097.50}{0.1275} \approx 589,122.55
   \]

4. **Calculate the percentage increase in sales**:
   \[
   \text{Percentage Increase in Sales} = \frac{\text{Required Increase in Revenue}}{\text{Current Revenue}} \times 100
   \]
   \[
   \text{Percentage Increase in Sales} = \frac{589,122.55}{6,750,000} \times 100 \approx 8.74\%
   \]

Therefore, the company would need to increase sales by **8.74%** to match the profit increase from a 2.65% savings on purchase expenses.

Would you like further details or have any questions? Here are some related questions you might consider:

1. What other strategies could the company explore to increase profits?
2. How does the net profit margin compare to industry standards?
3. What factors could affect the success of increasing sales?
4. How might the company track the effectiveness of its cost-saving measures?
5. What are the potential risks of relying solely on one strategy to increase profits?

**Tip:** Regularly reviewing both sales strategies and expense management can lead to more balanced growth and sustainability for the company.

A small company has $6,750,000 in (annual) revenue, spends 42% of its revenues on purchases, and has a net profit margin of 12.75%. They would like to increase their profits and they are looking at focusing in one of two directions. First, they think they can save 2.65% on their purchase expenses. Or second, they can focus on increasing sales. By what percentage would they have to increase sales in order to equal a 2.65% savings to purchasing expenses? (Write your answer as a percentage, and display your answer to two decimal places.)

Learn how a small company with $6,750,000 in revenue can determine the percentage sales increase required to match a 2.65% savings in purchase expenses. This problem covers percentage calculations, revenue analysis, and algebraic techniques for profit optimization, suitable for Grades 11-12 students.

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