Math Problem Statement
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.)
%
Solution
To find the percentage increase in sales that would equal a 2.65% savings on purchase expenses, we can follow these steps:
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Calculate the current purchase expenses:
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Calculate the savings from the purchase expenses:
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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:
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Calculate the percentage increase in sales:
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:
- What other strategies could the company explore to increase profits?
- How does the net profit margin compare to industry standards?
- What factors could affect the success of increasing sales?
- How might the company track the effectiveness of its cost-saving measures?
- 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.
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Math Problem Analysis
Mathematical Concepts
Percentage Calculation
Revenue and Profit Analysis
Algebra
Formulas
Purchase Expenses = Revenue × Percentage of Revenue spent on Purchases
Savings = Purchase Expenses × Savings Percentage
Required Increase in Revenue = Savings / Net Profit Margin
Percentage Increase in Sales = (Required Increase in Revenue / Current Revenue) × 100
Theorems
Proportional Relationships
Profit Margin Calculation
Suitable Grade Level
Grades 11-12
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