Math Problem Statement

SM.65 A marketing company prides itself on its sales prowess and is looking for ways to increase profits. Given the company culture, the president calls for a 11% increase in sales to meet the profitability goals. The company currently has revenues of $8,341,000 (annually), spends 46% of its revenues on purchases, and has a net profit margin of 6.75%.

You are a modest purchasing intern working for this company and you want to show the president that it may be easier to reach the profitability goals by lowering the purchasing expenses (while holding sales constant, that is, no need to increase sales by 11%).

If the company is able to reach its goal of increasing sales by 11%, by how how many dollars would its revenue increase? (Display your answer as a whole number.)

918,510

If the company is able to reach its goal of increasing sales by 11%, by how many dollars would its profit increase? (Display your answer as a whole number.)

Number

Assuming that revenues stayed flat (meaning the company did not try to increase sales by the 11 percent target), by what percentage would they have to decrease purchasing expenses to equal the increased profit that would have come from a 11 percent increase to revenues? (Write your answer as a percentage, and display your answer to two decimal places.)

%

Solution

To find the profit increase from an 11% increase in sales, let's start with the calculations:

  1. Revenue Increase:
    Current Revenue = $8,341,000
    Increase = 11% of $8,341,000
    Revenue Increase=0.11×8,341,000=918,510\text{Revenue Increase} = 0.11 \times 8,341,000 = 918,510

  2. Profit Increase:
    Current Profit = Current Revenue × Profit Margin
    Current Profit=8,341,000×0.0675=562,933.75\text{Current Profit} = 8,341,000 \times 0.0675 = 562,933.75
    New Revenue = Current Revenue + Revenue Increase
    New Revenue=8,341,000+918,510=9,259,510\text{New Revenue} = 8,341,000 + 918,510 = 9,259,510
    New Profit = New Revenue × Profit Margin
    New Profit=9,259,510×0.0675=624,731.43\text{New Profit} = 9,259,510 \times 0.0675 = 624,731.43
    Profit Increase = New Profit - Current Profit
    Profit Increase=624,731.43−562,933.75=61,797.68\text{Profit Increase} = 624,731.43 - 562,933.75 = 61,797.68
    Rounding this to a whole number gives $61,798.

  3. Percentage Decrease in Purchasing Expenses:
    Current Purchasing Expenses = 46% of Current Revenue
    Purchasing Expenses=0.46×8,341,000=3,832,860\text{Purchasing Expenses} = 0.46 \times 8,341,000 = 3,832,860
    To find the required decrease:
    Required Decrease = Profit Increase
    Required Decrease=61,798\text{Required Decrease} = 61,798
    New Purchasing Expenses = Current Purchasing Expenses - Required Decrease
    New Purchasing Expenses=3,832,860−61,798=3,771,062\text{New Purchasing Expenses} = 3,832,860 - 61,798 = 3,771,062
    Percentage Decrease = (Required Decrease / Current Purchasing Expenses) × 100
    Percentage Decrease=(61,7983,832,860)×100≈1.61%\text{Percentage Decrease} = \left(\frac{61,798}{3,832,860}\right) \times 100 \approx 1.61\%

Summary of Answers:

  • Profit Increase from 11% Sales Increase: $61,798
  • Percentage Decrease in Purchasing Expenses to Match Profit Increase: 1.61%

Would you like more details or have any questions? Here are some related questions:

  1. What factors could impact the profit margin if sales increase?
  2. How might the company effectively reduce purchasing expenses?
  3. What other strategies could be implemented to increase profitability?
  4. How does the net profit margin relate to the overall financial health of the company?
  5. What are the risks associated with not increasing sales while aiming to reduce costs?

Tip: Regularly monitor both sales and expenses to make informed adjustments for profitability.

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Math Problem Analysis

Mathematical Concepts

Percentages
Profit Calculation
Revenue Increase

Formulas

Revenue Increase = Current Revenue * 0.11
Current Profit = Current Revenue * Profit Margin
New Profit = New Revenue * Profit Margin
Profit Increase = New Profit - Current Profit
Percentage Decrease = (Required Decrease / Current Purchasing Expenses) * 100

Theorems

-

Suitable Grade Level

Grades 10-12

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