Suppose a company wishes to increase their return of capital employed (ROCE) to 15%. Currently, their ROCE is 10% and their working capital turnover rate is 1,5. However, they believe it would be difficult do much about their yearly turnover and average-tied up capital (assets).  What is the company’s current profit margin? What profit margin is the company aiming for?

To solve this problem, we need to find the current and target profit margins based on the Return on Capital Employed (ROCE) and the working capital turnover rate.

Given:
- Current ROCE: 10%
- Target ROCE: 15%
- Working capital turnover rate: 1.5
- Yearly turnover and average tied-up capital (assets) remain constant.

### Definitions and Formulas
1. **ROCE** is defined as:
   \[
   \text{ROCE} = \frac{\text{Operating Profit}}{\text{Capital Employed}} \times 100\%
   \]
   Rearranging for Operating Profit:
   \[
   \text{Operating Profit} = \text{ROCE} \times \text{Capital Employed}
   \]

2. **Working Capital Turnover Rate** is defined as:
   \[
   \text{Working Capital Turnover Rate} = \frac{\text{Yearly Turnover}}{\text{Average Tied-Up Capital (Assets)}}
   \]
   Rearranging for Yearly Turnover:
   \[
   \text{Yearly Turnover} = \text{Working Capital Turnover Rate} \times \text{Average Tied-Up Capital}
   \]

3. **Profit Margin** is defined as:
   \[
   \text{Profit Margin} = \frac{\text{Operating Profit}}{\text{Yearly Turnover}} \times 100\%
   \]

### Current Profit Margin Calculation
1. **Current Operating Profit**:
   \[
   \text{Operating Profit}_{\text{current}} = 0.10 \times \text{Capital Employed}
   \]

2. **Yearly Turnover** (based on working capital turnover rate):
   \[
   \text{Yearly Turnover} = 1.5 \times \text{Capital Employed}
   \]

3. **Current Profit Margin**:
   \[
   \text{Profit Margin}_{\text{current}} = \frac{\text{Operating Profit}_{\text{current}}}{\text{Yearly Turnover}} \times 100\%
   \]
   Substituting the values:
   \[
   \text{Profit Margin}_{\text{current}} = \frac{0.10 \times \text{Capital Employed}}{1.5 \times \text{Capital Employed}} \times 100\%
   \]
   Simplifying:
   \[
   \text{Profit Margin}_{\text{current}} = \frac{0.10}{1.5} \times 100\% = \frac{10}{1.5} \approx 6.67\%
   \]

### Target Profit Margin Calculation
1. **Target Operating Profit**:
   \[
   \text{Operating Profit}_{\text{target}} = 0.15 \times \text{Capital Employed}
   \]

2. **Target Profit Margin**:
   \[
   \text{Profit Margin}_{\text{target}} = \frac{\text{Operating Profit}_{\text{target}}}{\text{Yearly Turnover}} \times 100\%
   \]
   Substituting the values:
   \[
   \text{Profit Margin}_{\text{target}} = \frac{0.15 \times \text{Capital Employed}}{1.5 \times \text{Capital Employed}} \times 100\%
   \]
   Simplifying:
   \[
   \text{Profit Margin}_{\text{target}} = \frac{0.15}{1.5} \times 100\% = \frac{15}{1.5} = 10\%
   \]

### Summary
- The company’s **current profit margin** is approximately **6.67%**.
- The company is aiming for a **profit margin** of **10%**.

Would you like more details or have any questions?

Here are some related questions to consider:
1. How can the company increase its ROCE without increasing the profit margin?
2. What strategies can be implemented to improve the working capital turnover rate?
3. How does the profit margin affect the company's overall profitability?
4. What impact would increasing sales have on the profit margin if costs remain constant?
5. What are other key performance indicators (KPIs) the company should monitor?
6. How does the average tied-up capital influence the company's financial performance?
7. What role does operational efficiency play in achieving a higher ROCE?
8. How can reducing operational costs affect the profit margin and ROCE?

**Tip:** Regularly reviewing and optimizing both revenue streams and cost structures can help in achieving desired financial metrics like ROCE and profit margin.

Learn how to calculate current and target profit margins using Return on Capital Employed (ROCE) and working capital turnover rate. Understand the relationship between ROCE, profit margin, and capital efficiency. Suitable for professionals and analysts.

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