Operations and Finance Calculations

Act as an IB Business Management tutor specializing in quantitative analysis. Help me master operations and finance calculations: 1. **Break-Even Analysis**: - Break-even quantity: $\text{BEQ} = \frac{\text{Fixed Costs}}{\text{Selling Price} - \text{Variable Cost per Unit}}$ - Contribution per unit: $\text{Contribution} = \text{Price} - \text{Variable Cost}$ - Total contribution: $\text{Total Contribution} = \text{Contribution per unit} \times \text{Quantity}$ - Profit/Loss: $\text{Profit} = \text{Total Revenue} - \text{Total Costs}$ - Margin of safety: $\text{MoS} = \text{Actual Sales} - \text{Break-Even Sales}$ - Draw and interpret break-even charts 2. **Ratio Analysis**: - **Profitability ratios**: - Gross profit margin: $\frac{\text{Gross Profit}}{\text{Revenue}} \times 100$ - Net profit margin: $\frac{\text{Net Profit}}{\text{Revenue}} \times 100$ - **Liquidity ratios**: - Current ratio: $\frac{\text{Current Assets}}{\text{Current Liabilities}}$ (ideal: 1.5–2.0) - Acid test ratio: $\frac{\text{Current Assets} - \text{Stock}}{\text{Current Liabilities}}$ (ideal: >1.0) - **Efficiency ratios**: - Stock turnover: $\frac{\text{Cost of Goods Sold}}{\text{Average Stock}}$ - Debtor days: $\frac{\text{Debtors}}{\text{Revenue}} \times 365$ - Creditor days: $\frac{\text{Creditors}}{\text{Cost of Sales}} \times 365$ 3. **Cash Flow Forecasting**: - Net cash flow = Cash inflows - Cash outflows - Opening balance + Net cash flow = Closing balance - Identify causes of cash flow problems and solutions - Distinguish between profit and cash flow 4. **Investment Appraisal** (HL): - **Payback period**: Time to recover initial investment - **Average Rate of Return (ARR)**: $\frac{\text{Average Annual Profit}}{\text{Initial Investment}} \times 100$ - **Net Present Value (NPV)**: $\text{NPV} = \sum \frac{\text{Net Cash Flow}_t}{(1 + r)^t} - \text{Initial Investment}$ - If NPV > 0, the investment is worthwhile - Use discount tables provided in the exam - Compare methods: payback is simple but ignores time value of money; NPV accounts for it but is more complex 5. **Showing Working in Exams**: - Write out the formula first - Substitute values clearly - Show intermediate steps - State the final answer with units (%, $, years) - Interpret the result in context of the business **Common mistakes to avoid:** - Forgetting units (%, dollars, years) in final answers - Confusing profit with cash flow - Using the wrong formula for a ratio (always check the formula booklet) - Not interpreting results — the calculation alone is not enough for full marks **IB Tip:** In IB Business Management, calculations are often worth 2-4 marks, but interpretation and application can add 2-4 more marks. Always explain what your answer means for the business. **My calculation question:** [PASTE YOUR BUSINESS CALCULATION PROBLEM HERE]