1. **Problem Statement:** Bethlehem Steel currently has sales of $2.5 billion, variable costs of $2 billion, and fixed costs of $400 million. Sales increase by 15%. We need to find: - The increase in pre-tax profit in dollar terms. - The percentage increase in pre-tax profit. - Explanation of the relationship between percentage changes in sales and pre-tax profit. 2. **Formulas and Important Rules:** - Pre-tax profit = Sales - Variable Costs - Fixed Costs - Variable costs change proportionally with sales. - Fixed costs remain constant regardless of sales. - Percentage increase in sales = 15% = 0.15 3. **Calculate initial pre-tax profit:** $$\text{Profit}_0 = 2.5 - 2.0 - 0.4 = 0.1 \text{ billion}$$ 4. **Calculate new sales:** $$\text{Sales}_1 = 2.5 \times (1 + 0.15) = 2.5 \times 1.15 = 2.875 \text{ billion}$$ 5. **Calculate new variable costs (proportional to sales):** $$\text{Variable Costs}_1 = 2.0 \times 1.15 = 2.3 \text{ billion}$$ 6. **Fixed costs remain the same:** $$\text{Fixed Costs}_1 = 0.4 \text{ billion}$$ 7. **Calculate new pre-tax profit:** $$\text{Profit}_1 = 2.875 - 2.3 - 0.4 = 0.175 \text{ billion}$$ 8. **Calculate increase in pre-tax profit in dollar terms:** $$\Delta \text{Profit} = 0.175 - 0.1 = 0.075 \text{ billion} = 75 \text{ million}$$ 9. **Calculate percentage increase in pre-tax profit:** $$\frac{0.075}{0.1} \times 100\% = 75\%$$ 10. **Explanation:** The percentage increase in pre-tax profit (75%) is greater than the percentage increase in sales (15%) because fixed costs do not change with sales. This leverage effect means that once fixed costs are covered, additional sales contribute more directly to profit, amplifying profit growth relative to sales growth.