1. **State the problem:** We need to find the financial break-even point for Lin's Toys project, which is the number of toy cars sold where the net present value (NPV) of the project is zero. 2. **Given data:** - Machine cost (initial investment) = 485000 - Economic life = 7 years - Selling price per toy = 21 - Variable cost per toy = 6 - Fixed costs per year = 345000 - Corporate tax rate = 0.25 - Discount rate = 0.13 3. **Calculate annual depreciation using straight-line method:** $$\text{Depreciation} = \frac{485000}{7} = 69285.71$$ 4. **Define variables:** Let $Q$ be the number of toys sold per year. 5. **Calculate Earnings Before Tax (EBT):** $$\text{EBT} = (21 - 6)Q - 345000 - 69285.71 = 15Q - 414285.71$$ 6. **Calculate Net Income after tax:** $$\text{Net Income} = \text{EBT} \times (1 - 0.25) = (15Q - 414285.71) \times 0.75$$ 7. **Calculate Operating Cash Flow (OCF):** Add back depreciation (non-cash expense): $$\text{OCF} = \text{Net Income} + 69285.71 = 0.75(15Q - 414285.71) + 69285.71$$ Simplify: $$\text{OCF} = 11.25Q - 310714.28 + 69285.71 = 11.25Q - 241428.57$$ 8. **Financial break-even point occurs when NPV = 0:** NPV formula for an annuity: $$0 = -485000 + \frac{\text{OCF}}{r} \times \left(1 - \frac{1}{(1+r)^7}\right)$$ Where $r=0.13$. Calculate annuity factor: $$AF = \frac{1 - \frac{1}{(1+0.13)^7}}{0.13} = \frac{1 - \frac{1}{2.355}}{0.13} = \frac{1 - 0.4247}{0.13} = \frac{0.5753}{0.13} = 4.425$$ 9. **Set up equation:** $$0 = -485000 + (11.25Q - 241428.57) \times 4.425$$ 10. **Solve for $Q$:** $$485000 = (11.25Q - 241428.57) \times 4.425$$ $$\frac{485000}{4.425} = 11.25Q - 241428.57$$ $$109615.38 = 11.25Q - 241428.57$$ $$11.25Q = 109615.38 + 241428.57 = 351043.95$$ $$Q = \frac{351043.95}{11.25} = 31115.51$$ **Final answer:** The financial break-even point is **31115.51** toy cars per year.