1. **Problem Statement:** Calculate the Net Present Value (NPV), Internal Rate of Return (IRR), and payback period for a new hand drill project with given costs, sales, inflation, depreciation, tax, and risk parameters. 2. **Key Formulas and Concepts:** - NPV: $$NPV=\sum_{t=0}^n \frac{CF_t}{(1+r)^t}$$ where $CF_t$ is cash flow at year $t$, $r$ is discount rate. - IRR: The discount rate $r$ that makes $NPV=0$. - Payback Period: Time to recover initial investment from cumulative cash flows. - Depreciation (Straight-line): $$\text{Depreciation} = \frac{\text{Cost} - \text{Salvage Value}}{\text{Life}}$$ - Operating Working Capital (OWC): 10% of sales each year. - Sales and variable costs increase by 3% inflation after Year 0. - Tax rate: 25%. 3. **Step-by-step Calculation:** **Step 1: Initial Investment (Year 0)** - Equipment cost = 1,250,000 - Initial OWC = 10% of Year 0 sales - Year 0 sales = 7,500 units * 240 = 1,800,000 - Initial OWC = 0.10 * 1,800,000 = 180,000 - Total initial outflow = 1,250,000 + 180,000 = 1,430,000 **Step 2: Annual Sales and Costs for Years 1 to 5** - Sales price increases 3% annually: $$P_t = 240 \times (1.03)^t$$ - Variable cost increases 3% annually: $$VC_t = 175 \times (1.03)^t$$ - Units sold each year = 7,500 - Non-variable costs start at 100,000 in Year 1 and increase 3% annually: $$NVC_t = 100,000 \times (1.03)^{t-1}$$ **Step 3: Depreciation** - Depreciation per year = $\frac{1,250,000 - 50,000}{5} = 240,000$ **Step 4: Calculate EBIT for each year** $$EBIT_t = (P_t \times 7,500) - (VC_t \times 7,500) - NVC_t - Depreciation$$ **Step 5: Calculate Taxes and Net Income** - Taxes = $EBIT_t \times 0.25$ - Net Income = $EBIT_t - Taxes$ **Step 6: Calculate Operating Cash Flow (OCF)** $$OCF_t = Net\ Income + Depreciation$$ **Step 7: Calculate Change in OWC** - OWC each year = 10% of sales - Change in OWC = $OWC_t - OWC_{t-1}$ **Step 8: Calculate Net Cash Flow (NCF)** $$NCF_t = OCF_t - Change\ in\ OWC_t$$ **Step 9: Add Salvage Value and recover OWC at Year 5** - Salvage value = 100,000 - Recover OWC at Year 5 **Step 10: Calculate NPV** - Use discount rate 10% (average risk) - $$NPV = -Initial\ Investment + \sum_{t=1}^5 \frac{NCF_t}{(1.10)^t} + \frac{Salvage + OWC_5}{(1.10)^5}$$ **Step 11: Calculate IRR** - Find rate $r$ such that $$NPV=0$$ **Step 12: Calculate Payback Period** - Sum cumulative net cash flows until initial investment is recovered. 4. **Summary:** - Initial investment: 1,430,000 - Calculate yearly sales, costs, EBIT, taxes, OCF, changes in OWC, net cash flows. - Discount net cash flows at 10% to find NPV. - IRR is the discount rate making NPV zero. - Payback is year when cumulative cash flow turns positive. This model can be implemented in a spreadsheet for precise numeric results.