1. **Problem Statement:** Calculate the incremental free cash flow (FCF) from Year 0 to Year 4, then compute the Net Present Value (NPV), Payback Period, and Internal Rate of Return (IRR) for the project. 2. **Given Data:** - R&D costs: 40 million (sunk, exclude from cash flows) - Initial equipment investment: 2 million at Year 0 - Equipment salvage value: 1 million at Year 4 - Initial working capital: 0.2 million at Year 0, recovered at Year 4 - Wholesale price per bar: 2 - Variable cost per bar: 1 - Marketing/Admin costs Year 1: 20 million - Inflation rate: 3.5% per year from Year 2 to 4 - Tax rate: 35% - Sales volumes (millions): Y1=30, Y2=25, Y3=20, Y4=10 - Straight-line depreciation over 4 years - Discount rate: 15% 3. **Step 1: Calculate prices and costs for Years 2-4 with inflation** - Price Year 1 = 2 - Price Year 2 = $2 \times (1+0.035) = 2.07$ - Price Year 3 = $2.07 \times (1+0.035) = 2.14145$ - Price Year 4 = $2.14145 \times (1+0.035) = 2.2154$ Similarly, variable cost Year 1 = 1 - Variable cost Year 2 = $1 \times 1.035 = 1.035$ - Variable cost Year 3 = $1.035 \times 1.035 = 1.0712$ - Variable cost Year 4 = $1.0712 \times 1.035 = 1.1087$ Marketing/Admin costs only in Year 1 = 20 million (no inflation) 4. **Step 2: Calculate depreciation** - Equipment cost = 2 million - Depreciation per year = $\frac{2}{4} = 0.5$ million per year 5. **Step 3: Calculate EBIT (Earnings Before Interest and Taxes) for each year** Formula: $$\text{EBIT} = \text{Revenue} - \text{Variable Cost} - \text{Marketing/Admin} - \text{Depreciation}$$ Calculate revenue and variable cost for each year: - Year 1 Revenue = $2 \times 30 = 60$ million - Year 1 Variable Cost = $1 \times 30 = 30$ million - Year 1 EBIT = $60 - 30 - 20 - 0.5 = 9.5$ million - Year 2 Revenue = $2.07 \times 25 = 51.75$ million - Year 2 Variable Cost = $1.035 \times 25 = 25.875$ million - Year 2 EBIT = $51.75 - 25.875 - 0 - 0.5 = 25.375$ million - Year 3 Revenue = $2.14145 \times 20 = 42.829$ million - Year 3 Variable Cost = $1.0712 \times 20 = 21.424$ million - Year 3 EBIT = $42.829 - 21.424 - 0 - 0.5 = 20.905$ million - Year 4 Revenue = $2.2154 \times 10 = 22.154$ million - Year 4 Variable Cost = $1.1087 \times 10 = 11.087$ million - Year 4 EBIT = $22.154 - 11.087 - 0 - 0.5 = 10.567$ million 6. **Step 4: Calculate tax and net operating profit after tax (NOPAT)** - Tax = EBIT $\times$ 35% - NOPAT = EBIT $\times$ (1 - 0.35) Year 1 NOPAT = $9.5 \times 0.65 = 6.175$ million Year 2 NOPAT = $25.375 \times 0.65 = 16.49375$ million Year 3 NOPAT = $20.905 \times 0.65 = 13.58825$ million Year 4 NOPAT = $10.567 \times 0.65 = 6.86855$ million 7. **Step 5: Calculate operating cash flow (OCF)** OCF = NOPAT + Depreciation (non-cash expense) Year 1 OCF = $6.175 + 0.5 = 6.675$ million Year 2 OCF = $16.49375 + 0.5 = 16.99375$ million Year 3 OCF = $13.58825 + 0.5 = 14.08825$ million Year 4 OCF = $6.86855 + 0.5 = 7.36855$ million 8. **Step 6: Calculate net working capital (NWC) changes** - Initial NWC investment at Year 0 = -0.2 million - Recovered at Year 4 = +0.2 million 9. **Step 7: Calculate total cash flows including equipment and salvage** Year 0: Initial investment = -2 million (equipment) - 0.2 million (NWC) = -2.2 million Year 1: OCF = 6.675 million Year 2: OCF = 16.99375 million Year 3: OCF = 14.08825 million Year 4: OCF + Salvage + NWC recovery = 7.36855 + 1 + 0.2 = 8.56855 million 10. **Step 8: Calculate NPV** Formula: $$\text{NPV} = \sum_{t=0}^4 \frac{CF_t}{(1+0.15)^t}$$ Calculate each term: - Year 0: $\frac{-2.2}{(1.15)^0} = -2.2$ - Year 1: $\frac{6.675}{1.15} = 5.804$ - Year 2: $\frac{16.99375}{1.15^2} = \frac{16.99375}{1.3225} = 12.851$ - Year 3: $\frac{14.08825}{1.15^3} = \frac{14.08825}{1.5209} = 9.263$ - Year 4: $\frac{8.56855}{1.15^4} = \frac{8.56855}{1.749} = 4.899$ Sum: $-2.2 + 5.804 + 12.851 + 9.263 + 4.899 = 30.617$ million 11. **Step 9: Payback Period** Cumulative cash flows: - Year 0: -2.2 - Year 1: -2.2 + 6.675 = 4.475 (positive, payback occurs in Year 1) Payback period is between Year 0 and Year 1. Calculate fraction: $$\text{Payback} = 0 + \frac{2.2}{6.675} = 0.33 \text{ years}$$ 12. **Step 10: IRR** IRR is the discount rate $r$ that makes NPV = 0: $$0 = -2.2 + \frac{6.675}{1+r} + \frac{16.99375}{(1+r)^2} + \frac{14.08825}{(1+r)^3} + \frac{8.56855}{(1+r)^4}$$ Using trial or financial calculator, IRR $\approx 90\%$ (very high due to large cash inflows early). **Final answers:** - Incremental Free Cash Flows (million): Year 0: -2.2, Year 1: 6.675, Year 2: 16.99375, Year 3: 14.08825, Year 4: 8.56855 - NPV = 30.62 million - Payback Period = 0.33 years - IRR $\approx$ 90%