1. **Problem Statement:** Calculate the Net Present Value (NPV) for each of the three options available to Simtech Ltd. and advise on the best option. 2. **Formulas and Concepts:** - NPV formula: $$NPV = \sum_{t=0}^n \frac{C_t}{(1+r)^t}$$ where $C_t$ is net cash flow at time $t$, $r$ is discount rate (10%), and $n$ is project life. - Depreciation (straight-line): $$\text{Depreciation} = \frac{\text{Cost} - \text{Residual value}}{\text{Life}}$$ - Cash flows include revenues, costs, working capital changes, and opportunity costs. 3. **Option A: Manufacture the device** - Initial investment: Plant and equipment = 9 million, Working capital = 30 million - Depreciation per year: $$\frac{9 - 10}{5} = -0.2\text{ million (negative, so check residual value)}$$ Actually, residual value is 10 million, cost 9 million, so depreciation is zero or negative, meaning no depreciation expense. But since residual > cost, depreciation is zero. - Opportunity cost: Rent lost = 1 million per year - Market research cost (0.5 million) is sunk, ignore. - Sales units (in thousands): 800, 1400, 1800, 1200, 500 - Selling prices: Year 1 = 300, Years 2-4 = 220, Year 5 = 200 - Variable cost per unit = 140 - Fixed costs = 24 million per year (including depreciation) - Marketing costs = 20 million per year Calculate yearly revenues: Year 1: $800,000 \times 300 = 240,000,000$ Year 2: $1,400,000 \times 220 = 308,000,000$ Year 3: $1,800,000 \times 220 = 396,000,000$ Year 4: $1,200,000 \times 220 = 264,000,000$ Year 5: $500,000 \times 200 = 100,000,000$ Variable costs: Year 1: $800,000 \times 140 = 112,000,000$ Year 2: $1,400,000 \times 140 = 196,000,000$ Year 3: $1,800,000 \times 140 = 252,000,000$ Year 4: $1,200,000 \times 140 = 168,000,000$ Year 5: $500,000 \times 140 = 70,000,000$ Calculate EBIT (Earnings Before Interest and Tax): $$\text{EBIT} = \text{Sales} - \text{Variable Costs} - \text{Fixed Costs} - \text{Marketing Costs} - \text{Opportunity Cost}$$ Year 1: $$240,000,000 - 112,000,000 - 24,000,000 - 20,000,000 - 1,000,000 = 83,000,000$$ Year 2: $$308,000,000 - 196,000,000 - 24,000,000 - 20,000,000 - 1,000,000 = 67,000,000$$ Year 3: $$396,000,000 - 252,000,000 - 24,000,000 - 20,000,000 - 1,000,000 = 99,000,000$$ Year 4: $$264,000,000 - 168,000,000 - 24,000,000 - 20,000,000 - 1,000,000 = 51,000,000$$ Year 5: $$100,000,000 - 70,000,000 - 24,000,000 - 20,000,000 - 1,000,000 = -15,000,000$$ (loss) Add back depreciation (assumed zero due to residual > cost), so no adjustment. Calculate net cash flows (EBIT + Depreciation - Working capital changes): - Working capital invested immediately = 30 million (outflow at year 0) - Assume working capital recovered at end of year 5 (inflow) Year 0: -9,000,000 (plant) - 30,000,000 (working capital) = -39,000,000 Years 1-4: EBIT as above Year 5: EBIT + working capital recovery = -15,000,000 + 30,000,000 = 15,000,000 Discount cash flows at 10%: $$NPV = -39,000,000 + \frac{83,000,000}{1.1} + \frac{67,000,000}{1.1^2} + \frac{99,000,000}{1.1^3} + \frac{51,000,000}{1.1^4} + \frac{15,000,000}{1.1^5}$$ Calculate each term: $$\frac{83,000,000}{1.1} = 75,454,545$$ $$\frac{67,000,000}{1.21} = 55,371,901$$ $$\frac{99,000,000}{1.331} = 74,354,012$$ $$\frac{51,000,000}{1.4641} = 34,836,065$$ $$\frac{15,000,000}{1.61051} = 9,311,688$$ Sum: $$-39,000,000 + 75,454,545 + 55,371,901 + 74,354,012 + 34,836,065 + 9,311,688 = 210,328,211$$ NPV Option A = 210.33 million 4. **Option B: Royalty** - Sales increase by 10% over Option A units - Units per year (thousands): 880, 1540, 1980, 1320, 550 - Royalty per unit = 50 - Calculate royalty income per year: Year 1: $880,000 \times 50 = 44,000,000$ Year 2: $1,540,000 \times 50 = 77,000,000$ Year 3: $1,980,000 \times 50 = 99,000,000$ Year 4: $1,320,000 \times 50 = 66,000,000$ Year 5: $550,000 \times 50 = 27,500,000$ Discount these at 10%: $$NPV = \sum_{t=1}^5 \frac{\text{Royalty}_t}{(1.1)^t}$$ Calculate: $$\frac{44,000,000}{1.1} = 40,000,000$$ $$\frac{77,000,000}{1.21} = 63,636,364$$ $$\frac{99,000,000}{1.331} = 74,354,012$$ $$\frac{66,000,000}{1.4641} = 45,073,891$$ $$\frac{27,500,000}{1.61051} = 17,073,170$$ Sum: $$40,000,000 + 63,636,364 + 74,354,012 + 45,073,891 + 17,073,170 = 240,137,437$$ NPV Option B = 240.14 million 5. **Option C: Sell patent rights** - Payment: 240 million in two equal instalments - Instalments: 120 million now, 120 million in 2 years - NPV: $$NPV = 120,000,000 + \frac{120,000,000}{(1.1)^2} = 120,000,000 + 99,173,553 = 219,173,553$$ 6. **Advice:** - Option B has highest NPV (240.14 million), followed by Option A (210.33 million), then Option C (219.17 million). - Recommend Option B: Royalty agreement. 7. **Other factors to consider:** - Control over product and brand (Option A retains control, B and C do not). - Risk and resource commitment (Option A requires capital and operational risk; B and C transfer risk).