Let's solve the problem step by step. --- ### **a) i. Net Present Value (NPV)** #### **Step 1: Initial Data** - **R&D sunk cost** = K250,000 (already spent, ignore for decision-making) - **Initial investment (Plant & Equipment)** = K9,000,000 (depreciated straight-line over 4 years) - **Scrap value (Year 4)** = 10% × 9,000,000 = **K900,000** - **Selling price (Year 1)** = K80/unit; inflation = 4%/yr - **Variable cost (Year 1)** = K35/unit; inflation = 3%/yr - **Fixed cost (Year 1)** = K450,000/yr; inflation = 3%/yr - **Demand (units):** - Year 1: 50,000 - Year 2: 85,000 - Year 3: 100,000 - Year 4: 75,000 - **Tax rate** = 30% - **Real required return** = 12% (assume NPV discount rate is real, so inflate cash flows in real terms or use nominal rate with nominal cash flows) #### **Step 2: Project Cash Flows (Nominal)** Let’s forecast revenues, costs, and compute after-tax cash flows for each year. ##### **a) Revenue Calculation (inflated selling price):** | Year | Units | Price/unit | Revenue | |------|-------|------------|---------| | 1 | 50,000| 80.00 | 4,000,000 | | 2 | 85,000| 83.20 | 7,072,000 | | 3 |100,000| 86.53 | 8,653,000 | | 4 | 75,000| 89.99 | 6,749,250 | Calculation: - Year 2 Price = 80 × 1.04 = 83.20 - Year 3 Price = 83.20 × 1.04 = 86.528 - Year 4 Price = 86.528 × 1.04 = 89.989 ##### **b) Variable Cost Calculation (inflated cost):** | Year | Units | Cost/unit | Total Var Cost | |------|-------|-----------|---------------| | 1 |50,000 |35.00 | 1,750,000 | | 2 |85,000 |36.05 | 3,064,250 | | 3 |100,000|37.13 | 3,713,000 | | 4 |75,000 |38.24 | 2,868,000 | Calculation: - Year 2 Cost = 35 × 1.03 = 36.05 - Year 3 Cost = 36.05 × 1.03 = 37.1415 - Year 4 Cost = 37.1415 × 1.03 = 38.2557 ##### **c) Fixed Costs (inflated):** | Year | Fixed Cost | |------|------------| | 1 | 450,000 | | 2 | 463,500 | | 3 | 477,405 | | 4 | 491,727 | Calculation: - Year 2 = 450,000 × 1.03 = 463,500 - Year 3 = 463,500 × 1.03 = 477,405 - Year 4 = 477,405 × 1.03 = 491,727 ##### **d) Depreciation:** - Annual Depreciation = (Initial cost - Scrap value) / 4 - = (9,000,000 - 900,000) / 4 = 8,100,000 / 4 = **2,025,000 per year** ##### **e) Earnings Before Tax (EBT), Tax, Net Income, and Operating Cash Flow** | Year | Revenue | Var Cost | Fixed Cost | Depreciation | EBT | Tax (30%) | Net Income | Add Depreciation | Net Op. CF | |------|---------|----------|------------|--------------|----------|-----------|------------|------------------|------------| | 1 |4,000,000|1,750,000 |450,000 |2,025,000 |(225,000) | 0 | (225,000) | 2,025,000 | 1,800,000 | | 2 |7,072,000|3,064,250 |463,500 |2,025,000 |1,519,250 |455,775 |1,063,475 | 2,025,000 |3,088,475 | | 3 |8,653,000|3,713,000 |477,405 |2,025,000 |2,437,595 |731,279 |1,706,317 | 2,025,000 |3,731,317 | | 4 |6,749,250|2,868,000 |491,727 |2,025,000 |1,364,523 |409,357 |955,166 | 2,025,000 |2,980,166 | *Year 1 EBT is negative, so no tax.* #### **Step 3: Add Scrap Value and Tax on Scrap (Year 4)** - Sale of scrap: K900,000 - Book value at end: K9,000,000 - (2,025,000 × 4) = K900,000 - Gain/loss on sale: K900,000 - K900,000 = 0 - Thus, **no tax on sale of scrap**. So, **Year 4 total cash flow** = 2,980,166 + 900,000 = **3,880,166** #### **Step 4: Initial Outflow** - Initial investment = **K9,000,000** (Year 0, negative cash flow) #### **Step 5: NPV Calculation (discount at 12%)** NPV = -9,000,000 + (1,800,000/1.12¹) + (3,088,475/1.12²) + (3,731,317/1.12³) + (3,880,166/1.12⁴) Calculate the present value for each year: | Year | Cash Flow | Discount Factor (12%) | PV | |------|-----------|----------------------|------------| | 0 | -9,000,000| 1.000 | -9,000,000 | | 1 | 1,800,000 | 0.8929 | 1,607,220 | | 2 | 3,088,475 | 0.7972 | 2,460,908 | | 3 | 3,731,317 | 0.7118 | 2,656,126 | | 4 | 3,880,166 | 0.6355 | 2,464,212 | **Sum of PVs (years 1-4):** 1,607,220 + 2,460,908 + 2,656,126 + 2,464,212 = **9,188,466** **NPV = Total PV inflows - Initial Outflow** NPV = 9,188,466 - 9,000,000 = **K188,466** --- ### **a) ii. Internal Rate of Return (IRR)** IRR is the rate (r) at which NPV = 0. Set: 0 = -9,000,000 + (1,800,000)/(1+r)¹ + (3,088,475)/(1+r)² + (3,731,317)/(1+r)³ + (3,880,166)/(1+r)⁴ We'll estimate IRR by interpolation between two rates. Already calculated NPV at 12% = +188,466 Let's try at 15%: | Year | CF | Discount Factor (15%) | PV | |------|------------|----------------------|-----------| | 0 | -9,000,000 | 1.000 | -9,000,000| | 1 | 1,800,000 | 0.8696 | 1,565,280 | | 2 | 3,088,475 | 0.7561 | 2,334,334 | | 3 | 3,731,317 | 0.6575 | 2,452,795 | | 4 | 3,880,166 | 0.5718 | 2,217,070 | Total PV = 1,565,280 + 2,334,334 + 2,452,795 + 2,217,070 = 8,569,479 NPV at 15% = 8,569,479 - 9,000,000 = **-430,521** Now interpolate: IRR ≈ 12% + [188,466 / (188,466 + 430,521)] × (15% - 12%) = 12% + [188,466 / 618,987] × 3% = 12% + 0.3046 × 3% = 12% + 0.9138% = **12.91%** So, **IRR ≈ 12.9%** --- ### **b) Brief Discussion (2 marks)** **Findings:** - The NPV at a 12% discount rate is positive (K188,466), indicating the project is expected to create value for shareholders. - The IRR of about 12.9% is slightly above the company’s hurdle rate of 12%. **Advice:** Although the NPV is only slightly positive and the IRR just above the hurdle rate, the project appears to be marginally financially attractive. The company may proceed but should consider the sensitivity of results to key assumptions (e.g., demand, inflation). --- ### **c) Pros and Cons of Accounting Rate of Return (ARR) (5 marks)** **Pros:** 1. **Simplicity:** Easy to understand and calculate using accounting data. 2. **Uses familiar information:** Based on profit figures from financial statements. 3. **Useful for performance evaluation:** Can be compared to required return or other investments. 4. **Focus on profitability:** Highlights impact on reported earnings. **Cons:** 1. **Ignores time value of money:** Does not discount future profits. 2. **Based on accounting profits, not cash flows:** May misrepresent true economic benefit. 3. **Affected by accounting policies:** Depreciation, inventory methods, etc., can distort ARR. 4. **Ignores project size:** Cannot distinguish between projects of different scales with the same ARR. 5. **Ignores timing of profits:** Early vs. late profits treated equally, which can mislead decision making. --- ## **Summary Table** | Part | Value/Result | |------|-----------------| | NPV | K188,466 | | IRR | 12.9% | --- ## **Final Answers** ### **a) i. Net Present Value (NPV):** **K188,466** ### **a) ii. Internal Rate of Return (IRR):** **12.9%** ### **b) Brief discussion and advice:** > The project’s NPV is positive and the IRR is just above the company’s hurdle rate. The project is marginally attractive; management may proceed, but should be cautious as results are sensitive to assumptions. ### **c) Pros and Cons of ARR:** **Pros:** Simple, uses accounting data, easy to compare, performance focus. **Cons:** Ignores time value of money, uses profits not cash, affected by accounting policies, ignores project size and timing of returns. --- **If you need working in Excel or a spreadsheet, let me know!**