1. **Problem Statement:** Gecrogo Pte. Ltd. plans to develop an online sales system with development cost RM120,000 at Year 0. Operating costs and benefits for Years 1 to 5 are given. Discount rate is 11% with present value factors provided. We need to: (i) Develop a cost-benefit analysis table, calculate cumulative costs, benefits, and payback period. (ii) Calculate Return on Investment (ROI). (iii) Calculate Net Present Value (NPV). (iv) Justify economic feasibility. 2. **Formulas and Important Rules:** - Present Value (PV) = Future Value \times Present Value Factor - Cumulative Cost/Benefit = Sum of costs/benefits up to that year - Payback Period: Time when cumulative benefits equal cumulative costs - ROI = \frac{Total Benefits - Total Costs}{Total Costs} \times 100\% - NPV = \sum_{t=0}^n \frac{Net Cash Flow_t}{(1 + r)^t} = \sum_{t=0}^n Net Cash Flow_t \times PV Factor_t 3. **Calculations:** | Year | 0 | 1 | 2 | 3 | 4 | 5 | |-------|-----|-------|-------|-------|-------|-------| | Development Cost | 120000 | 0 | 0 | 0 | 0 | 0 | | Operating Cost | 0 | 28000 | 30000 | 35000 | 38000 | 50000 | | Total Cost | 120000 | 28000 | 30000 | 35000 | 38000 | 50000 | | Benefit | 0 | 60000 | 65000 | 70000 | 75000 | 80000 | - Cumulative Costs: - Year 0: 120000 - Year 1: 120000 + 28000 = 148000 - Year 2: 148000 + 30000 = 178000 - Year 3: 178000 + 35000 = 213000 - Year 4: 213000 + 38000 = 251000 - Year 5: 251000 + 50000 = 301000 - Cumulative Benefits: - Year 0: 0 - Year 1: 60000 - Year 2: 60000 + 65000 = 125000 - Year 3: 125000 + 70000 = 195000 - Year 4: 195000 + 75000 = 270000 - Year 5: 270000 + 80000 = 350000 - Payback Period: The year when cumulative benefits >= cumulative costs. - At Year 4, cumulative benefits = 270000 < cumulative costs = 251000 (benefits exceed costs here) - At Year 5, benefits = 350000 > costs = 301000 - Payback period is between Year 4 and Year 5. - Calculate exact payback period: $$\text{Payback Period} = 4 + \frac{251000 - 270000}{80000} = 4 + \frac{-19000}{80000} = 4 - 0.2375 = 3.76 \text{ years}$$ Since negative fraction means payback occurs before Year 4, re-check: Actually, cumulative benefits at Year 4 = 270000 > 251000 costs, so payback occurs during Year 4. Calculate fraction of Year 4: $$\text{Payback Period} = 3 + \frac{213000 - 195000}{75000} = 3 + \frac{18000}{75000} = 3 + 0.24 = 3.24 \text{ years}$$ Correct payback period is approximately 3.24 years. 4. **ROI Calculation:** - Total Benefits (sum over 5 years) = 60000 + 65000 + 70000 + 75000 + 80000 = 350000 - Total Costs = Development + Operating = 120000 + (28000 + 30000 + 35000 + 38000 + 50000) = 120000 + 181000 = 301000 - ROI: $$ROI = \frac{350000 - 301000}{301000} \times 100\% = \frac{49000}{301000} \times 100\% \approx 16.28\%$$ 5. **NPV Calculation:** - Calculate Net Cash Flow each year = Benefits - Operating Costs (Year 0 is development cost only): - Year 0: -120000 - Year 1: 60000 - 28000 = 32000 - Year 2: 65000 - 30000 = 35000 - Year 3: 70000 - 35000 = 35000 - Year 4: 75000 - 38000 = 37000 - Year 5: 80000 - 50000 = 30000 - Multiply each by Present Value Factor: - Year 0: -120000 \times 1.0000 = -120000 - Year 1: 32000 \times 0.9009 = 28829 - Year 2: 35000 \times 0.8116 = 28406 - Year 3: 35000 \times 0.7312 = 25592 - Year 4: 37000 \times 0.6587 = 24372 - Year 5: 30000 \times 0.5935 = 17805 - Sum all: $$NPV = -120000 + 28829 + 28406 + 25592 + 24372 + 17805 = 17504$$ - Rounded to nearest Ringgit: RM17504 6. **Economic Feasibility Justification:** - Payback period is about 3.24 years, which is less than project duration (5 years), indicating investment recovery within project life. - ROI is positive at 16.28%, showing profitability. - NPV is positive (RM17504), indicating the project adds value and is financially viable. **Final answers:** - Payback Period: Approximately 3.24 years - ROI: 16.28% - NPV: RM17504 These results suggest the project is economically feasible and worth pursuing.