1. **Problem Statement:** We are given costs and benefits of a tracking system over 5 years and need to perform cost-benefit analysis including Payback Period, ROI, and NPV with an 8% discount rate. 2. **Given Data:** | Year | Cost | Benefit | |------|-------|---------| | 0 | 50000 | 0 | | 1 | 20000 | 50000 | | 2 | 20000 | 50000 | | 3 | 20000 | 50000 | | 4 | 20000 | 50000 | 3. **Formulas and Rules:** - Payback Period: Time to recover initial investment from net benefits. - ROI = $\frac{\text{Total Benefits} - \text{Total Costs}}{\text{Total Costs}} \times 100$% - NPV = $\sum_{t=0}^n \frac{\text{Net Benefit}_t}{(1 + r)^t}$ where $r=0.08$ (discount rate) 4. **Step a) Payback Period Calculation:** - Calculate net benefit each year: $\text{Benefit} - \text{Cost}$ - Year 0: $0 - 50000 = -50000$ - Year 1: $50000 - 20000 = 30000$ - Year 2: $50000 - 20000 = 30000$ - Year 3: $50000 - 20000 = 30000$ - Year 4: $50000 - 20000 = 30000$ - Cumulative net benefit: - End Year 0: $-50000$ - End Year 1: $-50000 + 30000 = -20000$ - End Year 2: $-20000 + 30000 = 10000$ - Payback occurs between Year 1 and Year 2. - Fraction of Year 2 needed: $\frac{20000}{30000} = 0.67$ years - Payback Period = $1 + 0.67 = 1.67$ years 5. **Step b) ROI Calculation:** - Total Costs = $50000 + 20000 \times 4 = 50000 + 80000 = 130000$ - Total Benefits = $0 + 50000 \times 4 = 200000$ - ROI = $\frac{200000 - 130000}{130000} \times 100 = \frac{70000}{130000} \times 100 = 53.85$% 6. **Step c) NPV Calculation:** - Calculate present value of net benefits each year: - Year 0: $\frac{-50000}{(1+0.08)^0} = -50000.00$ - Year 1: $\frac{30000}{1.08^1} = 27777.78$ - Year 2: $\frac{30000}{1.08^2} = 25720.35$ - Year 3: $\frac{30000}{1.08^3} = 23815.69$ - Year 4: $\frac{30000}{1.08^4} = 22050.65$ - Sum NPV = $-50000 + 27777.78 + 25720.35 + 23815.69 + 22050.65 = 49364.47$ 7. **Step d) Evaluation:** - Payback Period of 1.67 years is short compared to project length (5 years), indicating quick recovery. - ROI of 53.85% shows a good return on investment. - Positive NPV of 49364.47 indicates the project adds value considering the discount rate. **Conclusion:** The tracking system is economically feasible based on payback period, ROI, and NPV analysis.