1. **Problem Statement:** PT. Sweet plans to invest 50,000,000 with projected revenues over 5 years. We need to analyze if the new location investment is accepted or rejected using Payback Period, NPV, IRR, and Profitability Index with a 20% interest rate and 20% tax. 2. **Given Data:** - Initial Investment: 50,000,000 - Revenues per year: 50,000,000; 75,000,000; 80,000,000; 140,000,000; 180,000,000 - Tax rate: 20% - Straight line depreciation with zero residual value over 5 years - Interest rate (discount rate): 20% 3. **Step 1: Calculate Annual Depreciation** $$\text{Depreciation} = \frac{\text{Initial Investment}}{\text{Life}} = \frac{50,000,000}{5} = 10,000,000$$ 4. **Step 2: Calculate Earnings Before Tax (EBT) each year** $$\text{EBT}_t = \text{Revenue}_t - \text{Depreciation}$$ Year 1: $50,000,000 - 10,000,000 = 40,000,000$ Year 2: $75,000,000 - 10,000,000 = 65,000,000$ Year 3: $80,000,000 - 10,000,000 = 70,000,000$ Year 4: $140,000,000 - 10,000,000 = 130,000,000$ Year 5: $180,000,000 - 10,000,000 = 170,000,000$ 5. **Step 3: Calculate Tax each year** $$\text{Tax}_t = 0.20 \times \text{EBT}_t$$ Year 1: $8,000,000$ Year 2: $13,000,000$ Year 3: $14,000,000$ Year 4: $26,000,000$ Year 5: $34,000,000$ 6. **Step 4: Calculate Net Income each year** $$\text{Net Income}_t = \text{EBT}_t - \text{Tax}_t$$ Year 1: $32,000,000$ Year 2: $52,000,000$ Year 3: $56,000,000$ Year 4: $104,000,000$ Year 5: $136,000,000$ 7. **Step 5: Calculate Cash Flow each year** Add back depreciation (non-cash expense): $$\text{Cash Flow}_t = \text{Net Income}_t + \text{Depreciation}$$ Year 1: $32,000,000 + 10,000,000 = 42,000,000$ Year 2: $52,000,000 + 10,000,000 = 62,000,000$ Year 3: $56,000,000 + 10,000,000 = 66,000,000$ Year 4: $104,000,000 + 10,000,000 = 114,000,000$ Year 5: $136,000,000 + 10,000,000 = 146,000,000$ 8. **Step 6: Calculate Payback Period** Cumulative cash flow: Year 1: 42,000,000 Year 2: 42,000,000 + 62,000,000 = 104,000,000 Payback period is between year 1 and 2 since initial investment 50,000,000 is recovered before year 2 ends. 9. **Step 7: Calculate NPV** $$\text{NPV} = \sum_{t=1}^5 \frac{\text{Cash Flow}_t}{(1+0.20)^t} - 50,000,000$$ Calculate present values: Year 1: $\frac{42,000,000}{1.2} = 35,000,000$ Year 2: $\frac{62,000,000}{1.44} \approx 43,055,556$ Year 3: $\frac{66,000,000}{1.728} \approx 38,194,444$ Year 4: $\frac{114,000,000}{2.074} \approx 54,969,696$ Year 5: $\frac{146,000,000}{2.488} \approx 58,682,634$ Sum PV = 35,000,000 + 43,055,556 + 38,194,444 + 54,969,696 + 58,682,634 = 229,902,330 NPV = 229,902,330 - 50,000,000 = 179,902,330 10. **Step 8: Calculate IRR** IRR is the discount rate $r$ where NPV = 0: $$0 = \sum_{t=1}^5 \frac{\text{Cash Flow}_t}{(1+r)^t} - 50,000,000$$ By trial or financial calculator, IRR is much higher than 20% since NPV at 20% is positive. 11. **Step 9: Calculate Profitability Index (PI)** $$\text{PI} = \frac{\sum_{t=1}^5 \frac{\text{Cash Flow}_t}{(1+0.20)^t}}{\text{Initial Investment}} = \frac{229,902,330}{50,000,000} = 4.598$$ 12. **Conclusion:** - Payback Period < 2 years (investment recovered quickly) - NPV > 0 (profitable investment) - IRR > 20% (above required rate) - PI > 1 (profitable) Therefore, the investment to add a new location should be **accepted**.