1. **Problem Statement:** Calculate the Net Present Value (NPV) and Internal Rate of Return (IRR) for PV Co's investment proposal to manufacture Product W33 using the given cash flows and discount rates. 2. **Given Data:** - Initial Investment at Year 0: $-2,000,000$ - Cash flows for Years 1 to 4: $560,000$, $696,028$, $1,350,773$, $392,874$ - Discount rates: 10% and 20% 3. **Formulas:** - NPV formula: $$\text{NPV} = \sum_{t=0}^n \frac{C_t}{(1+r)^t}$$ where $C_t$ is cash flow at year $t$, $r$ is discount rate. - IRR is the rate $r$ that makes $$\text{NPV} = 0$$. 4. **Calculate NPV at 10%:** $$\text{NPV}_{10\%} = -2,000,000 + \frac{560,000}{1.1} + \frac{696,028}{1.1^2} + \frac{1,350,773}{1.1^3} + \frac{392,874}{1.1^4}$$ Calculate each term: - $\frac{560,000}{1.1} = 509,091$ - $\frac{696,028}{1.21} = 575,225$ - $\frac{1,350,773}{1.331} = 1,014,944$ - $\frac{392,874}{1.4641} = 268,230$ Sum of discounted cash flows = $509,091 + 575,225 + 1,014,944 + 268,230 = 2,367,490$ NPV = $-2,000,000 + 2,367,490 = 367,490$ 5. **Calculate NPV at 20%:** $$\text{NPV}_{20\%} = -2,000,000 + \frac{560,000}{1.2} + \frac{696,028}{1.2^2} + \frac{1,350,773}{1.2^3} + \frac{392,874}{1.2^4}$$ Calculate each term: - $\frac{560,000}{1.2} = 466,667$ - $\frac{696,028}{1.44} = 483,364$ - $\frac{1,350,773}{1.728} = 781,349$ - $\frac{392,874}{2.0746} = 189,349$ Sum of discounted cash flows = $466,667 + 483,364 + 781,349 + 189,349 = 1,920,729$ NPV = $-2,000,000 + 1,920,729 = -79,271$ 6. **Calculate IRR:** IRR is the discount rate $r$ such that: $$-2,000,000 + \frac{560,000}{(1+r)} + \frac{696,028}{(1+r)^2} + \frac{1,350,773}{(1+r)^3} + \frac{392,874}{(1+r)^4} = 0$$ Using interpolation between 10% (NPV=367,490) and 20% (NPV=-79,271): $$\text{IRR} \approx 10\% + \frac{367,490}{367,490 + 79,271} \times (20\% - 10\%)$$ $$= 10\% + \frac{367,490}{446,761} \times 10\% \approx 10\% + 8.22\% = 18.22\%$$ 7. **Discussion and Recommendation:** - At 10% discount rate, NPV is positive ($367,490$), indicating the project adds value. - At 20%, NPV is negative ($-79,271$), indicating the project loses value at this higher cost of capital. - IRR is approximately 18.22%, which is between the two discount rates. - If the company’s required rate of return is below 18.22%, the project is financially acceptable. - If the required rate is above 18.22%, the project should be rejected. **Final answers:** - NPV at 10% = $367,490$ - IRR = $18.22\%$ - Investment is acceptable if required return < 18.22%, otherwise reject.