1. **State the problem:** We need to calculate the Net Present Value (NPV) of two projects, A and B, given their cash flows over 3 years and a discount rate of 10%. The NPV helps determine which project is more profitable by considering the time value of money. 2. **Formula for NPV:** $$\text{NPV} = \sum_{t=0}^n \frac{C_t}{(1+r)^t}$$ where $C_t$ is the cash flow at year $t$, $r$ is the discount rate, and $n$ is the number of years. 3. **Calculate NPV for Project A:** $$\text{NPV}_A = \frac{-100000}{(1+0.10)^0} + \frac{30000}{(1+0.10)^1} + \frac{40000}{(1+0.10)^2} + \frac{50000}{(1+0.10)^3}$$ 4. **Calculate each term:** $$\frac{-100000}{1} = -100000$$ $$\frac{30000}{1.10} = 27272.73$$ $$\frac{40000}{1.10^2} = \frac{40000}{1.21} = 33057.85$$ $$\frac{50000}{1.10^3} = \frac{50000}{1.331} = 37566.53$$ 5. **Sum the terms for Project A:** $$\text{NPV}_A = -100000 + 27272.73 + 33057.85 + 37566.53 = -100000 + 97897.11 = -2102.89$$ 6. **Calculate NPV for Project B:** $$\text{NPV}_B = \frac{-100000}{1} + \frac{20000}{1.10} + \frac{40000}{1.21} + \frac{60000}{1.331}$$ 7. **Calculate each term for Project B:** $$-100000$$ $$\frac{20000}{1.10} = 18181.82$$ $$\frac{40000}{1.21} = 33057.85$$ $$\frac{60000}{1.331} = 45079.83$$ 8. **Sum the terms for Project B:** $$\text{NPV}_B = -100000 + 18181.82 + 33057.85 + 45079.83 = -100000 + 96319.50 = -3680.50$$ 9. **Conclusion:** Project A has an NPV of approximately $-2102.89$ and Project B has an NPV of approximately $-3680.50$. Since both NPVs are negative, both projects lose value at a 10% discount rate, but Project A loses less and is therefore the better choice.