Subjects finance

Npv Project C F5B36E

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Determine if Project C is profitable given an initial investment of 150000 and cash inflows over 4 years with a required rate of return of 10%. 2. **Formula used:** We use the Net Present Value (NPV) formula: $$\text{NPV} = \sum_{t=1}^n \frac{C_t}{(1+r)^t} - C_0$$ where $C_t$ is the cash inflow at year $t$, $r$ is the required rate of return, and $C_0$ is the initial investment. 3. **Calculate present value of each cash inflow:** - Year 1: $\frac{50000}{(1+0.10)^1} = \frac{50000}{1.10} = 45454.55$ - Year 2: $\frac{60000}{(1+0.10)^2} = \frac{60000}{1.21} = 49586.78$ - Year 3: $\frac{70000}{(1+0.10)^3} = \frac{70000}{1.331} = 52573.17$ - Year 4: $\frac{30000}{(1+0.10)^4} = \frac{30000}{1.4641} = 20485.76$ 4. **Sum the present values:** $$45454.55 + 49586.78 + 52573.17 + 20485.76 = 168100.26$$ 5. **Calculate NPV:** $$\text{NPV} = 168100.26 - 150000 = 18100.26$$ 6. **Interpretation:** Since NPV is positive ($18100.26 > 0$), the investment is profitable. **Final answer:** The investment is profitable with an NPV of approximately 18100.26.