Npv Calculation 42Edca
1. **State the problem:** Calculate the Net Present Value (NPV) of a project with an initial outflow of 65000, Year 1 cash inflow of 22000, and cash inflows increasing by 5% in Years 2 and 3. The discount rate is 11%.
2. **Formula for NPV:**
$$\text{NPV} = -C_0 + \frac{C_1}{(1+r)^1} + \frac{C_2}{(1+r)^2} + \frac{C_3}{(1+r)^3}$$
where $C_0$ is initial outflow, $C_t$ is cash flow at year $t$, and $r$ is discount rate.
3. **Calculate cash flows:**
- Year 1: $C_1 = 22000$
- Year 2: $C_2 = 22000 \times 1.05 = 23100$
- Year 3: $C_3 = 23100 \times 1.05 = 24255$
4. **Calculate present values:**
- $PV_1 = \frac{22000}{(1+0.11)^1} = \frac{22000}{1.11} \approx 19819.82$
- $PV_2 = \frac{23100}{(1.11)^2} = \frac{23100}{1.2321} \approx 18744.88$
- $PV_3 = \frac{24255}{(1.11)^3} = \frac{24255}{1.3676} \approx 17733.51$
5. **Sum present values and subtract initial outflow:**
$$\text{NPV} = -65000 + 19819.82 + 18744.88 + 17733.51 = -65000 + 56398.21 = -8601.79$$
6. **Interpretation:** The NPV is approximately -8601.79, indicating the project would result in a net loss at the given discount rate.
**Final answer:** The closest choice is -8896.66.