Npv Project A 1D403F
1. **State the problem:** Calculate the Net Present Value (NPV) for Project A with an initial investment of 865000 and cash flows over 4 years, given a cost of capital of 13%.
2. **Formula for NPV:**
$$\text{NPV} = \sum_{t=1}^n \frac{C_t}{(1+r)^t} - C_0$$
where $C_t$ is the cash flow at year $t$, $r$ is the discount rate (cost of capital), and $C_0$ is the initial investment.
3. **Given data:**
- Initial investment $C_0 = 865000$
- Cash flows: $C_1=316000$, $C_2=350000$, $C_3=-20000$, $C_4=280000$
- Discount rate $r=0.13$
4. **Calculate present value of each cash flow:**
$$\frac{316000}{(1+0.13)^1} = \frac{316000}{1.13} \approx 279646.02$$
$$\frac{350000}{(1+0.13)^2} = \frac{350000}{1.2769} \approx 274010.94$$
$$\frac{-20000}{(1+0.13)^3} = \frac{-20000}{1.4429} \approx -13866.88$$
$$\frac{280000}{(1+0.13)^4} = \frac{280000}{1.6303} \approx 171712.85$$
5. **Sum the present values:**
$$279646.02 + 274010.94 - 13866.88 + 171712.85 = 711502.93$$
6. **Calculate NPV:**
$$\text{NPV} = 711502.93 - 865000 = -153497.07$$
7. **Interpretation:** The NPV is approximately -153497, which is closest to option b: -153384.40.
**Final answer:** b. -153384.40