1. **State the problem:** Calculate the Net Present Value (NPV) of Project K which costs 52125, has expected net cash inflows of 12000 per year for 8 years, and a Weighted Average Cost of Capital (WACC) of 12%.
2. **Formula for NPV:**
$$\text{NPV} = \sum_{t=1}^{n} \frac{C_t}{(1+r)^t} - C_0$$
where $C_t$ is the cash inflow at year $t$, $r$ is the discount rate (WACC), $n$ is the number of years, and $C_0$ is the initial investment.
3. **Important rule:** The cash inflows are discounted to their present value using the formula for the present value of an annuity since the inflows are equal each year.
4. **Calculate the present value of annuity:**
$$\text{PV} = C \times \frac{1 - (1+r)^{-n}}{r}$$
where $C=12000$, $r=0.12$, $n=8$.
5. **Substitute values:**
$$\text{PV} = 12000 \times \frac{1 - (1+0.12)^{-8}}{0.12}$$
6. **Calculate $(1+0.12)^{-8}$:**
$$1.12^{-8} = \frac{1}{1.12^8} \approx \frac{1}{2.476} = 0.4039$$
7. **Calculate the fraction:**
$$\frac{1 - 0.4039}{0.12} = \frac{0.5961}{0.12} = 4.9675$$
8. **Calculate PV:**
$$12000 \times 4.9675 = 59610$$
9. **Calculate NPV:**
$$\text{NPV} = 59610 - 52125 = 8485$$
10. **Interpretation:** The NPV is positive, so the project is expected to add value.
**Final answer:**
$$\boxed{8485}$$
Npv Project K 484F51
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