Assume a project has the following cash flows: an initial investment of \(-\$10,000\) at time 0, and returns of \$4,000 at the end of each year for 4 years. If the discount rate is 12\%, what is the Net Present Value (NPV) of this project?

• A. \$0
• B. \$2,486
• C. \$1,052
• D. $-1,052

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of Net Present Value (NPV). NPV is a method used to evaluate the profitability of an investment by calculating the present value of all cash inflows and outflows, discounted at a specific rate. The formula for NPV is: $\mathrm{NPV}=\sum \frac{C}{}$_t ( 1+r) t - C₀ Where: - Ct = Cash inflow at time t - r = Discount rate - t = Time period - C0 = Initial investment.
2. Step 2: Identify the cash flows and discount rate from the problem. The initial investment (C0) is $-\mathrm{10,000}$ at time 0, and the cash inflows (Ct) are $\mathrm{4,000}$ at the end of each year for 4 years. The discount rate (r) is $12\%$ or 0.12.
3. Step 3: Break down the NPV calculation into components. For each year (t = 1, 2, 3, 4), calculate the present value of the cash inflow using the formula: $\frac{C}{}$_t (1+r) t . Sum up the present values of all cash inflows.
4. Step 4: Subtract the initial investment (C0) from the total present value of cash inflows. This gives the Net Present Value (NPV). The formula is: $\mathrm{NPV}=\sum \frac{C}{}$_t (1+r) t - C₀ .
5. Step 5: Verify the calculation by ensuring all cash inflows are discounted correctly and the initial investment is subtracted accurately. This will yield the NPV, which can then be compared to the options provided in the problem.