Final answer:
The NPV of project A using a 15 percent discount rate is approximately $1,997.71, which is not one of the provided multiple-choice options. The NPV is calculated by summing the present values of each cash flow, discounted by the 15 percent rate.
correct option is A $1,857
Step-by-step explanation:
The question asks to calculate the Net Present Value (NPV) of a project using a 15 percent discount rate. The cash flows for Project A are as follows: initial investment Co = -3,000, cash inflow in year 1 C1 = +500, year 2 C2 = +1,500, and year 3 C3 = +5,000. We calculate NPV by discounting each of these cash flows to their present value using the formula PV = Cash Flow / (1 + r)^n, where r is the discount rate and n is the number of periods.
First, we calculate the present value for each cash flow:
- PV of C1 = $500 / (1 + 0.15)¹ = $434.78
- PV of C2 = $1,500 / (1 + 0.15)² = $1,133.88
- PV of C3 = $5,000 / (1 + 0.15)³ = $3,429.05
Now, we sum up all present values and subtract the initial investment:
NPV = Co + PV of C1 + PV of C2 + PV of C3 = -3,000 + 434.78 + 1,133.88 + 3,429.05 = $1,997.71
Therefore, none of the provided options (a) $1,857, (b) $3,201, (c) $5,000, and (d) $2,352 are correct. The NPV of the project using a 15 percent discount rate is approximately $1,997.71.