Question

What is the net present value of a project with the following cash flows if the discount rate is 12 percent? Year Cash flow 0 −$ 27,500 1 14,800 2 19,400 3 5,200

Multiple Choice $4,881.10 $11,900.00 $4,358.13 $11,035.24 $8,129.06

Answer 1

Net present value = Present value of cash inflows - present value of cash outflows

Net present value = -27,500 + 14,800 / (1 + 0.12)¹ + 19,400 / (1 + 0.12)² + 5,200 / (1 + 0.12)³

Net present value = -27,500 + 13,214.2857 + 15,465.5612 + 3,701.2573

Net present value = $4,881.10

Answer 2

To calculate the Net Present Value (NPV) of the project, we need to discount each cash flow back to present value and then sum them up. The formula for NPV is:

NPV = Σ(Cash flow / (1 + r)^t)

Where: Cash flow = Cash flow in each period r = Discount rate t = Time period

Given the cash flows and the discount rate:

r = 12% = 0.12 Cash flows: -27,500, 14,800, 19,400, 5,200

Let's calculate the NPV:

NPV = (-27,500 / (1 + 0.12)^0) + (14,800 / (1 + 0.12)^1) + (19,400 / (1 + 0.12)^2) + (5,200 / (1 + 0.12)^3)

NPV ≈ (-27,500) + (13,214.29) + (14,115.99) + (3,155.90)

NPV ≈ 2,984.38

So, the Net Present Value (NPV) of the project, with a discount rate of 12 percent, is approximately $2,984.38.

None of the provided multiple-choice options match the calculated NPV exactly. The closest option is $4,358.13, but the correct NPV is $2,984.38.