A project will produce operating cash flows of €45,000 a year for four years.During the life of the project,inventory will be lowered by €30,000 and trade receivables will increase by €15,000.Trade payables will decrease by €10,000.The project requires the purchase of equipment at an initial cost of €120,000.The equipment will be depreciated straight-line to a zero book value over the life of the project.The equipment will be salvaged at the end of the project creating a €25,000 after-tax cash flow.At the end of the project,net working capital will return to its normal level.What is the net present value of this project given a required return of 14%?

Question

Quizplus · Accepted Answer

To find the net present value (NPV) of the project, we need to calculate the present value of all the cash flows involved in the project, including the initial investment, operating cash flows, salvage value, and changes in working capital.

The initial investment is €120,000, which is a cash outflow at time zero. We can also calculate the present value of the salvage value using the formula (Salvage value/(1+r)^n), where r is the discount rate and n is the life of the project. In this case, salvage value = €25,000, r = 14%, and n = 4. The present value of the salvage value is €18,989.21.

The changes in working capital involve a decrease in inventory by €30,000, an increase in trade receivables by €15,000, and a decrease in trade payables by €10,000. These changes result in an initial cash outflow of €35,000. However, the working capital is expected to return to its normal level at the end of the project, resulting in a cash inflow of €35,000.

To calculate the present value of the operating cash flows, we can use the formula:
CFO*(1-T)/(1+r)^n, where CFO is the annual cash flow, T is the tax rate, r is the discount rate, and n is the year. In this case, CFO = €45,000, T = 0 (since we are given after-tax cash flows), and n = 1, 2, 3, and 4. The present values of the operating cash flows are €39,473.68, €34,693.10, €30,477.97, and €26,799.08, respectively.

Therefore, the total present value of cash flows is €39,473.68+€34,693.10+€30,477.97+€26,799.08-€120,000+€18,989.21+€35,000 = €24,433.96.

The NPV is the difference between the total present value of cash flows and the initial investment, which is €24,433.96-€120,000 = -€95,566.04. Since the NPV is negative, the project should be rejected. The correct answer is C.

A Project Will Produce Operating Cash Flows of €45,000 a Year