Question

You are considering the investment project summarized by the cash flows and timeline below. If the discount rate is 7.5%, what is the net present value of this project? Would you accept or reject the project?

a) Year 0: cash outflow (cost) of $2,000
b) Year 1: cash inflow of $1,000
c) Year 2: cash inflow of $1,200
d) Year 3: cash inflow of $1,350
e) Year 4: cash inflow of $750

Answer 1

The net present value (NPV) of the project at a discount rate of 7.5% is $588.35. Since this is a positive value, the project should be accepted as it is likely to add value to the firm.

Step-by-step explanation:

If the discount rate is 7.5%, the net present value (NPV) of the project is calculated by discounting each of the cash inflows and the initial cash outflow to their present values and then summing them up.

• Year 0: -$2,000 (this is already in present-day dollars)
• Year 1: $1,000 / (1 + 0.075)^1 = $930.23
• Year 2: $1,200 / (1 + 0.075)^2 = $1,038.69
• Year 3: $1,350 / (1 + 0.075)^3 = $1,086.96
• Year 4: $750 / (1 + 0.075)^4 = $532.47

To find the NPV, we add the discounted cash inflows and then subtract the initial investment:

NPV = (-$2000) + $930.23 + $1,038.69 + $1,086.96 + $532.47

NPV = $588.35

Since the NPV is positive, you would accept the project because it is expected to add value to the firm.