Question

NPV and IRR Benson Designs has prepared the following estimates for a​ long-term project it is considering. The initial investment is $26,940, and the project is expected to yield​ after-tax cash inflows of $3,000 per year for 14 years. The firm has a cost of capital of 8%.

a.  Determine the net present value​ (NPV) for the project.

b.  Determine the internal rate of return​ (IRR) for the project.

c.  Would you recommend that the firm accept or reject the​ project?

Answer 1

a)

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

net present value = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

net present value = 3,000 * [1 - 1 / (1 + 0.08)¹⁴] / 0.08 - 26,940

net present value = 3,000 * [1 - 0.34046] / 0.08 - 26,940

net present value = 3,000 * 8.24424 - 26,940

net present value = -2,207.29

b)

IRR is the rate of return that makes NPV equal to 0

net present value = 3,000 * [1 - 1 / (1 + R)¹⁴] / R - 26,940

Using trial and error method, i.e., after trying various values for R, let's try R as 6.56%

net present value = 3,000 * [1 - 1 / (1 + 0.0656)¹⁴] / 0.0656 - 26,940

net present value = 3,000 * 8.98098 - 26,940

net present value = 0

Therefore, IRR is 6.56%

3)

We would NOT recommend the project as it has negative NPV and IRR less than 8%