Question

​(NPV with varying required rates of return​) Big​ Steve's, a maker of swizzle​ sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of ​$130,000 and will generate free cash inflows of $ 18,000 per year for 12 years.

a. If the required rate of return is 7 ​percent, what is the​ project's NPV​?

b. If the required rate of return is 20 ​percent, what is the​ project's NPV​?

c. Would the project be accepted under part ​(a​) or ​(b​)?

d. What is the​ project's IRR​?

Answer 1

a)

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

NPV = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

NPV = 18,000 * [1 - 1 / (1 + 0.07)¹²] / 0.07 - 130,000

NPV = 18,000 * [1 - 0.444012] / 0.07 - 130,000

NPV = 18,000 * 7.942686 - 130,000

NPV = $12,968.35

b)

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

NPV = Annuity * [1 - 1 / (1 + r)ⁿ] / r - Initial investment

NPV = 18,000 * [1 - 1 / (1 + 0.2)¹²] / 0.2 - 130,000

NPV = 18,000 * [1 - 0.112157] / 0.2 - 130,000

NPV = 18,000 * 4.439217 - 130,000

NPV = -

$50,094.10

c)

Project under part A should be accepted as it has a positive NPV. Project under part B should not be accepted as it has a negative NPV.

d)

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

NPV = 18,000 * [1 - 1 / (1 + R)¹²] / R - 130,000

Using trial and error method, i.e., after trying various values for R, let's try R as 8.83%

NPV = 18,000 * [1 - 1 / (1 + 0.0883)¹²] / 0.0883 - 130,000

NPV = 0

Therefore, IRR is 8.83%