Question

(Net present value calculation) Big Steve's, makers of swizzle sticks, is considering the purchase of a new plastic stamping machine. This investment requires an initial outlay of $105 comma 000 and will generate net cash inflows of $21 comma 000 per year for 9 years.

a. What is the project's NPV using a discount rate of 7 percent ? Should the project be accepted? Why or why not?

b. What is the project's NPV using a discount rate of 14 percent? Should the project be accepted? Why or why not?

c. What is this project's internal rate of return? Should the project be accepted? Why or why not?

a. If the discount rate is 7 percent, then the project's NPV is $ nothing. (Round to the nearest dollar.)

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 = 21,000 * [1 - 1 / (1 + 0.07)⁹] / 0.07 - 105,000

NPV = 21,000 * [1 - 0.54393] / 0.07 - 105,000

NPV = 21,000 * 6.51523 - 105,000

NPV = $31,820

Project should be accepted as it has a positive NPV

b)

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

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

NPV = 21,000 * [1 - 1 / (1 + 0.14)⁹] / 0.14 - 105,000

NPV = 21,000 * [1 - 0.30751] / 0.14 - 105,000

NPV = 21,000 * 4.94637 - 105,000

NPV = -$1,126

Project should NOT be accepted as it has a negative NPV

c)

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

NPV = 21,000 * [1 - 1 / (1 + R)⁹] / R - 105,000

Using trial and error method, i.e., after trying various values for R, lets try R as 13.70%

NPV = 21,000 * [1 - 1 / (1 + 0.137)⁹] / 0.137 - 105,000

NPV = 0

Therefore IRR is 13.70% or 14%