Question

Deep Waters, Inc. is using the internal rate of return (IRR) when evaluating projects. Find the IRR for the company’s project. The initial outlay for the project is $397,200. The project will produce the following after-tax cash inflows of Round two decimal points

Year 1: 144,400

Year 2: 89,500

Year 3: 189,600

Year 4: 172,000

Answer 1

IRR is the discount rate which will equate the NPV of the project cash flows to zero.

NPV = -397200 + 144400/(1+r) + 89500/(1+r)² + 189600/(1+r)³ + 172000/(1+r)³ ; where r is the discount rate. Now IRR is the r for which the NPV = 0. We can do trial and error or use excel to calculate the IRR. By trial and error, we get for :

r = 10%, NPV = 67967.27 which is much higher than 0, hence we will try 20%

r = 20%, NPV = - 22044.1, since this is negative hence IRR is less than 20%

at r = 15%, NPV = 19046.71

at r = 17%, NPV = 1768.23

at r = 18%, NPV = -6437.51 ; hence IRR has to be between 17% and 18%. We can total the NPV (ignoring the sign) and divide the NPV at 17% with the total which will be = 1768.23/(1768.23 + 6437.51) = 0.21

Hence we will try at r = 17.21%, NPV = 21 only which is closest to zero. Hence IRR = 17.21%. We can also cross check this level from Excel and the answer is the same at 17.21%