Question

A colleague asks for your help in finding the discount rate where the NPV=0 for a set of cash flows. You quickly recall that this is the IRR for a project. Answer in %, rounding to 2 decimals.

Year 0 cash flow = -115,000
Year 1 cash flow = 38,000
Year 2 cash flow = 36,000
Year 3 cash flow = 41,000
Year 4 cash flow = 32,000

Answer 1

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

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

NPV = -115,000 + 38000 / (1 + R)¹ + 36,000 / (1 + R)² + 41,000 / (1 + R)³ + 32,000 / (1 + R)⁴

Using trial and error method,i.e., after trying various values for R, lets try R as 10.80%

NPV = -115,000 + 38000 / (1 + 0.1080)¹ + 36,000 / (1 + 0.1080)² + 41,000 / (1 + 0.1080)³ + 32,000 / (1 + 0.1080)⁴

NPV = -115,000 + 34,296.0289 + 29,323.9844 + 30,141.48017 + 21,232.00153

NPV = 0

Therefore, IRR is 10.80%