Question

Which of the following project(s) may have more than one IRR?
year    0 1 2 3 4 5 6 7
A -$1,000,000 230,000 340,000 90,000 120,000 180,000 200,000 80,000
B -$500,000 230,000 450,000 -120,000 340,000 330,000 -80,000 -20,000
C -$200,000 120,000 110,000 340,000 10,000 90,000 34,000 -100,000
A. A only
B. A and B only
C. B and C only
D. A and C only
E. all of the three

Answer 1

Multiple IRR's for a project will occur only when :

The multiple IRR occur only when at least one future cash inflow of a project is followed by cash outflow. In other words, there is at least one negative value after a positive one, or the signs of cash flows change more than once. Multiple IRR project's will have non-normal cash flow (non-conventional cash flow pattern). Non-normal cash flows are non-continuous streams of net cash outflows and net cash inflows, i.e. net cash outflows may occur at the start of the project, followed by net cash inflows, followed by further net cash outflows.

Project “A” will have only 1 IRR since it is a conventional cash flow pattern. (i.e.) it’s initial cash out flow is followed by 7 continuous periods of net cash inflows only.

The IRR for Project A is 6.61%

1 Project A 2 3 Year Cashflow 4 50 61 72 83 94 -10,00,000.00 2,30,000.00 3,40,000.00 90,000.00 1,20,000.00 1,80,000.00 2,00,000.00 80,000.00 105 11 6 127 13 14 IRR 6.61% 15 Formula Used EIRR(B5:B12) 16

Project B & Project C:

Project B may have multiple IRR's since it is a non-conventional cash-flow pattern, which has 4 sign changes.

Project C may have multiple IRR's since it is a non-conventional cash-flow pattern, which has 2 sign changes.

Thus, Project B & C only (option c) may have more than one IRR.