# Multiple IRRs

Multiple IRRs occur when a project has more than one internal rate of return. The problem arises where a project has non-normal cash flow (non-conventional cash flow pattern).

Internal rate of return (IRR) is one of the most commonly used capital budgeting tools. Investment decisions are made by comparing IRR of the project under consideration with the hurdle rate. If the IRR is greater than the hurdle rate, the project is accepted, otherwise it is rejected. When there are more than two IRRs, it is not exactly clear which IRR to compare with the hurdle rate.

Conventional cash flows (also called normal cash flows) is a cash flow pattern in which cash flows change sign only once, i.e. all net cash outflows occur at the start of the project, followed by all net cash inflows. In other words, there are continuous streams of net cash inflows or net cash outflows. Non-conventional (also called non-normal cash flows) are cash flows that have 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.

## Example

The following cash flows series illustrate the difference between conventional and non-conventional pattern of cash flows.

Period | 0 | 1 | 3 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

Conventional cash flows (Rs.) | -25,000 | 6,000 | 8,000 | 9,000 | 7,000 | 13,000 |

Non-conventional cash flows (Rs.) | -17,000 | 16,000 | 16,000 | 16,000 | 16,000 | -52,000 |

The first series is the conventional cash-flow pattern, which has one sign change, i.e. it has initial cash out flow followed by five continuous periods of net cash inflows. It has one IRR, which is 18.95%.

The second series is non-conventional cash-flow pattern, which has two sign changes. It has cash outflow followed by cash inflows followed by cash outflow. It has two IRRs, 6.77% and 65.36%. This is the range in which the net present value of the non-conventional cash flow series is positive. The multiple IRR problem poses a series problem to analysts because the decision is not obvious. IRR decision rule involves comparison of project IRR with the hurdle rate. If there are two values for IRR, we do not know which value to compare with hurdle rate.

Due to the multiple IRR problem and the unrealistic reinvestment rate assumption inherent in IRR methodology, net present value is the preferred capital budgeting tool.

Written by Obaidullah Jan, ACA, CFA and last modified on