Question

When does a project have multiple or no IRR?

In this situation, how do we make capital budgeting (investment decision)?

Answer 1

We have multiple or no IRRs when the project has non conventional cash flows that is if multiple sign changes are there or there are mutliple inflows and outflows during the life of the project.

In this case we use other capital budgeting technique such as NPV

Answer 2

A project can have multiple or no Internal Rate of Return (IRR) when there are changes in the cash flow patterns over time. This can happen under certain conditions, such as when there are unconventional cash flows, multiple sign changes in cash flows, or non-conventional investment and payout structures. Let's explore each scenario:

1. Multiple IRR:A project can have multiple IRRs when there are alternating periods of cash inflows and outflows, resulting in multiple changes in the direction of the cash flows. In this case, the IRR equation can have multiple roots, leading to multiple solutions for the IRR. Projects with irregular cash flows or complex investment structures, such as mutually exclusive projects, may exhibit multiple IRRs.

2. No IRR:A project can have no IRR when there are no real roots or when the IRR equation has no solutions. This situation typically arises when the cash flows are all negative or when the cash flows do not change sign (all cash inflows or all cash outflows).

Capital Budgeting and Investment Decision:When a project has multiple IRRs or no IRR, traditional IRR analysis becomes problematic. The reason is that the IRR, as a single rate of return, assumes that cash flows are reinvested at the same rate as the IRR itself. This assumption breaks down when there are multiple IRRs or no IRR.

In such cases, it is advisable to use other capital budgeting techniques to make investment decisions. Some of the common alternative techniques include:

1. Net Present Value (NPV):NPV calculates the present value of all future cash flows at a specified discount rate (usually the cost of capital). The decision rule is to accept a project if its NPV is positive. NPV takes into account the timing and magnitude of cash flows, making it a reliable method even in cases of multiple IRRs or no IRR.

2. Profitability Index (PI) or Benefit-Cost Ratio (BCR):PI is the ratio of the present value of cash inflows to the present value of cash outflows. Similarly, BCR is the ratio of the present value of benefits to the present value of costs. Both methods provide a relative measure of project profitability and help in ranking investment options.

3. Modified Internal Rate of Return (MIRR):MIRR addresses the issues of multiple IRRs and is more suitable for unconventional cash flow patterns. It involves discounting negative cash flows to the present and compounding positive cash flows to the end of the project. MIRR provides a single rate of return for ranking investment projects.

4. Payback Period:Payback period measures the time required to recover the initial investment. While it is a simple metric, it does not consider the time value of money and should be used in conjunction with other methods.

In summary, when a project exhibits multiple IRRs or no IRR, it is crucial to employ alternative capital budgeting techniques such as NPV, PI, MIRR, or payback period to make sound investment decisions. These methods provide a more robust evaluation of project profitability and viability, taking into account the complexities of cash flow patterns.