NPV vs. IRR

1. Introduction

Net Present Value (NPV) and Internal Rate of Return (IRR) are two widely used discounted cash flow (DCF) techniques for evaluating investment opportunities. While both consider the time value of money, they approach investment decisions from different angles, and under certain circumstances, can produce conflicting results.

2. NPV vs. IRR: Key Concepts

2.1. Net Present Value (NPV)

• Definition: NPV calculates the present value of all future cash flows (both inflows and outflows) associated with a project, using a specified discount rate (the required rate of return).
• Measure: It provides an absolute measure of the value that a project adds to the firm in today's dollars.
• Acceptance: Projects are accepted when NPV > 0 (positive value creation) and rejected when NPV < 0 (value destruction).

2.2. Internal Rate of Return (IRR)

• Definition: IRR is the discount rate at which the NPV of a project equals zero. In other words, it's the rate of return a project is expected to yield.
• Measure: It provides a relative measure, which is a percentage rate of return that can be compared with the required rate of return.
• Acceptance: Projects are accepted if IRR is higher than the opportunity cost of capital (the required rate of return). Projects are rejected if IRR < required return.

3. Equivalence of NPV and IRR (For Conventional Projects)

• Conventional Projects: These projects have an initial cash outflow followed by a series of cash inflows. The cash flow pattern has only one sign change (e.g., - + + +).
• Independent Projects: These are projects that do not compete with each other; acceptance of one does not affect the acceptance of others.
• Same Decisions: When evaluating independent conventional projects, both NPV and IRR generally lead to the same accept-or-reject decision:
  • If NPV is positive, IRR is typically greater than the required rate of return.
  • If NPV is negative, IRR is typically less than the required rate of return.
  • If NPV is 0, IRR = required rate of return.

4. Key Differences and When Conflicts Arise

Despite their similarities, NPV and IRR can lead to different decisions under certain situations:

1. Mutually Exclusive Projects:

   • These are projects where choosing one option automatically excludes the others.
   • In such situations, the NPV and IRR methods may rank projects differently based on the timing and size of cash flows.
   • NPV is a better choice here as it directly measures value created whereas IRR may have issues.

2. Non-Conventional Cash Flows:

   • These projects have multiple sign changes in their cash flow patterns (e.g., - + - +).
   • In such cases, IRR can produce multiple rates of return, making its interpretation difficult. The NPV should be preferred in such situations.

5. Key Points

• NPV is a measure of how much value a project adds in absolute terms (today's dollars).
• IRR is a measure of the rate of return of the project.
• NPV is superior because it is more robust and always consistent with wealth maximization.
• Conflicts can happen due to:
  • Timing of cashflows
  • Scale of investments
  • Project life spans.

6. Conclusion

In short, for most conventional independent projects, NPV and IRR give consistent accept-reject decisions. However, when you have mutually exclusive projects or non-conventional cash flows, rely on NPV as your primary method for making sound investment choices that focus on creating and maximizing value.