IRR vs NPV: Project Selection

Understanding NPV and IRR

Net Present Value (NPV) is a capital budgeting method that calculates the difference between the present value of cash inflows and the present value of cash outflows over a period of time. A positive NPV indicates that the project is expected to be profitable and adds value to the firm, while a negative NPV suggests the project will result in a loss. The formula for NPV is:

NPV = Σ [Cash Flow_t / (1 + r)^t] - Initial Investment

Where:

• Cash Flow_t = Cash flow in period t
• r = Discount rate (cost of capital)
• t = Time period

Internal Rate of Return (IRR), on the other hand, is the discount rate that makes the NPV of all cash flows from a particular project equal to zero. It represents the project’s expected rate of return. If the IRR is greater than the cost of capital, the project is considered acceptable. The IRR is calculated iteratively as it doesn’t have a direct algebraic solution.

Circumstances Leading to Comparable Recommendations

IRR and NPV often lead to the same investment decisions under the following circumstances:

• Conventional Cash Flows: When a project has a typical cash flow pattern – an initial outflow followed by a series of inflows – both methods usually agree.
• Similar Scale of Investment: If projects being compared have roughly the same initial investment, the ranking produced by NPV and IRR will likely be consistent.
• Constant Cost of Capital: When the cost of capital remains stable, the discount rate used in NPV calculations aligns with the interpretation of IRR.

For example, consider two projects, A and B, both with an initial investment of ₹100 crore. Project A has an NPV of ₹20 crore and an IRR of 15%, while Project B has an NPV of ₹15 crore and an IRR of 12%. Both methods would recommend choosing Project A.

Circumstances Leading to Conflicting Recommendations

Conflicts arise when:

• Non-Conventional Cash Flows: Projects with multiple sign changes in cash flows (e.g., initial outflow, inflows, then a large outflow for decommissioning) can lead to multiple IRRs or no IRR at all. This makes IRR unreliable.
• Mutually Exclusive Projects: When choosing between mutually exclusive projects (where accepting one precludes accepting the other), IRR can sometimes lead to suboptimal decisions, especially when projects differ significantly in scale.
• Reinvestment Rate Assumption: IRR implicitly assumes that cash flows are reinvested at the IRR itself, which may not be realistic. NPV assumes reinvestment at the cost of capital, a more conservative and realistic assumption.

Consider two mutually exclusive projects:

IRR would suggest Project X (20% > 15%), but NPV indicates Project Y is more valuable (₹20 > ₹10). This is because Project Y, despite a lower IRR, generates a higher overall value due to its larger scale.

Which Method to Use and Why?

In situations where NPV and IRR conflict, NPV should be used to select the project. This is because:

• Direct Measure of Value: NPV directly measures the increase in shareholder wealth, which is the primary goal of financial management.
• Realistic Reinvestment Rate: NPV uses the cost of capital for reinvestment, a more realistic assumption than IRR’s implicit reinvestment rate.
• Handles Non-Conventional Cash Flows: NPV provides a unique solution even with non-conventional cash flows, unlike IRR which can have multiple or no solutions.
• Consistent with Goal of Maximizing Shareholder Wealth: NPV aligns directly with the principle of maximizing shareholder wealth, a fundamental tenet of corporate finance.