Exploring the Possibility of Positive NPV when IRR is 0

Net Present Value (NPV) and Internal Rate of Return (IRR) are two key metrics used in financial analysis to evaluate the viability and profitability of an investment. It is often assumed that if the IRR is 0, the NPV must also be 0. However, this is not necessarily the case. This article explores the conditions under which NPV can be positive even when IRR is 0.

Definition Recap

Let's start by defining these two terms:

NPV (Net Present Value): NPV is the sum of the present values of all cash flows discounted at a specific rate. It indicates the additional value an investment adds to the investor. IRR (Internal Rate of Return): IRR is the discount rate that makes the NPV of all cash flows equal to zero. It represents the expected compound annual rate of return that can be realized on an investment.

Conditions for Positive NPV when IRR is 0

It is possible for NPV to be positive even when IRR is 0. This can occur when the cash inflows in later periods are large enough to outweigh the initial outflow when discounted at a higher rate. Here’s a detailed explanation of how this can happen:

Cash Flow Structure

Consider an investment with the following cash flows:

Year 0: Initial investment of $100 (negative cash flow) Year 1: Cash inflow of $10 Year 2: Cash inflow of $10 Year 3: Cash inflow of $10 Year 4: Significant cash inflow of $100

When calculating the IRR, the rate that equates the NPV to zero is determined. In this case, it might yield an IRR of 0 because the cumulative cash inflows during the first three years balance the initial outflow, but the fourth-year inflow is substantial.

Example

To illustrate this, let’s calculate the NPV using a discount rate greater than 0, say 5%:

NPV -100 10/(1 0.05)^1 10/(1 0.05)^2 10/(1 0.05)^3 100/(1 0.05)^4

Conclusion

In summary, even if IRR is 0, NPV can be positive if the investment generates substantial future cash flows that outweigh the initial investment when discounted at a higher rate. However, this distinction is crucial for investment evaluation.

Special Cases: Negative Discount Rates

It is important to note that this scenario can occur under special cases where the discount rate is negative. For example, if you are laundering money and your hurdle rate is -10%, you would be satisfied with an IRR of zero.

NPV and Discount Rates

If the discount rate of a series of cash flows is set to equal the IRR, then the NPV will be exactly zero. Conversely, if the NPV is negative, it means the discount rate exceeds the IRR.

Conventional Cash Flow Stream

In conventional cash flow streams, it is impossible for NPV to be positive if the IRR is zero. This is because there is always some cost involved in a project, which always bears at least a fraction of the cost of capital. Thus, if the IRR of a project is zero, the NPV cannot be positive.

Final Thoughts

To understand precisely when NPV is positive, it is helpful to review the principles of discounted cash flow analysis. The video provided in the reference can offer further insights into this concept.