Can a Project Have a Negative NPV but IRR be Greater than the Cost of Capital?

When evaluating the financial viability of a project, two key metrics are often considered: Net Present Value (NPV) and Internal Rate of Return (IRR). NPV measures the net present value of future cash inflows and outflows, while IRR is the discount rate at which the NPV of the project equals zero. In many cases, these two metrics align, but in certain scenarios, they can produce conflicting results.

The Role of Discount Rate

One of the key factors that can lead to a negative NPV but a positive IRR is the discount rate used. The discount rate, also known as the cost of capital, reflects the required rate of return for the investor. If the discount rate is set relatively high due to a high risk perception, the NPV will be lower or even negative.

Example Scenario

Consider a project with the following cash flows and a discount rate of 10%:

YearNet Cash Flow (€) 0-10,000 14,000 24,000 33,000 41,000

When the NPV is calculated using a discount rate of 10%, the result is:

NPV -10,000 4,000/(1 0.1) 4,000/(1 0.1)^2 3,000/(1 0.1)^3 1,000/(1 0.1)^4 -1,640 €

While the IRR for the same project is:

IRR 46.6%

Impact of Risk Perception on IRR and NPV

Assume that the perception of the project's risk by the investor (using a discount rate of 10%) is significantly higher than the risk perceived by the provider of funds, who is willing to lend at a cost of capital of only 3%. In this scenario, even if the IRR is high, the NPV will be negative:

NPV -10,000 4,000/(1 0.03) 4,000/(1 0.03)^2 3,000/(1 0.03)^3 1,000/(1 0.03)^4 -1,500 €

Here, the higher discount rate (10%) reflects a higher risk perception, resulting in a negative NPV, while the IRR is still positive but lower, at 46.6%.

Understanding Multiple IRRs

It is also worth considering the possibility of multiple IRRs, although this is less common. If the cash flow pattern of the project is such that it has multiple turning points, it can result in multiple IRRs. However, typically, only the highest IRR is considered, and it must be evaluated in the context of the cost of capital.

CASE STUDY: Multiple IRR Scenario

Consider a project with cash flows that could lead to multiple IRRs:

YearNet Cash Flow (€) 0-10,000 13,000 2-1,000 34,000 4-2,000 53,000

In this example, the IRR can be calculated using a financial calculator or software, and it might yield two different rates:

IRR1 12.3%
IRR2 30.1%

However, only IRR1 (12.3%) is typically considered if it exceeds the cost of capital. If IRR2 (30.1%) is less than the cost of capital, it is disregarded.

For a deeper understanding of how venture capital (VC) works and how these concepts apply to the start-up and entrepreneurial world, you can visit my space dedicated to Venture Capital for Entrepreneurs.