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How IRR and Cost of Capital Determine Project NPV

Article Quant Q&A · Author: Mohammed
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Summary

The document explains why a project's internal rate of return does not itself determine whether its net present value is positive. IRR is the discount rate that makes the present value of the project's cash flows equal zero; it is a break-even rate for those cash flows, not automatically the rate a firm should use to value them. The firm compares IRR with its cost of capital, which reflects the financing hurdle used to assess the project.

A simple example pairs borrowing at 10% with an investment returning 12%, leaving a positive net cash flow after one period. The explanation also notes that discounting the project's cash flows at its IRR would produce zero NPV, while discounting at a lower cost of capital produces positive NPV in the example. The discussion is conceptual and brief: it assumes the stated cash flows and rates, and does not explore complications such as nonstandard cash flow patterns, multiple IRRs, or differences between project and firm risk.

Key ideas

  • IRR is the discount rate that makes a project's NPV equal zero.
  • A firm assesses a project using its cost of capital rather than automatically discounting at IRR.
  • When project IRR exceeds the applicable cost of capital, the project has positive NPV under the described setup.
  • A project's cash flow pattern and risk affect whether a simple IRR comparison is appropriate.

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StatisticsRisk management
Full text
# How does a firm calculate whether a project will generate positive NPV?


# How does a firm calculate whether a project will generate positive NPV?












I am stuck on how a firm can calculate whether a project can generate positive NPV. In this scenario I will be assuming an efficient market hypothesis.

My lecturer said that if a project has IRR 12%, and the cost of capital is 10%, then you will generate positive NPV.

Though, I don't see why. Since regardless of the percentage cost of capital, the IRR is set at a breakeven point. So should the cost of capital be 20%, then you will still not be generating positive nor negative NPV.

An explanation into what I am missing or don't understand would be greatly appreciated.

Thank you in advance.

## Answer by wgajate (score 1, accepted)

https://quant.stackexchange.com/a/58823

> My lecturer said that if a project has IRR 12%, and the cost of capital is 10%, then you will generate positive NPV.

Let's take a concrete example:

```
Project    Borrow (at 10%)  Invest (at 12%)  Net cashflow
Period 0   + $100 (inflow)  - $100 (outflow)     $0
Period 1   - $110 (outflow) + $112 (inflow)    + $2
```

The net cashflow of $2 at period 1 can be discounted back to period 0 at any discount rate to create a positive NPV.

## Answer by Bob Jansen (score 2)

https://quant.stackexchange.com/a/58794

I think the confusion arises from the definition of break-even point. Given a set of cash flows the IRR is the rate such that negative and positive cash flows balance out. If you were to use this rate for discounting, the NPV would be $0$. However, there is no reason to use the IRR for discounting. It's just a number. A firm should use its cost of capital because that is what it uses to finance projects.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.