A brief guide to crunching numbers (Part 2)

In the second part of our series on number-crunching, we'll look at Net Present Value (NPV) and Internal Rate of Return (IRR).

A couple of weeks ago, we started to talk about financial methods that are commonly used to assess or justify projects, proposals, and business cases. Today, we'll continue by looking at the methods of Net Present Value (NPV) and Internal Rate of Return (IRR).  If you haven't yet read the first part of this article, please take a look at it here.

Writing about financial methods in a brief blog like this one is an interesting challenge. On the one hand, I have to be accurate; on the other hand, I'm careful not to overwhelm the reader with academic minutia. So, I have chosen to introduce the key principles and avoid the important but excruciating detail.

More on cash flows

There are three groups of cash flows: operating, investment, and financing. Operating cash flows come from the operating activities of the enterprise, such as receiving payments for goods or services, paying staff salary, purchasing inventory, and so on. Investment cash flows take place when capital assets (i.e., those with lasting value, such as equipment, machinery, etc.) are bought or sold, or when investments in securities are bought or sold. Finally, financing cash flows occur when the organization borrows money, issues shares (both inflows), or repays debt or repurchases shares (both outflows).

The two methods we're discussing today completely disregard financing cash flows. For instance, if the organization needs to borrow money to run the project being assessed, the initial cash inflow (loan received) and future cash outflows (repayments) never enter our analysis.

How to compute Net Present Value (NPV)

For a project considered for the immediate, this method provides the answer to the question "So, what is the value or cost of this initiative to us, in today's money?"

There are four steps to NPV, which are illustrated in a simple example at the end:

  1. Choose the investment horizon. How many years of future cash flows should you consider? Choose the number so that you are not ignoring any substantial future cash flows and, on the other hand, so that you don't appear trying to foretell the future. Five to ten years is typical, but may be different for capital-intensive initiatives or some public sector or "common good" projects (such as investment in healthcare or education). Use your best judgment.
  2. Plot future cash flows. Draw the timeline as selected in step 1 and plot projected net cash flows against each of the years. Net cash flow for a year is a sum of all cash flow projected for that year. Say you predict that in Year 5 you will make $5 million in additional profits but will have to pay extra $2 million in salaries and other costs. Well, the net cash flow for that year is $3 million. Remember to only include incremental cash flows that are directly attributable to this project. That is, if you are paying $800 a year in software maintenance today and the project you are considering will raise this number to $1,200, the incremental outflow of cash is $400. You will include it as negative $400 into your NPV calculations.
  3. Discount and sum up. The time value of money notion we discussed last time kicks in here. Net cash flows plotted against your timeline will have to be discounted starting from Year 2 in your investment horizon, but by how much? There is a well-developed theory behind the choice of the discount factor, but it's way out of the boundaries of this article. In short, it represents the cost of capital to the organization at this particular time. I suggest that you approach your financial manager, director or the CFO and say the following: "I'm using discounted cash flow methods to assess value of a project. What would you recommend to use as the discount factor?" Expect to hear a number of 5-15 per cent, much more in highly inflationary economies. Say you were told it is 8 per cent. Divide the second year net cash flow by 1.08, third year cash flow by 1.08 squared, fourth year cash flow by 1.08 cubed, and so on. Sum thus discounted net cash flows and you will have a number, which is your NPV.
  4. Test. Test the sensitivity of the derived NPV against assumptions you made. You may have predicted that as a result of your projects, profits will go up by 10 per cent year on year for the next 10 years. What if they won't? What if they go up by only 5 per cent? Wiggle the numbers to understand weaknesses of your analysis. (Figure A shows a simple case study.)

Figure A

NPV is probably one of the best methods available today, on a balance of usefulness and accuracy vs. complexity. A case can be made against using constant discount rate, and there are methods address this issue, but in practice, they are rarely used due to the level of complexity and the fragile nature of mounting assumptions necessary of their implementation.

The Internal Rate of Return (IRR) Method

Let's say you computed NPV for a project based on the predicted cash flows and some discount factor. You may have arrived to a positive or negative number. Suppose you wanted to know this: what is the discount factor (rate of return) that delivers a breakeven NPV of exactly zero? Such a calculation can be easily done numerically (e.g., in Excel using the Solver add-in). The resulting discount factor is what is known as the Internal Rate of Return.

Often, organizations establish hurdle rates, which a project needs to reach to be accepted. For instance, you may hear something like: "Only projects showing IRR of 20 per cent or higher will be considered."

There are a couple of issues with IRR, which you should be aware of:

  • In certain circumstances, the IRR calculation produces more than one solution. You may end up with, say, an IRR of 5 and 20 per cent. Which one should you choose? It's not clear.
  • IRR is biased towards projects with lower initial investment. It should not be used to compare mutually exclusive projects.
Payback redux

There is a modified payback method in which future cash flows are discounted. This approach removes one of the drawbacks of the payback method.

Final thoughts

Here are some final thoughts to keep in mind when you're digesting the financial information in this blog.

  • There may be plenty of reasons to undertake a project that are not attractive from the perspective of financial analysis. More on non-economic benefits next time.
  • Do not include sunk costs in your analysis. They are irrelevant.
  • Always clearly state all assumptions and data sources.
  • Include opportunity costs, but be realistic in estimating them.
  • A trivial but important observation: Prior to using NPV() function in Excel, very carefully read its description.
  • Comes to financial analysis, conservatism is a virtue.

Ilya Bogorad is the Principal of Bizvortex Consulting Group Inc, a management consulting company located in Toronto, Canada. Ilya can be reached at or (905) 278 4753.


Ilya Bogorad is the Principal of Bizvortex Consulting Group Inc, a management consulting company located in Toronto, Canada. Ilya specializes in building better IT organizations.