Ax Ax Ax

Table 5.1 shows the project balances at the end of each year for both 100% and 200% interest rates for the project in Example 5.7. The project starts with a cash inflow of S1000. At a 100% interest rate, the S1000 increases to S2000 over the first year. At the end of the first year, there is a S5000 disbursement, leaving a negative project balance of S3000. At 100% interest, this negative balance increases to $6000 over the second year. This negative S6000 is offset exactly by the S6000 inflow. This makes the project balance zero at the end of the second year. The project balance at the end of the project is the future worth of all the cash flows in the project. Y\ nen the future worth at the end of the project life is zero, the present worth is also zero. This verifies that the 100% is an IRR.

Table 5.1 Project Balances for Example 5.7

End of Year


Now consider the 200% interest rate. Over the first year, the S1000 inflow increases to S3000. At the end of the first year, $5000 is paid out, leaving a negative project balance of S2000. This negative balance grows at 200% to S6000 over the second year. This is offset exactly by the S6000 inflow so that the project balance is zero at the end of the second year. This verifies that the 200% is also an IRR!

Capital Budgeting and Financial Management Resources

The internet can be an excellent source of information about the project comparison methods presented in Chapters 4 and 5. A broad search for materials on the PW, AW, and IRR comparison methods might use key words such -AS financial management or capital budgeting. Such a search can yield very useful supports for practising engineers or financial managers responsible for making investment decisions. For example, one can find short courses on the process of project evaluation using present worth or IRR methods and how to determine the cost of capital in the Education Centre at http: / / Investopedia ( provides online investment resources, including definitions for a wide number of commonly used financial terms.

With more focused key words such as IRR one might find examples of how the internal rate of return is used in practice in a wide range of engineering and other applications. Some consulting companies publish promotional white papers on their websites that provide examples of project evaluation methods. For example, cautionary words on the use of the IRR method and advocacy for the use of ERR (also known as the modified internal rate of return or MIRR) can be found at AIcKinsey's online newsletter, McKinsey on Finance (www. corporate finance.

Source:}. Kelleher and J. .MacCormack, "Internal Rate of Return: A Cautionary Tale," McKinsey on Finance, Issue 12, accessed .May 8, 2008, as follows: http:// downloads/knowledge/ mckinsev_on_fi nance/A IoF_Issue_ 12.pdf

Looking at Table 5.1, it's actually fairly obvious that an important assumption is being made about the initial $1000 received. The IRR computation implicitly assumes that the SI000 is invested during the first period at either 100% or 200%, one of the two IRRs. However, during the first period, the project is not an investment. The project balance is positive. The project is providing money, not using it. This money cannot be reinvested immediatelv in the project. It is simply cash on hand. The $1000 must be invested elsewhere for one year if it is to earn any return. It is unlikely, however, that the $1000 provided by the project in this example would be invested in something else at 100% or 200%. More likely, it would be invested at a rate at or near the company's MYRR.

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