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The more I learn about the discount rate and IRR the more confused I get.... This is related to real estate.

My confusion is that I've read that you should use your desired rate of return for the discount rate. For example, if you want a 10% return, use 10% to discount the future cash flows. If that's telling you your return, what is IRR telling you? And why is it more relevant?

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The IRR is the Discount Rate r* that makes Net Present Value NPV(r*)==0. What this boils down to is two ways of making the same kind of profitability calculation. You can choose a project with NPV(10%)>0, or you can choose based on IRR>10%, and the idea is you get to the same set of projects. That's if everything is well behaved mathematically.

But that's not the end of this story of finance, math, and alphabet soup. For investments that have multiple positive and negative cash flows, finding that r* becomes solving for the roots of a polynomial in r*, so that there can be multiple roots. Usually people use the lowest positive root but really it only makes sense for projects where NPV(r)>0 for r<r* and NPV(r)<0 for r>r*.

To try to help with your understanding, you can evaluate a real estate project with r=10%, find the sum future discounted cash flows, which is the NPV, and do the project if NPV>0.

Or, you can take the future cash flows of a project, find the NPV as a function of the rate r, and find r* where NPV(r*)==0. That r* is the IRR. If IRR=r*>10% and the NPV function is well behaved as above, you can also do the project.

When we don't have to worry about multiple roots, the preceding two paragraphs will select the same identical sets of projects as meeting the 10% return requirement.

  • Thanks for the comments. Is the cost of capital almost always the discount rate? Is it better to use the return on Project X that you could otherwise invest in? I've seen both descriptions. Even though discount rates are subjective, are there some standard guidelines? – Moi Jun 17 '13 at 5:26
  • @Moi It is all just math. If you want to know if your project is profitable at a given interest rate, then you typically use that as the discount rate for DCF and sum to get NPV. You may have heard about DCF and NPV being used by the US Govt and Banks for rejecting loan modifications that otherwise fit some affordability criteria. For that, they allowed the banks to take the 30 yr Freddie Mac PMMS mortgage interest rate and add a premium of 0.0-2.0%. See sigtarp.gov/audit%20reports/npv_report.pdf‎ or perhaps my site armdisarm.com/UnofficialHAMPCalculator – Paul Jun 18 '13 at 6:03

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