## Financial Valuation Concepts – The Internal Rate of Return (IRR)

The **internal rate of return (or IRR)** is a common financial valuation metric used by financial analysts to calculate and assess the financial attractiveness / viability of capital intensive projects or investments.

As the **IRR** is normally easier to understand than the result of a discounted cash flow (DCF) analysis (i.e. the net present value or NPV) for non-financial executives, it is often used to explain and justify investment decisions, although a good financial modeler should know that the **IRR is after all an estimated value, especially when calculated in Excel**, and should be used in conjunction with other financial metrics such as the NPV and comparable valuation multiples when presenting a business or investment case.

So what exactly is the IRR? **The IRR is the interest rate that makes the net present value of all cash flow equal to zero**. In financial analysis terms, the IRR can be defined a discount rate at which the present value of a series of investments is equal to the present value of the returns on those investments.

All projects or investments with an IRR that has been calculated in a financial modeling exercise to be greater than the Weighted Average Cost of Capital (or WACC) should technically be considered as financially viable and accepted.

When choosing between projects or investments whose outcomes or performance are absolutely independent of one another, a good financial modeler should deem the project or investment with the highest calculated IRR to be the most financially attractive, **so long as we continue to keep in mind that the IRR value also needs to be higher than the WACC**.

**Modified Internal Rate Of Return (MIRR)**

The modified IRR (MIRR) is said to reflect the profitability of a project or investment more realistically than an IRR. The reason why this is so is because the IRR assumes the cash flow from an investment or project to be reinvested at the IRR, whereas **the modified IRR assumes that all cash flows to be reinvested at the investor’s / firm’s cost of capital**.

The MIRR is used extensively in **real estate financial analysis** due to the nature and timing of cash flows and investments for real estate investments.

**Dividend IRR**

The ongoing financial returns to investors who own and retain the equity of a business or project is essentially by way of financial / cash dividend payouts.

As equity investors are typically last in rank in the cash flow waterfall, and therefore face the greatest risk of not being paid should the investment turn sour when compared to holders of other forms of ownership in the same investment, equity investors would therefore expect the highest return.

The dividend IRR is therefore used extensively by equity investors to calculate and measure **the discount rate at which the present value of cash dividend payouts equal the present value of equity investments**.

… is because the IRR assumes the cash flow from an investment or project are reinvested at the IRR, …

The IRR does NOT assume that the cash flow (benefits) from an investment or project is reinvested at the IRR. The benefits are paid out of the project as determined by the cash flow.

If you can reinvest the benefits at the IRR, then this does not change the IRR of the project.

William, well spotted and just the check and balance we needed to ensure our content remains of the highest quality.

We have made the necessary edits to the article to make it more concise, and that line now reads “the IRR assumes the cash flow from an investment or project

to bereinvested at the IRR”.This is a very interesting point that you have raised, as it seems that many other sites such as Investopedia and others may have also made the same editorial error. This may potentially be misleading to many corporate finance / financial modeling practitioners and learners.

article is really intresting and useful.

Ball park formula for IRR…example investor put in $1 Million and gets a preferred return for 5 years of 10 percent of his/her monies. At the end of 5 years project sells and net cash flow or cashs proceeds from sale after debt service and expenses paid is $ 5 Million….at IRR of 25 percent on the investment money, how much of the $5 Million has to be paid to the investor realizing that the investor was being paid 10 percent annually for 5 years?

Is there a ball park formula to use without using all sorts of tables and discounted cash flows? Again, any rule of thumb? Anyway, please advise. Thank you.

The article is of great importance for people interested in cost-benefit analysis.

You have done a great job and the explanation is quite simple and understandable.

make the article more simpler so that an non commerce graduates would also be in a better position to understand it

nice one, but please make it simpler so that even a dummy can understand .. thanks

any one know about the detail of IRR calculation? please advice.Thanks

can anyone show an example of IRR when the CF’s for certain years are postive and negative ? thanks

pls give details of ratios under each classified ratio and show how it works independently and dependently for easy understanding.

can anyone explain how to tackle a problem when NPV fluctuates from negative to positive even if discount rate is increased. IRR in this case also keep fluctuating.

any one know about the detail of IRR calculation? please advice.Thanks

irr = A + {a*(B-A)/a+b

where

A = thelower discount rate whoch gives the +ve npv

B = the higher discount rate which gives the-ve npv

a = the value of the +ve npv

b = the value of the -ve npv

please note that a and b should be added toghether as the negative sign in b is ignored.

Trackback:Capital Budgeting and the Pros and Cons of IRR and NPVJan 19th, 2009 at 6:55 am

[…] metrics that have been traditionally used for this process: the net present value (NPV) and the internal rate of return (IRR), along with a secondary derivative of the IRR – the modified internal rate of return […]