### Project Description

The **internal rate of return** is a type of measurement that companies use for capital budgeting to determine the profitability of particular projects or investments. Individuals can also utilize the internal rate of return metric when it comes to decision-making for their own investments. Below is the specific formula for Net Present Value (NPV), which is used to derive the IRR.

where:

C_{t} = net cash inflow during the period t

C_{o}= total initial investment costs

r = discount rate, and

t = number of time periods

To calculate IRR using the above formula, simply set the NPV to zero, and then solve for *r *(the discount rate). However, due to the mathematical nature of this formula, the IRR cannot be calculated analytically, and you must either use simple trial-and-error to determine the correct value, or use software programmed to calculate IRR.

The good news is: financial calculators to easily and quickly determine IRR have been available for purchase for many years, and a simple Google search will yield dozens of **free online financial calculators** for computing IRR.

**What is IRR used for?**

IRR is an effective method for **measuring the rate of growth** that an investment or project is expected to provide over a specific period of time. For example, a company may be trying to decide whether to build a new manufacturing plant in a different location, or instead expand/renovate existing machinery.

The formula typically specifies the negative cash flow in the first year (all the costs of building or renovating the plant); and then takes into account all the positive cash flows (for example, profits) in the preceding years as a result of operating the new manufacturing plant. Below is an example of an investment project that costs $1,000,000 to undertake, and is expected to produce $200,000 in profits for 7 years. The IRR formula requires an end-point in the number of years for the project, so for simplicity’s sake let us assume this machinery only has a working life of exactly 7 years. The initial outlay at the beginning of the project is referred to as Year 0 (think of Year 0 as *“now”*)*, *while Year 1 refers to the positive cash flows received at the *end* of the first year.

Year 0 -1,000,000 (initial outlay, construction)

Year 1 +200,000 (profits from operations)

Year 2 +200,000

Year 3 +200,000

Year 4 +200,000

Year 5 +200,000

Year 6 +200,000

Year 7 +200,000

Again, for simplicity’s sake, assume the machinery only lasts for 7 years and at which point has no resale value.

Overall it can be viewed as costing $1,000,000 and returning $1,400,000; a seemingly 40% return over 7 years.

However, the IRR is not simply the present value of 40% total interest, reverse-compounded back 7 years. For that to be true would require the project to yield the $1,400,000 total profit all at once at the very end of the term. However, the positive cash flows begin almost immediately. As such, the actual yield on the investment, or the IRR is in fact **9.2% per annum**.

Theoretically, any investment project which produces an IRR that is higher than the company’s **cost of capital** is deemed to be profitable; and from a list of profitable investment options, a company should choose the one with the highest IRR.

** **

**How does IRR apply to me?**

As discussed in the article about budgeting and the 3 accounts, personal finance strategies often emulate corporate finance. (for example, matching short term liabilities with short term assets, medium term with medium, etc.) The same mimicry can be done with IRR. A common scenario for an individual investor would be with commercial real estate or **investment property planning**.

Assume the investor wants to buy a property for $500,000. The bank requires a 20% down payment, and will loan the remaining 80% at 4% interest. He or she plans to hold the property for 5 years, and then sell it on the open market; hoping the price will increase with inflation (3% increase per annum, or to 580,000 after 5 years). The unit will rent for $30,000 per year and the mortgage will cost $23,000. The cash flows would be:

**Year 0 ** -100,000 (down payment)

**Year 1 ** +7,000 (30k rent – 23k mortgage)

**Year 2** +7,000

**Year 3** +7,000

**Year 4** +7,000

**Year 5** +245,000 (+7k net rent, +580k sale price , -352k to pay off mortgage balance)

The above simplified example would produce an impressive **24.1% per annum internal rate of return**. This illustrates the power of leverage, and why it can be so enticing.

**What are the downsides to using IRR as a method of valuation?**

IRR is not a perfect valuation metric. Its most famous flaw is that the formula consists of many different built-in assumptions. Changing just one of the variables can have a large impact on the end result; changing two or more of the variables could yield a completely different outcome altogether.

Using the same investment property example, see below a new scenario that tests these variables:

In this scenario, the rental market will take a small downturn. Assume that in Year 2 the property has no tenant for six months out of the year. Then in Year 3, 4, and 5, the unit is tenanted but at a lower rent (20k instead of 30k). Naturally, decreased average rents tend to go hand in hand with decreased average property prices; and the investor is not able to sell at a small gain, but is instead forced to sell at a loss at the end of Year 5 (400k instead of 580k).

**Year 0** -100,000 (down payment)

**Year 1 ** +7,000 (30k rent – 23k mortgage)

**Year 2 ** -8,000 (only 6 months rent at 30k p.a. =15k rent, and -23k from mortgage)

**Year 3 ** -3,000 (20k rent – 23k mortgage)

**Year 4 ** -3,000

**Year 5 ** +45,000 (-3k net rent, +400k sale price, -352k to pay off mortgage balance)

The above scenario would yield an internal rate of return of **-17.1% per annum**. This illustrates the sobering effect of **leverage** when markets turn against you; and how some seemingly lower-risk investments like real estate can in fact be quite high risk if not properly selected.

**More to keep in mind with IRR**

Another shortcoming of the IRR and NPV methods of valuing investments is the uncertainty of a project’s sustainability or the timing of a large payoff. Some good examples would be an oil or precious metal exploration investment, a pharmaceutical developing a new drug, or a small technology startup. Their cash flows would look something like this:

**Year 0 ** -10,000,000

**Year 1 ** -1,000,000

**Year 2 ** -1,000,000

**Year 3** -1,000,000

**Year 4 ** -1,000,000

**Year 5 ** -1,000,000

**Year 6 ** -1,000,000

**Year 7 ** +200,000,000

This would produce a staggering +49.7% per annum IRR.

However, it begs the questions: What if the company goes bankrupt during the interim 7 years? What if there is some macro-economic or geopolitical event that completely disrupts the project? If everything hinges on one big success: what if they never find the new oil source, or the new medicine does not receive FDA approval, or the technology startup is not purchased by a larger company?

Once understood, and with the help of modern software, the math involved in IRR and NPV calculations is simple and direct. However, it is imperative to think very carefully about the **investment’s sensitivity to key variables**, and how they could impact the specific **annual cash flows**.

[sources]

– Forecasting Cashflows And Internal Rate Of Return – Rue, Joseph C; Volkan, Ara G; Walker, William H. *The Journal of Business Forecasting Methods & Systems ***Vol. 22
– **Uniqueness of the Internal Rate of Return with Variable Life of Investment – Kenneth J. Arrow and David Levhari

*The Economic Journal*Vol. 79

– Uses, Abuses, and Alternatives to the Net-Present-Value Rule – Stephen A. Ross –

*Financial Management*Vol. 24