Internal Rate of Return – IRR Definition, Formula and Calculation with Examples

internal-rate-of-return-formula

Everyone knows how important capital budgeting is in order to get a proper estimate of the profitability of potential investments. However, the metric used to calculate this is known as the internal rate of return (IRR). The IRR (internal rate of return) is a discount rate, which further makes the NPV (net present value) of every cash flow from a specific project equal to zero. You have to use the same formula to calculate IRR as you are required to calculate the NPV.

What is the formula for calculating the internal rate of return of a business?

It is of prime importance in business to calculate and make a note of the internal rate of return as it helps plan for the company’s future expansion and growth. Further mentioned below is the formula that can be used to effectively calculate the internal rate of return of a company.

IRR=NPV=t=1T(1+r)tCt​​C0=0

In this formula,

C0=total initial investment costs

Ct​=net cash inflow through the period

(t)

r=the discount rate, and

t=the number of time periods​

With this formula and the values, the internal rate of return (IRR) can be easily calculated. You will just have to set the net present value (NPV) to zero and solve the equation for the discount rate (r), which will give you the IRR. However, with this formula, you cannot calculate the IRR analytically, given the nature of the formula and should either try a trial and error method or you can use software which is programmed to calculate the IRR.

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Usually, it has been seen that the higher the internal rate of return of a project is, the more it is desirable to undertake. However, calculating the internal rate of return of a company can be very beneficial as it is uniform throughout the different types of investments and in addition to that, can also be used to rank multiple prospective projects on a comparatively even basis. Considering that the costs of investments are equal amongst all the given projects, whichever project has the highest internal rate of return will be deemed to be the best and will be undertaken first.

IRR is also sometimes referred to as the ‘discounted cash flow rate of return’ or the ‘economic rate of return’ in the market. The use of the word ‘internal’ here further tells that all external factors such as inflation or the cost of capital have to be omitted while calculating.

What is an alternative way to calculate IRR?

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Although using the formula is considered to be one of the most efficient and effective ways of calculating the IRR of a firm, there is an alternative as well. You can also use Excel to calculate IRR. Essentially, there are two main ways of calculating the internal rates of returns of business in Excel:

  • You can use any one of the three built-in IRR formulas provided in Excel.
  • You can break out the component cash flows and calculate each step separately. Once done, you can use the results from those calculations as inputs to the IRR formula mentioned above. (Since calculating the IRR is derivation, there is no easy way of getting around to the result directly.)

Although the first mentioned sounds much easier to execute, it is the second method that takes the prize and is more used. It is more preferable because a financial model works best when it is detailed, transparent, and easy to audit.

One of the main reasons why the first method is not as widely used is because pilling all the calculations into a formula along with being hectic, can hinder you from seeing what numbers are hard-coded or user inputs. Further mentioned below is an easy example showing how an IRR analysis works with cash flows that are consistent (one-year apart) and known.

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Let’s assume that a company is hired to assess the profitability of said ‘Project KK.’ It is seen the project KK requires funding of $250,000 and is expected to generate after cash flows of worth $100,000 on the first year and witness a growth of $50,000 for each year of the upcoming four years.

In such a case, the initial investment of business is negative as it represents an outflow. In a startup, you invest some money and anticipate a return later. Each estimated cash flow can either be negative or positive and is solely dependent on the estimates of what the project might deliver in the future.

For the example above, the IRR is calculated to be 55.77%. Along with the assumption of a WACC (weighted average cost of capital) of 10%. This project would surely add value.

It is very important to know that the internal rate of return of a company is not the literal dollar value of the project, and this is why the formula separates the NPV calculation from the rest of it. Also, in the formula, it assumes that the company can continually reinvest and further receive a return of 55.77%, which is highly unlikely. This is why it is necessary to assume incremental returns at a risk-free-rate and a MIRR, in this case, 2% and 33% respectively.

Why is Calculating the IRR Necessary?

In the business world, the IRR of a company is thought to be the rate at which a project is going to grow and how much returns it will generate. Although the actual value of the rate of return that the project would actually end up generating will always be different from the assumptions made, a project with a higher IRR value than the others can provide a much better chance of growth in the market.

The value of IRR is also very valuable for corporations to evaluate the stock buyback programs. It is very clear that if a company allocates a certain amount to a stock buyback, its own stock should have a better investment, in turn, a higher IRR, than any other use of the funds for other notable projects, or any other candidate according to the current market prices.

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