written by | April 25, 2022

Internal Rate of Return (IRR)- Meaning, Formula and Usage

Suppose that you work in a big organisation, and at hand, you have three projects quite similar to each other, but you can only choose two of them. How would you prioritise the projects? And how much will you invest? Using the Internal Rate of Return, companies can make good decisions in their capital budgeting, investing in a sound project that also provides higher returns.

Did you know?

The Internal Rate of Return (IRR) rule states that you should pursue a project or investment if its IRR is greater than the minimum required rate of return, also called the hurdle rate.

Also Read: Everything about Capital Budgeting - Processes and Calculations

What Is the Meaning of IRR in Finance?

What Is an IRR or Internal Rate of Return?

The Internal Rate of Return or IRR refers to the rate which equates to the present value of cash inflows and outflows. If the Net Present Value is positive, you can use a higher discount rate to bring it down to equalise the discount cash inflows and vice versa. You can also say that IRR is a discount rate that makes the NPV of a certain project equal to zero to calculate if the project is worth investing in. Hence, the Internal Rate of Return is the break-even financing rate for the project. Organisations use IRR because the calculation projects the compound annual rate of return earned on an investment. In most cases, the more the IRR for a project, the more attractive the investment option is than a different investment option.

Calculating Internal Rate of Return or IRR

IRR calculation is more complex and challenging than NPV. When you begin to calculate the Internal Rate of Return or IRR, you should consider specific cash flows for the investment and the NPV or Net Present Value should be zero. If that was hard to understand, look at it this way, the cost paid for the investment now will equal the present value of the future cash flows or returns. Hence, the Net Present Value = 0.

(Initial investment= PV of future cash flows= 0).

Typically, the meaning of IRR in finance is once you determine the IRR for a project, it is then compared to the company's cost of capital. If the IRR for the project is equal to or greater than the cost of capital to the company, then the company will think about investing in the project.

IRR Calculation Formula

For non-conventional cash flow, the formula would be

r= the internal rate of return

CFt= cash inflows at different times

Sn= salvage value in period n

Wn= working capital adjustment in period n

C= cash outlays at different periods

K= cut off rate, the rate below which a project will not be accepted, which is usually the cost of capital

n = life of the project

Decision Rule:

If Internal Rate of Return, i.e.

r> k (cut off rate) Accept the investment proposal

r < k Reject the investment proposal

r= k Indifferent.

In case there is more than one investment project, the company can rank the projects based on the IRR of each investment project. And then, the company can choose a project depending on its capacity and preference.

  • Future cash flows are estimated before taxes and before depreciation and interest.
  • The rate of discount that is equal to the present value of its future cash benefits its current investment.       
  • Choose the highest IRR amongst the different choices of investment, which all probably have different internal rates of return. The higher the rate of return, the higher the annual returns that a particular project gives to the company on their investment in the coming future.

Internal Rate of Return or IRR Calculation

The Internal Rate of Return computation is relatively complicated compared to the Present Net Value. One has to follow a trial and error exercise to ascertain the Internal Rate of Return (IRR) which equates to the cash inflows and outflows of the investment proposals. Under NPV, you know the value of K, but under this method.

NPV > 0 r> k (higher rate will be tried)

NPV = Or= k

NPV < 0r< k (lower rate

need to be tried)

RL = The lower rate of discount.

PVCFAT= Calculated present value of cash inflow.

PVC = Present value of cash outlay.

DPV = Difference in calculated present value.

Dr= Difference in rate of interest.

RH = The higher rate of discount.

Decision Rule:

If Internal Rate of Return, i.e.

r> k (cut off rate) Accept the investment proposal

r < k Reject the investment proposal

r= k Indifferent

Let's understand the calculation in different situations

  1. Uniform cash inflows
  2. Non-uniform cash inflows

Example

Let us consider a project where the initial investment of ₹18,000.

The annual inflow will be ₹5,600 for five years. You can calculate the internal rate of return as

F= I/C

where

F= factor to be located

1 = Initial investment

C= Average cash inflow

= ₹18,000/ ₹5600

 = 3.214

After calculating the factor as above, you can locate it in the different annuity tables on the line representing the number of years corresponding to the project's economic life.

In the above example, according to the annuity table, the factor closest to 3.21 for five years are 16% and 17%.

Rate of Discount

16%

 

17%

       

Total Present Value

5,600 x 3.274 =< 18,334.40

 

5,600 x 3.199 = < 17,914.40

Less: initial outlay

18,000.00

 

18,000.00

NPV

334.4

 

-85.6

Net Present Value is greater than zero ₹334.40 at a 16% discount rate, and we need a higher discount rate to equalise Net Present Value with total outlay. ₹ -85.60 at a 17% discount rate; we need a lower rate. So, the above exercise shows that the Internal Rate of Return lies between 16% and 17%. for the exact figure, you can use interpolation i.e.

PVCFAT = 18334.40

PVc = 18000

ΔPV = 420

Δr = 1

IRR = 16 + 334/420 x 1 = 16 + .8 = 16.8%

Similar to this, you can also alternatively use it for a higher rate of return.

Under non-uniform cash inflows,

You can understand the Internal Rate of Return process with the help of the following illustration, i.e. Company A is proposed to install a machine.

The cost of the said machine will be ₹16,200 with a lifespan of 3 years. The annual inflow shall be ₹8,000, ₹7,000, and ₹6,000 in the 3 years.

Calculate Internal Rate of Return.

The average cash inflow = 8000 + 7000+6000/3 = 7000

F = I/C = 16200/7000 = 2.314

The factor closest to 2.314 for 3 years is 14%, 15% and using 15% we get the NPV = 0.

Also Read: Know How To Calculate Cost of Capital With Examples

How Is the Internal Rate of Return Used For Capital Budgeting?

Management can use the IRR method to determine whether or not a project is economically feasible by simplifying projects to one number. An organisation may decide to proceed with a project if the IRR is greater than its required rate of return or if the project shows a net gain over time.

What Are the Shortcomings of this Method?

  1. Discounted cash flow is the most challenging of the methods discussed above for evaluating projects.
  2. A vital assumption implied by this method is that income will be reinvested (compounding) over the project's economic life at the rate of return on investment. If the Internal Rate of Return differs from the typical earnings rate of the company, the results of this method can be misleading. You can compute the IRR on a project to be 30%, while the company's average rate of return is 15%. The assumption of earning income on income at the rate of 30% is highly unrealistic.  
  3. Depending on calculations, the rate may be negative or a single rate or multiple rates. A project whose cash flow signs change over time may have more than one Internal Rate of Return.

Conclusion

The crucial takeaway about the Internal Rate of Return or IRR is that it is calculated using the same concept as the Net Present Value, except that the Net Present Value is equal to 0. The Internal Rate of Return is ideal when there are multiple investment opportunities and an understanding of the potential annual return rates over time. The Internal Rate of Return helps by enabling the decision-makers to rank the investment options from the highest IRR to the lowest IRR.
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FAQs

Q: Does the Internal Rate of Return consider compounding?

Ans:

While calculating IRR, you can also assume that all the inflow is invested in the business, and thus it doesn't directly take account of compounding.

Q: How to know if the IRR is better?

Ans:

A higher IRR is always better.

Q: Does the cash flow timing affect IRR?

Ans:

Yes, the timing affects the IRR. Calculating the Internal Rate of Return results is highly sensitive to the timing of the cash inflows.

Q: What factors affect the IRR?

Ans:

The rate is often determined while keeping and assessing the cost of capital, risks, opportunities in business, the return rate of similar investments, etc.

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