Internal Rate of Return (IRR) of An Investment

Internal Rate of Return (IRR) shows the actual percentage rate of return from the investment with taking discounting into consideration.

Why is Internal Rate of Return (IRR) of a project important? 

Internal Rate of Return (IRR) gives the rate of discount that yields Net Present Value (NPV) of zero considering the time value of money as it employs the discounting concept.

It uses discounted Cash Flows. Discounted Cash Flows are present values of future Cash Flows.

How to calculate Internal Rate of Return (IRR)?

Internal Rate of Return (IRR) is calculated by considering two Net Present Values (NPVs) with two different discount rates. One of the NPVs should be positive (NPV>0) and another one should be negative (NPV<0).

Internal Rate of Return (IRR) =   R_L + [N_L / (N_L – N_H)] × (R_H – R_L)

where:

R_H = Higher Interest Rate               

R_L = Lower Interest rate

N_L = Net Present Value (NPV) at Lower Interest Rate

N_H = Net Present Value (NPV) at Higher Interest Rate

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Example of calculating Internal Rate of Return (IRR)

A business is thinking about purchasing a new machine at a cost of USD15,000.

In Year 2, the Net Cash Flow is USD10,000.

In Year 4, the Net Cash Flow is USD1

           Year: 1%2%3%4%5%6%7%8%9%10%12%14%1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.893 0.877 2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.797 0.769 3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.712 0.675 4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.636 0.592 5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.567 0.519 6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.507 0.456 7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.452 0.400 8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.404 0.351 9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.361 0.308 10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.322 0.270 11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.287 0.237 12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.257 0.208 13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.229 0.182 14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.205 0.160 15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.183 0.140 16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.163 0.123 17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.146 0.108 18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.130 0.095 19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.116 0.083 20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.104 0.073 

The Net Cash Flows will then be discounted using the discount rate of 12% (R_L=12%) and 20% (R_H=20%) as the Net Present Value (NPV) equals zero somewhere in between these two discount rates. 

Discount Rate = 12%:

In Year 1, the Discounted Net Cash Flow is USD11,850

In Year 3, the Discounted Net Cash Flow is USD6,400.

Now, sum up all the Discounted Net Cash Flows. The total Discounted Net Cash Flows equal to Net Present Value (NPV) being USD3,700).

Discount Rate = 20%:

In Year 1, the Discounted Net Cash Flow is USD10,350

In Year 3, the Discounted Net Cash Flow is USD4,800.

Now, sum up all the Discounted Net Cash Flows. The total Discounted Net Cash Flows equal to Net Present Value (NPV) being -USD1,600).

R_H = 20%          

R_L = 12% 

N_L = 1,600

Internal Rate of Return (IRR) = R_L + [N_L / (N_L – N_H)] × (R_H – R_L)

Internal Rate of Return (IRR) = 12% + [3,700 – (-3,700 / can be compared. Also, different projects can be put in rank order to choose the best investment project – with the highest Internal Rate of Return (IRR). Managers will always be looking for the highest percentage returns from their investments. 

Allows to compare the IRR with the cost of capital. Internal Rate of Return (IRR) is easily compared with the rate of interest. This percentage return of Internal Rate of Return (IRR) can be compared with the expected rate of interest over the life of the investment to make sure that the Net Present Value (NPV) remains positive. 

Allows to compare the IRR with the business’s criterion. Internal Rate of Return (IRR) can also be compared against the pre-set cut-off rate, or criterion of return, so the firm can only choose the most appropriate investments it prefers.

Considers time value of money. Internal Rate of Return (IRR) does consider discounting. It brings to the present value the future Net Cash Flows. The timing of the Net Cash Flows and the size of them (their amounts) in arriving at the final appraisal are taken into consideration. Therefore, Value Internal Rate of Return (IRR) is helpful in evaluating investment projects as it compares project percentage returns from investment while taking the time value of money into account. 

Disadvantages of Internal Rate of Return (IRR) include:

1. Difficult to calculate and use. The calculation is very time consuming and tedious without using the Excel spreadsheet. Just take a look at the formula for calculating Internal Rate of Return (IRR) and what is needed to conduct this calculation.
2. Not comprehensive enough to make final investment decisions. Internal Rate of Return (IRR) should only be regarded as one of the methods to assess competing investments. It could be used as a screening tool to include and eliminate certain projects based on their percentage rate of return adjusted for inflation, but it is inappropriate as a basis for making any sophisticated investment decisions. The results can only be compared with other projects based on profitability, but not based on cash returns adjusted for inflation. A large project worth USD500,000, but the latter may have much higher profitability on a percentage basis. Internal Rate of Return (IRR) does not give a monetary return, so it usually is not considered by itself.

In summary, remember that Investment Appraisal is evaluating the profitability or desirability of an investment project. There are two ways to do it. Quantitative Investment Appraisal is using techniques to study the financial issues of investment (think quantity in terms of percentages and money). And, Qualitative Appraisal which is studying non-financial issues that may impact an investment decision (think quality and impact).