Last Updated on September 6, 2026 by Maged kamel
What is the definition of IRR-NPV?
The new Items are IRR and NPV. The first item is the IRR, which stands for the internal rate of Return. The internal rate of Return is the interest rate that makes the net present value equal to 0. The second item is NPV, or the net present value.
What is the NPV?
Net present value -NPV is the difference between the present value of cash inflows and the present value of cash outflows over a period of Time.
The NPV could be positive if your investment is good; if it is negative, it is bad. However, in this post, we are interested in finding the rate i that makes NPV = 0. We will have two examples of the positive and negative NPV quoted from the (math is fun ) site.
The first example is that someone who wants to earn a 10% Return lends his friend $500 now and will receive $550 after one year. It is necessary to calculate the NPV and determine whether it is positive or negative.
We draw the Time scale from 0 to 1, and the vertical axis represents cash inflows/outflows. The $500 will be drawn pointing downwards since it is an outflow.
After a one-year payment of $570 is received, a vertical arrow is drawn for that value. The idea behind estimating NPV is to discount all future inflows to their present value.
These inflows will be pointing upwards. The NPV is estimated by summing all cash inflows and outflows at Time t=0. We consider i=10%. The present value of $570 is =(0.909*570); this value will be added to ($-500). As shown on the next slide, the NPV is $18.18. The 10% investment is achieved as required.
The second case is when the Investor wants a 15% interest rate.
The sample example will be used, but this Time the interest rate i% will be set to 15%. The present value of $570 is obtained and will be =(570/1.15). The NPV is $4.35. This value indicates that this investment is not worthwhile.
A Solved Problem for IRR.
One invests $2000 now and receives 3 yearly payments of $100 each, and in the last year, he receives $2500. We draw the diagram as follows: $2000 is drawn downwards, ;ime is drawn at 0, 1,1, 2, 3-yearntervals,t Time 0 $,2000 is drawn downwards a;t the end of the first year, an00 is drawn upwards.
The same applies to the second and third years, and $2,500 is drawn upward at the end of the third year. We will set the present value to convert the payment to present value and estimate the net present value.
Here,,, the interest is not given;;; we are going to fint the value of I. For every future worth, we will convert it back to its present worth, and the Net present value =0, then $2000 =100*(1/1+i)+100*(1/1+i)^2+100*(1/1+i)^3+2500*(1/1+i)^3
Selecting different values for IRR.
Guessing I=10%.
We use trial and error, assuming i=10%, and then substitute. In this case, the left-hand side is 2000, the right-hand side is $2127.17, and the net present value is $127.17.
But we need the NPV to be zero. This is the case for i = 10%.
I’m guessing I = 12%. For a second trial, we will change the value of I; try I = 12%. The net present value is $6.325; we are approaching zero.
Guessing I=12.4%.Try i=12.4%. After substituting. The net present value is $0.937.
Use an Excel sheet to calculate the IRR.
Now, we open an Excel sheet in tabular form and review the steps we have taken. First, in the first column, we enter the Time values 0, 1, 2, and 3. In the second column, we list the cash flow values as shown in the Excel spreadsheet. For the third year, we allocated $2,600.
For the present value equation, the value equals cash flow/(1+i). The value is = cell B5/(1+c3), first trial as 10%, as referential cell $C$3. Because we will repeat the value with a common i, first estimate C5 = B5/(1 + C$3). Then, press Ctrl+D.
The present value of the cash flow, for instance, when the cash flow = $100, at Time = Time.
The present value=100/(1.10)^1=$90.901, when the cash flow =$100 at time =2 year, the present value=100/(1.10)^1=$82.6446 and etc.
We can use the built-in Excel function to estimate I directly; it’s called PV (present value). We use the negative sign to obtain the required value; the present value = PV ($C$3, A5, 0, B5, 0).
The first item is the value in $ C$ 3. The second item, A5, is the Time in Years. The third item, B5, is the cash flow value for the year.
The fourth item is 0. The PV function yields $ 0 0,000 in cell D5 and $90.91 in cell D6. Open one bracket (interest, the year,0, cash flow,0). The same values are shown in column D from Row 5 to Row 8, with the sum of C11 equal to D11.
For the Present Net Value, we calculate the sum from Time 0 to Time 3, yielding 126.39772. We solved our previous problem by setting i = 1010%, then i =12% (i2 =12)%, then i = 12.40%, for which we obtained -0.938.
For the IRR directly, we made trial-and-error adjustments to obtain a value closer to the IRR and then checked the value that approaches zero.
Use the built-in IRR function in Excel to calculate the IRR.
We use the IRR function in F31, as F31=IF31=IRR() directly gives the internal rate of Return of 12.3816%.
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For the following posts: 8A-What is Capital Recovery?
This is a link to post 5 -Step-by-step illustration of solved problems for P-F value.
For a useful external resource, Engineering Economy, here is a link: A good reference.