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How do you compute IRR?

Updated: 12/9/2022
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13y ago

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You can an online IRR Calculator as the one mentioned in the related section below or you can manually calculate IRR. Manual calculation requires Trial and Error method where we first find two rates at which one NPV is negative and the other positive. Once we have these two rates, we use linear interpolation to approximate the IRR

As an example, say you were considering a project that had an initial cost of $500,000 and you would be expecting six cash inflows at the end of each of the next six year in the following amount $120,000 $115,500 $130,000 $116,500 $117,250 and $200,000.

Here are the calculations as you can get from an online irr calculation tool listed in related link below

Net Cash FlowsCF0 = -500000

CF1 = 120000

CF2 = 115500

CF3 = 130000

CF4 = 116500

CF5 = 117250

CF6 = 200000

Discounted Net Cash Flows at 11%DCF1 = 120000/(1+11%)1 = 120000/1.11 = 108108.11

DCF2 = 115500/(1+11%)2 = 115500/1.2321 = 93742.39

DCF3 = 130000/(1+11%)3 = 130000/1.36763 = 95054.88

DCF4 = 116500/(1+11%)4 = 116500/1.51807 = 76742.16

DCF5 = 117250/(1+11%)5 = 117250/1.68506 = 69582.17

DCF6 = 200000/(1+11%)6 = 200000/1.87041 = 106928.17

NPV Calculation at 11%NPV = 108108.11 + 93742.39 + 95054.88 + 76742.16 + 69582.17 + 106928.17 -500000

NPV = 550157.88 -500000

NPV at 11% = 50157.88

Discounted Net Cash Flows at 16%DCF1 = 120000/(1+16%)1 = 120000/1.16 = 103448.28

DCF2 = 115500/(1+16%)2 = 115500/1.3456 = 85835.32

DCF3 = 130000/(1+16%)3 = 130000/1.5609 = 83285.5

DCF4 = 116500/(1+16%)4 = 116500/1.81064 = 64341.91

DCF5 = 117250/(1+16%)5 = 117250/2.10034 = 55824.25

DCF6 = 200000/(1+16%)6 = 200000/2.4364 = 82088.45

NPV Calculation at 16%NPV = 103448.28 + 85835.32 + 83285.5 + 64341.91 + 55824.25 + 82088.45 -500000

NPV = 474823.71 -500000

NPV at 16% = -25176.29

IRR with Linear InterpolationiL = 11%

iU = 16%

npvL = 50157.88

npvU = -25176.29irr = iL + [(iU-iL)(npvL)] / [npvL-npvU]

irr = 0.11 + [(0.16-0.11)(50157.88)] / [50157.88--25176.29]

irr = 0.11 + [(0.05)(50157.88)] / [75334.17]

irr = 0.11 + 2507.894 / 75334.17

irr = 0.11 + 0.0333

irr = 0.1433

irr = 14.33%

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What does IRR stand for?

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