How to calculate the IRR in finance?

If you know the net cash flows, such as initial cost of the project and expected benefits, you can then find IRR with paper and pencil as listed below . You will need to arrive at two different NPV values one which is positive and the other which is negative. Once we have two rates at which the NPV values are at opposing ends we can use linear interpolation to find IRR

These calculations below are from an online irr calculation tool listed in the related link section

Net Cash Flows

CF₀ = -400000
CF₁ = 100000
CF₂ = 100000
CF₃ = 100000
CF₄ = 100000
CF₅ = 100000
 

Discounted Net Cash Flows at 5%

DCF₁ = 100000/(1+5%)¹ = 100000/1.05 = 95238.1
DCF₂ = 100000/(1+5%)² = 100000/1.1025 = 90702.95
DCF₃ = 100000/(1+5%)³ = 100000/1.15763 = 86383.76
DCF₄ = 100000/(1+5%)⁴ = 100000/1.21551 = 82270.25
DCF₅ = 100000/(1+5%)⁵ = 100000/1.27628 = 78352.62
 

NPV Calculation at 5%

NPV = 95238.1 + 90702.95 + 86383.76 + 82270.25 + 78352.62 -400000
NPV = 432947.68 -400000
NPV at 5% = 32947.68
 

Discounted Net Cash Flows at 10%

DCF₁ = 100000/(1+10%)¹ = 100000/1.1 = 90909.09
DCF₂ = 100000/(1+10%)² = 100000/1.21 = 82644.63
DCF₃ = 100000/(1+10%)³ = 100000/1.331 = 75131.48
DCF₄ = 100000/(1+10%)⁴ = 100000/1.4641 = 68301.35
DCF₅ = 100000/(1+10%)⁵ = 100000/1.61051 = 62092.13
 

NPV Calculation at 10%

NPV = 90909.09 + 82644.63 + 75131.48 + 68301.35 + 62092.13 -400000
NPV = 379078.68 -400000
NPV at 10% = -20921.32
 

IRR with Linear Interpolation

iL = 5%
iU = 10%
npvL = 32947.68
npvU = -20921.32irr = iL + [(iU-iL)(npvL)] / [npvL-npvU]
irr = 0.05 + [(0.1-0.05)(32947.68)] / [32947.68--20921.32]
irr = 0.05 + [(0.05)(32947.68)] / [53869]
irr = 0.05 + 1647.384 / 53869
irr = 0.05 + 0.0306
irr = 0.0806
irr = 8.06%