Internal Rate of Return under Trail and Error Method using Interpolation and Extrapolation

IRR is the discount rate at which the Net Present Value (NPV) of all future cash flows equals zero. It represents the break-even interest rate or the rate of return expected on a project or investment.

Since solving for IRR analytically is difficult, the trial-and-error method with interpolation (and sometimes extrapolation) is used.

Steps to Calculate IRR (Trial & Error Method):

1. Assume two discount rates, say r1​ and r2​, such that:

   • NPV at r1​ is Positive

   • NPV at r2​ is Negative

2. Use the interpolation formula to find IRR:

Extrapolation (If Needed)

If both NPVs are negative, or the IRR is far beyond known rates, extrapolation may be used. The same formula can be adapted, but it’s less accurate than interpolation and rarely used unless IRR lies outside the expected range.