Internal Rate of Return (IRR) Tutorial
Key Snapshots
IRR Formulas
IRR formula for single cash flow:
![\[IRR = \sqrt[\leftroot{-2}\uproot{2}n]{\frac{CF_n}{I}} - 1\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-759c5cce080274dbb43923f51e8d0a1b_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Here, 
represents the Internal Rate of Return. 
reflects the cash flow that occurs at time 
, and 
denotes the initial investment.
IRR formula for multiple cash flows (using interpolation):
![\[IRR = r_1 + \frac{NPV_1}{NPV_1 - NPV_2}(r_2 - r_1)\]](https://www.ferventlearning.com/wp-content/ql-cache/quicklatex.com-a97fbaa4b78b77c156c7b1e12543de91_l3.svg?495a33&495a33 "Rendered by QuickLaTeX.com")
Here, represents the Internal Rate of Return.
represents the positive Net Present Value that is obtained by using a discount rate 
.
represents the negative Net Present Value that is obtained by using a discount rate 
.
The IRR formula here uses interpolation, relying on the fact that the IRR is the point at which NPV is equal to 0.
IRR formulas on Excel®:
- RATE
- IRR
IRR Use Cases
The IRR is relevant for:
- Capital Budgeting / Investment Appraisal
- Estimating the Yield to Maturity (YTM) of bonds
Related Resources
- Video tutorial on NPV: Net Present Value (NPV) Tutorial
- Articles:
- Course on Investment Appraisal / Capital Budgeting: Investment Appraisal Course
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