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IRR Approximation (Newton)

Approximate IRR for 3-year project. Free online IRR Approximation (Newton) for financial — instant, accurate results, mobile-friendly, no signup needed.

IRR
15.9753%

Derivation

  1. ├── 01Givencf0 = -10000, cf1 = 4000, cf2 = 4500, cf3 = 5000
  2. ├── 02Formula100 × o
  3. └── 03Compute IRR15.97532
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§01What is

Understanding the IRR Approximation (Newton)

The IRR Approximation (Newton) computes IRR from 4 inputs: initial (−), year 1, year 2, year 3. Approximate IRR for 3-year project.

Quick calculators for the math that shouldn’t need a notepad — instant, accurate, private to your browser. The IRR Approximation (Newton) sits in that toolkit — it approximate IRR for 3-year project. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

100 × o

Where

cf0
Initial (−)
cf1
Year 1
cf2
Year 2
cf3
Year 3
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Initial (−) = -10000, Year 1 = 4000, Year 2 = 4500, Year 3 = 5000.

  1. 01Start by noting the input — Initial (−): -10000.
  2. 02Start by noting the input — Year 1: 4000.
  3. 03Start by noting the input — Year 2: 4500.
  4. 04Start by noting the input — Year 3: 5000.
  5. 05Substitute these values into the formula: 100 × o
  6. 06Compute IRR: the calculator returns 15.9753.
  7. 07Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common IRR Approximation (Newton) Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Initial (−) halved

cf0 = -5000 (from -10000)

Keep every other input at its default and halve the initial (−). See how irr responds.

  1. 01New Initial (−): -5000
  2. 02Baseline IRR: 15.9753
  3. 03New IRR: 68.5769
  4. 04IRR increases by 329.3% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Initial (−) doubled

cf0 = -20000 (from -10000)

Keep every other input at its default and double the initial (−). See how irr responds.

  1. 01New Initial (−): -20000
  2. 02Baseline IRR: 15.9753
  3. 03New IRR: -16.8188
  4. 04IRR decreases by 205.3% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Year 1 halved

cf1 = 2000 (from 4000)

Keep every other input at its default and halve the year 1. See how irr responds.

  1. 01New Year 1: 2000
  2. 02Baseline IRR: 15.9753
  3. 03New IRR: 6.42653
  4. 04IRR decreases by 59.8% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Year 1 doubled

cf1 = 8000 (from 4000)

Keep every other input at its default and double the year 1. See how irr responds.

  1. 01New Year 1: 8000
  2. 02Baseline IRR: 15.9753
  3. 03New IRR: 38.5352
  4. 04IRR increases by 141.2% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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