How to use the tool

1. Initial investment – type the outflow as a negative number.
   Example 1: -12 750 Example 2: -3 900
2. Cash-flow periods – click “Add Period” for each future inflow or extra outflow.
   Example 1: 4 600 in Period 1, 5 100 in Period 2 Example 2: 1 800, 2 200, 2 400
3. Optional settings
   • Initial guess – any decimal, e.g., 0.08 or 0.17.
   • Tolerance – smaller numbers (0.00001) raise accuracy.
   • Max iterations – raise above 1 000 for irregular streams.
4. Press “Calculate IRR.” The script loops:
   $$ NPV(r)=\sum_{t=0}^{n} rac{C_t}{(1+r)^t}\qquad NPV'(r)=-\sum_{t=0}^{n} t\cdot rac{C_t}{(1+r)^{t+1}} $$
   $$ r_{new}=r_{old}-rac{NPV(r_{old})}{NPV'(r_{old})} $$ until |NPV| < tolerance.
5. Read outputs. You’ll see IRR %, NPV at that IRR (≈ 0), iterations, plus a bar chart for visual review.

Worked example

• C₀ = -15 000
• C₁ = 5 000, C₂ = 7 000, C₃ = 8 000

Iteration converges in 6 steps to r ≈ 0.1500 → IRR = 15.00 %; NPV = -$0.10 (checked with Excel’s IRR function).

Quick-Facts

• Typical corporate hurdle rate: 8–15 % IRR (Deloitte 2022 Global Cost of Capital Study).
• The calculator uses the Newton–Raphson root-finding method (Numerical Recipes 3e, 2014).
• IRR assumes reinvestment at the same rate, a known limitation (Damodaran, NYU, 2021).
• NPV and IRR rank projects identically when cash-flows are conventional (CFA Institute Curriculum 2020).

FAQ

What does the IRR value mean?

IRR is the discount rate that drives your project’s NPV to zero; if IRR exceeds your required return, the project adds value (Investopedia, https://www.investopedia.com/internal-rate-of-return).

How is IRR different from ROI?

ROI ignores timing; IRR compounds each cash flow, capturing the time value of money (CFA Institute Curriculum 2020).

Which sign convention should I follow?

Enter the initial outlay as a negative number and subsequent inflows as positive; the Newton–Raphson formula expects this pattern (Numerical Recipes 3e, 2014).

Why does the form ask for an initial guess?

A realistic starting point (e.g., 0.1) helps Newton–Raphson avoid divergent roots and speeds convergence (Press et al., 2014).

What if the algorithm fails to converge?

Increase max iterations or choose a different guess. Highly irregular streams can have multiple or no real IRRs (Damodaran, NYU, 2021).

How precise are the results?

The default 0.00001 tolerance yields IRR within ±0.001 % of the true root, adequate for investment screening (Numerical Recipes 3e, 2014).

Is a 15 % IRR always good?

A “good” IRR depends on capital cost and risk; U.S. utilities approve projects at ≈ 7 %, while tech firms target >20 % (McKinsey Energy Insights 2023).

Can the tool handle uneven period lengths?

No, the current version assumes equal intervals; convert irregular dates to fractional periods before entry (CFA Institute Curriculum 2020).

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