Pro Tier Module
IRR / NPV with Geometric Precision
Auditable IRR and NPV with the full solver trail and an honest verdict near the root.
See it run - a worked example, 100% in this browser tab
The problem
Deal and treasury analysts rely on IRR, but most tools return a single rate with no convergence proof and no warning when a near-cancellation makes that IRR ill-conditioned.
The local-first solution
This plugin computes exact in-browser DCF NPV and IRR with a transparent Newton-plus-bisection solver whose full iterate trail is surfaced as a convergence audit, and recomputes the NPV-at-rate sum through the GeoNum kernel to flag conditioning near the root. The cash-flow stream, dates, and rate are all your confirmed inputs and nothing is uploaded.
What it does
Net present value over a periodic cash-flow stream with period 0 today
Internal rate of return via Newton-Raphson with a bisection bracket fallback
XNPV and XIRR with Actual/365 day weighting from the earliest date
Full solver iterate trail (k, rate, NPV) as a convergence audit
Exact UTC calendar day-count arithmetic for irregular schedules
Sign-change warning for non-conventional streams plus a GeoNum conditioning verdict
Honest scope
NPV, its derivative, XNPV, the day counts, and the converged root are exact to the stated tolerance with the residual shown; there is no year-indexed table, so every number is your confirmed input. MIRR, multiple real IRRs beyond the first root found and a sign-change warning, continuous compounding, 30E/360 conventions, and currency are not modeled - a DEGRADED verdict means severe cancellation, not wrong arithmetic, and this is not investment, tax, or financial advice.
Authorities cited
- Brealey, R., Myers, S. & Allen, F. (2020). Principles of Corporate Finance, 13th ed., Ch. 5 - the Net Present Value rule and the definition NPV = sum CF_t/(1+r)^t.
- Brealey, Myers & Allen (2020), Ch. 5 - the Internal Rate of Return: the discount rate r* for which NPV(r*) = 0, and the non-conventional cash-flow / multiple-IRR pitfall.
- Burden, R. L. & Faires, J. D. (2011). Numerical Analysis, 9th ed., Sec. 2.3 - Newton-Raphson method, r_{k+1} = r_k - f(r_k)/f'(r_k), quadratic local convergence.
- Burden & Faires (2011), Sec. 2.1 - the Bisection method on a sign bracket [a,b] with f(a)f(b) < 0, guaranteed linear convergence (the safe fallback).
- Descartes' rule of signs - the number of positive real roots is bounded by the sign changes of the coefficient sequence; a single sign change in the cash-flow stream guarantees a unique real IRR.
- Microsoft Excel XIRR / XNPV documentation - the de-facto irregular-schedule convention: discount by (d_i - d_0)/365 (Actual/365) from the earliest date.
- Goldberg, D. (1991). What Every Computer Scientist Should Know About Floating-Point Arithmetic. ACM Computing Surveys 23(1), 5-48 - catastrophic cancellation of nearly-equal signed sums (why NPV near its root is ill-conditioned).
Compute IRR / NPV now
Run the engine in the browser and route results into a Sandbox workspace, a Worklog case, or a Gate client portal. Nothing is uploaded to anyone's cloud.