Pro Tier Module
IRR / NPV with Geometric Precision
Auditable IRR and NPV with the full solver trail and an honest verdict near the root.
This tool runs inside GDBS Pro. What it computes and the authorities it applies are below.
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).
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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.