# NPVCalc - Institutional Net Present Value & Capital Budgeting Platform

> NPVCalc (https://npvcalc.info) provides high-precision discounted cash flow (DCF), Net Present Value (NPV), and Internal Rate of Return (IRR) valuation tools, mathematical proofs, and spreadsheet implementations for corporate finance, commercial real estate, and investment appraisal.

## Core Calculators & Tools

- [NPV Calculator (Annual)](https://npvcalc.info/): Discount annual cash flows, calculate Profitability Index (PI) and discounted payback period, test hurdle rate sensitivity (5%–20%), and export CSV models.
- [IRR Calculator](https://npvcalc.info/irr-calculator): High-precision numerical bisection solver for Internal Rate of Return with Descartes' sign-reversal checks and NPV sensitivity curves.
- [Monthly NPV Calculator](https://npvcalc.info/monthly-npv-calculator): Periodic monthly discounting with mathematically exact effective compounding `r_m = (1+r)^(1/12) - 1` for commercial leases, SaaS MRR, and equipment loans.
- [NPV of Perpetuity Calculator](https://npvcalc.info/npv-of-perpetuity): Infinite series valuation for constant perpetuities `PV = C / r` and Gordon Growing Perpetuities `PV = C_1 / (r - g)` for DCF Terminal Value calculations.

## Theoretical Guides & Spreadsheet Solutions

- [NPV vs IRR Analysis](https://npvcalc.info/npv-vs-irr): Comparative guide solving mutually exclusive project conflicts, scale discrepancies, reinvestment rate paradoxes, and Incremental IRR (`ΔIRR`).
- [NPV Formula & Manual Calculation Steps](https://npvcalc.info/npv-formula): Mathematical derivation, Sigma notation, discount factor tables (5%–15%), and manual arithmetic walkthroughs.
- [NPV in Excel & The Year 0 Timing Bug](https://npvcalc.info/npv-in-excel): Formula generator and tutorial explaining why `=NPV(rate, CF0:CFn)` incorrectly discounts Year 0, and how `=NPV(rate, CF1:CFn) + CF0` and `=XNPV()` provide exact solutions.
- [Calculation Methodology & Proofs](https://npvcalc.info/methodology): Transparent documentation of numerical tolerances (`10^-7`), floating-point standards, and academic literature citations.
- [About & Editorial Standards](https://npvcalc.info/about): Information regarding the financial modeling engineering team, CFA review board, and editorial guidelines.

## Mathematical Formulas

- **Discrete Annual NPV:** `NPV = ∑ [ CF_t / (1 + r)^t ] - CF_0`
- **Internal Rate of Return:** Root `r` where `∑ [ CF_t / (1 + r)^t ] - CF_0 = 0`
- **Effective Monthly Rate:** `r_m = (1 + r_annual)^(1/12) - 1`
- **Constant Perpetuity:** `PV = C / r`
- **Growing Perpetuity:** `PV = C_1 / (r - g)` where `r > g`
- **Profitability Index:** `PI = (∑ PV of Future Cash Flows) / CF_0`

## Full Documentation

- [Full LLM Specification](https://npvcalc.info/llms-full.txt): Complete mathematical formulas, algorithm specifications, and entity definitions for AI models.