calculate-npv-irr

name	calculate-npv-irr
description	Use when evaluating capital investments, projects, or acquisitions using Net Present Value and Internal Rate of Return analysis
source	CFA Institute curriculum; Brealey Myers "Principles of Corporate Finance"; Fisher "The Theory of Interest" (1930)
tags	["corporate-finance","npv","irr","capital-budgeting"]
verified	true

Calculate NPV and IRR

Calculate Net Present Value (NPV) and Internal Rate of Return (IRR) to make capital allocation decisions that maximize shareholder value.

Why This Is Best Practice

Adopted by: CFA Institute (200,000+ members) teaches NPV as the theoretically superior capital budgeting technique; all investment banks use NPV/IRR in M&A, LBO, and project finance models; Brealey & Myers "Principles of Corporate Finance" is the standard reference for 50+ years across 400+ universities. Impact: Companies that use DCF-based capital budgeting (NPV/IRR) outperform companies using payback period alone by 15–20% on ROIC over 5 years; private equity firms achieving top-quartile returns (IRR >25%) consistently use disciplined NPV/IRR frameworks for all investment decisions. Why best: NPV directly measures value creation in dollars — the only metric that correctly accounts for the time value of money, risk (via discount rate), and the full duration of cash flows. IRR provides the rate-of-return complement for comparison purposes.

Sources: Fisher "The Theory of Interest" (1930); Brealey, Myers & Allen "Principles of Corporate Finance" 13th ed. (2019); CFA Institute — Corporate Issuers Level II; McKinsey "Valuation: Measuring and Managing the Value of Companies" 7th ed. (2020).

Steps

1. Define the investment and its incremental cash flows — identify all cash flows that are incremental to the investment decision: only those that change if the project is accepted. Exclude: sunk costs (already spent), allocated overhead (would exist regardless). Include: cannibalization of existing products, opportunity costs of resources used.

2. Estimate the initial capital outlay (Year 0) — sum all up-front costs: purchase price, installation, training, working capital increase (current assets − current liabilities needed to support the project), and any pre-project cleanup costs.

3. Project operating cash flows for each period — Operating CF = EBIT × (1 − Tax Rate) + Depreciation = Net Income + Depreciation + Non-Cash Charges − ΔWorking Capital. Use after-tax cash flows, not accounting income. Project for the full economic life of the investment.

4. Calculate the terminal value — for projects with value beyond the explicit forecast period: Terminal Value = Final Year CF × (1 + g) ÷ (WACC − g) for a growing perpetuity; or use a terminal multiple (EV/EBITDA × Terminal EBITDA). Include salvage value for equipment. Discount back to Year 0.

5. Select the appropriate discount rate — use WACC for the overall firm's cost of capital if the project has the same risk as the overall firm. Use a higher rate (add a risk premium) for riskier projects; use a lower rate for safer projects. For projects with different capital structures, use APV (Adjusted Present Value).

6. Calculate NPV — NPV = −Initial Investment + CF1/(1+r)^1 + CF2/(1+r)^2 + ... + CFn/(1+r)^n + Terminal Value/(1+r)^n. Decision rule: Accept if NPV > 0 (investment creates value); reject if NPV < 0. For mutually exclusive projects, choose the one with the highest positive NPV.

7. Calculate IRR — IRR is the discount rate at which NPV = 0. Solve iteratively (Excel: =IRR(cash flow range)). Decision rule: Accept if IRR > Hurdle Rate (WACC or required return); reject if IRR < Hurdle Rate. Caution: IRR assumes reinvestment at IRR (unrealistic for high-IRR projects — use MIRR).

8. Calculate Modified IRR (MIRR) where appropriate — MIRR corrects IRR's reinvestment rate assumption: future value of positive cash flows at reinvestment rate ÷ present value of negative cash flows at financing rate, adjusted to the number of periods. More reliable than IRR when cash flows change sign multiple times.

9. Perform sensitivity analysis — calculate NPV at: ±10% revenue, ±10% cost, ±1% discount rate, ±1 year project life. Create a tornado chart showing which variables most affect NPV. Calculate the breakeven value for each key assumption (what does revenue need to be for NPV = 0?).

Rules

• NPV supersedes IRR when they conflict: IRR may rank projects incorrectly; NPV is always the correct decision rule for value maximization.
• Never use accounting income (net income) in NPV calculations — use after-tax cash flows.
• Sunk costs are never included in NPV analysis; only incremental future cash flows matter.
• Model three scenarios (base, upside, downside) and weight them by probability — a single-case NPV overstates confidence.

Common Mistakes

• Ignoring working capital changes — increases in receivables and inventory use cash; inventory build-up at project start is a negative cash flow often missed in models.
• Using nominal cash flows with real discount rates (or vice versa) — inflation must be treated consistently; real cash flows require a real discount rate.
• Relying solely on IRR for mutually exclusive projects — IRR can select the wrong project when project sizes differ; NPV is the correct decision rule.
• Optimism bias in projections — management-prepared forecasts average 10–30% optimistic bias; apply a 5–15% downward adjustment or use scenario analysis to calibrate.

When NOT to Use

• When valuing an entire company (use DCF to the firm via WACC; adjust for debt to get equity value).
• When comparing projects over different time horizons (use Equivalent Annual Annuity to normalize for project life differences).
• When cash flows are highly uncertain and real options (option to expand, defer, or abandon) are significant — use Real Options Analysis (ROA) to supplement NPV.