Financial Statements

Financial Statements

Core Concepts

The Three Statements and How They Articulate

• Income statement: revenue minus expenses over a period, on an accrual basis. Ends in net income.
• Balance sheet: assets = liabilities + equity at a point in time. Net income (less dividends) rolls into retained earnings, linking the two statements.
• Cash flow statement: reconciles net income to actual cash movement, split into operating (CFO), investing (CFI), and financing (CFF) activities. It starts from net income, adds back non-cash charges (D&A, stock-based compensation, impairments), and adjusts for working capital changes. The ending cash ties back to the balance sheet cash line.

Accrual accounting means reported earnings and cash generation can diverge for long stretches. Most analytical work is about measuring and interpreting that divergence.

EBITDA and Its Adjustments

EBITDA = EBIT + Depreciation & Amortization. It approximates pre-tax, pre-financing operating cash generation and is capital-structure neutral, which is why EV/EBITDA multiples use it. "Adjusted EBITDA" further strips items management deems non-recurring (restructuring, litigation, stock-based compensation). Scrutinize each add-back: recurring "one-time" charges and stock-based compensation are real economic costs. EBITDA ignores capex entirely, so it flatters capital-intensive businesses.

Free Cash Flow — FCFF and FCFE

FCFF (free cash flow to the firm) is cash available to all capital providers:

• From CFO: FCFF = CFO + Interest × (1 − τ) − Capex
• From EBITDA/EBIT: FCFF = EBIT × (1 − τ) + D&A − ΔNWC − Capex, where EBIT = EBITDA − D&A and EBIT × (1 − τ) is NOPAT

FCFE (free cash flow to equity) is cash available to shareholders after debt service:

• FCFE = CFO − Capex + Net borrowing
• FCFE = FCFF − Interest × (1 − τ) + Net borrowing

FCFF pairs with WACC (enterprise DCF); FCFE pairs with cost of equity (equity DCF). Never mix them.

ROIC and the ROIC-vs-WACC Test

ROIC = NOPAT / Invested capital, where NOPAT = EBIT × (1 − τ) and invested capital = total debt + equity − excess cash (equivalently, net working capital + net fixed assets). A company creates value only when ROIC exceeds WACC; growth at ROIC below WACC destroys value. Persistent ROIC above WACC is the quantitative signature of a moat — it validates (or refutes) qualitative competitive-advantage claims.

Margin Analysis and DuPont Decomposition

• Gross margin = Gross profit / Revenue — pricing power and input costs
• Operating margin = EBIT / Revenue — adds operating cost discipline
• Net margin = Net income / Revenue — adds financing and tax effects

DuPont decomposes ROE into three levers:

ROE = (Net income / Revenue) × (Revenue / Assets) × (Assets / Equity) = Net margin × Asset turnover × Equity multiplier

Two companies with identical ROE can have very different quality: one earns it through margins and turnover, the other through leverage. Rising ROE driven solely by the equity multiplier is a risk signal, not an operating improvement.

Quality of Earnings

Earnings are high quality when backed by cash and generated by recurring operations:

• Accruals ratio = (Net income − CFO) / Average total assets. Persistently positive and rising accruals mean earnings outpace cash — historically a predictor of poor forward returns and restatements.
• Revenue recognition red flags: receivables growing much faster than revenue, heavy quarter-end shipments (channel stuffing), bill-and-hold sales, aggressive percentage-of-completion estimates, growing unbilled receivables.
• One-offs: recurring "restructuring" charges, gains on asset sales folded into operating income, reserve releases boosting earnings.
• Capitalization games: capitalizing costs that peers expense (software development, customer acquisition) shifts expense from the income statement to the balance sheet and inflates both earnings and CFO (the spend moves to CFI).

Working Capital Dynamics

Net working capital (NWC) = current operating assets − current operating liabilities (exclude cash and short-term debt). Growth normally consumes working capital; a rising cash conversion cycle consumes more. The cash conversion cycle:

CCC = DSO + DIO − DPO

where DSO = Receivables / Revenue × 365, DIO = Inventory / COGS × 365, DPO = Payables / COGS × 365. A lengthening CCC ties up cash and often precedes inventory write-downs or receivable problems; a negative CCC (customers pay before suppliers are paid) means growth generates cash.

Deferred Taxes and Cost Basis

Book (GAAP) and tax accounting diverge on timing. Accelerated tax depreciation makes cash taxes lower than book tax expense early in an asset's life, creating a deferred tax liability (DTL); it reverses later. Net operating losses and warranty reserves create deferred tax assets (DTAs), which are only worth carrying if future taxable income will absorb them. The US federal corporate rate applied in these calculations is 21% as of 2026.

For taxable investors, the same timing logic applies at the portfolio level. Cost basis is the purchase price (adjusted for reinvested distributions, return of capital, and wash sales); selling realizes the gain and triggers tax now, while holding defers it. The embedded tax liability of a position is:

Embedded tax = (Market value − Cost basis) × Applicable capital gains rate

with the top federal long-term rate at 23.8% (20% plus the 3.8% net investment income tax) as of 2026, and short-term gains taxed at ordinary rates. Deferral has real value: the unrealized tax is an interest-free loan from the government. This is the accounting foundation for tax-aware rebalancing — compare the tracking-error cost of holding an overweight against the tax cost of selling it, prefer high-basis lots (specific-lot identification), and remember basis steps up at death under current US law as of 2026.

Common Red Flags

• CFO persistently below net income (positive accruals ratio) for multiple years
• Receivables or inventory growing materially faster than revenue
• Frequent changes in accounting policies, estimates, or auditors
• Rising DSO alongside aggressive revenue growth
• Capex consistently far below D&A in a business that is not shrinking (under-investment)
• Serial "non-recurring" charges and heavy reliance on adjusted metrics
• Growing gap between adjusted EBITDA and CFO

Key Formulas

| Formula | Expression | Use Case |

|---------|-----------|----------|

| EBITDA | EBITDA = EBIT + D&A | Capital-structure-neutral operating profit |

| NOPAT | NOPAT = EBIT × (1 − τ) | After-tax operating profit for ROIC and FCFF |

| FCFF (from CFO) | FCFF = CFO + Int × (1 − τ) − Capex | Firm cash flow for enterprise DCF |

| FCFF (from EBIT) | FCFF = EBIT × (1 − τ) + D&A − ΔNWC − Capex | Same, built from the income statement |

| FCFE | FCFE = CFO − Capex + Net borrowing | Equity cash flow for equity DCF |

| ROIC | ROIC = NOPAT / Invested capital | Value creation test vs WACC |

| Invested capital | IC = Debt + Equity − Excess cash | Denominator for ROIC |

| DuPont ROE | ROE = Net margin × Asset turnover × Equity multiplier | Decompose the source of ROE |

| Accruals ratio | (NI − CFO) / Avg total assets | Earnings quality screen |

| Cash conversion cycle | CCC = DSO + DIO − DPO | Working capital efficiency |

| Embedded tax | (MV − Cost basis) × Cap gains rate | Tax cost of selling an appreciated position |

Worked Examples

Example 1: EBITDA, FCFF, and FCFE from the Statements

Given (fiscal year, $M): Revenue 500, COGS 300, SG&A 80, D&A 30, interest expense 10, tax rate 25%. Increase in net working capital 15, capex 35, net borrowing 5.

Solution:

• Gross profit = 500 − 300 = $200M (gross margin 40.0%)
• EBIT = 200 − 80 − 30 = $90M (operating margin 18.0%)
• EBITDA = EBIT + D&A = 90 + 30 = $120M
• Pre-tax income = 90 − 10 = $80M; taxes = 80 × 0.25 = $20M; net income = $60M (net margin 12.0%)
• CFO = NI + D&A − ΔNWC = 60 + 30 − 15 = $75M
• FCFF (from CFO) = 75 + 10 × (1 − 0.25) − 35 = 75 + 7.5 − 35 = $47.5M
• FCFF (from EBIT) = 90 × 0.75 + 30 − 15 − 35 = 67.5 + 30 − 15 − 35 = $47.5M — the two routes agree
• FCFE = CFO − Capex + Net borrowing = 75 − 35 + 5 = $45.0M
• Check: FCFE = FCFF − Int × (1 − τ) + Net borrowing = 47.5 − 7.5 + 5 = $45.0M

Note that net income ($60M) overstates distributable cash to the firm ($47.5M) because capex exceeds D&A and working capital consumed cash.

Example 2: ROIC vs WACC and DuPont Decomposition

Given (same company, $M): EBIT 90, tax rate 25%, total debt 150, shareholders' equity 300, excess cash 50, total assets 600, revenue 500, net income 60, WACC 9%.

Solution:

• NOPAT = 90 × (1 − 0.25) = $67.5M
• Invested capital = 150 + 300 − 50 = $400M
• ROIC = 67.5 / 400 = 16.875%
• ROIC − WACC = 16.875% − 9% = +7.9 pts — the company earns well above its cost of capital; reinvested growth creates value, consistent with a durable competitive advantage

DuPont:

• Net margin = 60 / 500 = 12.0%
• Asset turnover = 500 / 600 = 0.8333
• Equity multiplier = 600 / 300 = 2.0
• ROE = 0.12 × 0.8333 × 2.0 = 20.0% (check: 60 / 300 = 20.0%)

The ROE is earned mostly through margin and turnover with moderate leverage — a higher-quality 20% than one built on a 4x equity multiplier.

Example 3: Earnings Quality and Embedded Tax

Part A — Accruals. Two companies each report net income of $80M on average total assets of $500M. Company X has CFO of $30M; Company Y has CFO of $95M.

• X accruals ratio = (80 − 30) / 500 = +10.0% — earnings far ahead of cash; investigate receivables, inventory, and capitalization policy
• Y accruals ratio = (80 − 95) / 500 = −3.0% — earnings fully cash-backed

Part B — Cash conversion cycle (Company X, $M): receivables 75, inventory 60, payables 45, revenue 500, COGS 300.

• DSO = 75 / 500 × 365 = 54.75 days; DIO = 60 / 300 × 365 = 73.0 days; DPO = 45 / 300 × 365 = 54.75 days
• CCC = 54.75 + 73.0 − 54.75 = 73.0 days. If DSO was 40 days a year ago, the 15-day jump on flat revenue growth is a classic revenue-recognition red flag.

Part C — Embedded tax for rebalancing. A taxable client holds a fund position with market value $150,000 and cost basis $100,000, held over one year, top bracket.

• Embedded tax = (150,000 − 100,000) × 23.8% = $11,900 (20% LTCG + 3.8% NIIT, as of 2026)
• After-tax liquidation value = 150,000 − 11,900 = $138,100
• A full rebalancing sale costs $11,900 (7.9% of position value) today; that cost must be weighed against the risk reduction from trimming, and reduced where possible by selling the highest-basis lots first.

Common Pitfalls

• Treating EBITDA as cash flow — it ignores capex, working capital, cash taxes, and interest; capital-intensive businesses can post strong EBITDA and negative FCF indefinitely
• Discounting FCFF at the cost of equity or FCFE at WACC — mismatched cash flow and discount rate corrupts the valuation
• Accepting every adjusted-EBITDA add-back — stock-based compensation and serial "one-time" restructuring are recurring economic costs
• Computing ROIC with total assets instead of invested capital, or leaving excess cash in the denominator — both understate true operating returns
• Reading a high ROE as quality without DuPont — leverage can manufacture ROE while operations deteriorate
• Ignoring working capital in FCF — fast growth with a long cash conversion cycle can make a profitable company chronically cash-hungry
• Comparing margins across industries without context — a 4% net margin is excellent for a grocer and alarming for enterprise software
• Rebalancing taxable accounts as if they were IRAs — ignoring cost basis and embedded gains converts paper tax deferral into an immediate, avoidable tax bill
• Using average cost basis when specific-lot identification would allow selling high-basis lots and realizing smaller gains

Cross-References

• quantitative-valuation (wealth-management plugin): the FCFF, FCFE, and EBITDA figures derived here are the inputs to DCF and multiples-based valuation
• qualitative-valuation (wealth-management plugin): ROIC persistence, margin trends, and cash flow patterns provide the quantitative evidence for moat and management-quality claims
• equities (wealth-management plugin): statement analysis underpins fundamental stock selection and style classification (value vs growth metrics)
• tax-efficiency (wealth-management plugin): cost basis, embedded gains, and deferral value feed lot-selection, harvesting, and asset-location decisions
• statistics-fundamentals (core plugin): ratio trends and peer comparisons rely on distributional thinking (medians vs means, outlier handling)

Running the Script

uv run scripts/financial_statements.py

The PEP 723 header resolves the numpy dependency automatically. Alternatively run python3 scripts/financial_statements.py after pip install numpy.

• Bare run prints a demo covering the income-statement build, EBITDA and the FCFF/FCFE bridges, ROIC vs WACC, DuPont decomposition, accruals ratio, cash conversion cycle, and embedded tax liability.
• --verify re-runs the demo computations and asserts the outputs match this skill's worked examples (prints PASS/FAIL, nonzero exit on mismatch).
• --help lists the available classes.

The file is primarily meant to be imported as a module, e.g. from financial_statements import FreeCashFlow, Profitability, EarningsQuality, TaxBasis.