TSMC: Growth Is Strong.
The Shareholder Payoff Is Less Certain.

Operating context

Related analysis section: Investment Thesis

These reported figures supply the demand, competitor, funding and governance context used in the Analysis. They do not establish the ultimate profitability of the AI buildout or prove demand has been pulled forward.

TSMC's January–August 2026 revenue rose 39.3% from a year earlier. Management's July outlook called for full-year US-dollar revenue growth slightly above 40%, capital spending of $60–64 billion and a third-quarter operating margin of 56–58%. Monthly revenue establishes reported sales, not cash collection or the profitability of those sales. [S05, S06]

NVIDIA reported $96.221 billion of quarterly revenue and guided to $108 billion, excluding China data-center compute revenue. Broadcom reported $16.7 billion of AI revenue and guided to $21.7 billion for the next quarter. These reports support the demand picture without establishing whether ultimate users earn enough to sustain spending. [S07, S08]

Meta's quarterly operating cash was $31.86 billion against $31.08 billion of investment including finance-lease principal. Amazon reported negative trailing free cash flow despite strong operating cash and cloud growth. Microsoft had a larger gap between operating cash and cash equipment spending, but that measure omits some leases and other claims. Periods and definitions differ; summing the amounts would create a misleading total. Alphabet's latest detailed results were not recovered through the bounded research routes, so this is not a complete hyperscaler funding comparison. [S09–S11]

Samsung reports advanced-process orders and expansion plans, which do not demonstrate equal yields or economics. Intel's foundry reported $5.765 billion of quarterly revenue, including $5.477 billion from other Intel operations, alongside a $2.089 billion operating loss. Internal sales do not establish equivalent external market share. ASE's panel-packaging initiative targets initial production in 2027; it may provide an alternative for some packaging work while complementing wafer manufacturing. ASE's quarterly results were not recovered through the bounded routes, so no comparable competitor-return ranking is claimed. [S12–S14]

The Arizona entity reported NT$36.066 billion of first-half profit and JASM NT$1.678 billion, while ESMC remained loss-making at this stage. Subsidiary profits are not comparable unsubsidized returns: transfer pricing, subsidies, product mix and the stage of each ramp affect them. Management expects overseas expansion to dilute gross margin by roughly two to three percentage points early and three to four later. Relevant guidance already includes ramp effects; subtracting those costs again would double-count them. [S03–S05]

TSMC's June cash and current liquid securities of roughly NT$3,518 billion compared with about NT$1,032 billion of financial debt. These are June balances, not September cash. Precise covenant headroom is unknown. The model's reserve for operating needs is judgment, not proof that all remaining cash can be distributed. [S03]

The chief executive and chair roles are combined, with a majority-independent board. National Development Fund ownership and relatively low disclosed executive and director ownership excluding that fund do not, by themselves, prove interference or alignment. Long-term incentives include shareholder-return, financial and ESG components, but undisclosed weights prevent a precise claim about incentives to improve investment returns. Unqualified financial and control audit opinions do not certify the investment case. [S01, S02]

Decision probabilities

Related analysis section: Valuation and Alternatives

The estimates below are the researcher's actual decision beliefs at the reference price. They use the evidence through the stated research cutoff. They are neither historical frequencies nor calibrated predictions, and the later development of these probability estimates does not imply they existed in the earlier assessment.

The catastrophic Taiwan/ADR branch takes precedence over the ordinary outcomes. It covers sustained impairment of core production, shipping, payments or legal/market access that prevents ordinary going-concern ADR valuation. Otherwise, classify prospective recurring earnings per ADR for October 2027–September 2028, as anticipated by investors at the exit, relative to the fixed entry earnings anchor of $19.811622706 per ADR. Anticipated earnings need not equal later realized earnings; these categories do not replace the original thesis tests.

The four ordinary weights already sum to 98% of the total. Do not multiply them by 98% again. Each boundary belongs to the higher range. Filings support the economic mechanisms, not the exact whole-percent choices.

Within every ordinary range, the model uses the same normal-shaped weighting function with location 1.12 and scale 0.20. It restricts that function to the range, normalizes the remaining area to one, and then gives it the independently chosen outcome weight. The result is a piecewise mixture, not a single globally normal forecast. The location balances continued growth against cost pressure; the 20-percentage-point scale allows substantial variation in earnings. Neither was estimated from a sampled time series, and the location is not necessarily the mean of the final mixture.

For readers reproducing the averages, let x be the earnings ratio, μ = 1.12, σ = 0.20, and [a,b] the range. If φ and Φ are the standard-normal density and cumulative distribution, the restricted mass is Φ((b−μ)/σ) − Φ((a−μ)/σ). The conditional mean is μ + σ × [φ((a−μ)/σ) − φ((b−μ)/σ)] / mass. The first and last ranges extend to negative and positive infinity. Pricing integrates max(x,0) instead of x: negative earnings receive a zero earnings-based price floor, an assumption rather than a statement that loss-making companies are worthless. Ordinary dividends are separate and may have been received before the loss.

Entry TSM P/E is 22.766938716. The severe range's mean positive ratio for pricing is 0.757584532, slightly above its raw earnings mean because of the price floor. The other pricing means equal their earnings means. The underlying shape's raw masses across the ordinary ranges are 8.850799%, 27.466136%, 37.898454% and 25.784611%. The selected weights conditional on no catastrophe are 8.163265%, 25.510204%, 40.816327% and 25.510204%. Their proximity is a coherence check, not evidence of calibration.

Ordinary TSM return is mean positive earnings ratio × exit P/E / entry P/E − 1 + 3.45625 / 451.05. The $3.45625 distribution assumes four NT$7 entitlements, five shares per ADR, NT$32/USD and 21% Taiwan withholding. Four future payments are not all declared, and fees and personal US taxes remain excluded from this forecast. SPY return is (1 + earnings growth) × exit P/E / 21.31 − 1 + 0.0109 − 0.000945, with its gross indicated yield and fund fee counted once. [S15, S21, S24]

Tail returns are inclusive: no extra dividend or cost is added. Their economic impairment marks do not guarantee a tradable price. Actual return evaluation still uses the original nontradability rules.

Multiplying each unrounded state return by its total probability gives TSM 10.572412%, SPY 6.754332%, and excess return 3.818080 percentage points. Conditional on no catastrophic outcome, the respective averages are 12.420829% and 7.606462%; those exclude a material risk and are not substitutes for the headline totals.

Both securities face the same five economic states. That does not imply perfectly correlated realized returns. SPY's state returns are representative conditional means, without a separately estimated earnings distribution. Within-state variation and covariance are insufficiently specified to estimate an exact probability of outperformance. Changing correlation alone while leaving marginal means fixed cannot change mean excess return.

TSM's accelerating-state multiple rises about 5.4%, against about 7.9% for SPY. This is an independent valuation judgment: TSM starts at a higher modeled multiple and retains direct concentration and reinvestment risk, while broader risk appetite can lift SPY from its lower starting multiple. Those facts do not prove the exact choice. Matching TSM's proportional increase to SPY's raises TSM's weighted return to 11.433963% and the advantage to 4.679631 points.

Probability sensitivities

Related analysis section: Risks and Countercase

Readers can substitute weights using the returns above, with weights totaling 100%, and calculate each weighted total as the sum of probability times return. These alternative sets preserve the earnings and valuation assumptions while changing beliefs about which outcomes occur. The order is severe, soft, durable, accelerating, catastrophic.

Weaker conversion would favor the more cautious rating 5 in the researcher's judgment. These alternatives are not additional additive outcomes. Holding all returns and other weights fixed, transferring about 14.36 percentage points from accelerating to soft conversion equalizes the mean returns. That leaves about 10.64% in the accelerating outcome. It is an equation, not a rating cutoff.

Shape matters independently of weights. The following grid changes the normal-shaped function's location and scale, keeping the selected outcome probabilities and valuation rules fixed. Each entry shows TSM's weighted return followed by its advantage over the unchanged 6.754332% SPY estimate.

These settings are plausible alternative judgments, not confidence limits. Looking only inside the durable-growth range also exposes sensitivity: a uniform distribution gives a 1.15 earnings ratio and 3.91 points of total advantage; a linearly declining triangular distribution gives 1.116667 and 2.58 points; a steep declining exponential with rate 29 gives 1.083875 and 1.27 points. Each substitutes only that category's mean while holding the other current means and weights fixed. No one of these shapes is established by the published business facts.

An independent reviewer's more severe ordinary-downside belief uses an earnings ratio of 0.596, compared with 0.757585 in the base model. With other assumptions unchanged, that gives TSM 9.550396% against SPY 6.754332%, a 2.796064-point advantage. The reviewer retains concern that a smooth distribution may understate cancellation and funding cascades. Separately, making 10% or 25% of the severe ordinary outcome a total shareholder loss leaves advantages of 3.33 or 2.60 points. Those fractions are within the existing 8% outcome, not extra total probability, and SPY's corresponding return is unchanged in those particular stresses.

Catastrophic probability and severity are separate uncertainties. The table below proportionally rescales ordinary weights when the catastrophic probability changes. It shows paired inclusive impairment returns, with each cell giving TSM / SPY weighted totals and their difference.

At the base −80%/−35% losses, the tail-only probability that equalizes mean returns is about 9.66%, with ordinary proportions otherwise fixed. That is not an estimate that tail risk is acceptably low, a confidence bound or a rating rule.

Other assumptions can matter sooner than tail-only parity. A 5% reduction only in TSM's ordinary multiples gives TSM 5.10% versus SPY 6.75%, a 1.65-point disadvantage. Cutting both ordinary multiples by 10% gives −0.37% and −3.69%, preserving a 3.32-point relative edge while both lose money. Replacing all ordinary SPY returns with the single 8.9955% illustration, while retaining its catastrophic branch, gives SPY 8.12% and a TSM advantage of 2.46 points. That changes comparator means, not merely correlation.

A $0.10 ADR fee in ordinary TSM outcomes reduces its weighted return by about 0.0217 percentage points; it is a stress, not a verified fee. Holding all dollar endpoints, including tail recovery, fixed gives entry-price mean parity of about $467.18. This diagnostic is not a price target, buy limit or automatic rating threshold. Changing price can call for a new assessment rather than mechanically applying that number.

Financial history

Related analysis section: Financial Quality and Funding

All amounts are NT$ billions except diluted earnings per ordinary share, shown in NT$. Annual figures use IASB IFRS; quarters use Taiwan IFRS. They are kept separate because tax timing and a small unreconciled associate-related residual affect the bases. Neither series is a complete restatement of recurring earnings. [S01–S03, S25, S26]

Quarterly cash flows are discrete quarters, not repeated cumulative totals. Equipment spending alone omits other claims on cash. The full first-half cash calculation uses unrounded financial-statement amounts.

Recurring earnings

Related analysis section: Financial Quality and Funding

The VIS-only second-quarter adjustment is (27.25 − 2.24) × 5 / 31.601 = $3.957 per ADR; multiplying by four gives $15.829. The five-share conversion and the quarter's exchange rate matter. The NT$63.202 billion pretax gain and NT$24.301 billion sale cash are different quantities, and the rounded management EPS attribution is not an audited gain-specific tax allocation. [S03, S05, S24]

Removing the NT$10.641 billion prior-year tax benefit separately reduces the quarterly proxy to $3.892 per ADR. This is a sensitivity, not a rule that every tax adjustment is nonrecurring. The independent first-half recurring anchor is operating profit plus interest income less finance expense, taxed at an assumed 18%, less minority income. It excludes VIS and other nonoperating gains while retaining normal R&D, compensation, inventory costs and depreciation.

The insurance disclosure changes from a cumulative NT$3 billion net loss to a cumulative NT$4.3 billion net gain. It does not isolate the exact second-quarter benefit. Subtracting the full NT$7.3 billion change before tax as a stress reduces annualized normalized ADR earnings from $14.605 to $14.533, about 0.5%. This bounds the uncertainty rather than declaring it zero. Do not also remove the prior-year tax benefit from an anchor already normalized to an 18% tax assumption.

Cash after investment

Related analysis section: Financial Quality and Funding

The historical calculation uses first-half 2026 Taiwan-IFRS amounts, in NT$ billions. [S03]

Operating cash already contains rents and paid taxes; those are not deducted twice. The formula excludes asset-sale proceeds, grants and new financing. Insurance cash and the cash attributable to minority owners are not separately measurable; the latter's NT$0.541 billion profit is small but is not an exact cash allocation.

The simultaneous timing stress subtracts NT$80.927934 billion for the tax accrual/payment gap, NT$114.790916 billion for equipment payables, NT$102.502167 billion for other noncurrent-liability inflow and NT$70.327983 billion for bonus accrual, leaving NT$296.027278 billion. These are timing diagnostics rather than four additional recurring expenses. Customer temporary receipts are not deducted again from the other-liability stress. Equipment payables explain only part of the NT$115.252915 billion gap between equipment additions and cash payments; other reconciliation items account for the rest.

Annualizing solely for scale, using NT$32 per US dollar and the reference equity value, gives yields of 1.78% for the historical proxy and 0.79% for the stressed proxy. Neither is a forecast.

Forward central cash, in US$ billions, is 102.751 parent profit + 32.25 depreciation and amortization − 75.25 cash equipment spending − 4.15 other investment − 1.68 incremental working capital = 53.921. Dividing by $2,339.33 billion of equity value gives 2.304980%.

Other investment comprises a $2 billion first-year Sony-venture allowance and a $2.15 billion reserve for otherwise uncovered lease, intangible and capitalized borrowing-cost cash. Stock compensation and ordinary rents remain in earnings once. The reserve excludes them. Historical lease/intangible cash and a capitalized-interest accrual provide a scale comparison, not a verified future cash budget. Adequacy and Sony subscription timing remain uncertain; each additional $1 billion of cash claims reduces the yield by about 0.043 percentage points. A $5 billion additional-investment stress reduces it by about 0.21 points. Multi-year factory announcements are not added again to annual spending. [S03, S15]

Working capital is modeled at 4% of sales above a $173 billion calendar planning base. Comparing a rolling forecast with that calendar base is a period-mismatched proxy, not a precise matching of receivables and inventories. The operating cash-flow valuation uses a separate 1% reinvestment allowance that excludes financing interest. Identical allowance percentages do not mean identical cost boundaries.

Forward valuation

Related analysis section: Valuation and Alternatives

This section preserves the operating anchor and earlier unweighted single-path sensitivities. Its six cases overlap and receive no additional probabilities. The decision-probabilities section controls the current expected returns. In particular, the 15%-growth/57%-margin path is not the average of the durable-growth outcome, and the 6.1% ordinary-disappointment path is not the current soft-growth average.

All sales and net-interest inputs below are US$ billions. Year 1 is October 2026–September 2027; year 2 is October 2027–September 2028. Those quarterly periods end six days after the fixed September 24 return endpoint, a disclosed approximation to prospective earning capacity rather than a change of dates.

The $215 billion sales assumption starts with FY2025 actual-period US-dollar revenue of $122.424 billion. Interpreting “slightly above 40%” as 41%, then removing first-quarter $35.90 billion, second-quarter $40.20 billion and the third-quarter guidance midpoint of $45.2 billion, implies a fourth quarter of $51.31784 billion. The 40% and 42% alternatives imply $50.0936 billion and $52.54208 billion. Management did not guide those fourth-quarter numbers. [S04–S06, S25]

Four quarters beginning with the middle implied fourth quarter and increasing 3% sequentially total $214.694701 billion, rounded to $215 billion. A flat path gives $205.27 billion. These paths are assumptions, not orders or a claim of calendar-year growth. The separate 15% year-2 growth assumption comes from the long-term model; it is not the annualized result of the 3% quarterly path.

Parent profit equals (sales × operating margin + net interest) × (1 − tax rate) − minority profit. Divide by 5.1864 billion ADR equivalents × (1 + dilution) for EPS. The ADR-equivalent count is derived from 25.932 billion ordinary shares, not the actual number of deposited ADRs. Minority profit is $0.2 billion in each scenario.

Year 2 retains each case's margin, tax, interest and dilution assumptions. The ordinary case uses the central entry multiple; resetting its entry multiple to its own lower earnings would cancel the disappointment. Central profit is $102.751 billion and EPS $19.811623, so entry P/E is $451.05 / $19.811623 = 22.766939. Year-2 sales of $247.25 billion give EPS $22.718003.

Return equals (Y2 EPS × exit multiple + projected net distributions) / 451.05 − 1. Projected distributions are $3.45625 per ADR: four assumed NT$7 entitlements, five ordinary shares per ADR, NT$32/USD and 21% Taiwan withholding. One announced entitlement is not four declared payments. Personal US taxes and unverified ADR fees are excluded from these scenario returns; a $0.10 fee is a sensitivity, not a verified charge. No dividend reinvestment is assumed. [S15, S24]

At an unchanged multiple and central margins, 0%, 5%, 10%, 15% and 20% second-year growth produce approximately 0.8%, 5.7%, 10.5%, 15.4% and 20.3% returns. Growth of about 8.41% matches the SPY illustration if other central conditions hold. None is an estimated probability. Holding a price-derived entry multiple constant tests conditional earnings growth; it does not prove fair value at any price.

Long-term cash value

Related analysis section: Valuation and Alternatives

The ten-year discounted cash-flow model starts with operating profit after tax, adds depreciation and amortization, and deducts cash equipment spending, other operating investment, incremental working capital and a minority allowance of 0.1% of sales. Financing interest is excluded. The annual assumptions are:

Other operating investment is 1% of sales plus $2 billion in year 1. Working capital is 4% of incremental sales, with the $173 billion planning base for year 1 and prior-year modeled sales thereafter. Discounting uses a judgmental 10% required return, not a measured cost of capital or insurance against catastrophe. Terminal growth is 3%; incremental return on capital is assumed to be 20%, requiring reinvestment of 15% of terminal operating profit after tax. This replaces explicit terminal net investment rather than deducting it twice.

Terminal cash is Y10 sales × 1.03 × [terminal margin × (1 − terminal tax) × (1 − 0.03 / 0.20) − 0.001]. Its value is terminal cash divided by (0.10 − 0.03), then discounted ten years. Add discounted annual cash and $54.803 billion of modeled surplus cash, and divide by 5.1864 billion ADR equivalents. The surplus-cash estimate deducts debt, customer receipts, declared dividends, pension claims and a $5 billion operating reserve from June cash and liquid securities. A zero-surplus-cash sensitivity recognizes uncertainty about availability. Leases serviced through modeled cash are not deducted again at book value.

The $215 billion start yields about $280 per ADR. The separate $200 billion starting-sales case yields $261, with a $218–335 range across 9–11% required returns and 2–4% terminal growth. That range belongs to the $200 billion case. About 60% of its enterprise value comes from terminal value, illustrating reliance on distant assumptions. A stronger durable-growth case reaches about $414 at the same 10% required return, with year-ten sales of $582 billion and 58% long-run margins. It is a separate sensitivity, not the central forecast. Lower required returns or better reinvestment economics can justify more; the model does not establish one observed intrinsic value.

Benchmark and alternatives

Related analysis section: Valuation and Alternatives

SPY's September 23 sponsor data show forward forecast P/E of 21.31, trailing index P/E of 25.09, gross indicated index dividend yield of 1.09%, fund distribution yield near 0.99% and a 0.0945% expense ratio. Technology was around 39% and NVIDIA alone around 8%. These concentrations limit claims of independence from AI or Taiwan risk. [S21]

The illustration is (1 + earnings growth) × exit P/E / 21.31 − 1 + 0.0109 − 0.000945. At 8% growth and unchanged P/E, it gives 8.9955%. A separate net-distribution-yield approach gives 8.99%, with no further fee deduction. The two yield measures differ in period and denominator; their spread is not an exact fee reconciliation. Actual observed SPY returns already bear fund expenses.

SPY stress assumes earnings down 10% and an 18 multiple, producing about −23.0%; favorable conditions assume 15% growth and a 23 multiple, producing about +25.1%. The current decision table pairs these with TSM under the same state probabilities and includes a soft-growth SPY condition of 3% earnings growth and a 20 multiple. The old single-path common-multiple stress gives TSM 3.969336% and SPY −1.8045%; the current weighted common-multiple result is separately −0.369735% and −3.693542%. Do not substitute either single-path return for its weighted counterpart.

The September 24 Treasury reference of 4.51% is a one-year par-curve yield, not a quote for a specific executable security. Selling before maturity brings price risk, and inflation can reduce purchasing power. The Marcus twelve-month 3.90% APY offer requires at least $500 and assumes interest remains deposited; an early withdrawal can cost 90 days' interest. Eligibility and FDIC coverage depend on account and ownership category, including other deposits at the same bank. Neither reference establishes a future reinvestment rate or a return after personal taxes. [S22, S23]

Thesis tests

Related analysis section: What Would Change Our View

The fixed measured period is January 1–June 30, 2027. Reporting is anticipated in July/August 2027, not a verified appointment. These tests are not yet observable and are not averaged into a score.

T03's original formula is operating cash minus cash equipment, intangibles and cash right-of-use acquisition, plus interest and dividends received, minus total interest paid, lease principal and economic stock-compensation cost. Its original first-half 2026 baseline was NT$664.595257 billion, about $20.77 billion at NT$32/USD. It omitted the separate lease-prepayment line. The corrected diagnostic deducts that line as well, giving a historical baseline of NT$664.576278 billion. Evaluate both against the unchanged $22 billion threshold, showing met, missed or unobservable for each and explaining any difference. A pass under only one convention is not proof of durable cash conversion. Historical timing-stress estimates were correspondingly corrected from NT$296.046036 billion to NT$296.027278 billion.

T04's original planning baseline was $70 billion / $200 billion = 35%; the current central assumption is $75.25 billion / $215 billion, also 35%. The threshold remains 38%.

Use final issuer-filed interim statements, then condensed results, then issuer releases. Retain originally reported and restated figures, with explanations of changed outcomes. For USD revenue, use issuer period conversion; for T03 use the issuer's first-half average exchange rate or quarter-weighted issuer averages. Do not round before threshold comparisons. Missing material data or an unreconciled accounting-basis change makes the result unobservable, not met. These tests do not capture every competitive, demand or Taiwan risk and do not automatically trigger a trade.

Prices and return rules

Related analysis section: What Would Change Our View

The original reference-session snapshots are TSM $451.05 and SPY $767.29, September 24, 2026. Later provider rows show $451.15 and $767.18. Neither original snapshot is presented as a certified finalized close. With all modeled dollar endpoints fixed, the later marks give weighted returns of 10.547903% for TSM and 6.769639% for SPY, an advantage of 3.778264 points rather than 3.818080. The initial prices and twelve-month clock remain intact. [S20, S21]

The valued ending session is September 24, 2027, or the latest prior regular session for both securities if no session exists that day. Use ChartExchange historical closes, then official exchange closes, issuer/sponsor market closes, then another established vendor with its method and row preserved. Explain source differences rather than selecting favorable marks.

Record the first authorized observation at or after the next trading day's regular-session close following the endpoint, including timestamp and timezone. That observation still values the specified ending session. If the review occurs later, disclose the delay. Subsequent vendor corrections remain separate, with their effects shown alongside the initially observed result. This establishes observation terms without scheduling monitoring.

Return is (ending value of original units + entitled distributions − observed ADR fees) / starting value − 1. Include distributions with ex-dates after the start and no later than the endpoint, showing paid cash and determinable receivables separately. The October 8, 2026 TSM payment has a September 16 ex-date and is not earned by this starting position. Do not reinvest dividends or credit interest on them. Use actual depositary USD distributions when known, not forecast exchange rates. [S24]

The primary TSM return deducts actual Taiwan withholding and depositary fees; also show gross return before withholding. Unknown fees remain unknown. SPY distributions are before personal tax and after fund expenses; no second expense-ratio deduction applies. Personal US taxes, foreign-tax-credit recovery, commissions and bid/ask costs are excluded.

Splits adjust original units without creating return. Rights and spin-offs include evidenced cash or saleable value; optional purchases are excluded. Merger cash is held uninvested, and mandatory new securities retained, through the endpoint. Suspension, nontradability or an event preventing defensible valuation makes the comparison unobservable. Show the last quote and liquidity conditions separately instead of inventing an executable exit.

Report absolute returns and TSM net return minus SPY return in percentage points. Outperformance alone cannot prove the thesis or analytical skill. A later assessment may use a new price and cutoff but cannot rewrite these terms.

Sources and limits

Related analysis section: Risks and Countercase

The source register identifies the filings, issuer releases and other evidence supporting this dated assessment. The research and model assumptions received independent analytical scrutiny. Conventional earnings multiples and discounted cash-flow methods are not presented as original inventions.

Company disclosures establish what management reports; they do not audit customer orders, production yields or future cash returns. Financial PDFs were read through text extraction, not a visual audit of every table cell. Alphabet's latest detailed results and ASE's quarterly results were not recovered through the research's bounded routes, so this article does not claim a complete hyperscaler funding comparison or a comparable competitor-return ranking. Dynamic news and price pages also limit completeness. Review did not calibrate the subjective probabilities or earnings shapes, establish exact covenant headroom or standalone packaging returns, or measure the probability and severity of Taiwan disruption. The numerical probabilities and impairment assumptions are disclosed judgments under those limits.