# 单位经济、成本结构与经营杠杆
用CAT历史桥解释变化，再用独立教材模型推导经营杠杆的精确有限变化；产能台阶显式改变条件。
Entry: zh-bf17 | Node: BF-17 | Language: zh | Editorial revision: 2026-09-21
## Teaching instructions
你正在教 BF-17《单位经济、成本结构与经营杠杆》，材料版本2026-09-21。学习任务：核八项历史OI桥与A/B直接重算，证明线性条件下百分比恒等式。
本篇没有行业分支；Caterpillar历史桥与OpenStax A/B教学模型均为核心必读，二者身份必须分开。 optional只有读者启用后才变为必读。先实际打开指定公开原文单元，分页读到单元结束，必要表图核原页，记录标题/版本/位置/范围与当前用途。文献目录、工具返回标题或作者先前已读记录都不能代替本次读取；runtime_reading_log从空数组开始。读取失败先找同版本正式等价原文，仍缺则说明该单元缺口，不凭摘要补讲。
诊断任务：{"core": "核八项历史OI桥与A/B直接重算，证明线性条件下百分比恒等式。"}。补充任务：A销量下降20%，先用贡献利润算55,400，再从基点DOL得到同一结果。
随后沿本包完整正文、实际输入、静态实验与题解推进一个完整任务，先让读者解释或计算再反馈；已会的基础跳过。默认迁移是在同一虚构A/B模型改变销量并核恒等式，再回到Caterpillar判断缺失结构输入；没有额外行业分支。通过尺度：有限变化固定参数时两结果完全一致；跨台阶另算新增成本，基点利润0不返回可用比率。
保持真实披露、分析计算、教学模型三种身份，参数只改变模型，不反写真实公司数据。资料不足处不要补造差额或估值。最后明确：读者已经能独立重建什么，换一份材料时还需先核哪些条件？
Before substantive teaching, actually retrieve every required reading unit for the selected scope. Read its complete designated section, including necessary assumptions, tables and footnotes. A working URL or an editorial access date is not a runtime reading receipt. Record the actual version, location, scope and what it supports. If unavailable, use a previously verified equivalent source; if the required unit remains unavailable, identify that gap rather than teach it from memory. Start runtime_reading_log empty. Once reading is complete, use a substantive diagnostic or follow the reader's request for direct explanation. Advance one complete reasoning task at a time; skip mastered basics. Distinguish original facts, supplied teaching assumptions and inference.
## Required readings and runtime protocol
```json
{
"export_mode": "public",
"default_branch": "core",
"branch_options": [
"core"
],
"branch_tasks": {
"core": "核八项历史OI桥与A/B直接重算，证明线性条件下百分比恒等式。"
},
"selection_rules": {
"common": "始终必读",
"selected": "只读所选主分支",
"all": "读所有主分支",
"optional": "读者启用后再读；cat/epw/cross不同入口"
},
"required_readings": [
{
"source_id": "BBC-C04",
"title": "Caterpillar Inc. — FY2025 Form 10-K",
"authors": [
"Caterpillar Inc."
],
"version": "FY ended 2025-12-31; comparatives recast in this filing after July 1, 2025 organization changes",
"access": {
"kind": "html_full_text",
"uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231.htm"
},
"required_unit": {
"locator": "MD&A pp31–35 and Definitions pp36–38",
"scope": "完整历史收入/利润说明、p33经营利润图全部八项、四个具名Definitions",
"purpose": "历史归因与模型输入区别",
"figure_uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231_g4.jpg"
},
"supports": "制造与出租资产用途、公司历史驱动定义、报告分部到收入/税前利润的完整桥。不得把volume包含的组合效果当结构性贡献率。",
"branch": "common"
},
{
"source_id": "BFDE-CVP",
"title": "Principles of Accounting Vol2 §3.5 — Margin of Safety and Operating Leverage",
"authors": [
"Mitchell Franklin",
"Patty Graybeal",
"Dixon Cooper",
"OpenStax"
],
"version": "2019",
"access": {
"kind": "html_full_text",
"uri": "https://openstax.org/books/principles-managerial-accounting/pages/3-5-calculate-and-interpret-a-companys-margin-of-safety-and-operating-leverage"
},
"required_unit": {
"locator": "§3.5 Operating Leverage and Company A/B",
"scope": "完整相关设置、表、变化与相关范围段",
"purpose": "正向CVP重算与有限变化恒等式"
},
"supports": "Company A/B虚构输入与经营杠杆；按原始表复算，不采用网页不一致的1.71、31.9%/46.9%。有限变化精确式由本篇条件推导。",
"branch": "common"
}
],
"optional_readings": [],
"runtime_reading_log": [],
"supplied_inputs": {
"input_id": "BFDE-SHARED-20260921-v1",
"historical": {
"scope": [
"BF-12",
"BF-13",
"BF-14",
"BF-18",
"BF-17",
"BF-16"
],
"retrieved_on": "2026-09-21",
"identity": "Historical financial-statement observations; teaching cases are separately labelled. Values are not stock valuation inputs.",
"costco": {
"source_id": "BF-S-COST-FY2025-PDF",
"unit": "USD million",
"periods": [
"2025-08-31",
"2024-09-01"
],
"fiscal_weeks": [
52,
52
],
"ppe": {
"locator": "FY2025 annual-report PDF printed pp42–43; PDF pp48–49",
"land": [
10323,
9447
],
"buildings_improvements": [
25508,
23727
],
"equipment_fixtures": [
13127,
12387
],
"construction_in_progress": [
1882,
1389
],
"gross": [
50840,
46950
],
"accumulated_depreciation_amortization_positive": [
18931,
17918
],
"net": [
31909,
29032
]
},
"flows": {
"locator": "Printed pp35,39; PDF pp41,45",
"net_sales": [
269912,
249625
],
"merchandise_costs": [
239886,
222358
],
"cash_ppe_additions_outflow_positive": [
5498,
4710
],
"consolidated_depreciation_amortization": [
2426,
2237
],
"capex_included_in_liabilities_supplemental_noncash": [
193,
203
],
"cashflow_inventory_adjustment": [
559,
-2068
],
"cashflow_accounts_payable_adjustment": [
404,
1938
],
"cfo": [
13335,
11339
]
},
"working_capital": {
"locator": "Printed p37 balance sheet; pp41–42 Receivables, Net; p39 cash flow",
"inventory": [
18116,
18647
],
"accounts_payable": [
19783,
19421
],
"receivables_net": [
3203,
2721
],
"deferred_membership_fees": [
2854,
2501
],
"receivables_identity": "Includes vendor, credit-card, reinsurance and tax receivables; do not use total as customer credit-sale receivables.",
"payable_days_denominator": "Merchandise costs proxy, not independently observed credit purchases."
},
"leases_2025": {
"locator": "Note5 printed pp50–51; PDF pp56–57; policy printed p43",
"operating_rou_asset": 2725,
"finance_lease_asset_net": 1488,
"finance_asset_balance_sheet_location": "Other long-term assets",
"operating_liability_current": 208,
"operating_liability_noncurrent": 2460,
"finance_liability_current": 78,
"finance_liability_noncurrent": 1401,
"operating_cost": 271,
"finance_asset_amortization": 102,
"finance_interest_expense": 63,
"variable_cost": 182,
"total_cost_reported": 618,
"cash_operating_leases": 255,
"cash_finance_interest": 58,
"cash_finance_principal": 147,
"cash_scope": "Cash paid for amounts included in measurement of lease liabilities; not total lease cash payments including variable payments.",
"new_modified_operating_rou": 294,
"new_modified_finance_rou": 131,
"remaining_term_years_operating_finance": [
20,
25
],
"payment_buckets": [
"FY2026",
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"Thereafter"
],
"operating_payments": [
267,
250,
235,
204,
184,
2451
],
"operating_payments_total": 3591,
"operating_interest_deduction": 923,
"operating_liability": 2668,
"finance_payments": [
133,
132,
135,
122,
109,
1780
],
"finance_payments_total": 2411,
"finance_interest_deduction": 932,
"finance_liability": 1479,
"signed_not_commenced_payments_excluded": 1094,
"future_operating_sublease_income_not_netted": 92
}
},
"salesforce": {
"source_id": "BBC-C01",
"unit": "USD million",
"periods": [
"2026-01-31",
"2025-01-31"
],
"income": {
"locator": "Consolidated Statements of Operations p58 including notes1–2; MD&A Research and Development",
"total_revenue": [
41525,
37895
],
"rd_expense": [
5993,
5493
],
"rd_sbc_included": [
1162,
1091
],
"acquired_intangibles_amortization_cost_of_revenue": [
692,
750
],
"acquired_intangibles_amortization_sales_marketing": [
995,
901
]
},
"working_capital": {
"locator": "Balance sheet p57; Note2 Unearned Revenue p71; MD&A seasonal nature pp39–40",
"accounts_receivable_net": [
14339,
11945
],
"unearned_revenue": [
24317,
20743
],
"unearned_opening_2026": 20743,
"billings_and_other_2026": 45099,
"revenue_over_time_2026": 39041,
"revenue_point_in_time_2026": 2484,
"unearned_acquired_informatica": 651,
"identity": "Billings and other includes FX, contract assets and business combinations; neither cash receipts nor organic billings."
},
"leases_2026": {
"locator": "Note6 Leases and Other Commitments pp75–77; Note1 Leases pp67–68",
"operating_rou_asset": 2003,
"finance_lease_asset_gross": 1427,
"finance_accumulated_amortization_positive": 813,
"finance_lease_asset_net": 614,
"finance_asset_balance_sheet_location": "Property and equipment",
"operating_liability_current": 548,
"operating_liability_noncurrent": 2189,
"finance_liability_current": 275,
"finance_liability_noncurrent": 260,
"operating_cost": 614,
"finance_asset_amortization": 375,
"finance_interest_expense": 25,
"cash_operating_leases": 695,
"cash_finance_interest": 25,
"cash_finance_principal": 367,
"remaining_term_years_operating_finance": [
7,
3
],
"payment_buckets": [
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"FY2031",
"Thereafter"
],
"operating_payments": [
615,
571,
493,
338,
268,
790
],
"operating_payments_total": 3075,
"operating_interest_deduction": 338,
"operating_liability": 2737,
"finance_payments": [
289,
120,
76,
58,
26,
0
],
"finance_payments_total": 569,
"finance_interest_deduction": 34,
"finance_liability": 535
},
"informatica_2025_ppa": {
"locator": "Note7 Informatica, Inc., pp77–79",
"acquisition_period": "November 2025",
"status": "Preliminary purchase-price allocation at FY2026 filing; measurement period not complete",
"consideration_components": {
"cash": 9538,
"preexisting_relationship": 62,
"assumed_equity_purchase_component": 36
},
"consideration_total": 9636,
"assets": {
"cash": 1405,
"receivables": 233,
"ppe": 128,
"operating_rou": 27,
"other_assets": 149,
"goodwill": 5257,
"identifiable_intangibles": 3818
},
"liabilities_positive": {
"payables_accruals_current": 221,
"unearned_revenue": 651,
"operating_lease_liabilities": 30,
"other_noncurrent": 36,
"deferred_tax_liability": 443
},
"intangibles": [
{
"name": "Cloud developed technology",
"amount": 1350,
"life_years": 7
},
{
"name": "Other developed technology",
"amount": 270,
"life_years": 3
},
{
"name": "Customer relationships",
"amount": 1840,
"life_years": 10
},
{
"name": "Trade names",
"amount": 79,
"life_years": 4
},
{
"name": "Backlog",
"amount": 279,
"life_years": 2
}
],
"assumed_equity_fair_value": 330,
"assumed_equity_future_service_component": 294
},
"intangible_roll": {
"locator": "Note8 pp80–81; addition/retirement columns are net movements, not gross acquisition or amortization flows",
"gross_opening": 10183,
"additions_and_retirements_net": 3956,
"gross_closing": 14139,
"accum_amortization_opening_positive": 5755,
"expense_and_retirements_net_positive": 1569,
"accum_amortization_closing_positive": 7324,
"net_opening": 4428,
"net_closing": 6815,
"goodwill_opening": 51283,
"regrello": 704,
"informatica": 5257,
"other_acquisitions_adjustments": 697,
"goodwill_closing": 57941
},
"segment_identity": "One operating segment; Note1 p63 CODM assesses consolidated net income. Product offering revenue categories are not separately reported operating segments."
},
"caterpillar": {
"source_id": "BBC-C04",
"unit": "USD million",
"periods": [
"2025-12-31",
"2024-12-31"
],
"comparative_identity": "2024 figures as retrospectively adjusted in FY2025 filing after July 1, 2025 segment changes",
"ppe": {
"locator": "Note9 p89; Note1D pp64–65",
"land": [
616,
612
],
"buildings": [
7761,
7281
],
"machinery_equipment": [
13737,
12523
],
"capitalized_software": [
1696,
1609
],
"equipment_leased_to_others": [
6004,
5701
],
"construction_in_progress": [
2092,
1751
],
"gross": [
31906,
29477
],
"accumulated_depreciation_positive": [
16766,
16116
],
"net": [
15140,
13361
],
"consolidated_depreciation": [
2093,
1983
],
"cat_financial_leased_to_others_depreciation": [
699,
722
]
},
"operating_profit_bridge": {
"locator": "MD&A p33 Consolidated Operating Profit Comparison, original chart cat-20251231_g4.jpg; Definitions pp36–38",
"opening_2024": 13072,
"drivers": {
"sales_volume_including_product_mix": 1218,
"price_realization": -817,
"manufacturing_costs": -2148,
"sga_rd": -336,
"currency": -32,
"financial_products": 49,
"restructuring": -85,
"other": 230
},
"closing_2025": 11151,
"bridge_identity": "Company historical attribution, not structural marginal profit coefficients."
},
"revenue_bridge": {
"locator": "MD&A p31 Sales and Revenues Comparison",
"opening_2024": 64809,
"drivers": {
"sales_volume": 3389,
"price_realization": -817,
"currency": 45,
"financial_products": 163
},
"closing_2025": 67589
},
"segments_2025": {
"locator": "Note23 pp115–121; external-column Financial Products footnote is integral",
"rows": [
{
"name": "Construction Industries",
"external_column": 24800,
"intersegment_column": 260,
"total_sales": 25060,
"profit": 4675
},
{
"name": "Resource Industries",
"external_column": 12185,
"intersegment_column": 289,
"total_sales": 12474,
"profit": 1988
},
{
"name": "Power & Energy",
"external_column": 27143,
"intersegment_column": 5058,
"total_sales": 32201,
"profit": 6418
},
{
"name": "Financial Products",
"external_column": 4220,
"intersegment_column": 0,
"total_sales": 4220,
"profit": 966
}
],
"financial_products_external_column_includes_group_revenue": 712,
"reportable_sales_total": 73955,
"all_other_sales": 327,
"corporate_eliminations_sales": -6693,
"consolidated_sales": 67589,
"all_other_external_column": 46,
"all_other_intersegment_column": 281,
"corporate_external_column": -805,
"corporate_intersegment_column": -5888,
"reportable_profit_total": 14047,
"profit_reconciling_items": {
"all_other": -8,
"cost_centers": -11,
"corporate_costs": -1006,
"timing": -175,
"restructuring": -445,
"inventory_method": 49,
"postretirement_benefit": 185,
"sbc": -230,
"financing_costs": -180,
"currency": -81,
"goodwill_impairment": 0,
"other_income_expense_method": -470,
"other_method": -134
},
"consolidated_pretax_profit": 11541,
"interest_expense_excluding_financial_products": 502,
"other_income": 892,
"consolidated_operating_profit": 11151
}
},
"teaching_cvp": {
"source_id": "BFDE-CVP",
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"assumptions": "Constant prices and unit variable costs, fixed product mix, unchanged fixed costs within the relevant range; reported income here is model operating income.",
"companies": [
{
"name": "A",
"sales": 250000,
"variable_costs": 102000,
"fixed_costs": 63000,
"income": 85000
},
{
"name": "B",
"sales": 315000,
"variable_costs": 105000,
"fixed_costs": 125000,
"income": 85000
}
],
"sales_changes": [
0.1,
-0.2
]
}
},
"supplemental": {
"costco_ppe_original_labels": [
[
"land",
"Land",
"土地",
"N/A"
],
[
"buildings_improvements",
"Buildings and improvements",
"建筑及改良",
"5–50 years"
],
[
"equipment_fixtures",
"Equipment and fixtures",
"设备及装置",
"3–20 years"
],
[
"construction_in_progress",
"Construction in progress",
"在建工程",
"N/A"
],
[
"gross",
null,
"原值合计（原表该行无行名）",
null
],
[
"accumulated_depreciation_amortization_positive",
"Accumulated depreciation and amortization",
"累计折旧摊销（减项）",
null
],
[
"net",
"Property and equipment, net",
"物业及设备净额",
null
]
],
"cat_ppe_original_labels": [
[
"land",
"Land",
"土地",
"—"
],
[
"buildings",
"Buildings and land improvements",
"建筑及土地改良",
"20–45 years"
],
[
"machinery_equipment",
"Machinery, equipment and other",
"机器、设备及其他",
"2–10 years"
],
[
"capitalized_software",
"Software",
"软件",
"3–7 years"
],
[
"equipment_leased_to_others",
"Equipment leased to others",
"出租给他人的设备",
"1–7 years"
],
[
"construction_in_progress",
"Construction-in-process",
"在建工程",
"—"
],
[
"gross",
"Total property, plant and equipment, at cost",
"物业厂房设备成本合计",
null
],
[
"accumulated_depreciation_positive",
"Less: Accumulated depreciation",
"减：累计折旧",
null
],
[
"net",
"Property, plant and equipment–net",
"物业厂房设备净额",
null
]
],
"costco_receivables_exact_scope": {
"source_id": "BF-S-COST-FY2025-PDF",
"locator": "IR PDF printed pp41–42; SEC pp43–44, Receivables, Net",
"original_categories": [
"vendor",
"credit card incentive",
"reinsurance",
"third-party pharmacy",
"other receivables"
],
"explanation_zh": "其他应收主要为对政府的应收，多与税款有关。信用卡奖励应收不是顾客刷卡货款；结算期不超过四天的顾客刷卡货款另依现金政策列示。"
},
"costco_lease_2024": {
"operating_rou_asset": 2617,
"finance_lease_asset_net": 1433,
"operating_liability_current": 179,
"operating_liability_noncurrent": 2375,
"finance_liability_current": 147,
"finance_liability_noncurrent": 1351,
"total_assets": 4050,
"total_liabilities": 4052,
"operating_cost": 284,
"finance_asset_amortization": 97,
"finance_interest_expense": 58,
"variable_cost": 163,
"total_cost_reported": 602,
"cash_operating_leases": 274,
"cash_finance_interest": 58,
"cash_finance_principal": 136,
"remaining_term": [
19,
23
],
"discount_rate_percent": [
2.67,
4.59
]
},
"salesforce_lease_2025": {
"operating_rou_asset": 2157,
"operating_liability_current": 579,
"operating_liability_noncurrent": 2380,
"finance_lease_asset_gross": 1520,
"finance_accumulated_amortization_positive": 708,
"finance_lease_asset_net": 812,
"finance_liability_current": 337,
"finance_liability_noncurrent": 341,
"operating_cost": 684,
"finance_asset_amortization": 303,
"finance_interest_expense": 28,
"cash_operating_leases": 628,
"cash_finance_interest": 27,
"cash_finance_principal": 380,
"remaining_term": [
7,
3
]
},
"intangible_rows": [
{
"label_original": "Acquired developed technology",
"label_zh": "购入已开发技术",
"gross_open": 2958,
"gross_change_net": 1838,
"gross_close": 4796,
"accum_open": 1753,
"accum_change_net": 654,
"accum_close": 2407,
"net_open": 1205,
"net_close": 2389,
"remaining_years": 4.4
},
{
"label_original": "Customer relationships",
"label_zh": "客户关系",
"gross_open": 6894,
"gross_change_net": 1765,
"gross_close": 8659,
"accum_open": 3820,
"accum_change_net": 820,
"accum_close": 4640,
"net_open": 3074,
"net_close": 4019,
"remaining_years": 6.3
},
{
"label_original": "Other (1)",
"label_zh": "其他（商号、未开票订单、区域权利）",
"gross_open": 331,
"gross_change_net": 353,
"gross_close": 684,
"accum_open": 182,
"accum_change_net": 95,
"accum_close": 277,
"net_open": 149,
"net_close": 407,
"remaining_years": 2.1
}
],
"future_amortization": {
"buckets": [
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"FY2031",
"Thereafter"
],
"amounts": [
1842,
1412,
1104,
710,
448,
1299
]
},
"cat_profit_rows_original": [
[
"all_other",
"Profit from All Other Segment",
"其他分部利润"
],
[
"cost_centers",
"Cost centers",
"成本中心"
],
[
"corporate_costs",
"Corporate costs",
"公司共同成本"
],
[
"timing",
"Timing",
"确认时点差异"
],
[
"restructuring",
"Restructuring costs",
"重组成本"
],
[
"inventory_method",
"Inventory/cost of sales",
"存货／销售成本计量"
],
[
"postretirement_benefit",
"Postretirement benefit income (expense)",
"退休后福利收益（费用）"
],
[
"sbc",
"Stock-based compensation expense",
"股权薪酬费用"
],
[
"financing_costs",
"Financing costs",
"融资成本"
],
[
"currency",
"Currency",
"汇率"
],
[
"goodwill_impairment",
"Goodwill impairment charge",
"商誉减值"
],
[
"other_income_expense_method",
"Other income/expense methodology differences",
"其他损益计量方法差异"
],
[
"other_method",
"Other methodology differences",
"其他方法差异"
]
],
"cat_segment_costs_2025": {
"cost_of_goods_sold": [
18393,
9018,
22474,
0
],
"sga_rd": [
1902,
1513,
3330,
829
],
"other_segment_items": [
90,
-45,
-21,
2425
]
},
"cat_segments_2024": {
"rows": [
[
"Construction Industries",
25344,
111,
25455,
6165
],
[
"Resource Industries",
12100,
371,
12471,
2538
],
[
"Power & Energy",
24088,
4766,
28854,
5736
],
[
"Financial Products Segment",
4053,
0,
4053,
932
]
],
"total_profit": 15371,
"reconciling": [
43,
-1,
-889,
133,
-359,
33,
67,
-223,
-126,
145,
0,
-740,
-81
],
"pretax": 13373,
"revenue": 64809,
"reportable_revenue": 70833,
"all_other_revenue": 344,
"corporate_revenue": -6368
},
"cat_segment_name_overrides": {
"Financial Products": "Financial Products Segment"
},
"origins": {
"costco_lease_2024": "BF-S-COST-FY2025-PDF Note5 printed pp50–51 / PDF pp56–57, reopened 2026-09-21",
"salesforce_lease_2025": "BBC-C01 Note6 pp75–77, same-session full reading",
"intangible_rows": "BBC-C01 Note8 pp80–81, same-session full reading",
"cat_segment_costs_2025": "BBC-C04 Note23 p120, same-session full reading",
"cat_segments_2024": "BBC-C04 Note23 pp118,120–121; comparatives as recast in FY2025 filing"
}
},
"teaching": {
"asset": {
"identity": "Author synthetic example, not company transactions",
"unit": "teaching currency units",
"cost": 100,
"residual": 0,
"life_months": 60,
"initial_cash": 150,
"payment": "2026-01",
"acquisition": "2026-02",
"ready": "2026-04",
"start": "2026-01",
"months": 12,
"convention": "Events at month start; same-day acquisition then ready then payment; depreciation at month end starting ready month, full months, no tax/interest/disposal, depreciation expensed in this example."
},
"intangible": {
"identity": "Author synthetic accumulation model, not EPW estimates or Salesforce valuation",
"unit": "teaching currency units",
"rd": [
100,
120,
80
],
"sga_excluding_rd": [
60,
60,
60
],
"alpha": 1,
"gamma": 0.3,
"delta_r": 0.2,
"delta_s": 0.2,
"initial_r": 0,
"initial_s": 0,
"order": "Opening stock depreciates first; eligible current investment added at each period end. R&D and SG&A inputs do not overlap."
},
"cvp_extension": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"retail_cycle": {
"identity": "Author synthetic inventory/cash-timing example, not Costco days",
"unit": "teaching currency units and relative days",
"cost": 100,
"price": 150,
"acquire_day": 0,
"sale_day": 20,
"collect_day": 23,
"pay_day": 30,
"order": "Day start: acquire, sell, collect, pay. Same-day effects follow this explicit convention; cumulative net cash can be negative as a financing-gap measure, not an observed bank balance."
},
"subscription_cycle": {
"identity": "Author synthetic subscription funding example, not actual Salesforce contract",
"unit": "teaching currency units and relative 30-day months",
"amount": 120,
"invoice_day": 0,
"collection_day": 30,
"term_months": 12,
"monthly_cost": 6,
"month_days": 30,
"order": "Invoice and unconditional right at day0; each service month completed on day30*n; collection precedes same-day service cash cost. No refunds/tax, no costs before day30. Advances cover remaining service obligations."
}
},
"provenance": {
"lead_input_sha256": "5300ec0d05b830f8d6aa2ce72fd367beb3dc6bbfe044ff6cd28146e8beb7c68b",
"lead_input_lines": 209,
"transcription": "All supplied keys and amounts reproduced semantically; original byte hash identifies connector source, not this JSON serialization. Labels clarified in supplemental, raw observations unchanged.",
"reference_plan_sha256": "d6a351ea333643dc50af7704a7984a43fb623f24a058db74726b12c418a1494b"
},
"canonical_file": "https://ou-liu-red-sugar.github.io/notebook/labs/bf-de/inputs.json"
},
"default_outputs": {
"drivers": {
"identity": "Company historical attribution, not structural coefficients",
"unit": "USD million",
"revenue": {
"opening": 64809,
"rows": [
{
"label": "Sales Volume（含新产品）",
"value": 3389,
"before": 64809,
"after": 68198
},
{
"label": "Price Realization",
"value": -817,
"before": 68198,
"after": 67381
},
{
"label": "Currency",
"value": 45,
"before": 67381,
"after": 67426
},
{
"label": "Financial Products",
"value": 163,
"before": 67426,
"after": 67589
}
],
"computed": 67589,
"reported": 67589,
"residual": 0
},
"profit": {
"opening": 13072,
"rows": [
{
"label": "Sales Volume（含产品组合）",
"value": 1218,
"before": 13072,
"after": 14290
},
{
"label": "Price Realization",
"value": -817,
"before": 14290,
"after": 13473
},
{
"label": "Manufacturing Costs",
"value": -2148,
"before": 13473,
"after": 11325
},
{
"label": "SG&A / R&D",
"value": -336,
"before": 11325,
"after": 10989
},
{
"label": "Currency",
"value": -32,
"before": 10989,
"after": 10957
},
{
"label": "Financial Products",
"value": 49,
"before": 10957,
"after": 11006
},
{
"label": "Restructuring",
"value": -85,
"before": 11006,
"after": 10921
},
{
"label": "Other",
"value": 230,
"before": 10921,
"after": 11151
}
],
"computed": 11151,
"reported": 11151,
"residual": 0
}
},
"cvp": [
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": 0.1,
"new_sales": 275000,
"new_variable_costs": 112200.00000000001,
"added_fixed_cost": 0,
"linear_oi": 99800,
"new_oi": 99800,
"relative_oi_change": 0.17411764705882352,
"constant_parameter_identity": 0.17411764705882354,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": -0.2,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": -0.2,
"new_sales": 200000,
"new_variable_costs": 81600,
"added_fixed_cost": 0,
"linear_oi": 55400,
"new_oi": 55400,
"relative_oi_change": -0.34823529411764703,
"constant_parameter_identity": -0.3482352941176471,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "B",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 315000,
"base_variable_costs": 105000,
"fixed_costs": 125000,
"contribution": 210000,
"base_oi": 85000,
"dol": 2.4705882352941178,
"sales_change": 0.1,
"new_sales": 346500,
"new_variable_costs": 115500.00000000001,
"added_fixed_cost": 0,
"linear_oi": 106000.00000000003,
"new_oi": 106000.00000000003,
"relative_oi_change": 0.2470588235294121,
"constant_parameter_identity": 0.24705882352941178,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "B",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": -0.2,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 315000,
"base_variable_costs": 105000,
"fixed_costs": 125000,
"contribution": 210000,
"base_oi": 85000,
"dol": 2.4705882352941178,
"sales_change": -0.2,
"new_sales": 252000,
"new_variable_costs": 84000,
"added_fixed_cost": 0,
"linear_oi": 43000,
"new_oi": 43000,
"relative_oi_change": -0.49411764705882355,
"constant_parameter_identity": -0.49411764705882355,
"exact_linear_identity_applies": true
}
],
"cvp_step": {
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.2,
"step_enabled": true,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": 0.2,
"new_sales": 300000,
"new_variable_costs": 122400,
"added_fixed_cost": 10000,
"linear_oi": 114600,
"new_oi": 104600,
"relative_oi_change": 0.23058823529411765,
"constant_parameter_identity": 0.3482352941176471,
"exact_linear_identity_applies": false
}
},
"prompt": "你正在教 BF-17《单位经济、成本结构与经营杠杆》，材料版本2026-09-21。学习任务：核八项历史OI桥与A/B直接重算，证明线性条件下百分比恒等式。\n本篇没有行业分支；Caterpillar历史桥与OpenStax A/B教学模型均为核心必读，二者身份必须分开。 optional只有读者启用后才变为必读。先实际打开指定公开原文单元，分页读到单元结束，必要表图核原页，记录标题/版本/位置/范围与当前用途。文献目录、工具返回标题或作者先前已读记录都不能代替本次读取；runtime_reading_log从空数组开始。读取失败先找同版本正式等价原文，仍缺则说明该单元缺口，不凭摘要补讲。\n诊断任务：{\"core\": \"核八项历史OI桥与A/B直接重算，证明线性条件下百分比恒等式。\"}。补充任务：A销量下降20%，先用贡献利润算55,400，再从基点DOL得到同一结果。\n随后沿本包完整正文、实际输入、静态实验与题解推进一个完整任务，先让读者解释或计算再反馈；已会的基础跳过。默认迁移是在同一虚构A/B模型改变销量并核恒等式，再回到Caterpillar判断缺失结构输入；没有额外行业分支。通过尺度：有限变化固定参数时两结果完全一致；跨台阶另算新增成本，基点利润0不返回可用比率。\n保持真实披露、分析计算、教学模型三种身份，参数只改变模型，不反写真实公司数据。资料不足处不要补造差额或估值。最后明确：读者已经能独立重建什么，换一份材料时还需先核哪些条件？",
"selected_branch": "core",
"required_readings_by_branch": {
"core": [
{
"source_id": "BBC-C04",
"title": "Caterpillar Inc. — FY2025 Form 10-K",
"authors": [
"Caterpillar Inc."
],
"version": "FY ended 2025-12-31; comparatives recast in this filing after July 1, 2025 organization changes",
"access": {
"kind": "html_full_text",
"uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231.htm"
},
"required_unit": {
"locator": "MD&A pp31–35 and Definitions pp36–38",
"scope": "完整历史收入/利润说明、p33经营利润图全部八项、四个具名Definitions",
"purpose": "历史归因与模型输入区别",
"figure_uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231_g4.jpg"
},
"supports": "制造与出租资产用途、公司历史驱动定义、报告分部到收入/税前利润的完整桥。不得把volume包含的组合效果当结构性贡献率。",
"branch": "common"
},
{
"source_id": "BFDE-CVP",
"title": "Principles of Accounting Vol2 §3.5 — Margin of Safety and Operating Leverage",
"authors": [
"Mitchell Franklin",
"Patty Graybeal",
"Dixon Cooper",
"OpenStax"
],
"version": "2019",
"access": {
"kind": "html_full_text",
"uri": "https://openstax.org/books/principles-managerial-accounting/pages/3-5-calculate-and-interpret-a-companys-margin-of-safety-and-operating-leverage"
},
"required_unit": {
"locator": "§3.5 Operating Leverage and Company A/B",
"scope": "完整相关设置、表、变化与相关范围段",
"purpose": "正向CVP重算与有限变化恒等式"
},
"supports": "Company A/B虚构输入与经营杠杆；按原始表复算，不采用网页不一致的1.71、31.9%/46.9%。有限变化精确式由本篇条件推导。",
"branch": "common"
}
]
},
"required_readings_all_branches": [
{
"source_id": "BBC-C04",
"title": "Caterpillar Inc. — FY2025 Form 10-K",
"authors": [
"Caterpillar Inc."
],
"version": "FY ended 2025-12-31; comparatives recast in this filing after July 1, 2025 organization changes",
"access": {
"kind": "html_full_text",
"uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231.htm"
},
"required_unit": {
"locator": "MD&A pp31–35 and Definitions pp36–38",
"scope": "完整历史收入/利润说明、p33经营利润图全部八项、四个具名Definitions",
"purpose": "历史归因与模型输入区别",
"figure_uri": "https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231_g4.jpg"
},
"supports": "制造与出租资产用途、公司历史驱动定义、报告分部到收入/税前利润的完整桥。不得把volume包含的组合效果当结构性贡献率。",
"branch": "common"
},
{
"source_id": "BFDE-CVP",
"title": "Principles of Accounting Vol2 §3.5 — Margin of Safety and Operating Leverage",
"authors": [
"Mitchell Franklin",
"Patty Graybeal",
"Dixon Cooper",
"OpenStax"
],
"version": "2019",
"access": {
"kind": "html_full_text",
"uri": "https://openstax.org/books/principles-managerial-accounting/pages/3-5-calculate-and-interpret-a-companys-margin-of-safety-and-operating-leverage"
},
"required_unit": {
"locator": "§3.5 Operating Leverage and Company A/B",
"scope": "完整相关设置、表、变化与相关范围段",
"purpose": "正向CVP重算与有限变化恒等式"
},
"supports": "Company A/B虚构输入与经营杠杆；按原始表复算，不采用网页不一致的1.71、31.9%/46.9%。有限变化精确式由本篇条件推导。",
"branch": "common"
}
],
"branch_selection_protocol": "网页已选分支和展开的选读优先；切换后以相应 required_readings_by_branch 的完整数组替换必读，cross/all才读取所有主分支。运行日志从空开始。",
"experiment_ids": [
"EXP-BF17-HISTORICAL-VS-STRUCTURAL"
]
}
```
## Supplied entry
收入和利润把许多经营变化压成几个总额。要解释变化，我们需要重新展开销量、价格、组合、投入成本和共同费用；要预测一个条件变化的后果，还需要更明确的模型。本篇把这两项工作分开：先走完 Caterpillar 的真实历史驱动桥，再用参数透明的线性模型理解经营杠杆。完成以后，你应能判断一项数字究竟是历史归因，还是可以用于变式计算的模型参数。
主线约 15–20 分钟。历史公司图和教学模型使用不同单位与身份，实验也将它们分在两个视图。我们不把某家教材虚构公司改名成 Caterpillar。
## 1. 从历史总额回到变化来源
Caterpillar FY2025 将 2024 年收入 64,809 百万美元接到 2025 年 67,589。按其披露类别，完整桥为：[^bf17-cat]
| Sales and Revenues Comparison／收入桥原类别 | 影响，百万美元 |
|---|---:|
| 2024 Sales and revenues／期初年度收入 | 64,809 |
| Sales Volume／销售量相关影响 | +3,389 |
| Price Realization／价格实现 | −817 |
| Currency／汇率 | +45 |
| Financial Products／金融产品 | +163 |
| 2025 Sales and revenues／期末年度收入 | 67,589 |
收入增长了 2,780，但经营利润反而由 13,072 降至 11,151。公司原始经营利润比较图给出八个因素，全部列出才能核回终点：
| Consolidated Operating Profit Comparison／经营利润桥原类别 | 影响，百万美元 |
|---|---:|
| 2024 Operating profit | 13,072 |
| Sales Volume | +1,218 |
| Price Realization | −817 |
| Manufacturing Costs | −2,148 |
| SG&A / R&D | −336 |
| Currency | −32 |
| Financial Products | +49 |
| Restructuring | −85 |
| Other | +230 |
| 2025 Operating profit | 11,151 |
正向关系已经很清楚：本次披露中销量相关影响为正，但制造成本、价格及其他费用的不利影响更大，最终利润净减少 1,921。这是公司对历史变化的分类与解释。下一步要读定义，才能知道这些名字究竟捕捉了什么，而不是把每一行直接当教科书里的独立变量。
## 2. “Volume”不总是纯数量
Caterpillar 的 Definitions 说明：收入桥中的 Sales Volume 包含数量与新产品推出的影响；经营利润桥里的同名项目还包含产品组合。Price Realization 包含地域价格组合；Manufacturing Costs 包含按产量调整后的变动成本变化，以及期间制造成本的绝对变化。Financial Products 的汇率等影响又留在其自身类别中。[^bf17-def]
这意味着，$1,218/3,389\approx35.94\%$ 可以叫“这次两项披露效果之比”，却不是已经识别出的每台设备边际贡献率。你甚至还没有一个纯数量单位和对应单位变动成本。真实驱动桥依然有用：它指向要继续核验的成本、组合和定价证据；只是它所回答的是“公司怎样解释这一年”，不是“下一年每增加一台设备必然赚多少”。
现在我们主动换一种对象：建立一个条件足够清楚的小模型，让后一个问题可以被严格回答。
## 3. 线性模型里，经营杠杆为什么出现
假定只有一种产品，或固定产品组合；单位价格为 $p$，单位变动成本为 $v$，销量为 $q$，相关产量范围内固定成本为 $F$。那么销售额为 $S=pq$，贡献利润为 $C=(p-v)q$，经营利润为 $OI=C-F$。贡献利润先承担固定成本，余下部分才是模型经营利润。这里的“固定”是针对决策期间和产量范围而言，并非永远不能调整。
经营杠杆系数在基点利润非零时为 $DOL=C/OI$。把价格、单位变动成本、组合及固定成本保持不变，只让销量变化比例 $x$，新的贡献利润就是 $C(1+x)$，所以利润增量为 $Cx$。因此：
$$\frac{\Delta OI}{OI}=\frac{C}{OI}x=DOL\frac{\Delta S}{S}$$
在上述线性且参数不变的模型里，这对该次有限变化是精确恒等式，不是只能在极小变化下成立的近似。它也有局部弹性的含义；两种表述并不矛盾。直接重算与右式应给出相同结果。[^bf17-cvp]
OpenStax 的虚构 Company A／B 给出一个有区分力的基准，单位是普通美元，不是上面的百万美元：
| 模型项目 | Company A | Company B |
|---|---:|---:|
| Sales／销售额 | 250,000 | 315,000 |
| Variable costs／变动成本 | 102,000 | 105,000 |
| Contribution margin／贡献利润 | 148,000 | 210,000 |
| Fixed costs／固定成本 | 63,000 | 125,000 |
| Operating income／经营利润 | 85,000 | 85,000 |
| 由上述原始输入计算的DOL | 1.741176 | 2.470588 |
两者利润相同，但 B 有更大的贡献利润和固定成本。销售上升时，有更多新增贡献利润越过已覆盖的固定成本；下降时，同一固定成本又会使利润降得更快。
| 在固定参数内的销量／销售变化 | A新利润 | A利润变化 | B新利润 | B利润变化 |
|---|---:|---:|---:|---:|
| +10% | 99,800 | +17.4118% | 106,000 | +24.7059% |
| −20% | 55,400 | −34.8235% | 43,000 | −49.4118% |
例如 A 的 −20% 情景，直接算 $148,000\times0.8-63,000=55,400$；同样由 $1.741176\times(-20\%)$ 得利润下降约 34.8235%。两条路径相等。表格全部由原始输入复算，正文中的系数与百分比不采用教材网页中和这些输入不一致的数值。
## 4. 模型边界要用另一个计算展示
接近盈亏平衡时，基点利润小，DOL 会很大；这不代表企业获得了免费的高回报能力。当 $OI=0$ 时该比率无定义，程序应显示“基点利润为零”，而不是给一个能继续乘的无穷大。
再给 Company A 加一个明确的教学条件：销量比基准高出 15% 以后，必须新增 10,000 固定成本。若销量增加 20%，旧线性式先给 $148,000\times1.2-63,000=114,600$；跨产能台阶后实际模型利润为 104,600。此时参数已改变，旧 DOL 预测的 34.8235% 与新模型利润增长约 23.0588% 不再相等，差异来自新增固定成本，而非 DOL 公式突然不准确。
真实企业还可能改变售价、折扣、产品组合和投入方式。与其把这些全部塞进一个“调整后杠杆”，不如先说明是哪项条件变化，再建立新的成本桥。这样模型的差异能被经营资料核验。
## 5. 固定历史桥，与可变教学模型并排看
历史视图完整保留 Caterpillar 的两条桥，不用滑块把历史变成预测。模型视图允许选择 A／B、改变销量比例，并开启上面定义的产能台阶。图同时显示直接重算与恒定参数恒等式结果；在线性模式两条线重合，台阶模式才发生有解释的分离。每次图的变化都附有数值表，不依赖颜色猜结论。
## 6. 从推演回到资料
计算任务。Company B 在固定参数下销量下降 20%，请同时用贡献利润直接重算和 DOL 等式求结果。然后说明要把同样的模型用于 Caterpillar，还缺哪些输入。
解析。直接算 $210,000\times0.8-125,000=43,000$；利润下降 42,000，占原85,000的49.4118%。DOL为 $210,000/85,000=2.470588$，乘 −20% 得相同变化。迁移到 Caterpillar，仍需定义销量单位、纯价格、单位变动成本、产品组合、相关范围及固定成本，并处理报告桥里已混合的组合与新产品影响。
解释任务。Caterpillar 收入上升而利润下降，与 DOL 模型矛盾吗？
解析。不矛盾。固定参数模型没有允许售价、单位成本与固定成本同时变化，而公司历史桥恰恰披露了价格、制造成本等多项变化。正确的工作次序是先用真实定义解释历史，再判断是否具备建立某个条件模型的证据；不是拿一个模型系数覆盖全部经营过程。
[^bf17-cat]: Caterpillar FY2025 10-K，MD&A pp31–35，Sales and Revenues Comparison 与 Consolidated Operating Profit Comparison；[SEC 原件](https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231.htm)，[经营利润原图](https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231_g4.jpg)。两期为2024→2025，单位百万美元，取得日2026-09-21。
[^bf17-def]: 同一原件 Definitions pp36–38：Manufacturing Costs、Price Realization、Sales Volume、Financial Products。披露归因不等于独立因果识别或可外推结构参数。
[^bf17-cvp]: OpenStax, *Principles of Accounting, Volume 2: Managerial Accounting* (2019)，§3.5 的 Operating Leverage 与虚构 Company A/B 输入。[公开全节](https://openstax.org/books/principles-managerial-accounting/pages/3-5-calculate-and-interpret-a-companys-margin-of-safety-and-operating-leverage)。有限变化恒等式由本篇列明的线性假设推导；产能台阶为另设教学变式。
## Additional teaching material
## BF-17｜单位经济、成本结构与经营杠杆：静态实验
输入身份 `BFDE-SHARED-20260921-v1`。公司金额为百万美元；教学设备、现金例和资本模型为教学金额；CVP 为美元。
### 固定的CAT历史归因
| 原行／关系 | 影响金额 | 累计值 |
|---|---|---|
| 期初 | 64,809 | 64,809 |
| Sales Volume（含新产品） | 3,389 | 68,198 |
| Price Realization | -817 | 67,381 |
| Currency | 45 | 67,426 |
| Financial Products | 163 | 67,589 |
| 原表终点 | 67,589 | 67,589 |
| 原行／关系 | 影响金额 | 累计值 |
|---|---|---|
| 期初 | 13,072 | 13,072 |
| Sales Volume（含产品组合） | 1,218 | 14,290 |
| Price Realization | -817 | 13,473 |
| Manufacturing Costs | -2,148 | 11,325 |
| SG&A / R&D | -336 | 10,989 |
| Currency | -32 | 10,957 |
| Financial Products | 49 | 11,006 |
| Restructuring | -85 | 10,921 |
| Other | 230 | 11,151 |
| 原表终点 | 11,151 | 11,151 |
Volume含新产品，利润volume还含组合；price realization含地域组合。1218/3389不是结构性边际贡献率。
### 独立线性CVP
| 公司 | 收入 | 变动成本 | 固定成本 | OI |
|---|---|---|---|---|
| A | 250,000 | 102,000 | 63,000 | 85,000 |
| B | 315,000 | 105,000 | 125,000 | 85,000 |
| 公司 | sales变化% | 初始DOL | 新OI | 实际OI变化% | DOL×sales变化% |
|---|---|---|---|---|---|
| A | 10 | 1.741176 | 99,800 | 17.411765 | 17.411765 |
| A | -20 | 1.741176 | 55,400 | -34.823529 | -34.823529 |
| B | 10 | 2.470588 | 106,000 | 24.705882 | 24.705882 |
| B | -20 | 2.470588 | 43,000 | -49.411765 | -49.411765 |
固定价格、单位变动成本、组合与固定成本，且基点利润非零时，有限变化等式精确成立。局部弹性解释与此不矛盾。
| 台阶变式：A增加20% | 金额 |
|---|---|
| 恒定参数利润 | 114,600 |
| 超过15%新增固定成本 | 10,000 |
| 台阶后利润 | 104,600 |
新增固定成本是作者教学设定。基点OI=0时DOL及相对变化返回null，不显示无穷百分比为可用结果。
## Experiment inputs and static equivalents
```json
[
{
"id": "EXP-BF17-HISTORICAL-VS-STRUCTURAL",
"title": "单位经济、成本结构与经营杠杆：同源实验",
"anchor": "bf17-experiment",
"description": "真实桥固定历史输入。教学CM=sales-variable_costs；OI=CM-fixed_costs；DOL=CM/OI。固定参数时newOI=(1+x)CM-F，有限百分比关系精确；台阶另加10,000，基点OI零拒绝百分比。",
"inputs": {
"input_id": "BFDE-SHARED-20260921-v1",
"source": "https://ou-liu-red-sugar.github.io/notebook/labs/bf-de/inputs.json",
"identity": "历史观察与教学设定分别标识",
"values": {
"schema_version": "BFDE-1.0",
"input_id": "BFDE-SHARED-20260921-v1",
"revised": "2026-09-21",
"historical": {
"scope": [
"BF-12",
"BF-13",
"BF-14",
"BF-18",
"BF-17",
"BF-16"
],
"retrieved_on": "2026-09-21",
"identity": "Historical financial-statement observations; teaching cases are separately labelled. Values are not stock valuation inputs.",
"costco": {
"source_id": "BF-S-COST-FY2025-PDF",
"unit": "USD million",
"periods": [
"2025-08-31",
"2024-09-01"
],
"fiscal_weeks": [
52,
52
],
"ppe": {
"locator": "FY2025 annual-report PDF printed pp42–43; PDF pp48–49",
"land": [
10323,
9447
],
"buildings_improvements": [
25508,
23727
],
"equipment_fixtures": [
13127,
12387
],
"construction_in_progress": [
1882,
1389
],
"gross": [
50840,
46950
],
"accumulated_depreciation_amortization_positive": [
18931,
17918
],
"net": [
31909,
29032
]
},
"flows": {
"locator": "Printed pp35,39; PDF pp41,45",
"net_sales": [
269912,
249625
],
"merchandise_costs": [
239886,
222358
],
"cash_ppe_additions_outflow_positive": [
5498,
4710
],
"consolidated_depreciation_amortization": [
2426,
2237
],
"capex_included_in_liabilities_supplemental_noncash": [
193,
203
],
"cashflow_inventory_adjustment": [
559,
-2068
],
"cashflow_accounts_payable_adjustment": [
404,
1938
],
"cfo": [
13335,
11339
]
},
"working_capital": {
"locator": "Printed p37 balance sheet; pp41–42 Receivables, Net; p39 cash flow",
"inventory": [
18116,
18647
],
"accounts_payable": [
19783,
19421
],
"receivables_net": [
3203,
2721
],
"deferred_membership_fees": [
2854,
2501
],
"receivables_identity": "Includes vendor, credit-card, reinsurance and tax receivables; do not use total as customer credit-sale receivables.",
"payable_days_denominator": "Merchandise costs proxy, not independently observed credit purchases."
},
"leases_2025": {
"locator": "Note5 printed pp50–51; PDF pp56–57; policy printed p43",
"operating_rou_asset": 2725,
"finance_lease_asset_net": 1488,
"finance_asset_balance_sheet_location": "Other long-term assets",
"operating_liability_current": 208,
"operating_liability_noncurrent": 2460,
"finance_liability_current": 78,
"finance_liability_noncurrent": 1401,
"operating_cost": 271,
"finance_asset_amortization": 102,
"finance_interest_expense": 63,
"variable_cost": 182,
"total_cost_reported": 618,
"cash_operating_leases": 255,
"cash_finance_interest": 58,
"cash_finance_principal": 147,
"cash_scope": "Cash paid for amounts included in measurement of lease liabilities; not total lease cash payments including variable payments.",
"new_modified_operating_rou": 294,
"new_modified_finance_rou": 131,
"remaining_term_years_operating_finance": [
20,
25
],
"payment_buckets": [
"FY2026",
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"Thereafter"
],
"operating_payments": [
267,
250,
235,
204,
184,
2451
],
"operating_payments_total": 3591,
"operating_interest_deduction": 923,
"operating_liability": 2668,
"finance_payments": [
133,
132,
135,
122,
109,
1780
],
"finance_payments_total": 2411,
"finance_interest_deduction": 932,
"finance_liability": 1479,
"signed_not_commenced_payments_excluded": 1094,
"future_operating_sublease_income_not_netted": 92
}
},
"salesforce": {
"source_id": "BBC-C01",
"unit": "USD million",
"periods": [
"2026-01-31",
"2025-01-31"
],
"income": {
"locator": "Consolidated Statements of Operations p58 including notes1–2; MD&A Research and Development",
"total_revenue": [
41525,
37895
],
"rd_expense": [
5993,
5493
],
"rd_sbc_included": [
1162,
1091
],
"acquired_intangibles_amortization_cost_of_revenue": [
692,
750
],
"acquired_intangibles_amortization_sales_marketing": [
995,
901
]
},
"working_capital": {
"locator": "Balance sheet p57; Note2 Unearned Revenue p71; MD&A seasonal nature pp39–40",
"accounts_receivable_net": [
14339,
11945
],
"unearned_revenue": [
24317,
20743
],
"unearned_opening_2026": 20743,
"billings_and_other_2026": 45099,
"revenue_over_time_2026": 39041,
"revenue_point_in_time_2026": 2484,
"unearned_acquired_informatica": 651,
"identity": "Billings and other includes FX, contract assets and business combinations; neither cash receipts nor organic billings."
},
"leases_2026": {
"locator": "Note6 Leases and Other Commitments pp75–77; Note1 Leases pp67–68",
"operating_rou_asset": 2003,
"finance_lease_asset_gross": 1427,
"finance_accumulated_amortization_positive": 813,
"finance_lease_asset_net": 614,
"finance_asset_balance_sheet_location": "Property and equipment",
"operating_liability_current": 548,
"operating_liability_noncurrent": 2189,
"finance_liability_current": 275,
"finance_liability_noncurrent": 260,
"operating_cost": 614,
"finance_asset_amortization": 375,
"finance_interest_expense": 25,
"cash_operating_leases": 695,
"cash_finance_interest": 25,
"cash_finance_principal": 367,
"remaining_term_years_operating_finance": [
7,
3
],
"payment_buckets": [
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"FY2031",
"Thereafter"
],
"operating_payments": [
615,
571,
493,
338,
268,
790
],
"operating_payments_total": 3075,
"operating_interest_deduction": 338,
"operating_liability": 2737,
"finance_payments": [
289,
120,
76,
58,
26,
0
],
"finance_payments_total": 569,
"finance_interest_deduction": 34,
"finance_liability": 535
},
"informatica_2025_ppa": {
"locator": "Note7 Informatica, Inc., pp77–79",
"acquisition_period": "November 2025",
"status": "Preliminary purchase-price allocation at FY2026 filing; measurement period not complete",
"consideration_components": {
"cash": 9538,
"preexisting_relationship": 62,
"assumed_equity_purchase_component": 36
},
"consideration_total": 9636,
"assets": {
"cash": 1405,
"receivables": 233,
"ppe": 128,
"operating_rou": 27,
"other_assets": 149,
"goodwill": 5257,
"identifiable_intangibles": 3818
},
"liabilities_positive": {
"payables_accruals_current": 221,
"unearned_revenue": 651,
"operating_lease_liabilities": 30,
"other_noncurrent": 36,
"deferred_tax_liability": 443
},
"intangibles": [
{
"name": "Cloud developed technology",
"amount": 1350,
"life_years": 7
},
{
"name": "Other developed technology",
"amount": 270,
"life_years": 3
},
{
"name": "Customer relationships",
"amount": 1840,
"life_years": 10
},
{
"name": "Trade names",
"amount": 79,
"life_years": 4
},
{
"name": "Backlog",
"amount": 279,
"life_years": 2
}
],
"assumed_equity_fair_value": 330,
"assumed_equity_future_service_component": 294
},
"intangible_roll": {
"locator": "Note8 pp80–81; addition/retirement columns are net movements, not gross acquisition or amortization flows",
"gross_opening": 10183,
"additions_and_retirements_net": 3956,
"gross_closing": 14139,
"accum_amortization_opening_positive": 5755,
"expense_and_retirements_net_positive": 1569,
"accum_amortization_closing_positive": 7324,
"net_opening": 4428,
"net_closing": 6815,
"goodwill_opening": 51283,
"regrello": 704,
"informatica": 5257,
"other_acquisitions_adjustments": 697,
"goodwill_closing": 57941
},
"segment_identity": "One operating segment; Note1 p63 CODM assesses consolidated net income. Product offering revenue categories are not separately reported operating segments."
},
"caterpillar": {
"source_id": "BBC-C04",
"unit": "USD million",
"periods": [
"2025-12-31",
"2024-12-31"
],
"comparative_identity": "2024 figures as retrospectively adjusted in FY2025 filing after July 1, 2025 segment changes",
"ppe": {
"locator": "Note9 p89; Note1D pp64–65",
"land": [
616,
612
],
"buildings": [
7761,
7281
],
"machinery_equipment": [
13737,
12523
],
"capitalized_software": [
1696,
1609
],
"equipment_leased_to_others": [
6004,
5701
],
"construction_in_progress": [
2092,
1751
],
"gross": [
31906,
29477
],
"accumulated_depreciation_positive": [
16766,
16116
],
"net": [
15140,
13361
],
"consolidated_depreciation": [
2093,
1983
],
"cat_financial_leased_to_others_depreciation": [
699,
722
]
},
"operating_profit_bridge": {
"locator": "MD&A p33 Consolidated Operating Profit Comparison, original chart cat-20251231_g4.jpg; Definitions pp36–38",
"opening_2024": 13072,
"drivers": {
"sales_volume_including_product_mix": 1218,
"price_realization": -817,
"manufacturing_costs": -2148,
"sga_rd": -336,
"currency": -32,
"financial_products": 49,
"restructuring": -85,
"other": 230
},
"closing_2025": 11151,
"bridge_identity": "Company historical attribution, not structural marginal profit coefficients."
},
"revenue_bridge": {
"locator": "MD&A p31 Sales and Revenues Comparison",
"opening_2024": 64809,
"drivers": {
"sales_volume": 3389,
"price_realization": -817,
"currency": 45,
"financial_products": 163
},
"closing_2025": 67589
},
"segments_2025": {
"locator": "Note23 pp115–121; external-column Financial Products footnote is integral",
"rows": [
{
"name": "Construction Industries",
"external_column": 24800,
"intersegment_column": 260,
"total_sales": 25060,
"profit": 4675
},
{
"name": "Resource Industries",
"external_column": 12185,
"intersegment_column": 289,
"total_sales": 12474,
"profit": 1988
},
{
"name": "Power & Energy",
"external_column": 27143,
"intersegment_column": 5058,
"total_sales": 32201,
"profit": 6418
},
{
"name": "Financial Products",
"external_column": 4220,
"intersegment_column": 0,
"total_sales": 4220,
"profit": 966
}
],
"financial_products_external_column_includes_group_revenue": 712,
"reportable_sales_total": 73955,
"all_other_sales": 327,
"corporate_eliminations_sales": -6693,
"consolidated_sales": 67589,
"all_other_external_column": 46,
"all_other_intersegment_column": 281,
"corporate_external_column": -805,
"corporate_intersegment_column": -5888,
"reportable_profit_total": 14047,
"profit_reconciling_items": {
"all_other": -8,
"cost_centers": -11,
"corporate_costs": -1006,
"timing": -175,
"restructuring": -445,
"inventory_method": 49,
"postretirement_benefit": 185,
"sbc": -230,
"financing_costs": -180,
"currency": -81,
"goodwill_impairment": 0,
"other_income_expense_method": -470,
"other_method": -134
},
"consolidated_pretax_profit": 11541,
"interest_expense_excluding_financial_products": 502,
"other_income": 892,
"consolidated_operating_profit": 11151
}
},
"teaching_cvp": {
"source_id": "BFDE-CVP",
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"assumptions": "Constant prices and unit variable costs, fixed product mix, unchanged fixed costs within the relevant range; reported income here is model operating income.",
"companies": [
{
"name": "A",
"sales": 250000,
"variable_costs": 102000,
"fixed_costs": 63000,
"income": 85000
},
{
"name": "B",
"sales": 315000,
"variable_costs": 105000,
"fixed_costs": 125000,
"income": 85000
}
],
"sales_changes": [
0.1,
-0.2
]
}
},
"supplemental": {
"costco_ppe_original_labels": [
[
"land",
"Land",
"土地",
"N/A"
],
[
"buildings_improvements",
"Buildings and improvements",
"建筑及改良",
"5–50 years"
],
[
"equipment_fixtures",
"Equipment and fixtures",
"设备及装置",
"3–20 years"
],
[
"construction_in_progress",
"Construction in progress",
"在建工程",
"N/A"
],
[
"gross",
null,
"原值合计（原表该行无行名）",
null
],
[
"accumulated_depreciation_amortization_positive",
"Accumulated depreciation and amortization",
"累计折旧摊销（减项）",
null
],
[
"net",
"Property and equipment, net",
"物业及设备净额",
null
]
],
"cat_ppe_original_labels": [
[
"land",
"Land",
"土地",
"—"
],
[
"buildings",
"Buildings and land improvements",
"建筑及土地改良",
"20–45 years"
],
[
"machinery_equipment",
"Machinery, equipment and other",
"机器、设备及其他",
"2–10 years"
],
[
"capitalized_software",
"Software",
"软件",
"3–7 years"
],
[
"equipment_leased_to_others",
"Equipment leased to others",
"出租给他人的设备",
"1–7 years"
],
[
"construction_in_progress",
"Construction-in-process",
"在建工程",
"—"
],
[
"gross",
"Total property, plant and equipment, at cost",
"物业厂房设备成本合计",
null
],
[
"accumulated_depreciation_positive",
"Less: Accumulated depreciation",
"减：累计折旧",
null
],
[
"net",
"Property, plant and equipment–net",
"物业厂房设备净额",
null
]
],
"costco_receivables_exact_scope": {
"source_id": "BF-S-COST-FY2025-PDF",
"locator": "IR PDF printed pp41–42; SEC pp43–44, Receivables, Net",
"original_categories": [
"vendor",
"credit card incentive",
"reinsurance",
"third-party pharmacy",
"other receivables"
],
"explanation_zh": "其他应收主要为对政府的应收，多与税款有关。信用卡奖励应收不是顾客刷卡货款；结算期不超过四天的顾客刷卡货款另依现金政策列示。"
},
"costco_lease_2024": {
"operating_rou_asset": 2617,
"finance_lease_asset_net": 1433,
"operating_liability_current": 179,
"operating_liability_noncurrent": 2375,
"finance_liability_current": 147,
"finance_liability_noncurrent": 1351,
"total_assets": 4050,
"total_liabilities": 4052,
"operating_cost": 284,
"finance_asset_amortization": 97,
"finance_interest_expense": 58,
"variable_cost": 163,
"total_cost_reported": 602,
"cash_operating_leases": 274,
"cash_finance_interest": 58,
"cash_finance_principal": 136,
"remaining_term": [
19,
23
],
"discount_rate_percent": [
2.67,
4.59
]
},
"salesforce_lease_2025": {
"operating_rou_asset": 2157,
"operating_liability_current": 579,
"operating_liability_noncurrent": 2380,
"finance_lease_asset_gross": 1520,
"finance_accumulated_amortization_positive": 708,
"finance_lease_asset_net": 812,
"finance_liability_current": 337,
"finance_liability_noncurrent": 341,
"operating_cost": 684,
"finance_asset_amortization": 303,
"finance_interest_expense": 28,
"cash_operating_leases": 628,
"cash_finance_interest": 27,
"cash_finance_principal": 380,
"remaining_term": [
7,
3
]
},
"intangible_rows": [
{
"label_original": "Acquired developed technology",
"label_zh": "购入已开发技术",
"gross_open": 2958,
"gross_change_net": 1838,
"gross_close": 4796,
"accum_open": 1753,
"accum_change_net": 654,
"accum_close": 2407,
"net_open": 1205,
"net_close": 2389,
"remaining_years": 4.4
},
{
"label_original": "Customer relationships",
"label_zh": "客户关系",
"gross_open": 6894,
"gross_change_net": 1765,
"gross_close": 8659,
"accum_open": 3820,
"accum_change_net": 820,
"accum_close": 4640,
"net_open": 3074,
"net_close": 4019,
"remaining_years": 6.3
},
{
"label_original": "Other (1)",
"label_zh": "其他（商号、未开票订单、区域权利）",
"gross_open": 331,
"gross_change_net": 353,
"gross_close": 684,
"accum_open": 182,
"accum_change_net": 95,
"accum_close": 277,
"net_open": 149,
"net_close": 407,
"remaining_years": 2.1
}
],
"future_amortization": {
"buckets": [
"FY2027",
"FY2028",
"FY2029",
"FY2030",
"FY2031",
"Thereafter"
],
"amounts": [
1842,
1412,
1104,
710,
448,
1299
]
},
"cat_profit_rows_original": [
[
"all_other",
"Profit from All Other Segment",
"其他分部利润"
],
[
"cost_centers",
"Cost centers",
"成本中心"
],
[
"corporate_costs",
"Corporate costs",
"公司共同成本"
],
[
"timing",
"Timing",
"确认时点差异"
],
[
"restructuring",
"Restructuring costs",
"重组成本"
],
[
"inventory_method",
"Inventory/cost of sales",
"存货／销售成本计量"
],
[
"postretirement_benefit",
"Postretirement benefit income (expense)",
"退休后福利收益（费用）"
],
[
"sbc",
"Stock-based compensation expense",
"股权薪酬费用"
],
[
"financing_costs",
"Financing costs",
"融资成本"
],
[
"currency",
"Currency",
"汇率"
],
[
"goodwill_impairment",
"Goodwill impairment charge",
"商誉减值"
],
[
"other_income_expense_method",
"Other income/expense methodology differences",
"其他损益计量方法差异"
],
[
"other_method",
"Other methodology differences",
"其他方法差异"
]
],
"cat_segment_costs_2025": {
"cost_of_goods_sold": [
18393,
9018,
22474,
0
],
"sga_rd": [
1902,
1513,
3330,
829
],
"other_segment_items": [
90,
-45,
-21,
2425
]
},
"cat_segments_2024": {
"rows": [
[
"Construction Industries",
25344,
111,
25455,
6165
],
[
"Resource Industries",
12100,
371,
12471,
2538
],
[
"Power & Energy",
24088,
4766,
28854,
5736
],
[
"Financial Products Segment",
4053,
0,
4053,
932
]
],
"total_profit": 15371,
"reconciling": [
43,
-1,
-889,
133,
-359,
33,
67,
-223,
-126,
145,
0,
-740,
-81
],
"pretax": 13373,
"revenue": 64809,
"reportable_revenue": 70833,
"all_other_revenue": 344,
"corporate_revenue": -6368
},
"cat_segment_name_overrides": {
"Financial Products": "Financial Products Segment"
},
"origins": {
"costco_lease_2024": "BF-S-COST-FY2025-PDF Note5 printed pp50–51 / PDF pp56–57, reopened 2026-09-21",
"salesforce_lease_2025": "BBC-C01 Note6 pp75–77, same-session full reading",
"intangible_rows": "BBC-C01 Note8 pp80–81, same-session full reading",
"cat_segment_costs_2025": "BBC-C04 Note23 p120, same-session full reading",
"cat_segments_2024": "BBC-C04 Note23 pp118,120–121; comparatives as recast in FY2025 filing"
}
},
"teaching": {
"asset": {
"identity": "Author synthetic example, not company transactions",
"unit": "teaching currency units",
"cost": 100,
"residual": 0,
"life_months": 60,
"initial_cash": 150,
"payment": "2026-01",
"acquisition": "2026-02",
"ready": "2026-04",
"start": "2026-01",
"months": 12,
"convention": "Events at month start; same-day acquisition then ready then payment; depreciation at month end starting ready month, full months, no tax/interest/disposal, depreciation expensed in this example."
},
"intangible": {
"identity": "Author synthetic accumulation model, not EPW estimates or Salesforce valuation",
"unit": "teaching currency units",
"rd": [
100,
120,
80
],
"sga_excluding_rd": [
60,
60,
60
],
"alpha": 1,
"gamma": 0.3,
"delta_r": 0.2,
"delta_s": 0.2,
"initial_r": 0,
"initial_s": 0,
"order": "Opening stock depreciates first; eligible current investment added at each period end. R&D and SG&A inputs do not overlap."
},
"cvp_extension": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"retail_cycle": {
"identity": "Author synthetic inventory/cash-timing example, not Costco days",
"unit": "teaching currency units and relative days",
"cost": 100,
"price": 150,
"acquire_day": 0,
"sale_day": 20,
"collect_day": 23,
"pay_day": 30,
"order": "Day start: acquire, sell, collect, pay. Same-day effects follow this explicit convention; cumulative net cash can be negative as a financing-gap measure, not an observed bank balance."
},
"subscription_cycle": {
"identity": "Author synthetic subscription funding example, not actual Salesforce contract",
"unit": "teaching currency units and relative 30-day months",
"amount": 120,
"invoice_day": 0,
"collection_day": 30,
"term_months": 12,
"monthly_cost": 6,
"month_days": 30,
"order": "Invoice and unconditional right at day0; each service month completed on day30*n; collection precedes same-day service cash cost. No refunds/tax, no costs before day30. Advances cover remaining service obligations."
}
},
"provenance": {
"lead_input_sha256": "5300ec0d05b830f8d6aa2ce72fd367beb3dc6bbfe044ff6cd28146e8beb7c68b",
"lead_input_lines": 209,
"transcription": "All supplied keys and amounts reproduced semantically; original byte hash identifies connector source, not this JSON serialization. Labels clarified in supplemental, raw observations unchanged.",
"reference_plan_sha256": "d6a351ea333643dc50af7704a7984a43fb623f24a058db74726b12c418a1494b"
}
}
},
"outputs": {
"default": {
"drivers": {
"identity": "Company historical attribution, not structural coefficients",
"unit": "USD million",
"revenue": {
"opening": 64809,
"rows": [
{
"label": "Sales Volume（含新产品）",
"value": 3389,
"before": 64809,
"after": 68198
},
{
"label": "Price Realization",
"value": -817,
"before": 68198,
"after": 67381
},
{
"label": "Currency",
"value": 45,
"before": 67381,
"after": 67426
},
{
"label": "Financial Products",
"value": 163,
"before": 67426,
"after": 67589
}
],
"computed": 67589,
"reported": 67589,
"residual": 0
},
"profit": {
"opening": 13072,
"rows": [
{
"label": "Sales Volume（含产品组合）",
"value": 1218,
"before": 13072,
"after": 14290
},
{
"label": "Price Realization",
"value": -817,
"before": 14290,
"after": 13473
},
{
"label": "Manufacturing Costs",
"value": -2148,
"before": 13473,
"after": 11325
},
{
"label": "SG&A / R&D",
"value": -336,
"before": 11325,
"after": 10989
},
{
"label": "Currency",
"value": -32,
"before": 10989,
"after": 10957
},
{
"label": "Financial Products",
"value": 49,
"before": 10957,
"after": 11006
},
{
"label": "Restructuring",
"value": -85,
"before": 11006,
"after": 10921
},
{
"label": "Other",
"value": 230,
"before": 10921,
"after": 11151
}
],
"computed": 11151,
"reported": 11151,
"residual": 0
}
},
"cvp": [
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": 0.1,
"new_sales": 275000,
"new_variable_costs": 112200.00000000001,
"added_fixed_cost": 0,
"linear_oi": 99800,
"new_oi": 99800,
"relative_oi_change": 0.17411764705882352,
"constant_parameter_identity": 0.17411764705882354,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": -0.2,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": -0.2,
"new_sales": 200000,
"new_variable_costs": 81600,
"added_fixed_cost": 0,
"linear_oi": 55400,
"new_oi": 55400,
"relative_oi_change": -0.34823529411764703,
"constant_parameter_identity": -0.3482352941176471,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "B",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.1,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 315000,
"base_variable_costs": 105000,
"fixed_costs": 125000,
"contribution": 210000,
"base_oi": 85000,
"dol": 2.4705882352941178,
"sales_change": 0.1,
"new_sales": 346500,
"new_variable_costs": 115500.00000000001,
"added_fixed_cost": 0,
"linear_oi": 106000.00000000003,
"new_oi": 106000.00000000003,
"relative_oi_change": 0.2470588235294121,
"constant_parameter_identity": 0.24705882352941178,
"exact_linear_identity_applies": true
},
{
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "B",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": -0.2,
"step_enabled": false,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 315000,
"base_variable_costs": 105000,
"fixed_costs": 125000,
"contribution": 210000,
"base_oi": 85000,
"dol": 2.4705882352941178,
"sales_change": -0.2,
"new_sales": 252000,
"new_variable_costs": 84000,
"added_fixed_cost": 0,
"linear_oi": 43000,
"new_oi": 43000,
"relative_oi_change": -0.49411764705882355,
"constant_parameter_identity": -0.49411764705882355,
"exact_linear_identity_applies": true
}
],
"cvp_step": {
"identity": "OpenStax §3.5 fictional Company A/B example; not actual company observations",
"unit": "USD",
"company": "A",
"parameters": {
"identity": "Author optional capacity-step variation; not OpenStax original inputs or CAT facts",
"sales_change": 0.2,
"step_enabled": true,
"threshold": 0.15,
"step_fixed_cost": 10000
},
"base_sales": 250000,
"base_variable_costs": 102000,
"fixed_costs": 63000,
"contribution": 148000,
"base_oi": 85000,
"dol": 1.7411764705882353,
"sales_change": 0.2,
"new_sales": 300000,
"new_variable_costs": 122400,
"added_fixed_cost": 10000,
"linear_oi": 114600,
"new_oi": 104600,
"relative_oi_change": 0.23058823529411765,
"constant_parameter_identity": 0.3482352941176471,
"exact_linear_identity_applies": false
}
},
"all_defaults_file": "https://ou-liu-red-sugar.github.io/notebook/labs/bf-de/default-results.json"
},
"algorithm": "真实桥固定历史输入。教学CM=sales-variable_costs；OI=CM-fixed_costs；DOL=CM/OI。固定参数时newOI=(1+x)CM-F，有限百分比关系精确；台阶另加10,000，基点OI零拒绝百分比。",
"boundaries": "有限变化固定参数时两结果完全一致；跨台阶另算新增成本，基点利润0不返回可用比率。",
"local_url": "/notebook/labs/bf-de/interactions.html#EXP-BF17-HISTORICAL-VS-STRUCTURAL",
"static_equivalent": {
"html": "https://ou-liu-red-sugar.github.io/notebook/labs/bf-de/static.html#EXP-BF17-HISTORICAL-VS-STRUCTURAL",
"markdown": "https://ou-liu-red-sugar.github.io/notebook/labs/bf-de/static-equivalents.md"
}
}
]
```
## Sources
- [Caterpillar Inc. FY2025 Form 10-K](https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231.htm): 制造库存四阶段、部分LIFO与FIFO可比调整，以及NCI利润/权益归属；公司同时包含Financial Products。
- [Caterpillar FY2025 Consolidated Operating Profit Comparison](https://www.sec.gov/Archives/edgar/data/18230/000001823026000008/cat-20251231_g4.jpg): 期初13,072、八项归因及期末11,151；这是公司历史解释，不是独立因果估计。
- [Principles of Accounting Vol2 §3.5 — Margin of Safety and Operating Leverage](https://openstax.org/books/principles-managerial-accounting/pages/3-5-calculate-and-interpret-a-companys-margin-of-safety-and-operating-leverage): Company A/B虚构输入与经营杠杆；按原始表复算，不采用网页不一致的1.71、31.9%/46.9%。有限变化精确式由本篇条件推导。
## Content relations
```json
[
{
"from": "zh-bf17",
"relation": "part_of",
"to": "business-capital",
"reason": "主要 topic 归属"
},
{
"from": "zh-bf17",
"relation": "supported_by",
"to": "BBC-C04",
"reason": "指定原文支持本篇采用范围；不扩展为整份原件已读",
"locator": [
"Note1D pp64–65; Note9 p89",
"MD&A pp31–35; Definitions pp36–38",
"Note23 A/B/C pp115–118; profit p120; pretax reconciliation p121"
],
"scope": "制造与出租资产用途、公司历史驱动定义、报告分部到收入/税前利润的完整桥。不得把volume包含的组合效果当结构性贡献率。"
},
{
"from": "zh-bf17",
"relation": "supported_by",
"to": "BFDE-CAT-CHART",
"reason": "指定原文支持本篇采用范围；不扩展为整份原件已读",
"locator": [
"MD&A p33 original chart"
],
"scope": "期初13,072、八项归因及期末11,151；这是公司历史解释，不是独立因果估计。"
},
{
"from": "zh-bf17",
"relation": "supported_by",
"to": "BFDE-CVP",
"reason": "指定原文支持本篇采用范围；不扩展为整份原件已读",
"locator": [
"§3.5 full section; Operating Leverage; Company A/B tables and relevant-range discussion"
],
"scope": "Company A/B虚构输入与经营杠杆；按原始表复算，不采用网页不一致的1.71、31.9%/46.9%。有限变化精确式由本篇条件推导。"
},
{
"from": "zh-bf17",
"relation": "illustrated_by",
"to": "CASE-BFDE-CAT-BF17-20260921",
"reason": "固定期间的教学案例，不指向动态最新研究"
},
{
"from": "zh-bf17",
"relation": "uses_method",
"to": "zh-bf18",
"reason": "局部调用资源/计量/边界关系，可在本文补齐；不是整篇硬先修"
},
{
"from": "bf17-experiment",
"relation": "illustrated_by",
"to": "EXP-BF17-HISTORICAL-VS-STRUCTURAL",
"reason": "真实桥固定历史输入。教学CM=sales-variable_costs；OI=CM-fixed_costs；DOL=CM/OI。固定参数时newOI=(1+x)CM-F，有限百分比关系精确；台阶另加10,000，基点OI零拒绝百分比。",
"at_section": "bf17-experiment",
"conditions": "有限变化固定参数时两结果完全一致；跨台阶另算新增成本，基点利润0不返回可用比率。"
}
]
```
## Related entries
## Optional reading path
拆一份企业财报: step 9/14
把公司历史利润桥与明确条件的经营杠杆模型分开。
同样的经营利润，也会因收付款时间形成不同的资金需要。
Next: [营运资本与现金周转](https://ou-liu-red-sugar.github.io/zh/notebook/working-capital-and-cash-cycle/)