The selected simplified SGR formula本文选定的简化 SGR 公式
This page defines sustainable growth rate (SGR) = retention ratio × return on equity (ROE). Retention = 1 − ordinary-dividend payout; ROE = common-attributable net income ÷ average common equity. The model estimates growth compatible with retained earnings when profitability, payout, asset use and leverage stay stable and no common equity is raised. It is not a revenue, earnings, book-value or share-price forecast. Buybacks, special dividends, weak denominators and external financing need separate treatment.
本文定义：可持续增长率（SGR）＝留存率×净资产收益率（ROE）；其中，留存率＝1−普通股股利支付率，ROE＝归属于普通股股东的净利润÷平均普通股权益。该模型估计在盈利能力、分配政策、资产使用和杠杆保持稳定且不增发普通股时，留存收益能够支持的增长速度。它不是收入、利润、账面价值或股价增长的预测或保证。回购、特别股利、负盈利、异常权益分母及外部融资必须另行处理。
Close the model before trusting the output先封闭模型，再使用结果
| Model condition | Simplified SGR assumes | When the condition breaks |
|---|---|---|
| Profitability | ROE remains near the selected normalized level | Margin, tax, asset impairment or cycle changes retained earnings |
| Payout policy | The ordinary-dividend payout ratio remains stable | Special dividends, omitted dividends or buybacks change owner distributions |
| Asset intensity | Asset turnover remains stable as the business grows | New plants, inventory or receivables require a different asset base |
| Leverage | The assets-to-equity relationship is maintained | Deleveraging constrains funding; additional debt can fund faster growth at higher risk |
| External equity | No new common equity is issued | An issuance expands funds but also changes average equity and measured ROE |
| Accounting scope | Earnings and equity belong to the same common shareholders | NCI, preferred claims, disposal or restatement creates a scope mismatch |
| 模型条件 | 简化 SGR 的假设 | 条件失效时 |
|---|---|---|
| 盈利能力 | ROE 保持在所选正常水平附近 | 利润率、税项、资产减值或周期改变留存收益 |
| 分配政策 | 普通股股利支付率保持稳定 | 特别股利、停派股利或回购改变所有者分配 |
| 资产强度 | 业务增长时资产周转保持稳定 | 新厂、库存或应收款需要不同资产基数 |
| 杠杆 | 资产与权益关系保持稳定 | 去杠杆限制资金；新增债务可支持更快增长但风险更高 |
| 外部权益 | 不增发普通股 | 增发扩大资金，同时改变平均权益与已测 ROE |
| 会计范围 | 盈利与权益属于同一组普通股股东 | NCI、优先权益、处置或重述造成范围错配 |
“Sustainable” means financing consistency here, not environmental performance or indefinite competitive endurance. If management retains the stated common earnings and repeats the ROE without changing leverage or issuing equity, internal equity can support similar proportional expansion. The model does not specify what grows: turnover can move revenue faster, while OCI or owner transactions change book equity differently.
这里的“可持续”指在这些假设下融资关系能够保持一致，不是环境可持续性，也不是竞争优势可以无限延续。它更像一个有条件的容量：如果管理层留存既定比例的普通股盈利，以既定 ROE 经营，同时不改变杠杆且不增发权益，那么内部权益增长可以支持相近比例的扩张。模型没有规定究竟哪项必须按该速度增长。资产周转改善时收入可能更快；其他综合收益、所有者交易或会计调整又会让账面权益采用不同速度。
Construct retention and ROE from matched claims用归属匹配的项目构建留存率与 ROE
Use common-attributable net income. Deduct preferred dividends where needed; do not pair income including NCI with parent common equity. Separate reported and normalized earnings.
普通股盈利分子使用归属于普通股股东的净利润；必要时扣除优先股股利，也不能把包含 NCI 的合并净利润与母公司普通股权益相配。已报告盈利与正常化盈利应分列。
Simple average = (opening + closing common equity) ÷ 2. Major mid-period issuances, repurchases or distributions may require time weighting.
平均普通股权益分母简单平均值＝（期初普通股权益＋期末普通股权益）÷2。若期中发生重大增发、回购、分配或收购，还应采用时间加权或事件感知分析。
Payout = ordinary common dividends ÷ common net income. Use recognized dividends consistently and explain proposed or post-period dividends.
普通股股利支付率支付率＝归属于普通股股东的普通股股利÷其净利润。分析期间内应一致采用已确认股利；拟派或期后股利需要明确说明处理。
Retention = 1 − payout, or (common income − ordinary dividends) ÷ common income when positive. Buybacks require a separately defined total-payout version.
留存率留存率＝1−支付率；当利润为正时，也等于（普通股净利润−普通股股利）÷普通股净利润。除非另建总分配口径，这个捷径并不包含回购。
| Input condition | Arithmetic result | Analytical treatment |
|---|---|---|
| Net income is zero | Dividend payout division is undefined | Do not calculate retention or SGR from this formula |
| Net loss | Payout and retention signs become economically confusing | Report loss, distributions and equity change in currency |
| Average equity is zero | ROE is undefined | Mark SGR not meaningful |
| Average equity is negative | ROE can reverse sign or appear favorable | Do not interpret the product as growth capacity |
| Dividend exceeds earnings | Payout >100%; retention <0% | Identify special distribution or under-earning; negative SGR is not a forecast |
| Very small positive equity | ROE and SGR become extreme | Show numerator and denominator amounts; avoid a precise capacity claim |
| 输入条件 | 算术结果 | 分析处理 |
|---|---|---|
| 净利润为零 | 股利支付率除法无定义 | 不能用本公式计算留存率或 SGR |
| 净亏损 | 支付率与留存率符号失去直观经济含义 | 用金额报告亏损、分配与权益变化 |
| 平均权益为零 | ROE 无定义 | 把 SGR 标为无意义 |
| 平均权益为负 | ROE 可能反转符号或看似有利 | 不能把乘积解释为增长能力 |
| 股利超过盈利 | 支付率超过 100%，留存率低于 0% | 识别特别分配或盈利不足；负 SGR 不是预测 |
| 很小的正权益 | ROE 与 SGR 变得极端 | 展示分子和分母金额，避免精确容量结论 |
Worked model: Kestrel Valve funds a steady year案例模型：Kestrel Valve 为稳定年度融资
Kestrel Valve Services is a fictional industrial-valve maintenance company. Amounts are illustrative CU millions for 20X4. Revenue is 180, common-attributable net income 18 and ordinary dividends 7.2. Opening common equity is 94.6 and closing equity 105.4. Assume no preferred dividends, NCI, issuance, repurchase or OCI; the CU10.8 increase equals retained earnings.
Kestrel Valve Services 是虚构的工业阀门巡检与维护公司。所有金额均为截至 20X4 年 12 月 31 日年度的 CU 百万演示数据。公司收入 180，归属于普通股股东净利润 18，普通股股利 7.2；期初普通股权益 94.6，期末 105.4。假设层：没有优先股股利、NCI、增发、回购或其他综合收益；权益增加 CU10.8 正好等于留存收益。
| Baseline step | Formula | Result |
|---|---|---|
| Average common equity | (94.6 + 105.4) ÷ 2 | 100.0 |
| ROE | 18 ÷ 100.0 | 18.0% |
| Ordinary-dividend payout ratio | 7.2 ÷ 18 | 40.0% |
| Retention ratio | 1 − 40.0% | 60.0% |
| Simplified SGR | 60.0% × 18.0% | 10.8% |
| 基准步骤 | 公式 | 结果 |
|---|---|---|
| 平均普通股权益 | （94.6＋105.4）÷2 | 100.0 |
| ROE | 18÷100.0 | 18.0% |
| 普通股股利支付率 | 7.2÷18 | 40.0% |
| 留存率 | 1−40.0% | 60.0% |
| 简化 SGR | 60.0%×18.0% | 10.8% |
The 10.8% model rate differs from actual equity growth: (105.4 − 94.6) ÷ 94.6 = 11.42%. ROE uses average equity while the roll-forward uses beginning equity. On beginning equity, ROE = 18 ÷ 94.6 = 19.03% and SGR = 60% × 19.03% = 11.42%. Average equity reflects period capital, but its timing convention must remain attached.
10.8% 是模型速率，并非期末权益的精确变化。普通股权益实际增长＝（105.4−94.6）÷94.6＝11.42%。差异来自本文用平均权益计算 ROE，而权益滚动表用期末与期初比较。若用期初权益，ROE＝18÷94.6＝19.03%，60%×19.03%＝11.42%，恰好等于留存收益除以期初权益。平均权益更能反映期间内使用的资本，但必须把时点约定附在结果旁。
Facts: the fictional amounts. Calculations: average equity, ROE, payout, retention and growth comparisons. Assumptions: aligned scope, no other equity movements and stable relationships. Interpretation: 10.8% is the simplified internally funded rate. Missing: dividend dates, buybacks, debt policy, asset needs, normalized margins and repeatability of ROE.
证据状态事实层：仅包括上述虚构金额。计算层：平均权益、ROE、支付率、留存率及两个增长比较。假设层：普通股股东范围匹配、没有其他权益变动且未来关系稳定。解释层：10.8% 是简化模型下 Kestrel 的内部融资速率。缺失证据：股利宣告日期、回购、债务政策、资产需求、维护积压、正常化利润率、税项及 20X4 年 ROE 能否重复。
Open ROE with a DuPont control panel用杜邦控制面板拆开 ROE
Assume average assets of CU200. The DuPont identity is ROE = net margin × asset turnover × equity multiplier. Kestrel’s margin = 18 ÷ 180 = 10.0%; turnover = 180 ÷ 200 = 0.90×; multiplier = 200 ÷ 100 = 2.00×. The product is 18.0% ROE.
ROE 输入不能被视为固定黑箱。案例假设平均总资产为 CU200。三因素杜邦恒等式为：ROE＝净利率×资产周转率×权益乘数。Kestrel 净利率＝18÷180＝10.0%；资产周转率＝180÷200＝0.90 倍；权益乘数＝200÷100＝2.00 倍。三者相乘为 10.0%×0.90×2.00＝18.0% ROE。
| Control | Raises model SGR when… | Question before accepting it |
|---|---|---|
| Net margin | Pricing, mix or efficiency raises profit per revenue unit | Is the gain recurring, cash-supported and after tax? |
| Asset turnover | Existing workshops and service vehicles support more revenue | Did receivables, spares or leased assets move outside the selected asset base? |
| Equity multiplier | More assets are funded for each unit of equity | Did debt, lease or refinancing risk rise? |
| Retention | Less common profit is distributed as ordinary dividends | Can retained cash be reinvested at the historical ROE? |
| 控制项 | 何时提高模型 SGR | 接受前要问 |
|---|---|---|
| 净利率 | 定价、组合或效率提高每单位收入利润 | 改善是否可重复、有现金支持且为税后结果？ |
| 资产周转 | 现有车间与服务车辆支持更多收入 | 应收、备件或租赁资产是否移出所选资产基数？ |
| 权益乘数 | 每单位权益为更多资产融资 | 债务、租赁或再融资风险是否上升？ |
| 留存率 | 作为普通股股利分配的利润减少 | 留存现金能否继续以历史 ROE 再投资？ |
Margin and turnover gains may reflect stronger operations, but need evidence. A higher equity multiplier raises ROE and SGR without operational improvement because equity supports more obligations. Higher retention supplies capital, yet poor incremental returns can still destroy value.
该恒等式避免把更高 SGR 自动视为利好。利润率与周转改善可能反映更强经营，但各自仍需证据。权益乘数上升即使没有任何经营改善，也能推高 ROE 与 SGR，因为同一权益支撑了更多资产和义务。提高留存确实提供更多内部资本，但若新增投资回报很差，即使用“可持续”命名也不会创造价值。
Change one funding control at a time每次只改变一个资金控制项
| Illustrative scenario | Recalculation | What the number does not say |
|---|---|---|
| Net margin falls from 10% to 8% | ROE = 8% × 0.90 × 2.00 = 14.4%; SGR = 60% × 14.4% = 8.64% | Whether margin recovers or payout changes |
| Asset turnover rises from 0.90× to 1.05× | ROE = 10% × 1.05 × 2.00 = 21.0%; SGR = 12.6% | Whether CU210 revenue can use CU200 assets without service deterioration |
| Equity multiplier rises from 2.00× to 2.50× | ROE = 10% × 0.90 × 2.50 = 22.5%; SGR = 13.5% | The extra debt or other liabilities and their repayment risk |
| Dividend payout rises from 40% to 70% | Retention = 30%; SGR = 30% × 18% = 5.4% | Whether the higher distribution is regular or temporary |
| CU20 common equity issued at period start; income unchanged | Average equity = 120; ROE = 18 ÷ 120 = 15%; simplified SGR = 60% × 15% = 9.0% | External equity added CU20 funding, so the no-issuance model no longer describes total capacity |
| 演示情景 | 重新计算 | 数字没有说明什么 |
|---|---|---|
| 净利率从 10% 降至 8% | ROE＝8%×0.90×2.00＝14.4%；SGR＝60%×14.4%＝8.64% | 利润率会否恢复或分配政策会否改变 |
| 资产周转从 0.90 倍升至 1.05 倍 | ROE＝10%×1.05×2.00＝21.0%；SGR＝12.6% | CU200 资产能否承载 CU210 收入且服务不恶化 |
| 权益乘数从 2.00 倍升至 2.50 倍 | ROE＝10%×0.90×2.50＝22.5%；SGR＝13.5% | 新增债务或其他负债及其偿还风险 |
| 股利支付率从 40% 升至 70% | 留存率＝30%；SGR＝30%×18%＝5.4% | 更高分配是常规还是暂时 |
| 期初增发 CU20 普通股，利润不变 | 平均权益＝120；ROE＝18÷120＝15%；简化 SGR＝60%×15%＝9.0% | 外部权益增加 CU20 资金，因此无增发模型不再描述总容量 |
These are mechanical scenarios, not forecasts. After issuance, SGR falls because income is divided by more equity, yet the company has more cash. Calling 9.0% reduced total capacity would invert the economics. Leverage likewise raises modeled SGR while weakening resilience. Rebuild funding needs instead of selecting the highest output.
这些都是每次只改变一个变量的机械情景，不是预测。增发情景尤其重要：相同利润除以更多权益使 SGR 降低，但公司拥有更多现金可投资。若把 9.0% 解读为总增长能力下降，就颠倒了经济含义。同样，杠杆可以提高模型 SGR，却削弱韧性。该表用于定位变化的假设，之后应重建资产负债表与现金需求，而不是挑选最高结果。
Classic retention subtracts dividends, not repurchases. A labeled total-payout ratio can use (dividends + net repurchases) ÷ common income. Adding CU6 repurchases gives payout = (7.2 + 6) ÷ 18 = 73.33% and retention = 26.67%. Because buybacks reduce equity and can lift future ROE, adjust both payout and the ROE denominator.
回购需要第二种分配口径经典留存率扣除普通股股利，不包含股份回购。可另列“总分配率”＝（普通股股利＋净回购）÷普通股净利润。在 Kestrel 基准上加入 CU6 净回购，总分配率＝（7.2＋6）÷18＝73.33%，总留存率＝26.67%；但回购还会减少权益并机械推高未来 ROE。不能只在等式一边加入回购，却不调整 ROE 分母。
Reconcile actual growth without calling the gap failure调节实际增长，但不要把差距直接称为失败
| Observed relationship | Possible funding explanation | Evidence required |
|---|---|---|
| Actual revenue growth above SGR | Unused cash, more debt, new equity, higher turnover, acquisition or temporary margin | Cash roll-forward, financing note, asset turnover and acquisition contribution |
| Actual revenue growth below SGR | Demand constraint, deliberate deleveraging, capacity delay or distribution | Order/service data, debt repayment, capex schedule and equity statement |
| Book equity grows above simplified SGR | Equity issuance, OCI, share-based compensation or scope change | Statement of changes in equity and transaction notes |
| ROE rises while operations are flat | Buyback, impairment-shrunken equity or added leverage | Equity roll-forward, impairment and debt notes |
| High SGR but weak cash generation | Profit is tied up in receivables, inventory or capital expenditure | Cash-flow statement, working accounts and investment commitments |
| 观察关系 | 可能的资金解释 | 所需证据 |
|---|---|---|
| 实际收入增速高于 SGR | 闲置现金、更多债务、新权益、更高周转、收购或临时利润率 | 现金滚动、融资附注、资产周转与收购贡献 |
| 实际收入增速低于 SGR | 需求受限、主动去杠杆、产能延迟或所有者分配 | 订单／服务数据、偿债、资本开支计划与权益变动表 |
| 账面权益增长高于简化 SGR | 权益增发、OCI、股份薪酬或范围变化 | 权益变动表与交易附注 |
| 经营平稳但 ROE 上升 | 回购、减值压缩权益或新增杠杆 | 权益滚动、减值及债务附注 |
| SGR 高但现金创造弱 | 利润被应收、库存或资本开支占用 | 现金流量表、营运账户与投资承诺 |
Report 10.8% with its period and definitions; separate supported assumptions from those merely held constant; then explain any actual-growth gap through financing or operations. Growth above SGR is not automatically excessive, nor growth below it inefficient. The model diagnoses funding; demand, incremental returns and risk determine whether using capacity makes sense.
有效结论包含三层。第一，报告 10.8% 及其期间和输入定义。第二，说明哪些假设有证据支持，哪些只是暂时保持不变。第三，指出解释实际增长差距的融资行动或经营变化。不能把高于 SGR 的增长自动称为过度，也不能把低于 SGR 的增长称为低效。该模型诊断的是资金关系；是否值得使用这项容量，还取决于战略、需求、增量回报与风险。
Build an auditable SGR input pack建立可审计的 SGR 输入包
InfiniSynapse operates Stock Explained and publishes this page. Upload multi-period income statements, balance sheets, equity statements, dividends, preferred and NCI schedules, repurchases, debt, issuances, assets and revenue. Ask the tool to preserve holder scope, dates, units and source pages while separating reported inputs from normalized scenarios.
Use output as an evidence index, not a forecast. Check every profit, equity, dividend, repurchase, debt and issuance against the originals; recompute average equity, payout, retention, DuPont components and SGR. Do not infer dividend policy, buyback execution, future leverage, incremental return, current market data or durability.
InfiniSynapse 运营“一眼看懂这只股票”并发布本页。上传多期利润表、期初与期末资产负债表、权益变动表、股利宣告、优先股与 NCI 明细、回购记录、债务及租赁附注、股份增发、资产与收入数据，以及管理层自定义 ROE 调节。要求工具保留权益持有人范围、日期、单位和来源页，并把已报告输入与正常化情景分开。
输出只能作为证据索引，不能作为增长预测。每项利润、权益、股利、回购、债务与增发金额都要回到上传原件核验；平均权益、支付率、留存率、杜邦组成与 SGR 必须独立复算。不要推断未提供的股利政策、回购执行、未来杠杆、增量回报、资本需求、当前市场数据或增长持续性。
Upload earnings, equity, dividends, repurchases, debt and issuance notes; preserve holder scope and dates before calculating the conditional funding rate.
上传盈利、权益、股利、回购、债务与增发附注，在计算条件资金速率前保留持有人范围与日期。
Open Stock Explained打开“一眼看懂这只股票”Questions after calculating sustainable growth计算可持续增长率后的常见问题
No. The simplified SGR is a funding-consistency estimate built from retention and ROE. Revenue can differ because asset turnover, pricing, capacity, acquisition, currency or demand changes. Treat any comparison with revenue growth as a reconciliation question, not a forecast error.
可持续增长率等于预期收入增速吗？不等于。简化 SGR 是基于留存率与 ROE 的资金一致性估计。资产周转、定价、产能、收购、汇率或需求变化都会使收入增速不同。把两者的差异当作需要调节的问题，而不是预测误差。
This page uses average common equity to represent capital employed through the period. Beginning equity can make retained earnings growth tie exactly in a simple end-of-period model, as Kestrel demonstrates. State the choice, keep holder scope aligned and use the same convention across periods; major equity events may require time weighting.
ROE 应使用期初权益还是平均权益？本文使用平均普通股权益，以代表期间内投入资本。Kestrel 案例显示，在简单期末模型中，使用期初权益可让留存收益增长精确勾稽。必须声明选择、统一持有人范围并跨期一致；重大权益事项可能需要时间加权。
Not in the classic dividend-only definition. Show repurchases separately or create a clearly labeled total-payout version. Because a buyback also reduces equity, it may raise later ROE mechanically. Adjust both the payout analysis and equity denominator rather than treating repurchases as dividends on only one side.
股份回购会降低留存率吗？在经典的仅股利定义中不会。应单独展示回购，或建立明确标记的总分配版本。回购还会减少权益，机械推高后续 ROE；因此必须同时调整分配分析与权益分母，不能只在一边把回购当股利。
If a higher equity multiplier raises ROE while margin and turnover stay fixed, retention × ROE rises mechanically. The model has not measured interest coverage, maturity or refinancing risk. A leverage-driven increase therefore signals a changed financing assumption, not free operating growth.
为什么增加债务会提高 SGR？若净利率与周转率不变，较高权益乘数会提高 ROE，留存率×ROE 也会机械上升。模型并未测量利息保障、到期或再融资风险。因此，杠杆推动的增幅代表融资假设改变，不是免费获得的经营增长。
The arithmetic may produce signs, but the economic interpretation usually fails. A loss makes dividend payout and retention misleading; zero equity makes ROE undefined; negative or tiny equity can reverse or explode ROE. Report the underlying amounts and mark SGR not meaningful until the denominator and earnings normalize.
净亏损或负权益时可以计算 SGR 吗？算术可能产生符号，但经济解释通常失效。亏损会让股利支付率与留存率误导；权益为零使 ROE 无定义；负权益或很小权益会反转或放大 ROE。应报告基础金额，并在分母与盈利恢复前把 SGR 标为无意义。
No. Retention supplies internal funds, but the model assumes those funds earn the selected ROE. If incremental projects earn less, absorb cash for longer or increase risk, retaining more can lower value even while formula SGR rises. Compare incremental returns and capital needs separately.
更高留存率一定提高增长质量吗？不一定。留存提供内部资金，但模型假设这些资金能获得所选 ROE。若新增项目回报更低、占用现金更久或增加风险，即使公式 SGR 上升，更多留存仍可能降低价值。必须另行比较增量回报与资本需求。
Authoritative sources and model boundary权威来源与模型边界
The CFA Institute source discusses the simplified retention-rate × ROE relationship. SEC financial-statement guidance supplies statement context; FASB Concepts Statement 8 describes equity and owner distributions; IAS 1 supplies presentation context for owner changes and dividends; SEC Rule 10b-18 FAQs supply issuer-repurchase disclosure context. None prescribes Kestrel’s inputs, normalization, DuPont scenarios, total-payout variant or a universally appropriate SGR.
Kestrel Valve Services and all amounts, policies and scenarios are fictional. SGR is sensitive to accounting framework, attribution, equity timing, distributions, leverage and normalization. It is not a revenue or earnings forecast, financing commitment, solvency opinion, valuation, return guarantee or individualized investment recommendation.
CFA Institute 来源讨论了留存率×ROE 的简化关系。SEC 财报指南提供报表背景；FASB 概念公告第 8 号第 4 章说明权益与所有者分配；IAS 1 提供所有者权益变动与股利列报背景；SEC Rule 10b-18 问答提供发行人回购披露背景。任何来源都未规定 Kestrel 输入、正常化、杜邦情景、总分配变体或通用适当 SGR。
Kestrel Valve Services 及全部金额、政策与情景均为虚构。SGR 对会计框架、归属、权益时点、分配、杠杆与正常化高度敏感。它不是收入或利润预测、融资承诺、偿付能力意见、估值、收益保证或个性化投资建议。
- CFA Institute Research and Policy Center — Inflation’s Impact on Financial Statements and ROE
- U.S. Securities and Exchange Commission — Beginners’ Guide to Financial Statements
- Financial Accounting Standards Board — Concepts Statement 8, Chapter 4: Elements
- IFRS Foundation — IAS 1 Presentation of Financial Statements
- U.S. Securities and Exchange Commission — Rule 10b-18 Issuer Repurchase FAQs