麦肯锡公司估值模型教学——【炒股必备估值模型 精】
股票投资价值评估的基本模型
股票投资价值评估的基本模型以股票投资价值评估的基本模型为标题的文章股票投资是一种常见的投资方式，而对于投资者来说，了解股票的价值是至关重要的。
股票的价值评估是投资决策的基础，它可以帮助投资者判断股票是否被低估或高估，并作出相应的买入或卖出决策。
股票投资价值评估的基本模型有多种，其中最常用的是股票估值模型和比较估值模型。
股票估值模型是根据公司的财务指标和市场预期对股票进行估值的一种方法。
常见的股票估值模型包括股票的市盈率（P/E ratio）、市净率（P/B ratio）和市销率（P/S ratio）等。
这些比率可以反映公司的盈利能力、资产质量和市场销售情况，从而评估股票的价值。
一般来说，市盈率越低，股票就越被低估；市净率越低，股票就越被低估；市销率越低，股票就越被低估。
投资者可以通过比较公司的估值指标与行业平均水平或历史水平，判断股票的投资价值。
比较估值模型是将公司与其他类似公司进行比较，以确定股票的价值。
常见的比较估值模型包括市盈率比较法、市净率比较法和市销率比较法等。
投资者可以选择与目标公司业务相似、规模相近且盈利能力较好的公司进行比较，从而评估股票的价值。
一般来说，如果目标公司的估值指标低于类似公司的平均水平，那么股票就可能被低估；反之，如果目标公司的估值指标高于类似公司的平均水平，那么股票就可能被高估。
除了股票估值模型和比较估值模型，还有其他一些辅助模型可以用于股票投资价值评估。
例如，股票的盈利预测模型可以根据公司的财务数据和市场预期，预测未来的盈利情况，进而评估股票的价值。
股票的风险评估模型可以根据公司的财务风险和市场风险，评估股票的风险水平，从而考虑风险与收益的平衡。
在进行股票投资价值评估时，投资者还需考虑一些其他因素。
例如，宏观经济环境、行业发展趋势、公司的竞争优势和管理团队的素质等。
这些因素也会影响股票的价值，投资者需要综合考虑这些因素，做出更准确的投资决策。
股票投资价值评估是投资决策的基础，它可以帮助投资者判断股票的投资价值，从而做出更明智的投资决策。
股票估值模型公式
股票估值模型公式股票估值是一项十分重要的股市分析工具，为投资者提供了较为客观的参考标准。
股票估值模型公式则是股票估值的核心，以下将介绍两种较为常用的股票估值模型公式。
常见股票估值模型公式1. 资产法资产法是根据企业的资产价值来进行估值的方法，其主要公式为：股票估值 = 企业净资产 * 股权摊薄比例其中，股权摊薄比例即为指定股权的持有者所占股份的百分比。
2. 盈利法盈利法则是通过企业的盈利能力来进行估值的方法，其主要公式为：股票估值 = 每股收益 * 盈利倍数其中，每股收益为企业每一股的纯利润，即净利润/总股本；盈利倍数则是指对企业未来盈利的预期倍数，其计算方法有多种。
盈利倍数的计算方法盈利倍数是股票估值中十分关键的指标，在计算中需要根据企业的实际情况来确定。
以下介绍几种常用的盈利倍数的计算方法。
1. PE（市盈率）PE（市盈率）是指股票价格与每股收益之比，其计算公式为：市盈率 = 股票价格 / 每股收益在计算市盈率时需要注意，不同行业之间的市盈率存在较大的差异。
2. PB（市净率）PB（市净率）是指股票价格与净资产之比，其计算公式为：市净率 = 股票价格 / 每股净资产在计算市净率时需要注意，不同行业之间的市净率存在较大的差异。
3. PS（市销率）PS（市销率）是指股票价格与销售收入之比，其计算公式为：市销率 = 股票价格 / 每股销售收入在计算市销率时需要注意，不同行业之间的市销率存在较大的差异。
结语股票估值模型公式是股票估值分析的核心内容之一，不同的股票估值模型适用于不同行业和企业的细节特征。
因此，在进行股票投资时，投资者需要对企业进行全方位的分析，采用多种股票估值模型进行比较。
投资学中的股票估值模型
投资学中的股票估值模型股票估值是投资学中的一个重要课题，通过对股票进行合理估值可以帮助投资者做出明智的投资决策。
本文将介绍一些常用的股票估值模型，并对其原理和适用范围进行分析。
一、股票估值模型的概念和应用范围股票估值模型是一种通过对公司财务数据和市场信息进行分析，对公司股票的未来价值进行预测的工具。
它可以帮助投资者判断股票的价格是否被市场低估或高估，从而指导投资决策。
常用的股票估值模型有：股利折现模型（Dividend Discount Model，简称DDM）、盈利折现模型（Earnings Discount Model，简称EDM）、自由现金流估值模型（Free Cash Flow Valuation Model，简称FCF）、市盈率估值模型（Price-Earnings Ratio，简称P/E Ratio）等。
二、股利折现模型（DDM）股利折现模型认为，股票的价值等于其未来股利的现值之和。
即将未来的股利折现到当前时点。
该模型适用于稳定且有持续分红的公司，对于高风险或不分红的公司不适用。
股利折现模型的计算公式如下：股票价值= Σ (D/(1+r)^t)其中，D为未来每期的股利，r为期望收益率，t为投资期数。
三、盈利折现模型（EDM)盈利折现模型是将公司未来的盈利折现到当前时点，从而推算出股票的价值。
该模型适用于稳定且有稳定盈利增长率的公司。
盈利折现模型的计算公式如下：股票价值= Σ (E/(1+r)^t)其中，E为未来每期的盈利，r为期望收益率，t为投资期数。
四、自由现金流估值模型（FCF）自由现金流估值模型是将公司未来的自由现金流折现到当前时点，从而得出股票的价值。
自由现金流是指企业从业务活动中产生的可自由支配的现金。
自由现金流估值模型的计算公式如下：股票价值= Σ (FCF/(1+r)^t)其中，FCF为未来每期的自由现金流，r为期望收益率，t为投资期数。
五、市盈率估值模型（P/E Ratio）市盈率估值模型是通过对公司的市盈率进行估值。
股票估价模型计算公式
股票估价模型计算公式
股票估价模型有很多，以下列出几种常见的股票估价模型及其计算公式：
1. 贴现现金流模型(DCF)
DCF模型的基本思想是将未来的现金流贴现回现在，再加上终止时的剩余价值来决定企业的价值。
计算公式：V = Σ(CFt/(1+r)^t) + PV(终值)
其中V为企业的价值，CFt为第t年的自由现金流，r为贴现率，PV(终值)为终止时的剩余价值。
2. 增长股票模型(GGM)
GGM模型假设未来的股票分红随着时间以固定比率增长，因此可以用当前的股票分红和未来的增长率来估计企业价值。
计算公式：V = D/(r-g)
其中V为企业的价值，D为当前年度的股票分红，r为资本成本率，g为分红增长率。
3. 市盈率模型(P/E)
P/E模型假设企业的股价与每股收益的比率是稳定的，因此可以用当前的每股收益和市场平均P/E比率来估计股票的公允价值。
计算公式：V = EPS x P/E
其中V为股票价值，EPS为每股收益，P/E为市盈率。
4. 资产定价模型(CAPM)
CAPM模型是衡量投资风险和回报的一种经济学模型，基于市场风险溢价和资产特有风险溢价来估计资产的预期回报率。
计算公式：r = Rf + β(Rm - Rf)
其中r为资产的预期回报率，Rf为无风险利率，β为资产的市场风险系数，Rm 为市场的预期回报率。
需要注意的是，以上的股票估价模型只是理论模型，实际应用中需要考虑估价模型的局限性以及财务数据的质量等诸多因素。
章股票估值模型
• 公司的价值等于公司预期现金流按公司资本成本进 行折现，将预期的未来自由现金流用加权平均资本 成本折现到当前价值来假设公司价值，
– 其次，求出股权的价值
• 公司价值减去债务的价值，得到股权的价值 .
• 1.自由现金流稳定增长的估值模型
– 假定公司以某一稳定的增长率保持增长，估值公 式为：
12.2 自由现金流估价方法
• 弄清楚了企业将会产生的各种现金流，那么我们 就可以把这些所有的现金流进行贴现在求和，从 而得到公司的价值。这就是利用自由现金流来对 公司进行估价的基本思想。
• 该方法的基本原理是一项资产的价值等于该资产 预期在未来所产生的全部现金流的现值总和。
12.2.1公司自由现金流估价方法
1
等于FCFF（ n 1 gn )；
ke依据资本资产定价模型计量的股权成本
• 3.自由现金流量估值的三阶段模型
– 二阶段：初始阶段增长率很高，增长率转换，最后阶 段增长率稳定，且持续时间较长
– 公式：
V
FCFF0 (1 g ) （WACC g )
（WF AC CF CF 1 g )
其中，FCFF0为当前的自由现金流量， FCFF1为预期下一期的自由现金流量， WACC为加权平均资本成本（折现率），
• 公司自由现金流（free cash flow of firm，FCFF）
– 是公司支付了所有营运费用、进行了必需的固定资产与 营运资产投资后可以向所有的权利要求者（股东和债权 人，或者所有资本供给者）分派的税后现金流。
gt
gagagb Nhomakorabeat A B A
, ga gb
• FCFF贴现模型的思路
•
g
股票估值的估值模型
股票估值的估值模型
股票估值的估值模型有多种，以下是一些常见的模型：
1.DCF模型（现金流折现模型）：该模型是一种基于未来现金流的股票估值模型，其核心思想是将未来现金流折现到现在的价值，以计算公司的内在价值。
2.P/E比率模型（市盈率模型）：该模型是一种将公司的市盈率与同行业或市场平均值进行比较，以评估其是否被低估或高估的模型。
3.PEG比率模型（市盈率增长比模型）：该模型是市盈率模型的一种扩展，将公司的市盈率与未来增长率进行比较，以评估公司的成长性。
4.EV/EBITDA模型（企业价值/息税折旧及摊销前利润比率模型）：该模型是一种将企业价值与其息税折旧及摊销前利润进行比较，以评估公司的估值水平的模型。
5.P/BV比率模型（市净率模型）：该模型是一种将公司的股价与其每股净资产进行比较，以评估公司的估值水平的模型。
需要注意的是，不同的估值模型适用于不同的公司和行业，以及不同的投资目标和风险偏好。
因此，在选择使用哪种模型进行股票估值时，需要根据具体情况进行选择和调整。
股权投资中的企业估值模型与方法
股权投资中的企业估值模型与方法在股权投资领域，企业估值是一项关键的任务，它能够帮助投资者准确判断企业的价值，为投资决策提供基础。
本文将介绍股权投资中常用的企业估值模型与方法，从而帮助投资者更好地进行估值分析。
一、市场与收益相关模型市场与收益相关模型是最常用的股权投资估值方法之一，它基于企业在市场中的表现以及预期收益来计算企业的估值。
常见的市场与收益相关模型包括市盈率模型、市销率模型和市净率模型。
1. 市盈率模型市盈率是指公司股票的市值与公司盈利的比率，它可以反映投资者对企业未来盈利能力的期望。
通过与行业内其他企业的市盈率进行比较，可以确定企业的估值水平。
市盈率模型的公式为：估值 = 盈利 * 市盈率。
2. 市销率模型市销率是指公司股票的市值与公司销售收入的比率，它可以反映企业的市场份额以及销售业绩。
与市盈率类似，市销率模型将企业的销售收入与行业内其他企业进行比较，从而确定企业的估值水平。
市销率模型的公式为：估值 = 销售收入 * 市销率。
3. 市净率模型市净率是指公司股票的市值与公司净资产的比率，它可以反映企业的资产质量以及市场价值。
市净率模型将企业的净资产与行业内其他企业进行比较，从而确定企业的估值水平。
市净率模型的公式为：估值 = 净资产 * 市净率。
二、现金流量相关模型现金流量相关模型是一种基于企业现金流量情况来计算估值的方法，它关注的是企业经营活动所产生的现金流量。
常见的现金流量相关模型包括折现现金流量模型和自由现金流量模型。
1. 折现现金流量模型折现现金流量模型（DCF）是一种将企业未来的现金流量折现至现值的方法，它能够全面考虑企业的经营状况和未来发展潜力。
DCF模型通过确定企业的自由现金流量以及折现率，计算出企业的估值。
DCF模型的公式为：估值= ∑(未来现金流量 / (1+折现率)^年数)。
2. 自由现金流量模型自由现金流量模型（FCFF）是一种将企业未来可自由支配的现金流量折现至现值的方法，它关注的是企业经营活动所产生的净现金流量。
麦肯锡模型及其详解
麦肯锡模型及其详解麦肯锡模型（McKinsey model）是一种管理工具，用于分析和解决复杂的商业问题。
它由全球领先的管理咨询公司麦肯锡公司（McKinsey & Company）开发并广泛应用。
在本篇文章中，我们将详细解释麦肯锡模型的各个方面，包括其定义、应用场景、步骤和示例。
一、什么是麦肯锡模型麦肯锡模型是一种商业问题解决框架，旨在提供结构化的方法来分析和解决各种商业挑战。
该模型由麦肯锡公司的顾问们根据多年的实践经验开发而成，并在全球范围内得到广泛应用。
其核心思想是将问题分解为不同的要素，并通过相互关联的分析来提供解决方案。
二、麦肯锡模型的应用场景麦肯锡模型适用于各种商业问题解决和战略制定的场景。
无论是市场分析、竞争对手研究、产品定位、供应链优化还是企业规模扩张，麦肯锡模型都可以提供有力的解决方案。
该模型被广泛应用于各行各业，包括制造业、金融业、咨询业等。
三、麦肯锡模型的步骤麦肯锡模型的应用通常包括以下几个步骤：1. 定义问题：明确要解决的具体问题，并确保所有相关方都对问题的定义达成一致。
2. 数据收集：收集必要的数据和信息，包括市场数据、竞争信息等，以支持后续的分析和决策。
3. 分析框架：选择适当的分析框架，将问题分解为不同的要素，并建立它们之间的关联。
4. 数据分析：在分析框架的指导下，对收集到的数据进行分析，识别关键问题和机会。
5. 解决方案：基于数据分析的结果，提出切实可行的解决方案，并进行评估和优化。
6. 实施计划：将解决方案转化为可执行的计划，并明确责任和时间表。
7. 监控和调整：跟踪解决方案的实施情况，定期评估并进行必要的调整。
四、麦肯锡模型的示例为了更好地理解麦肯锡模型的应用，以下是一个实际案例的示例：假设一个新兴的科技公司面临市场份额下降的问题。
他们希望通过使用麦肯锡模型来找到解决方案。
遵循麦肯锡模型的步骤，他们首先明确问题为市场份额下降，并与团队成员一致对问题进行定义。
估值(FCFF and FCFE)
FCFF and FCFE2010-01-01 21:52:38| 分类：估值法|字号订阅作为估值模型之一的DCF，其中Cash flow的选择有三种。
其中自由现金流算是其中比较重要的概念。
最近在阅读Analysis of equity valuation，发现之前对于FCF的理解还是很肤浅，CFA对于FCF的解读简单明了，逻辑清晰。
由于支撑销售的资产，如生产线等固定资产会有折旧，按照会计核算的基本假定，公司持续经营，FCFF的概念由此而生：Free cash flow to the firm--公司自由现金流量, cash flow from operations minus capital expenditures.即营运现金流减去资本支出。
资本支出包括reinvestment in new assets,working capital included.简单来说，公司自由现金流是可供股东与债权人分配的最大现金额。
FCFE：Free cash flow to equity就是FCFF去掉财务杠杆。
从概念而言，FCFF是含债务的现金流概念，FCFE是不含债务的现金流债务概念。
关于网友对于FCFF的讨论，我粘贴了一些，都是很好的意见，大家可以参考：1.FCFE/FCFF的来龙去脉1、美国学者Franco Modigliani和Mertor Miller于1958年创立了关于资本结构的著名的MM理论，明确提出企业经营的目标是价值最大化，而不是“利润最大化”。
他们于1961年首次阐述了公司价值和其他资产价值一样，也取决于其未来产生的现金流量的理念。
2、于1975年发生的美国W.T.Grant公司破产事件，推动了业界与学界对现金流研究的重视。
W.T.Grant公司曾是美国最大的商品零售企业，且按照“应计会计制”（即：权责发生制）核算的盈利能力优良。
但由于该公司过于重视会计利润而忽视了现金流管理，应收账款回收无力、存货周转缓慢，导致企业营运资本占用资金越来越大，迫使企业持续大量举债，财务风险不断积聚，最终导致公司无法运转而破产。
股票估价的基本模型
股票估价的基本模型股票估价是市场经济中重要的一环，它体现了企业价值和市场需求之间的平衡关系。
在投资领域，股票估价是最为基础和必要的分析工具之一，有效的股票估价可以帮助投资者掌握股市行情，及时作出投资决策。
本文将介绍股票估价的基本模型。
一、股票估价的要素股票估价模型是以公司基本面指标为基础，综合考虑公司的业绩、财务状况、市场前景、行业竞争等多种因素的计算模型。
主要包括以下要素：1、现金流量公司的现金流量是股票估价的重要指标。
投资者可以通过分析公司的经营现金流和自由现金流来确定公司的价值。
2、盈利能力盈利能力是公司的核心竞争力。
投资者可以通过计算公司的净利润、利润率、股息支付率等指标来评估公司的盈利能力。
3、资产负债表资产负债表可以反映公司的资产结构、负债结构、资产负债率等关键指标。
通过分析资产负债表，可以评估公司财务状况的稳定性和长远发展能力。
4、市场前景市场前景是投资者着重关注的因素，行业竞争格局的变化、新产品的上市和市场需求的变化都可能对公司的发展产生影响。
股票估价是一种基于未来现金流的估值方法。
其本质就是以公司未来的现金流入为基础，通过估算公司未来的盈利情况，确定公司在未来的现金流入，从而推算出股票的现值。
（1）股票的基本价值 = 稳定增长期的自由现金流 / (折现率–成长率)公式中，稳定增长期自由现金流指的是未来稳定增长期内，公司所剩下的自由现金流，折现率指的是资本成本费用，成长率指的是未来现金流的增长率。
这个公式适用于稳定增长期较长的公司。
（2）股票的基本价值 = 第一年自由现金流 / (折现率–成长率) + 第二年自由现金流 / (折现率–成长率)^2 + … + 第n年自由现金流 / (折现率–成长率)^n公式中，n指的是股票预期现金流时限，以此为基础来确定股票的现值。
（3）残余收益法残余收益法是一种基于企业经济利润的估值方法。
该方法中，公司的基本价值等于净资产价值加上公司未来的经济收益。
股票估值模型
股票估值模型
股票估值模型是通过把股票价值分解为溢价计价和事实计价两部分，以指导投资决策的重要方法。
一般来说，溢价计价按照股价的走势以及未来的预期考虑，而事实计价则按照股值本身的要素分析，如收入、资产、企业内部运行等等，对股票进行估值。
溢价计价是股票估值中最重要和最常用的估值方法，它直接反映了市场对某股未来发展的乐观度。
采用溢价计价法进行股票估值时，一般会考虑市场热度、行业发展趋势、风险水平、政策变化等，以及企业未来的发展前景等因素，确定股票的合理价格，以作为其价值的参考。
事实计价是根据股票收益、资产及其他企业基础要素进行估值。
常见的方法有净资产估值法、市盈率法、市净率法和市现率法等。
首先，通过公司上市报表分析公司净资产，以贴现现金流量的方式，以公允价值计算出股票的价值。
其次，通过共有的价格和归属母公司的净利润的比较，以及净资产价值和当前市场价格的比较，来确定股票的估值水平。
最后，以市盈率的估值法，将股份的价格除以每股收益，即市净率、市销率计算出估值水平。
股票估值模型也可以结合事实计价和溢价计价对股票估值进行综合估值。
当投资者利用溢价计价法来预测公司业绩时，可以参考事实计价法，以确定公司股价水平。
当投资者考虑市场未来趋势时，同样可以参考事实计价法，以了解预期收益率是否合理。
总之，股票估值模型通过综合溢价计价法和事实计价法，能够更好地完成股票估值，从而更好地指导投资决策。
FCFF
FCFF模型(重定向自公司自由现金流模型)FCFF模型(Free Cash Flow for the Firm,公司自由现金流模型)FCFF的定义和计算方法公司自由现金流（Free cash flow for the firm）是对整个公司进行估价，而不是对股权。
美国学者拉巴波特（Alfred Rappaport）20 世纪80 年代提出了自由现金流概念：企业产生的、在满足了再投资需求之后剩余的、不影响公司持续发展前提下的、可供企业资本供应者/各种利益要求人（股东、债权人）分配的现金。
麦肯锡(McKinsey & Company, Inc.)资深领导人之一的汤姆·科普兰(Tom Copeland)教授于1990年阐述了自由现金流量的概念并给出了具体的计算方法:自由现金流量等于企业的税后净经营利润(Net Operating Profit less Adjusted Tax, NOPAT,)即将公司不包括利息费用的经营利润总额扣除实付所得税税金之后的数额)加上折旧及摊销等非现金支出,再减去营运资本的追加和物业厂房设备及其他资产方面的投资。
其经济意义是:公司自由现金流是可供股东与债权人分配的最大现金额。
具体公式为:公司自由现金流量(FCFF) =(税后净利润+ 利息费用+ 非现金支出)- 营运资本追加- 资本性支出这个只是最原始的公式,继续分解得出:公司自由现金流量(FCFF)=(1-税率t)×息税前利润(EBIT)+折旧-资本性支出(CAPX)-净营运资金(NWC)的变化这个就是最原始的计算FCFF的公式。
其中:息税前利润(EBIT)=扣除利息、税金前的利润,也就是扣除利息开支和应缴税金前的净利润。
具体还可以将公式转变为:公司自由现金流量(FCFF)=(1-税率t)× 息前税前及折旧前的利润(EBITD)+税率t×折旧-资本性支出(CAPX)-净营运资金(NWC)的变化公司自由现金流量(FCFF)=(1-税率t)× 息税前利润(EBITD)-净资产(NA)的变化其中:息前税前及折旧前的利润(EBITD)= 息税前利润+折旧净营运资金的变化有时称为净营运资金中的投资[编辑]FCFF模型概述FCFF模型认为公司价值等于公司预期现金流量按公司资本成本进行折现。
股票财务估值模型
股票财务估值模型一、股票估值模型的定义股票估值模型是根据股票的财务数据和市场环境等因素，对股票进行估算的一种方法。
通常采用股票基本面分析和技术面分析相结合的方法，以确定股票的实际价值，并为投资者提供投资决策的参考。
二、财务估值模型的分类1. 相对估值模型：基于公司的财务数据和行业比较分析，通过对各种财务指标进行比较，计算出公司的相对估值。
2. 绝对估值模型：基于公司的财务数据和预期收益分析，通过分析公司的未来盈利能力，预测公司的未来现金流，并计算公司的未来现金流折现价值，得到公司的绝对估值。
三、主要的股票财务估值模型1. 市盈率估值模型（PE）：PE模型是一种相对估值模型，通过比较公司的市盈率和同行业的平均市盈率来确定公司的股票价格。
如果公司的市盈率低于行业平均水平，则股票被认为是低估的；如果公司的市盈率高于行业平均水平，则股票被认为是高估的。
2. 市净率估值模型（PB）：PB模型是主要用于估算金融、房地产等行业的股票，通过比较公司的市净率和同行业的平均市净率来确定公司的股票价格。
如果公司的市净率低于行业平均水平，则股票被认为是低估的；如果公司的市净率高于行业平均水平，则股票被认为是高估的。
3. 资产负债表估值模型（ROA）：ROA模型是一种绝对估值模型，通过分析公司的资产负债表，计算出公司的总资产和总负债，并分析公司的收益率和风险水平来确定公司的股票价格。
如果公司的收益率高于风险水平，则股票被认为是低估的；如果公司的收益率低于风险水平，则股票被认为是高估的。
4. 自由现金流估值模型（DCF）：DCF模型是一种绝对估值模型，通过分析公司的未来现金流水平，预测公司的未来现金流，并计算公司的未来现金流折现价值来确定公司的股票价格。
如果公司的未来现金流折现价值高于当前股票价格，股票被认为是低估的；如果公司的未来现金流折现价值低于当前股票价格，则股票被认为是高估的。
四、结论股票财务估值模型是股票投资的重要参考工具，不同类型的估值模型适用于不同的行业和企业，选择适合自己的估值模型可以提高投资者的投资效益。
麦肯锡公司价值评估经典模型
A Tutorial on the Discounted Cash FlowModel for Valuation of CompaniesL.Peter Jennergren∗Sixth revision,August25,2006SSE/EFI Working Paper Series in Business Administration No.1998:1AbstractAll steps of the discounted cashflow model are outlined.Essential steps are: calculation of free cashflow,forecasting of future accounting data(income state-ments and balance sheets),and discounting of free cashflow.There is particularemphasis on forecasting those balance sheet items which relate to Property,Plant,and Equipment.There is an exemplifying valuation included(of a company calledMcKay),as an illustration.A number of other valuation models(abnormal earn-ings,adjusted present value,economic value added,and discounted dividends)arealso discussed.Earlier versions of this working paper were entitled“A Tutorial onthe McKinsey Model for Valuation of Companies”.Key words:Valuation,free cashflow,discounting,accounting dataJEL classification:G31,M41,C60∗Stockholm School of Economics,Box6501,S-11383Stockholm,Sweden.The author is indebted to Tomas Hjelstr¨o m,Joakim Levin,Per Olsson,Kenth Skogsvik,and Ignacio Velez-Pareja for discussions and comments.1IntroductionThis tutorial explains all the steps of the discounted cashflow model,prominently featured in a book by an author team from McKinsey&Company(Tim Koller,Marc Goedhart,and David Wessels:Valuation:Measuring and Managing the Value of Compa-nies,Wiley,Hoboken,New Jersey;4th ed.2005).The purpose is to enable the reader to set up a complete valuation model of his/her own,at least for a company with a simple structure.The discussion proceeds by means of an extended valuation example.The company that is subject to the valuation exercise is the McKay company.1 The McKay example in this tutorial is somewhat similar to the Preston example (concerning a trucking company)in thefirst two editions of Valuation:Measuring and Managing the Value of Companies(Copeland et al.1990,Copeland et al.1994).How-ever,certain simplifications have been made,for easier understanding of the model.In particular,the capital structure of McKay is composed only of equity and debt(i.e., no convertible bonds,etc.).Also,McKay has no capital leases or capitalized pension liabilities.2McKay is a single-division company and has no foreign operations(and con-sequently there are no translation differences).There is no goodwill and no minority interest.The purpose of the McKay example is merely to present all essential aspects of the discounted cashflow model as simply as possible.Some of the historical income statement and balance sheet data have been taken from the Preston example.However, the forecasted income statements and balance sheets are totally different from Preston’s. All monetary units are unspecified in this tutorial(in the Preston example in Copeland et al.1990,Copeland et al.1994,they are millions of US dollars).This tutorial is intended as a guided tour through one particular implementation of the discounted cashflow model and should therefore be viewed only as exemplifying:This is one way to set up a valuation model.Some modelling choices that have been made will be pointed out later on.However,it should be noted right away that the specification given below of net Property,Plant,and Equipment(PPE)as driven by revenues agrees with Koller et al.2005.Thefirst two editions of Valuation:Measuring and Managing the Value of Companies contain two alternative model specifications relating to investment1Previous versions of this tutorial were entitled“A Tutorial on the McKinsey Model for Valuation of Companies”,since they focused on the McKinsey implementation of the discounted cashflow model. However,after several revisions of the McKinsey book as well as of this tutorial,there are now some differences in emphasis and approach between the two,motivating the title change.Otherwise,the most important changes in the sixth revision of this tutorial are as follows:The working capital items inventories and accounts payable are now driven by operating expenses,rather than by revenues.Section 15and Appendix2are new.2Pension contributions in McKay may hence may be thought of as paid out to an outside pension fund concurrently with the salaries generating those contributions,so no pension debt remains on the company’s books.in PPE(cf.Levin and Olsson1995).In the following respect,this tutorial is an extension of Koller et al.2005:It contains a more detailed discussion of capital expenditures,i.e.,the mechanism whereby cash is absorbed by investments in PPE.This mechanism centers on two particular forecast assumptions,[this year’s net PPE/revenues]and[depreciation/last year’s net PPE].3It is explained below how those assumptions can be specified consistently.On a related note, the treatment of deferred income taxes is somewhat different,and also more detailed, compared to Koller et al.2005.In particular,deferred income taxes are related to a forecast ratio[timing differences/this year’s net PPE],and it is suggested how to set that ratio.There is also another extension in this tutorial:Alternative valuation models are also discussed.In fact,in the end McKay is valued throughfive different models.The McKay valuation is set up as a spreadsheetfile in Excel named MCK.XLS.That file is an integral part of this tutorial.The model consists of the following parts(as can be seen by downloading thefile):Table1.Historical income statements,Table2.Historical balance sheets,Table3.Historical free cashflow,Table4.Historical ratios for forecast assumptions,Table5.Forecasted income statements,Table6.Forecasted balance sheets,Table7.Forecasted free cashflow,Table8.Forecast assumptions,Value calculations.Tables in the spreadsheetfile and in thefile printout that is included in this tutorial are hence indicated by numerals,like Table1.Tables in the tutorial text are indicated by capital letters,like Table A.The outline of this tutorial is as follows:Section2gives an overview of essential model features.Section3summarizes the calculation of free cashflow.Section4is an introduction to forecastingfinancial statements and also discusses forecast assumptions relating to operations and working capital.Sections5,6,and7deal with the specification of the forecast ratios[this year’s net PPE/revenues],[depreciation/last year’s net PPE], and[retirements/last year’s net PPE].Section8considers forecast assumptions about taxes.Further forecast assumptions,relating to discount rates andfinancing,are discussed in Section9.Section10outlines the construction of forecastedfinancial statements and free cashflow,given that all forecast assumptions have beenfixed.Section11outlines a3Square brackets are used to indicate specific ratios that appear in tables in the spreadsheetfiles.slightly different version of the McKay example,with another system for accounting for deferred income taxes.4The discounting procedure is explained in Section12.Section13 gives results from a sensitivity analysis,i.e.,computed values of McKay’s equity when certain forecast assumptions are revised.Section14discusses another valuation model, the abnormal earnings model,and indicates how McKay’s equity can be valued by that model.Section15considers a differentfinancing policy for McKay.Under thatfinancing policy,McKay is valued byfive different models(discounted cashflow,adjusted present value,economic value added,discounted dividends,and abnormal earnings).5Section 16contains concluding remarks.Appendix1discusses how a data base from Statistics Sweden can be used as an aid in specifying parameters related to the forecast ratios[this year’s net PPE/revenues],[depreciation/last year’s net PPE]and[retirements/last year’s net PPE].Appendix2is a note on the value driver formula that is recommended for continuing value by Koller et al.2005.2Model overviewEssential features of the discounted cashflow model are the following:1.The model uses published accounting data as input.Historical income statements and balance sheets are used to derive certain criticalfinancial ratios.Those historical ratios are used as a starting point in making predictions for the same ratios in future years.2.The object of the discounted cashflow model is to value the equity of a going concern.Even so,the asset side of the balance sheet is initially valued.The value of the interest-bearing debt is then subtracted to get the value of the equity.Interest-bearing debt does not include deferred income taxes and trade credit(accounts payable and other current liabilities).Credit in the form of accounts payable is paid for not in interest but in higher operating expenses(i.e.,higher purchase prices of raw materials)and is therefore part of operations rather thanfinancing.Deferred income taxes are viewed as part of equity;cf.Sections9and10.It may seem like an indirect approach to value the assets and deduct interest-bearing debt to arrive at the equity(i.e.,it may seem more straight-forward to value the equity directly,by discounting future expected dividends). However,this indirect approach is the recommended one,since it leads to greater clarity and fewer errors in the valuation process(cf.Koller et al.2005,pp.126-128).4This version of the McKay example is contained in the Excelfile MCK B.XLS.A printout from that file is also included in this tutorial.The two versions of the McKay example are equivalent as regards cashflow and resulting value.In other words,it is only the procedure for computing free cashflow that differs(slightly)between them.5See thefile MCK EXT.XLS.A printout from thatfile is also included here.3.The value of the asset side is the value of operations plus excess marketable secu-rities.The latter can usually be valued using book values or published market values. Excess marketable securities include cash that is not necessary for operations.For valu-ation purposes,the cash account may hence have to be divided into two parts,operating cash(which is used for facilitating transactions relating to actual operations),and ex-cess cash.(In the case of McKay,excess marketable securities have been netted against interest-bearing debt at the date of valuation.Hence there are actually no excess mar-ketable securities in the McKay valuation.This is one of the modelling choices that were alluded to in the introduction.)4.The operations of thefirm,i.e.,the total asset side minus excess marketable secu-rities,are valued by the WACC method.In other words,free cashflow from operations is discounted to a present value using the WACC.There is then a simultaneity problem (actually quite trivial)concerning the WACC.More precisely,the debt and equity values enter into the WACC weights.However,equity value is what the model aims to determine.5.The asset side valuation is done in two parts:Free cashflow from operations is forecasted for a number of individual years in the explicit forecast period.After that, there is a continuing(post-horizon)value derived from free cashflow in thefirst year of the post-horizon period(and hence individual yearly forecasts must be made for each year in the explicit forecast period and for one further year,thefirst one immediately following the explicit forecast period).The explicit forecast period should consist of at least10-15years(cf.Koller et al.2005,p.230).The explicit forecast period can be thought of as a transient phase during a turn-around or after a take-over.The post-horizon period, on the other hand,is characterized by steady-state development.This means that the explicit forecast period should as a minimal requirement be sufficiently long to capture transitory effects,e.g.,during a turn-around operation.Actually,it is a requirement of the present implementation of the discounted cashflow model that the explicit forecast period should not be shorter than the economic life of the PPE.6.For any future year,free cashflow from operations is calculated from forecasted income statements and balance sheets.This means that free cashflow is derived from a consistent scenario,defined by forecastedfinancial statements.This is probably the main strength of the discounted cashflow model,since it is difficult to make reasonable forecasts of free cashflow in a direct fashion.Financial statements are forecasted in nominal terms (which implies that nominal free cashflow is discounted using a nominal discount rate).7.Continuing value is computed through an infinite discounting formula.In this tutorial,the Gordon formula is used(cf.Brealey et al.2006,pp.40,65).In other words, free cashflow in the post-horizon period increases by some constant percentage from year to year,hence satisfying a necessary condition for infinite discounting.(The Gordon formula is another one of the modelling choices made in this tutorial.)As can be inferred from this list of features,and as will be explained below,the discounted cashflow model combines three rather different tasks:Thefirst one is the production of forecastedfinancial statements.This is not trivial.In particular,it involves issues relating to capital expenditures that are fairly complex.(The other valuation models use forecastedfinancial statements,just like the discounted cashflow model,so thefirst task is the same for those models as well.)The second task is deriving free cashflow from operations fromfinancial statements. At least in principle,this is rather trivial.In fairness,it is not always easy to calculate free cashflow from complicated historical income statements and balance sheets.However,all financial statements in this tutorial are very simple(and there is,in any case,no reason to forecast accounting complexities if the purpose is one of valuation).The third task is discounting forecasted free cashflow to a present value.While not exactly trivial,this task is nevertheless one that has been discussed extensively in the corporatefinance literature, so there is guidance available.This tutorial will explain the mechanics of discounting in the discounted cashflow model.However,issues relating to how the relevant discount rates are determined will largely be brushed aside.Instead,the reader is referred to standard text books(for instance,Brealey et al.2006,chapters9,17,and19).3Historicalfinancial statements and the calculation of free cashflowThe valuation of McKay is as of Jan.1year1.Historical input data are the income statements and balance sheets for the years−6to0,Tables1and2.Table1also includes statements of retained earnings.It may be noted in Table1that operating expenses do not include depreciation.In other words,the operating expenses are cash costs.At the bottom of Table2,there are a couple offinancial ratio calculations based on historical data for the given years.Short-term debt in the balance sheets(Table2)is that portion of last year’s long-term debt which matures within a year.It is clear from Tables1and 2that McKay’sfinancial statements are very simple,and consequently the forecasted statements will also have a simple structure.As already mentioned earlier,McKay has no excess marketable securities in the last historical balance sheet,i.e.,at the date of valuation.From the data in Tables1and2,historical free cashflow for the years−5to0 is computed in Table3.Each annual free cashflow computation involves two balance sheets,that of the present year and the previous one,so no free cashflow can be obtained for year−6.Essentially the same operations are used to forecast free cashflow for year1and later years(in Table7).The free cashflow calculations assume that the clean surplus relationship holds.This implies that the change in book equity(including retainedearnings)equals net income minus net dividends(the latter could be negative,if there is an issue of common equity).The clean surplus relationship does not hold,if PPE is written down(or up)directly against common equity(for instance).Such accounting operations may complicate the calculation of free cashflow from historicalfinancial statements(and if so,that calculation may not be trivial).However,there is usually no reason to forecast deviations from the clean surplus relationship in a valuation situation.EBIT in Table3means Earnings Before Interest and Taxes.NOPLAT means Net Op-erating Profits Less Adjusted Taxes.Taxes on EBIT consist of calculated taxes according to the income statement(from Table1)plus[this year’s tax rate]×(interest expense) minus[this year’s tax rate]×(interest income).Interest income and interest expense are taken from Table1.The tax rate is given in Table4.Calculated taxes according to the income statement reflect depreciation of PPE over the economic life.Change in deferred income taxes is this year’s deferred income taxes minus last year’s deferred income taxes. In the McKay valuation example,it is assumed that deferred income taxes come about for one reason only,timing differences in depreciation of PPE.That is,fiscal depreciation takes place over a period shorter than the economic life.Working capital is defined net.Hence,working capital consists of the following balance sheet items:Operating cash plus trade receivables plus other receivables plus inventories plus prepaid expenses minus accounts payable minus other current liabilities.Accounts payable and other current liabilities are apparently considered to be part of the operations of thefirm,not part of thefinancing(they are not interest-bearing debt items).Change in working capital in Table3is hence this year’s working capital minus last year’s working capital.Capital expenditures are this year’s net PPE minus last year’s net PPE plus this year’s depreciation.Depreciation is taken from Table1,net PPE from Table2.It should be emphasized that depreciation in Table1(and forecasted depreciation in Table5)is according to plan,over the economic life of the PPE.Free cashflow in Table3is hence cash generated by the operations of thefirm,after paying taxes on operations only,and after expenditures for additional working capital and after capital expenditures.(“Additional working capital”could of course be negative.If so,free cashflow is generated rather than absorbed by working capital.)Hence,free cash flow represents cash that is available for distribution to the holders of debt and equity in thefirm,and for investment in additional excess marketable securities.Stated somewhat differently,free cashflow is equal tofinancial cashflow,which is the utilization of free cashflow forfinancial purposes.Table3also includes a break-down offinancial cashflow. By definition,free cashflow must be exactly equal tofinancial cashflow.We now return briefly to thefinancial ratios at the end of Table2.Invested capi-tal is equal to working capital plus net PPE.Debt at the end of Table2in the ratio [debt/invested capital]is interest-bearing(short-term and long-term).Thefinancial ratio[NOPLAT/invested capital]is also referred to as ROIC(Return on Invested Capital).It is a better analytical tool for understanding the company’s performance than other return measures such as return on equity or return on assets,according to Koller et al.(2005,p. 183).Invested capital in the ratio[NOPLAT/invested capital]is the average of last year’s and this year’s.It is seen that McKay has provided a decreasing rate of return in recent years.It can also be seen from Table3that the free cashflow has been negative,and that the company has handled this situation by increasing its debt.It is evident from the bottom of Table2that the ratio of interest-bearing debt to invested capital has increased substantially from year−6to year0.Table4contains a set of historicalfinancial ratios.Those ratios are important,since forecasts of the same ratios will be used to produce forecasted income statements and balance sheets.Most of the items in Table4are self-explanatory,but a few observations are called PPE(which is taken from Table2)enters into four ratios.In two of those cases,[depreciation/net PPE]and[retirements/net PPE],the net PPE in question is last year’s.In the other two cases,[net PPE/revenues]and[timing differences/net PPE],the net PPE in question is this year’s.Retirements are defined as depreciation minus change in accumulated depreciation between this year and last year(accumulated depreciation is taken from Table2).This must hold,since last year’s accumulated de-preciation plus this year’s depreciation minus this year’s retirements equals this year’s accumulated depreciation.The timing differences for a given year are measured between accumulatedfiscal depre-ciation of PPE and accumulated depreciation according to PPE economic life.For a given piece of PPE that is about to be retired,accumulatedfiscal depreciation and accumulated depreciation according to economic life are both equal to the original acquisition value. Consequently,non-zero timing differences are related to non-retired PPE only.The ratio [timing differences/net PPE]in Table4has been calculated byfirst dividing the deferred income taxes for a given year by the same year’s corporate tax rate(also given in Table 4).This gives that year’s timing differences.After that,there is a second division by that year’s net PPE.4Forecast assumptions relating to operations and working capitalHaving recorded the historical performance of McKay in Tables1-4,we now turn to the task of forecasting free cashflow for years1and later.Individual free cashflow forecasts are produced for each year1to12.The free cashflow amounts for years1to11 are discounted individually to a present value.The free cashflow for year12and all later years is discounted through the Gordon formula,with the free cashflow in year12as astarting value.Years1to11are therefore the explicit forecast period,and year12and all later years the post-horizon period.As required,the explicit forecast period is longer than the economic life of the PPE(the latter is assumed to be10years in Section7).Tables5-8have the same format as Tables1-4.In fact,Table5may be seen as a continuation of Table1,Table6as a continuation of Table2,and so on.We start the forecasting job by setting up Table8,the forecast ing assumptions (financial ratios and others)in that table,and using a couple of further direct forecasts of individual items,we can set up the forecasted income statements,Table5,and the forecasted balance sheets,Table6.From Tables5and6,we can then in Table7derive the forecasted free cashflow(just like we derived the historical free cashflow in Table3, using information in Tables1and2).Consider now the individual items in Table8.It should be noted in Table8that all items are the same for year12,thefirst year of the post-horizon period,as for year11,the last year of the explicit forecast period.Since thefirst year in the post-horizon period is representative of all subsequent post-horizon period years,all items are the same for every post-horizon period year as for the last year of the explicit forecast period.This is actually an important condition(cf.Levin and Olsson1995,p.38;Lundholm and O’Keefe2001, pp.321-322):If that condition holds,then free cashflow increases by the same percentage (the nominal revenue growth rate for year12in Table8,cell T135)between all successive years in the post-horizon period.This means that a necessary condition for discounting by means of the Gordon formula in the post-horizon period is satisfied.The revenue growth in each future year is a combination of inflation and real growth. More precisely,nominal revenue growth is“one plus real growth multiplied by one plus expected inflation minus one”.Actually,in years10and11there is no real growth,and the same assumption holds for all later years as well(in the application of the Gordon formula).The underlying assumption in Table8is apparently that real operations will initially expand but will eventually(in year10)settle down to a steady state with no further real growth.Inflation,on the other hand,is assumed to be3%in all coming years(including after year12).The ratio of operating expenses to revenues is assumed to improve immediately,e.g.,as a consequence of a determined turn-around effort.Ap-parently,it is set to90%year1and all later years.To avoid misunderstandings,this forecast assumption and the other ones displayed in Table8are not necessarily intended to be the most realistic ones that can be imagined.The purpose is merely to demonstrate the mechanics of the discounted cashflow model for one particular scenario.A table in Levin and Olsson1995(p.124;based on accounting data from Statistics Sweden)contains information about typical values of the ratio between operating expenses and revenues in various Swedish industries(cf.also Appendix1for a further discussion of the Statistics Sweden data base).A number of items in the forecasted income statements and balance sheets are directly driven by revenues.That is,those items are forecasted as percentages of revenues.In particular,this holds for most of the working capital items.It is thus assumed that as revenues increase,the required amounts of working capital for these items increase correspondingly.It is not important whether revenues increase due to inflation or real growth,or a combination of both.Working capital turns over very quickly,and therefore it is a reasonable assumption that these working capital items are simply proportional to revenues.The ratios between the different working capital items and revenues for future years in Table8have been set equal to the average values of the corresponding historical percentages in Table4.Again,this is only for illustrative purposes.Another table in Levin and Olsson1995(p.125),again based on data from Statistics Sweden, reports average values of the ratio between(aggregate)working capital and revenues in different Swedish industries.Two of the working capital items,inventories and accounts payable,are forecasted as percentages of operating expenses rather than as percentages of revenues.This is actually not a very important distinction(i.e.,one may perhaps just as well forecast all working capital items as percentages of revenues;cf.Koller et al.2005, pp.243-244).The ratios between these two working capital items and operating expenses for future years are also set as average historical values.5Forecast assumptions relating to property,plant, and equipmentThe forecast assumptions relating to PPE will be considered next(this section and the following two).The equations that determine capital expenditures may be stated as follows(subscripts denote years):(capital expenditures)t=(net PPE)t−(net PPE)t−1+depreciation t,(net PPE)t=revenues t×[this year’s net PPE/revenues],depreciation t=(net PPE)t−1×[depreciation/last year’s net PPE].To this set of equations,we may add three more that are actually not necessary for the model:retirements t=(net PPE)t−1×[retirements/last year’s net PPE],(accumulated depreciation)t=(accumulated depreciation)t−1+depreciation t−retirements t, (gross PPE)t=(net PPE)t+(accumulated depreciation)t.In particular,this second set of three equations is needed only if one wants to produce forecasted balance sheets showing how net PPE is related to gross PPE minus accumulated depreciation.It should be noted that such detail is not necessary,since thefirst set ofthree equations suffices for determining net PPE,depreciation,and consequently also capital expenditures.6It is clear from thefirst three equations that forecasts have to be made for two partic-ular ratios,[this year’s net PPE/revenues]and[depreciation/last year’s net PPE].Setting those ratios in a consistent fashion involves somewhat technical considerations.In this section and the following one,one way of proceeding,consistent with the idea of the company developing in a steady-state fashion in the post-horizon period,will be outlined.To begin with,the idea of the company developing in a steady-state fashion has to be made more precise.As indicated in Section4,the forecast assumptions should be specified in such a manner that nominal free cashflow increases by a constant percentage every year in the post-horizon period.This is a necessary condition for infinite discounting by the Gordon formula.But if so,capital expenditures must also increase by the same constant percentage in every post-horizon period year.For this condition on capital expenditures to hold,there must be an even age distribution of nominal acquisition values of successive PPE cohorts.More precisely,it must hold that the acquisition value of each PPE cohort develops in line with the assumed constant growth percentage that is applicable to the post-horizon period.As also mentioned in Section4,that constant percentage is the same as the assumed nominal revenue growth in the post-horizon period,3%in the McKay example.The general idea is now to set steady-state values of the two ratios[this year’s net PPE/revenues]and[depreciation/last year’s net PPE]for the last year of the explicit forecast period(year11in the McKay example).Those steady-state values will then also hold for every year in the post-horizon period(since all forecast assumptions have to be the same in thefirst year of the post-horizon period as in the last year of the explicit forecast period,as already explained in Section4).During the preceding years of the explicit forecast period,steady-state values of[this year’s net PPE/revenues]and[depreciation/last year’s net PPE]are not assumed.Values for these two ratios in the preceding explicit forecast period years arefixed in the following heuristic fashion in the McKay example:For thefirst year of the explicit forecast period, they are set as averages of the corresponding values for the historical years.7Values for6If the historicalfinancial statements do not show gross PPE and accumulated depreciation,only net PPE,then it seems pointless to try to include these items in the forecastedfinancial statements.If so, the second set of three equations is deleted.In the McKay case,the historical statements do indicate gross PPE and accumulated depreciation.For that(aesthetic)reason,those items will also be included in the forecasted statements.7The value for the last year of the explicit forecast period of[retirements/last year’s net PPE]is also set as a steady-state value.For thefirst year of the explicit forecast period,that ratio is set equal to the corresponding value for the last historical year.An average of corresponding values for all historical years is not used in this case,since[retirements/last year’s net PPE]appears to have been unstable during。