麦肯锡公司估值模型教学
麦肯锡业绩评估操作手册
案例二：某国有企业业绩评估改革
要点一
总结词
要点二
详细描述
该国有企业通过逐步推进评估体系改革，实现了从单一 考核到综合评估的转变，提高了员工的工作积极性和企 业竞争力。
该国有企业原有业绩评估体系存在不科学、不合理之处 ，导致员工工作积极性不高。引入麦肯锡的业绩评估方 法后，逐步推进评估体系改革，实现了从单一考核到综 合评估的转变，提高了员工的工作积极性和企业竞争力 。
公司战略调整
根据评估结果，对公司的战略目 标和业务策略进行调整。
04
02
业绩评估中的关键要素
目标设定与衡量标准
明确目标
01
在制定业绩评估计划时，首先需要明确每个岗位的工作目标和
业务目标，确保所有员工都了解并认同这些目标。
设定关键绩效指标（KPI）
02
为了衡量业绩，需要设定一些关键绩效指标，这些指标应该是
03
业绩评估中的常见问题与 对策
目标难以达成
原因
目标设置过高，缺乏实现的基础；目标缺乏清晰度，导致理解不足；缺乏有效的执行计划和资源支持 。
对策
设置合理且可实现的目标，基于历史数据和实际情况进行评估；明确目标，确保所有人都清楚理解； 提供必要的资源和支持，制定有效的执行计划。
数据不准确或不全
原因
案例三：某创业公司的业绩评估策略调整
总结词
该创业公司通过调整评估策略，实现了从短期考核到长 期激励的转变，有效提高了员工的归属感和公司业绩。
详细描述
该创业公司原有业绩评估策略过于注重短期考核，导致 员工流失率较高。引入麦肯锡的业绩评估方法后，调整 评估策略，从短期考核转向长期激励，有效提高了员工 的归属感和公司业绩。
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。
财务管理模型--麦肯锡经典资料
• 单位产品成本
• 劳动生产率 • 废品率
各层级的业绩指标举例：一家欧洲领先银行 的分行零售业务
战略议题/目标 关键管理问题 员工是否在富有 成效地工作 分行的 人员编制 是否有效 长期雇员成本 是否在控制中 支持性员工是否争取 了足够的重点潜在客户 分行成本是否 在预算之内 我们是否 在有效率 地使用 资源 是否最大程度地 优化了现金平衡 我们是否在 控制“运作”亏损 是否保持了 客户服务标准 分行是否在积极地 达到标准 相应管理信息 预估业务量和人员需求量(各项职能) 预估量和实际人员数量的对比 将实际的小时数分解为全职、兼职、随叫随到和加班 使用的员工为所需员工的% 每笔业务的人工费成本 网点中 的各工 作领域
差幅=投资资本回报(ROIC)—加权平均资本成本(WACC)
中国公司必须开阔思路
从只关注 到关注更多指标，包括
• 产量 • 市场占有率 • 销售收入 • 净利润 • 每股收益
• 投资资本回报 • 差幅 • 经济利润 • 折现现金流量价值 • 股票市值(适用于上
市公司)
为中国经济及消费者带来利益 •更好的资源配置，将有限的资源投入到最好的投资上 •减少对国外资本投入的需求 •创造更多的财富
价值管理是一个综合性的管理工具
• 将整个公司的价值创造与一线
工作小组和雇员的日常运作活 动联系起来
• 指导战略，资源配置及经营运
作的决策
• 的 业绩评估方法
• 推动公司业绩的迅速发展
价值管理将股东与管理者及一线工作小组 联系起来
经营价值驱动 因素，例如 • 生产周期时间 驱动因素 • 销售收入 • 单位成本 • 废品率 • 劳动生产率
185 138 101
17 18
净利润 人民币亿元
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。
麦肯锡价值模型
input: yellow; link: blue; calculation: white
Equity Finance Tax
Forecast Inputs (Cont’d.)
Phase 2 and CV Drivers
Phase 2: six major inputs CV period: ROIC & growth
Constants and Dates
Results & Valuation Summary
McKinsey Valuation Model
A brief Introduction
Important notes
Make sure that the Analysis ToolPak and Report Manager Add-ins are installed before you use the model
Historical Inputs
You can enter up to 10 years of data Historical Income Statement Statement of Changes in Equity Historical Balance Sheet Off Balance Sheet Items
The model is in read-only format. Any changes you make must be saved under a different file name
现代企业战略管理工具麦肯锡七步分析法
现代企业战略管理工具麦肯锡七步分析法（1）解析：麦肯锡七步分析法又称“七步分析法”是麦肯锡公司根据他们做过的大量案例，总结出的一套对商业机遇的分析方法。
它是一种在实际运用中，对新创公司及成熟公司都很重要的思维、工作方法。
第一步：确定新创公司的市场在哪里这里一是要搞清楚市场是什么？再一个是在市场中的价值链的哪一端？确定自己的市场在哪里，才能比较谁和你竞争，你的机遇在哪里？第二步：分析影响市场的每一种因素知道自己的市场定位后，就要分析该市场的抑制、驱动因素。
要意识到影响这个市场的环境因素是什么？哪些因素是抑制的，哪些因素是驱动的。
此外还要找出哪些因素是长期的？哪些因素是短期的？如果这个抑制因素是长期的，那就要考虑这个市场是否还要不要做？还要考虑这个抑制因素是强还是弱？第三步：找出市场的需求点在对市场各种因素进行分析之后，就很容易找出该市场的需求点在哪里，这就要对市场进行分析，要对市场客户进行分类，了解每一类客户的增长趋势。
如中国的房屋消费市场增长很快，但有些房屋消费市场却增长很慢。
这就要对哪段价位的房屋市场增长快，哪段价位的房屋市场增长慢做出分析，哪个阶层的人是在买这一价位的，它的驱动因素在哪里？要在需求分析中把它弄清楚，要了解客户的关键购买因素，即客户来买这件东西时，最关心的头三件事情、头五件事情是什么？第四步：做市场供应分析即多少人在为这一市场提供服务，在这一整个的价值链中，所有的人都在为企业提供服务，因位置不同，很多人是你的合作伙伴而不是竞争对手。
如在奶制品市场中，有养奶牛的，有做奶产品的，有做奶制品分销的。
如公司要做奶制品分销，那前两个上游企业都是合作伙伴。
不仅如此，还要结合对市场需求的分析，找出供应伙伴在供应市场中的优劣势。
第五步：找出新创空间机遇供应商如何去覆盖市场中的每一块？从这里能找出一个商机，这就是新创公司必需要做的这一块。
这样分析后最大的好处是，在关键购买因素增长极快的情况下，供应商却不能满足它，而新的创业模式正好能补充它，填补这一空白，这也就是创业机会。
麦肯锡市场营销全套分析模型
最佳做法
常见错误
3. 宣传价值
包装
1. 选择价值
了解消费者的需要
选择目标对象
确定价值组合
2. 提供价值
产品设计
采购/生产
定价
销售
送货
广告
促销/公关
价值定位：最佳做法和常见错误
致胜的营销及销售战略和计划包括 创建有竞争吸引力的价值定位 通过有重点的新产品开发、销售、送货及定价计划来交付这一价值 向消费者和销售渠道清楚地宣传这一价值 成功的营销者通过连续的评估程序不断地改进这些计划
细分市场可以通过描述性数据(例如人口特征)或对几个有关分类问题的回答来识别和瞄准
公司必须能将其宣传主旨以及产品和服务交付给各细分市场
公司具备实施该细分方案的技能和系统，或能发展这种技能和系统；简单的细分方案与复杂的方案相比更为可行
不同细分市场的消费者需求截然不同
啤酒实例
占总消费量的百分比
低档产品
主流产品
3. 宣传价值
包装
1. 选择价值
了解消费者的需要
选择目标对象
确定价值组合
2. 提供价值
产品设计
采购/生产
定价
广告
销售
送货
促销/公关
了解消费者的需要及偏好 清晰可行的市场细分 具有竞争吸引力的产品服务定位 一刀切式的定位 根据产品性能来定位
根据顾客的需要设计产品 高效率及高效能的销售和分销商管理 根据价值来定价 积极地对过程进行管理 产品的设计、生产和交付没有与消费者需求相连接 对所有客户、地区和渠道平均使用力量 根据成本来定价
开发产品概念、原形，并通过座谈会进行产品测试
FCFE模型
FCFE模型FCFE模型的来源是现金流贴现定价模型。
FCFE估值模型的框架首先要看看：FCFE和FCFF的最大区别就是：前者只是公司股权拥有者（股东）可分配的最大自由现金额，后者是公司股东及债权人可供分配的最大自由现金额。
因此FCFE要在FCFF基础上减去供债权人分配的现金（即利息支出费用等）。
整个模型的原理就是：你买入的是公司未来自由现金流（可供分配的现金，不等同于股息，除非分红率100%，但是理论上，这些现金都是可以分配的）在当期的贴现值。
这和早期的红利贴现模型最大的区别就是：红利贴现模型并不符合实际，因为很多高成长的企业有理由不分配而将资金投入到新项目中去。
按照前面分析的贴现模型，需要明确的就是：公司预期未来的自由现金流、适当的贴现率、贴现的方法。
因此，一套FCFE/FCFF估值模型的要素就包括：1、如何定义当期的FCFE/FCFF。
2、如何确定未来各期的FCFE/FCFF。
3、如何选择适当的贴现率（WACC）。
4、按照何种方法进行贴现？可以看出：这个模型的难点就在于：1、预测未来各期的FCFE/FCFF难度太大！2、适当的贴现率WACC对于模型最终结果影响很大，但是该贴现率的算法很难有统一的标准。
3、采用何种方式进行贴现关系到如何定义该企业在企业经营周期中处的地位，以及预测企业发展周期的时间。
这个其实和第一点一样非常难。
但是学习这个模型也可以给我们带来几点启发：1、多关注企业的自由现金流，而不是仅仅关注收益。
但是需要注意不同行业的现金流存在形式是不同的。
2、WACC实际上就是企业所有负债的加权平均期望成本。
也就是说，企业发行了股票，向银行借贷用于生产，它必须承担一定的成本。
因此，企业拿着这些钱必须投向比WACC收益率更高的领域才能保证生存和发展。
因此，要关注企业募集资金或借贷资金投入项目的预期收益率与WACC相比是否存在明显的优势。
3、要关注企业所处行业周期和企业经营周期。
在不同的时期应当给于不同的估值水平。
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。