The Option to Abandon

废止的选择权

If the option to expand has value, what about the decision to bail out? Projects don’t just go on until assets expire of old age. The decision to terminate a project is usually taken by management, not by nature. Once the project is no longer profitable, the company will cut its losses and exercise its option to abandon the project.¹⁷

如果扩张的选择权具有价值，那么终止的决定又如何呢？项目不会就持续到资产陈旧到期。终止一个项目的决定常由管理层而不是自然性质做出。一旦项目不再盈利，公司就会削减其损失并行使其废止该项目的选择权¹⁷。

¹⁷The abandonment option was first analyzed by A. A. Robichek and J. C. Van Horne, “Abandonment Value in Capital Budgeting,” Journal of Finance 22 (December 1967), pp. 577–590.

¹⁷废止选择权最早是由A. A. Robichek和J. C. Van Horne所分析, “Abandonment Value in Capital Budgeting,” Journal of Finance 22 (December 1967), pp. 577–590.

Some assets are easier to bail out of than others. Tangible assets are usually easier to sell than intangible ones. It helps to have active secondhand markets, which really exist only for standardized items. Real estate, airplanes, trucks, and certain machine tools are likely to be relatively easy to sell. On the other hand, the knowledge accumulated by a software company’s research and development program is a specialized intangible asset and probably would not have significant abandonment value. (Some assets, such as old mattresses, even have negative abandonment value; you have to pay to get rid of them. It is costly to decommission nuclear power plants or to reclaim land that has been strip-mined.)

       某些资产较其他资产更易处置。有形资产通常比无形资产容易出售。有活跃的二手市场会比较有帮助，当然它也仅为标准化的物品而存在。房地产、飞机、卡车和某些机器工具可能相对容易出售。另一方面，一家软件公司的在研发程序中累积的知识是一种专门的无形资产，而且可能不会有很大的处置价值。（某些资产，如旧床垫（mattress — the soft part of a bed that you lie on），其处置价值甚至为负值；你不得不花钱来处理它们。拆除（decommission — to stop using a ship, weapon, or nuclear reactor and to take it to pieces）核电站或者重新平整露天矿山的土地都是代价不菲的。）

Example. Managers should recognize the option to abandon when they make the initial investment in a new project or venture. For example, suppose you must choose between two technologies for production of a Wankel-engine outboard motor.

1. Technology A uses computer-controlled machinery custom-designed to produce the complex shapes required for Wankel engines in high volumes and at low cost. But if the Wankel outboard doesn’t sell, this equipment will be worthless.

2. Technology B uses standard machine tools. Labour costs are much higher, but the machinery can be sold for $10 million if the engine doesn’t sell.

Technology A looks better in a DCF analysis of the new product because it was designed to have the lowest possible cost at the planned production volume. Yet you can sense the advantage of technology B’s flexibility if you are unsure about whether the new outboard will sink or swim in the marketplace.

例 管理者应该在做出一个新项目或者新企业的初始投资时就确认废止的选择权。例如，假设你必须在生产转子发动机（Wankel engine — A rotary internal combustion engine invented by Felix Wankel (1902-1988). It consists of an equilateral triangular member with curved sides orbiting about an eccentric on a shaft inside a stationary housing whose inner working surface is in the shape of an epitrochoid. The rotor is in sliding contact with the eccentric and imparts power to the eccentric shaft as a connecting rod does to a crankshaft. With one-third of a rotor revolution per shaft revolution and a power impulse for each of the three rotor sides, the Wankel generates one power impulse per revolution per rotor--twice that of what the four-cycle piston engine produces. Thus it has become accepted practice to multiply the geometry displacement of the Wankel by a factor of two for comparison with otto-cycle piston engines. The Wankel's advantages include compact size, light weight and smooth operation because there are no reciprocating parts. Its drawbacks include relatively high exhaust emission, possible sealing problems and low fuel economy. Mazda, however, has made significant improvements in all three areas.大量的汽车术语看不明白，就知道马自达在这方面颇有建树）式船外马达的两种技术之间选择。

1. A技术运用定制的计算机控制机械来高产量低成本的生产转子发动机所需的复杂样式。但是如果发动机卖不出去，这一设备将毫无价值。

2. B技术运用标准化的机械工具。人工成本高得多，但是如果引擎卖不出去该机械可以1000万美元出售。

以DCF来分析新产品A技术看上去更佳，因为它就是被设计在计划产量下有最低的成本。然而你可以感觉到B技术的灵活性带来的优势，如果你不能确定新的产品是否会在市场中起起落落。

We can make the value of this flexibility concrete by expressing it as a real option. Just for simplicity, assume that the initial capital outlays for technologies A and B are the same. Technology A, with its low-cost customized machinery, will provide a payoff of $18.5 million if the outboard is popular with boat owners and $8.5 million if it is not. Think of these payoffs as the project’s cash flow in its first year of production plus the present value of all subsequent cash flows. The corresponding payoffs to technology B are $18 million and $8 million.

       我们可以通过将其表述为一种实物期权而使这一灵活性的价值变得实在。为简化起见，假定技术A和技术B的初始资本支出相同。技术A，低成本的定制机械，如果马达受到船东的欢迎将提供1850万美元的收益，如果不是则为850万美元。将这些收益想成项目投产第一年的现金流加上所有后续现金流的现值。技术B对应的收益为1800万美元和800万美元。

If you are obliged to continue in production regardless of how unprofitable the project turns out to be, then technology A is clearly the superior choice. But remember that at year-end you can bail out of technology B for $10 million. If the outboard is not a success in the market, you are better off selling the plant and equipment for $10 million than continuing with a project that has a present value of only $8 million.

       如果你一定要继续生产而不论这个项目最终有多么的不盈利，那么很明显A技术是更优的选择。但是请记住在年末你能够以1000万美元处置B技术。如果马达在市场上未获成功，你就可以从出售工厂和设备中得到1000万美元而不是维持一个现值只有800万美元的项目。

Figure 10.7 summarizes this example as a decision tree. The abandonment option occurs at the right-hand boxes for Technology B. The decisions are obvious: continue if demand is buoyant, abandon otherwise. Thus the payoffs to Technology B are:

Buoyant demand → continue production → own business worth $18 million

Sluggish demand → exercise option to sell assets → receive $10 million

       图示10.7用决策树概括了这个例子。废止选择权发生在B技术的右边方块处。决策是显然的：如果需求踊跃就继续，否则就放弃。因此B技术的收益是：

需求踊跃→继续生产→拥有价值1800万美元的业务

需求疲软→行使出售资产的选择权→得到1000万美元

Technology B provides an insurance policy: If the outboard’s sales are disappointing, you can abandon the project and recover $10 million. You can think of this abandonment option as an option to sell the assets for $10 million. The total value of the project using technology B is its DCF value, assuming that the company does not abandon, plus the value of the abandonment option. When you value this option, you are placing a value on flexibility.

       B技术（相当于）提供一张保单：如果马达的销售令人失望，你可以废止这个项目并收回1000万美元。你可以把这个废止选择权想成一个以1000万美元出售资产的选择权。运用B技术的项目的总价值是其DCF价值，假定公司没有放弃的话，再加上该废止选择权的价值。当你对这一选择权进行估值的时候，你就是在为灵活性估价。

10.3 REAL OPTIONS AND DECISION TREES

10.3实物期权和决策树

If financial managers treat projects as black boxes, they may be tempted to think only of the first accept–reject decision and to ignore the subsequent investment decisions that may be tied to it. But if subsequent investment decisions depend on those made today, then today’s decision may depend on what you plan to do tomorrow.

如果财务管理者们像对待黑匣子那样对待投资项目，他们就可能被诱导至仅仅思考第一个接受—拒绝决策并且还会忽略可能与之有关的后续投资的决策。但是如果后续投资决策取决于今日所作出的决策，那么今日的决策也会取决于你明日所作之计划。

When you use discounted cash flow (DCF) to value a project, you implicitly assume that the firm will hold the assets passively. But managers are not paid to be dummies. After they have invested in a new project, they do not simply sit back and watch the future unfold. If things go well, the project may be expanded; if they go badly, the project may be cut back or abandoned altogether. Projects that can easily be modified in these ways are more valuable than those that don’t provide such flexibility. The more uncertain the outlook, the more valuable this flexibility becomes.

       当你运用贴现现金流（DCF）来对一个项目进行估值的时候，你不假思索的假定该企业会被动地持有这些资产。但是（企业）支付管理者报酬并不是让他们成为摆放在橱窗里的模特（dummy — a model that is the shape and size of a person, especially used in order to show clothes in a shop or when you are making clothes）。在他们投资了一个新项目之后，管理者并不是撒手不管（sit back — to relax and make no effort to get involved in something or influence what happens）仅仅是坐视未来逐步展现。如果一切顺利，这个项目可能会扩大；如果不如人意，项目也许会缩减或废止。能够容易地以这些方式来建模的项目比那些不能提供这样灵活性的项目具有更大的价值。前景越不确定，这一灵活性的具有的价值就越大。

That sounds obvious, but notice that sensitivity analysis and Monte Carlo simulation do not recognize the opportunity to modify projects.¹⁵ For example, think back to the Otobai electric scooter project. In real life, if things go wrong with the project, Otobai would abandon to cut its losses. If so, the worst outcomes would not be as devastating as our sensitivity analysis and simulation suggested.

       这听上去很显然，但是请注意敏感性分析与蒙特卡罗模拟均未确认为项目建模的机会¹⁵。例如，回想Otobai的电动助动车项目。在现实生活中，如果项目不顺利，Otobai会废止以减少损失。如果这样，最糟糕的结果就不会如我们的敏感性分析和（蒙特卡罗）模拟所提示的那样不可收拾。

¹⁵Some simulation models do recognize the possibility of changing policy. For example, when a pharmaceutical company uses simulation to analyze its R&D decisions, it allows for the possibility that the company can abandon the development at each phase.

¹⁵某些模拟模型确实会确认政策改变的可能性。例如，当一家医药公司运用模拟来分析其R&D决策时，它会在每一阶段都纳入公司可以放弃研发的可能性。

Options to modify projects are known as real options. Managers may not always use the term real option to describe these opportunities; for example, they may refer to “intangible advantages” of easy-to-modify projects. But when they review major investment proposals, these option intangibles are often the key to their decisions.

       修改项目的选择权被称之为实物期权。管理者也许不会总是用实物期权这个术语来描述这些机会；例如，他们也许会称其为容易修改项目的“无形优势”。但是当他们评估重要投资提议的时候，这些无形选择权常常是他们决策的关键所在。

The Option to Expand

扩大的选择权

In 2000 FedEx placed an order for 10 Airbus A380 superjumbo transport planes for delivery in the years 2008–2011. Each flight of an A380 freighter will be capable of making a 200,000 pound dent in the massive volume of goods that FedEx carries each day, so the decision could have a huge impact on FedEx’s worldwide business. If FedEx’s long-haul airfreight business continues to expand and the superjumbo is efficient and reliable, the company will need more superjumbos. But it cannot be sure they will be needed.

FedEx（联邦快递）于2000年订购了10架空中客车A380超大型喷气式货运飞机，交付时间为2008–2011。一架A380货机的每一次航班都可以从FedEx每天运送的大量货物中瓜分走（dent in — a reduction in the amount of something）200,000磅，所以这个决策会对FedEx的全球业务有巨大的影响。如果FedEx的长程空运业务持续增长且A380效率高可靠，公司就会需要更多的A380。但是（现在）无法肯定它们一定就是需要的。

Rather than placing further firm orders in 2000, FedEx has secured a place in the Airbus production line by acquiring options to buy a “substantial number” of additional aircraft at a predetermined price. These options do not commit the company to expand but give it the flexibility to do so.

       FedEx没有在2000年下更多的确认订单，代替的是它通过取得以一个预设的价格购买数量庞大的新飞机的选择权从而在空中客车的生产线上确保了一席之地。这些选择权没有约束公司进行扩张，但是给了其这样做的灵活性。

Figure 10.6 displays FedEx’s expansion option as a simple decision tree. You can think of it as a game between FedEx and fate. Each square represents an action or decision by the company. Each circle represents an outcome revealed by fate. In this case there is only one outcome in 2007,¹⁶ when fate reveals the airfreight demand and FedEx’s capacity needs. FedEx then decides whether to exercise its options and buy additional A380s. Here the future decision is easy: Buy the airplanes only if demand is high and the company can operate them profitably. If demand is low, FedEx walks away and leaves Airbus with the problem of selling the planes that were reserved for FedEx to some other customer.

       图示10.6将FedEx的扩张选择权以一个简单的决策树展示出来。你可以把它想成一个FedEx和命运之间的游戏。每个方块代表公司的一个行动或决策。每个圆圈代表命运所揭示的一个结果。这个案例中当命运揭示了空运需求以及FedEx 的运力需要的时候，2007年只会有一种结果¹⁶。然后FedEx决定是否行使其选择权购买更多的A380。这里的未来决策是容易的：仅在需求高涨且公司能够运营使之盈利的情况下购买飞机。如果需求低迷，FedEx就拍拍屁股走人，把销售为FedEx保留的飞机给其他顾客的问题留给空中客车去解决。

¹⁶We assume that FedEx can wait until 2007 to decide whether to acquire the additional planes.

¹⁶我们假定FedEx可以等到2007年再来决定是否购买新飞机。

You can probably think of many other investments that take on added value because of the further options they provide. For example

• When launching a new product, companies often start with a pilot program to iron out possible design problems and to test the market. The company can evaluate the pilot and then decide whether to expand to full-scale production.

• When designing a factory, it can make sense to provide extra land or floor space to reduce the future cost of a second production line.

• When building a four-lane highway, it may pay to build six-lane bridges so that the road can be converted later to six lanes if traffic volumes turn out to be higher than expected.

Such options to expand do not show up in the assets that the company lists in its balance sheet, but investors are very aware of their existence. If a company has valuable real options that can allow it to invest in new profitable projects, its market value will be higher than the value of its physical assets now in place.

       你或许还能想到其他许多的投资，它们因其所提供的更多的选择权而具有附加值。例如：

• 当投入一种新产品的时候，通常公司会用一个试行计划来着手，以便能够解决（iron something ↔ out — phrasal verb to solve or get rid of problems or difficulties, especially small ones）可能的设计问题以及测试市场。公司可以评估试行计划，然后决定是否扩大至大规模生产。

• 当设计一家新工厂的时候，提供额外的产地或者楼层面积以降低未来第二条生产线的成本是有其道理的。

• 当建造一条四车道的高速公路的时候，建造一座六车道的桥梁以便如果交通流量高于预期时这条公路可以转为六车道是值得的。

这些扩张的选择权并没有显示在公司资产负债表所列的资产之中，但是投资者非常注意它们的存在。如果一家公司有可以使其投资新的赢利项目的价值不菲的实物期权，它的市值就会高于其现有物理资产的价值。

In Chapter 4 we showed how the present value of growth opportunities (PVGO) contributes to the value of a company’s common stock. PVGO equals the forecasted total NPV of future investments. But it’s better to think of PVGO as the value of the firm’s options to invest and expand. The firm is not obliged to grow. It can invest more if the number of positive-NPV projects turns out high or slow down if that number turns out low. The flexibility to adapt investment to future opportunities is one of the factors that makes PVGO so valuable.

       在第4章我们展示了增长机会的现值（PVGO）是如何对一家公司的普通股的价值作出贡献的。PVGO等于预计的未来投资的NPV总额。但是将PVGO想成企业投资和扩张选择权的价值更佳。企业不是一定要成长。如果正NPV项目的数目很多它就可以投资更多，或者该数目很少它就减少投资。适应未来机会的投资的灵活性是使PVGO如此有价值的因素之一。

Simulation of Pharmaceutical Research and Development

模拟医药研发

Simulation, though sometimes costly and complicated, has the obvious merit of compelling the forecaster to face up to uncertainty and to interdependencies. By constructing a detailed Monte Carlo simulation, you will gain a better understanding of how the project works and what could go wrong with it. You will have confirmed, or improved, your forecasts of future cash flows, and your calculations of project NPV will be more confident.

模拟，尽管有些时候成本高昂且复杂，但是其具有强制预测者面对不确定性和相互关联关系的明显优点。通过构建一个精细的蒙特卡罗模拟模型，你会对于项目如何运作以及可能出差错的地方有一个更好的理解。你将会证实或者改进你对未来现金流的预测，而你的项目NPV的计算也会更有信心。

Several large pharmaceutical companies have used Monte Carlo simulation to analyze investments in research and development (R&D) of new drugs. Figure 10.5 sketches the progression of a new drug from its infancy, when it is identified as a promising chemical compound, all the way through the R&D required for approval for sale by the Food and Drug Administration (FDA). At each phase of R&D, the company must decide whether to press on to the next phase or halt. The R&D effort lasts 10 to 12 years from preclinical testing to FDA approval and can cost $300 million or more.¹²

       有些大型医药公司运用蒙特卡罗模拟来分析新药研发(R&D)的投资。图示10.5描绘了一种新药从其孕育，即找到了一种有希望的化学成分,到获得食品和药品监管局(FDA)批准销售的整个研发的过程。在R&D的每个阶段，公司必须决定是否进入下一阶段还是停止。R&D从临床前测试到FDA批准需要10到12年的时间并且可以耗费3亿美元或更多¹²。

¹²Myers and Howe estimated the average cost of bringing one new drug to market as about $300 million after tax. The estimate was based on R&D costs and success rates from the 1970s and 1980s, but adjusted for inflation through 1994. See S. C. Myers and C. Howe, “A Life-Cycle Model of Pharmaceutical R&D,” MIT Program on the Pharmaceutical Industry, April 1997.

¹²Myers和Howe估计把一种新药投入市场的平均成本约为税后3亿美元。这一估计是基于R&D成本和二十世纪七八十年代以来的成功率，并从1994年起调整通货膨胀后得出的。参见S. C. Myers and C. Howe, “A Life-Cycle Model of Pharmaceutical R&D,” MIT Program on the Pharmaceutical Industry, April 1997.

The pharmaceutical companies face two kinds of uncertainty:

1. Will the compound work? Will it have harmful side effects? Will it ultimately gain FDA approval? (Most drugs do not: Of 10,000 promising compounds, only 1 or 2 may ever get to market. The 1 or 2 that are marketed have to generate enough cash flow to make up for the 9,999 or 9,998 that fail.)

2. Market success. FDA approval does not guarantee that a drug will sell. A competitor may be there first with a similar (or better) drug. The company may or may not be able to sell the drug worldwide. Selling prices and marketing costs are unknown.

       医药公司面对着两种不确定性：

1.      成分是否有效？其是否会有不良副作用？是否最终会得到FDA批准？（多数新药不会：10,000种有希望的成分，只有1或2种可能进入市场。这1或2种必须产生足够的现金流来弥补那失败的9,999或9,998种。）

2.      市场成功。FDA的批准不保证这种新药就能销售。竞争者可能已有一种类似（或更好）的药。公司可能或者可能不能在全球范围内销售这种药。售价和营销成本也都是未知。

Imagine that you are standing at the top left of Figure 10.5. A proposed research program will investigate a promising class of compounds. Could you write down the expected cash inflows and outflows of the program up to 25 or 30 years in the future? We suggest that no mortal could do so without a model to help; simulation may provide the answer.¹³

       想象一下你正站在图示10.5的左上角。一个提议的研究项目会检查一组有希望的成分。你能够写出这个项目未来25年或30年的期望现金流入和流出吗？我们认为没有一个凡人（mortal — ordinary people, as compared with people who are more important, more powerful, or more skilled - used humorously）在没有模型的帮助下可以做到这一点；模拟也许可以提供答案¹³。

¹³N. A. Nichols, “Scientific Management at Merck: An Interview with CFO Judy Lewent,” Harvard Business Review 72 (January–February 1994), p. 91.

Simulation may sound like a panacea for the world’s ills, but, as usual, you pay for what you get. Sometimes you pay for more than you get. It is not just a matter of the time and money spent in building the model. It is extremely difficult to estimate interrelationships between variables and the underlying probability distributions, even when you are trying to be honest.¹⁴ But in capital budgeting, forecasters are seldom completely impartial and the probability distributions on which simulations are based can be highly biased.

       模拟听上去像能医百病的灵丹妙药（panacea — something that people think will make everything better and solve all their problems），但是通常地，有付出才有得到。有时候你付出的比得到的多。它不仅仅是在构建模型中所花费的时间和金钱。估计变量之间的相互关系和基本的概率分布是极其困难的，即便是你试图诚实面对的时候也是如此¹⁴。但是在资本预算中，预测者们极少完全公平，而且模拟所基于的概率分布也可能是高度偏向的。

¹⁴These difficulties are less severe for the pharmaceutical industry than for most other industries. Pharmaceutical companies have accumulated a great deal of information on the probabilities of scientific and clinical success and on the time and money required for clinical testing and FDA approval.

¹⁴这些困难对医药行业来说较其对其他多数行业程度轻。医药公司在科学概率、临床成功、临床测试所需的时间和金钱以及FDA批准方面已经积累了大量的数据信息。

In practice, a simulation that attempts to be realistic will also be complex. Therefore the decision maker may delegate the task of constructing the model to management scientists or consultants. The danger here is that, even if the builders understand their creation, the decision maker cannot and therefore does not rely on it. This is a common but ironic experience: The model that was intended to open up black boxes ends up creating another one.

       实践中，一个试图反映现实的模型也将会是复杂的。因此决策者也许会把构建模型的任务授权给管理学者和咨询顾问去完成。这样做的危险在于，即使构建者理解他们的创造成果，决策者却不能理解，因此也不会去依靠它做出决策。这是一件很常见但是个很讽刺的事情：为试图打开黑匣子而构建的模型最终却创造出了另一个黑匣子。

10.2 MONTE CARLO SIMULATION

10.2 蒙特卡罗模拟

Sensitivity analysis allows you to consider the effect of changing one variable at a time. By looking at the project under alternative scenarios, you can consider the effect of a limited number of plausible combinations of variables. Monte Carlo simulation is a tool for considering all possible combinations. It therefore enables you to inspect the entire distribution of project outcomes. The use of simulation in capital budgeting was first advocated by David Hertz⁷ and McKinsey and Company, the management consultants.

敏感性分析允许你考虑一次改变一个变量造成的效果。通过关注处在不同情境下的项目，你可以考虑限定数量的可行变量组合造成的效果。蒙特卡罗模拟是一个用来考虑所有可能组合的工具。因此它使你能够检视项目结果的全部的分布情况。在资本预算中运用（蒙特卡罗）模拟首先是由David Hertz和麦肯锡管理咨询公司提出的。

⁷See D. B. Hertz, “Investment Policies that Pay Off,” Harvard Business Review 46 (January–February 1968), pp. 96–108.

⁷参见D. B. Hertz, “Investment Policies that Pay Off,” Harvard Business Review 46 (January–February 1968), pp. 96–108

Imagine that you are a gambler at Monte Carlo. You know nothing about the laws of probability (few casual gamblers do), but a friend has suggested to you a complicated strategy for playing roulette. Your friend has not actually tested the strategy but is confident that it will on the average give you a 21⁄2 percent return for every 50 spins of the wheel. Your friend’s optimistic estimate for any series of 50 spins is a profit of 55 percent; your friend’s pessimistic estimate is a loss of 50 percent. How can you find out whether these really are the odds? An easy but possibly expensive way is to start playing and record the outcome at the end of each series of 50 spins. After, say, 100 series of 50 spins each, plot a frequency distribution of the outcomes and calculate the average and upper and lower limits. If things look good, you can then get down to some serious gambling.

       想象一下你是一个在蒙特卡罗的赌徒。你对概率论一无所知（很少有随兴的赌徒知道），但是你的一位朋友向你推荐了一个用来玩轮盘赌（roulette — a game in which a small ball is spun around on a moving wheel, and people try to win money by guessing which hole the ball will fall into）的非常复杂的策略。你的朋友没有实际测试过这一策略，但是对于平均来说转盘每50转它就会给你带来21⁄2的回报率很有信心。你朋友对任一50转的乐观估计是获利55%；悲观估计是损失50%。你怎么才能发现这些是否就是真实的概率呢？一种容易但是可能很花钱的方法是就这么开始玩并在每50转后记下结果。在比方说100次50转之后，用图示画出一个结果的概率分布图并计算平均值和上下限。如果结果看上去不错，那么你就可以开始玩大的了。

An alternative is to tell a computer to simulate the roulette wheel and the strategy. In other words, you could instruct the computer to draw numbers out of its hat to determine the outcome of each spin of the wheel and then to calculate how much you would make or lose from the particular gambling strategy.

       一个替代方法是告诉计算机来模拟转盘和策略。换句话说，你可以命令计算机抽取（be drawn/pulled/picked out of the/a hat — if someone's name is drawn out of a hat, they are chosen, for example as the winner of a competition, because their name is the first one that is taken out of a container containing the names of all the people involved）数字来决定转轮每次转的结果，然后计算你可以从特定的赌博策略中赚多少或输多少。

That would be an example of Monte Carlo simulation. In capital budgeting we replace the gambling strategy with a model of the project, and the roulette wheel with a model of the world in which the project operates. Let’s see how this might work with our project for an electrically powered scooter.

       这就是蒙特卡罗模拟的一个例子。在资本预算中，我们以一个项目的模型来代替赌博策略，一个项目运营所在的世界的模型来代替转盘。让我们看看这会如何适用于我们的电动助动车项目。

Simulating the Electric Scooter Project

模拟电动助动车项目

Step 1: Modeling the Project The first step in any simulation is to give the computer a precise model of the project. For example, the sensitivity analysis of the scooter project was based on the following implicit model of cash flow:

Cash flow = (revenues - costs – depreciation) × (1 - tax rate) + depreciation

Revenues = market size × market share × unit price

Costs = (market size × market share × variable unit cost) + fixed cost

第一步：项目建模 任何模拟的第一步都是给计算机一个项目的精确模型。例如，助动车项目的敏感性分析是基于如下隐含的现金流模型：

现金流 = (收入 – 成本 – 折旧) × (1 – 税率) + 折旧

收入 = 市场规模 × 市场份额 × 单位售价

成本 = (市场规模 × 市场份额 × 单位变动成本) + 固定成本

This model of the project was all that you needed for the simpleminded sensitivity analysis that we described above. But if you wish to simulate the whole project, you need to think about how the variables are interrelated.

       这一项目模型提供了所有你需要用来进行如我们之前所述的简单的敏感性分析的信息。但是如果你希望模拟整个项目，你就需要思考各变量是如何相互关联的。

For example, consider the first variable—market size. The marketing department has estimated a market size of 1 million scooters in the first year of the project’s life, but of course you do not know how things will work out. Actual market size will exceed or fall short of expectations by the amount of the department’s forecast error:

Market size, year 1 = expected market size, year 1 × (1 + forecast error, year 1)

You expect the forecast error to be zero, but it could turn out to be positive or negative. Suppose, for example, that the actual market size turns out to be 1.1 million. That means a forecast error of 10 percent, or +.1:

Market size, year 1 = 1 × (1 + .1) = 1.1 million

       举个例子，考虑第一个变量—市场规模。营销部门估计该项目第一年的市场规模为100万年辆，当然你不知道到底是不是如估计这样。实际的市场规模将会超过或少于预期，数额就是营销部门的预测误差：

Market size, year 1 = expected market size, year 1 × (1 + forecast error, year 1)

你期望预期误差为零，但是它可以是正的也可以是负的。假设，例如，实际市场规模为110万辆。这就意味预测误差为10%，即+.1:

Market size, year 1 = 1 × (1 + .1) = 1.1 million

You can write the market size in the second year in exactly the same way:

Market size, year 2 = expected market size, year 2 × (1 + forecast error, year 2)

But at this point you must consider how the expected market size in year 2 is affected by what happens in year 1. If scooter sales are below expectations in year 1, it is likely that they will continue to be below in subsequent years. Suppose that a shortfall in sales in year 1 would lead you to revise down your forecast of sales in year 2 by a like amount. Then

Expected market size, year 2 = actual market size, year 1

Now you can rewrite the market size in year 2 in terms of the actual market size in the previous year plus a forecast error:

Market size, year 2 = market size, year 1 × (1 + forecast error, year 2)

In the same way you can describe the expected market size in year 3 in terms of market size in year 2 and so on.

       你可以用完全相同的方法写出第二年的市场规模：

Market size, year 2 = expected market size, year 2 × (1 + forecast error, year 2)

但是这个时候你必须考虑第1年所发生的情况对第2年的期望市场规模有何影响。如果第1年的助动车销售低于预期，那么可能在后续年度销售会持续走低。假设第1年销售的缺口会使你以类似的数额向下修正对第2年的销售预测。那么

Expected market size, year 2 = actual market size, year 1

现在你可以用前一年的实际市场规模加上预测误差来重写第2年的市场规模：

Market size, year 2 = market size, year 1 × (1 + forecast error, year 2)

同样的方法你可以第2年的市场规模来描述第3年的预期市场规模，并依次类推。

This set of equations illustrates how you can describe interdependence between different periods. But you also need to allow for interdependence between different variables. For example, the price of electrically powered scooters is likely to increase with market size. Suppose that this is the only uncertainty and that a 10 percent shortfall in market size would lead you to predict a 3 percent reduction in price. Then you could model the first year’s price as follows:

Price, year 1 = expected price, year 1 × ( 1 + .3 × error in market size forecast, year 1)

Then, if variations in market size exert a permanent effect on price, you can define the second year’s price as

Price, year 2 = expected price, year 2 × ( 1 + .3 × error in market size forecast, year 2)

                      = actual price, year 1 × ( 1 + .3 × error in market size forecast, year 2)

       以上这组等式描绘了你如何才能够描述不同期间之间的相互依赖性。但是你还需要纳入不同变量之间的相互依赖性。例如，电动助动车的价格可能随市场规模而上涨。假设这是仅有的不确定因素，且市场规模缺口10%会使你预测价格下降3%。这样的话你就可以将第1年的价格建模如下：

Price, year 1 = expected price, year 1 × ( 1 + .3 × error in market size forecast, year 1)

然后，如果市场规模的变动对价格有永久的影响，你就可以定义第2年的价格为

Price, year 2 = expected price, year 2 × ( 1 + .3 × error in market size forecast, year 2)

                      = actual price, year 1 × ( 1 + .3 × error in market size forecast, year 2)

Notice how we have linked each period’s selling price to the actual selling prices (including forecast error) in all previous periods. We used the same type of linkage for market size. These linkages mean that forecast errors accumulate; they do not cancel out over time. Thus, uncertainty increases with time: The farther out you look into the future, the more the actual price or market size may depart from your original forecast.

       请注意我们如何将每一期的销售价格与所有以前期间的实际销售价格（包括预测误差）联系起来。我们运用了和市场规模同样类型的联系方式。这些连接意味着预测误差会累积；它们不会随时间流逝而消失。因此，不确定性随着时间而增加：你所关注的未来越是遥远，实际价格或市场规模就越是会偏离你的初始预测。

The complete model of your project would include a set of equations for each of the variables: market size, price, market share, unit variable cost, and fixed cost. Even if you allowed for only a few interdependencies between variables and across time, the result would be quite a complex list of equations.⁸ Perhaps that is not a bad thing if it forces you to understand what the project is all about. Model building is like spinach: You may not like the taste, but it is good for you.

       项目的完整模型将会包含每一个变量所对应的一组等式：市场规模、价格、市场份额、单位变动成本和固定成本。即便你只容许仅仅少数的变量和时间之间的相互依赖关系，结果还会是一个相当复杂的等式列表⁸。也许这不是一件坏事情，如果它迫使你全面了解这个项目的话。建模就好比菠菜：你也许不喜欢这个味道，但是它却对你有益。（菠菜，想到大力水手了：-）

⁸Specifying the interdependencies is the hardest and most important part of a simulation. If all components of project cash flows were unrelated, simulation would rarely be necessary.

⁸明确相互依赖关系时模拟中最难和最重要的一个环节。如果项目现金流的所有组成部分相互无关联，那么就基本不必模拟了。

Step 2: Specifying Probabilities Remember the procedure for simulating the gambling strategy? The first step was to specify the strategy, the second was to specify the numbers on the roulette wheel, and the third was to tell the computer to select these numbers at random and calculate the results of the strategy:

Step 1 Model the strategy

Step 2 Specify numbers on roulette wheel

Step 3 Select numbers and calculate results of strategy

The steps are just the same for your scooter project:

Step 1 Model the project

Step 2 Specify probabilities for forecast errors

Step 3 Select numbers for forecast errors and calculate cash flows

步骤2 明确概率 还记得用来模拟那个赌博策略的步骤吗？第一步是明确这个策略，第二步是明确转盘上的数字，而第三步是告诉计算机随即选择这些数字并计算出这个策略的结果：

第1步 策略建模

第2步 明确转盘上数字

第3步 选择数字并计算策略的结果

对你的助动车项目来说，步骤是完全相同的：

第1步 项目建模

第2步 明确预测误差的概率

第3步 选择预测误差的数值并计算现金流

Think about how you might go about specifying your possible errors in forecasting market size. You expect market size to be 1 million scooters. You obviously don’t think that you are underestimating or overestimating, so the expected forecast error is zero. On the other hand, the marketing department has given you a range of possible estimates. Market size could be as low as .85 million scooters or as high as 1.15 million scooters. Thus the forecast error has an expected value of 0 and a range of plus or minus 15 percent. If the marketing department has in fact given you the lowest and highest possible outcomes, actual market size should fall somewhere within this range with near certainty.⁹

       考虑一下你会如何确定在预测市场规模中可能的误差。你预计市场规模为100万辆。很明显你并不认为你会低估或高估，所以期望预测误差为零。另一方面，营销部门给了你一个可能估计的范围。市场规模可能低至85辆，也可能高至115万辆。因此预测误差的期望值为0加减15%。如果营销部门事实上给出了最低和最高的可能结果，实际市场规模就近乎肯定的会落在这一区间内⁹。

⁹Suppose “near certainty” means “99 percent of the time.” If forecast errors are normally distributed, this degree of certainty requires a range of plus or minus three standard deviations.

Other distributions could, of course, be used. For example, the marketing department may view any market size between .85 and 1.15 million scooters as equally likely. In that case the simulation would require a uniform (rectangular) distribution of forecast errors.

⁹假设“近乎肯定”意味“99%的概率”。如果预测误差是正态分布的话，这一确定程度要求加减三个标准差。

       当然，其他的分布也可使用。例如，营销部门也许认为85万辆到115万辆之间的任何市场规模的可能性相等。这种情况下的模拟就要求预测误差的一个均匀（矩形）分布。

That takes care of market size; now you need to draw up similar estimates of the possible forecast errors for each of the other variables that are in your model.

       市场规模的问题解决了；现在你需要为模型中的其他每个变量写出相似的可能预测误差的估计。

Step 3: Simulate the Cash Flows The computer now samples from the distribution of the forecast errors, calculates the resulting cash flows for each period, and records them. After many iterations you begin to get accurate estimates of the probability distributions of the project cash flows—accurate, that is, only to the extent that your model and the probability distributions of the forecast errors are accurate. Remember the GIGO principle: “Garbage in, garbage out.”

步骤3 模拟现金流 现在计算机从预测误差的分布中进行取样，计算每一期的现金流并把它们记录下来。在多次迭代（iterate — if a computer iterates, it goes through a set of instructions before going through them for a second time）之后你开始得到项目现金流的概率分布的精确的估计—精确，仅仅是就你的模型和预测误差的概率分布是精确的而言的。请记住GIGO法则：“Garbage in, garbage out.”

Figure 10.4 shows part of the output from an actual simulation of the electric scooter project.¹⁰ Note the positive skewness of the outcomes—very large outcomes are more likely than very small ones. This is common and realistic when forecast errors accumulate over time. Because of the skewness the average cash flow is somewhat higher than the most likely outcome; in other words, a bit to the right of the peak of the distribution.¹¹

       图示10.4显示了电动助动车项目的一次实际模拟的部分结果¹⁰。注意结果表现出的正向偏态—非常大的数值较非常小的数值更为可能。当预测误差随时间而累积的时候出现这种情况是常见和现实的。因为偏态，平均现金流稍就高于最可能的；换句话说，就是在分布峰值的右边一点¹¹。

¹⁰These are actual outputs from Crystal Ball™ software used with an EXCEL spreadsheet program. The simulation assumed annual forecast errors were normally distributed and ran through 10,000 trials. We thank Christopher Howe for running the simulation.

¹⁰这些是运用Crystal Ball™ 软件和EXCEL电子表格程序所得到的实际结果。该模拟假定年预测误差为正态分布，并执行了10,000试验。我们感谢Christopher Howe所做的这次模拟。

¹¹When you are working with cash-flow forecasts, bear in mind the distinction between the expected value and the most likely (or modal) value. Present values are based on expected cash flows—that is, the probability-weighted average of the possible future cash flows. If the distribution of possible outcomes is skewed to the right as in Figure 10.4, the expected cash flow will be greater than the most likely cash flow.

¹¹当你处理现金流预测的时候，请将期望值和最可能（或modal）值之间的区别牢记在心。现值是基于期望现金流的—即，可能的未来现金流的概率加权平均数。如果可能结果的分布如图示10.4一样向右偏态，期望现金流将会大于最可能的现金流。

Step 4: Calculate Present Value The distributions of project cash flows should allow you to calculate the expected cash flows more accurately. In the final step you need to discount these expected cash flows to find present value.

步骤4 计算现值 项目现金流的分布应容许你更加精确的计算期望现金流。在这最后一个步骤中，你需要贴现这些期望现金流来找出现值。

 

I have hired quite a few finance directors over the years. Some were outstanding; others did not work out so well. Inevitably, I have acquired some views about what makes a great numbers guy.

I prefer working with someone fundamentally conservative. Bullish chief finance officers are dangerous. The leader of a business needs to be an optimist, and sales-oriented. But every business needs at least one person at the top alongside them to worry about the downside. I insist that the senior finance person is a qualified accountant. Whether they are a certified public accountant or a chartered accountant, they will have been taught how vital prudence is when preparing accounts, budgets and so forth. I am always astonished at how huge US corporations, like Enron and leading investment banks, can hire go-go MBAs as their CFOs. No wonder they got into trouble.

The CFO must be able to assemble and analyse financial statements themselves: I do not want a quick-talking professional who has risen so far that they do not understand the business's accounting systems. But they must also be able to see the whole picture and not get so immersed in detail that they overlook major issues – a surprisingly common failing.

The CFO must also be able to explain treatments, policies and consequences so that every executive can understand them. The best accountants do not hide behind jargon or technical mumbo-jumbo. Great accountants are so familiar with the company's books that they can swiftly identify each entry, liabilities and assets, every item of income and expense, flows of cash, margins and all the rest, where material.

Some CFOs get bored with things like management accounts, and really want to be corporate financiers. They would rather be doing deals, having power lunches and indulging in the whole merry-go-round, rather than crunching the numbers. Those tasks have their place, but they are not the first order of business. Principally, the CFO must be in absolute command of the figures and financial basics, such as tax, debt and key ratios. Only once they have total mastery of vital administration should they be thinking about the sexy stuff like M&As.

As well as highly numerate, a modern CFO must be something of an IT expert. There are still a surprising number of finance professionals who struggle to use even unsophisticated accounting software. It must be a devastating disadvantage for anyone performing a high level finance job in the 21st century. Similarly, a rounded CFO will have a thorough knowledge of property – leases, financing and the rest – and insurance, as well as a good grounding in corporate law and company secretarial affairs.

The best CFOs have a close, mutually respectful, but not subservient relationship with the chief executive. Those who never disagree and do not stand up to their boss on key matters are not worth having. Ultimately, shareholders and the board place huge faith in the CFO. Whoever fills the post must be independently minded and a strong enough character to deliver the truth to the owners and non-executives – no matter how unpalatable. While every CFO should be a partner to the CEO, they should always believe they report to the board and owners of a corporation.

As with every senior role, an ability to manage people and a sense of humour are critical. But with a CFO, absolute integrity and a capacity for hard work are even more important. During difficult times the role cannot be executed in 40 hours a week and a holiday entitlement of six weeks. Periods of crisis call for all hands to the pump. CFOs are the ones who are managing costs, coping with foreign exchange risks, dealing with pressing bankers and covenants, collecting overdue money and ensuring the auditors do not qualify the accounts. A proper company cannot function without a decent finance director at the helm, supervising, informing and warning.

They may not win all the applause as corporate heroes, but without their contribution even the sexiest business would soon be in trouble.

 

 

Operating Leverage and Break-Even Points

经营杠杆和盈亏平衡点

Break-even charts like Figure 10.1 help managers appreciate operating leverage, that is, project exposure to fixed costs. Remember from Section 9.5 that high operating leverage means high risk, other things equal, of course.

类似图示10.1的盈亏平衡图有助于管理者察觉经营杠杆，即，项目承担的固定成本。还记得Section 9.5，高的经营杠杆意味着高的风险，当然是在其他条件相同的情况下。

The electric scooter project had low fixed costs, only ￥3 billion against projected revenues of ￥37.5 billion. But suppose Otobai now considers a different production technology with lower variable costs of only ￥120,000 per unit (versus ￥300,000 per unit) but higher fixed costs of ￥19 billion. Total forecasted production costs are lower (12 + 19 = ￥31 billion versus ￥33 billion), so profitability improves— compare Table 10.6 to Table 10.1. Project NPV increases to ￥9.6 billion.

	Year 0	Years 1-10
Investment 1.Revenue 2.Variable cost 3.Fixed cost 4.Depreciation 5.Pretax profit(1-2-3-4) 6.Taxes 7.Net profit(5-6) 8.Operating cash flow(4+7) Net cash flow	15                 -15	37.5 12.0 19.0 1.5 5.0 2.5 2.5 4.0 +4.0
NPV=

Table 10.6

Cash-flow forecasts and PV for the electric scooter project, here assuming a production technology with high fixed costs but low total costs (figures in ￥ billions). Compare Table 10.1.

       电动助动车项目的固定成本很低，相对预计销售的375亿日元仅有30亿日元。但是假定Otobai现在考虑一种不同的生产技术，其变动成本更低仅为每辆￥120,000（相对以前的每辆￥300,000），但是固定成本更高为190亿日元。预测总的生产成本会更低（12 + 19 = ￥31 billion versus ￥33 billion，310亿对330亿），这样一来盈利能力会提升—比较表格10.6和10.1。项目的NPV增加至96亿日元。

	0年	1-10年
投资 1.收入 2.变动成本 3.固定成本 4.折旧 5.税前利润(1-2-3-4) 6.税收 7.净利润(5-6) 8.经营现金流(4+7) 净现金流	15                 -15	37.5 12.0 19.0 1.5 5.0 2.5 2.5 4.0 +4.0
NPV=

表格10.6

电动助动车项目的现金流预测和PV, 这里假设一种固定成本高但是总成本低的生产技术 (金额单位：10亿日元).。与表格10.1比较。

Figure 10.3 is the new break-even chart. Break-even sales have increased to 88,000 (that’s bad), even though total production costs have fallen. A new sensitivity analysis would show that project NPV is much more exposed to changes in market size, market share, or unit price. All of these differences can be traced to the higher fixed costs of the alternative production technology.

       图示10.3是新的盈亏平衡图。盈亏平衡销量增加到了88,000（这可不妙），即便总生产成本下降了。新的敏感性分析会显示项目的NPV更加暴露于市场规模、市场份额或单位售价的变动之下。所有这些差别都可以追溯至新的生产技术带来的更高的固定成本。

Is the alternative technology better than the original one? The financial manager would have to consider the alternative technology’s higher business risk, and perhaps recompute NPV at a higher discount rate, before making a final decision.⁶

       新的生产技术优于最初的那种吗？财务经理在作出最后的决策之前，将必须考虑新技术更高的经营风险，而且或许会用更高的贴现率来重新计算NPV⁶。

⁶He or she could use the procedures outlined in Section 9.5 to recalculate beta and come up with a new discount rate.

⁶他/她可以运用Section 9.5中归纳的流程来重算beta并取得一个新的贴现率。

Managers frequently calculate break-even points in terms of accounting profits rather than present values. Table 10.5 shows Otobai’s after-tax profits at three levels of scooter sales. Figure 10.2 once again plots revenues and costs against sales. But the story this time is different. Figure 10.2, which is based on accounting profits, suggests a break-even of 60,000 scooters. Figure 10.1, which is based on present values, shows a break-even at 85,000 scooters. Why the difference?

Table 10.5

The electric scooter project’s accounting profit under different assumptions about unit sales (figures in ￥ billions except as noted).

       管理者常常用会计利润而不是现值来计算盈亏平衡点。表格10.5列出了在三个助动车销售水平上Otobai的税后利润。图示10.2再次标出了相对于销售量的收入和成本。但是这次的情况有所不同。图示10.2，基于会计利润，表明盈亏平衡为60,000辆。图示10.1，基于现值，表明盈亏平衡为85,000辆。为什么会有差别？

表格10.5

不同销售量假设下电动助动车项目的会计利润(除标明外金额单位为10亿日元).

When we work in terms of accounting profit, we deduct depreciation of ￥1.5 billion each year to cover the cost of the initial investment. If Otobai sells 60,000 scooters a year, revenues will be sufficient both to pay operating costs and to recover the initial outlay of ￥15 billion. But they will not be sufficient to repay the opportunity cost of capital on that ￥15 billion. If we allow for the fact that the ￥15 billion could have been invested elsewhere to earn 10 percent, the equivalent annual cost of the investment is not ￥1.5 billion but ￥2.44 billion.⁴

       当我们致力于会计利润的时候，我们扣除了每年15亿日元的折旧以弥补初始投资的成本。如果Otobai一年销售60,000辆助动车，收入将足以支付经营成本和弥补150亿日元的初始指支出。但是它们将不足以抵偿这150亿日元的资本机会成本。如果我们引入这150亿日元可以被投资到他处来赚取10%的回报，那么投资的等价年成本就不是15亿日元而是24.4亿日元。⁴

⁴To calculate the equivalent annual cost of the initial ￥15 billion investment, we divide by the 10-year annuity factor for a 10 percent discount rate:

Equivalent annual cost

See Section 6.3.

The annual revenues at 85,000 scooters per year are about ￥31.9 billion. You can check that this is sufficient to cover variable costs, fixed costs, and taxes and still leave ￥2.44 billion per year to recover the ￥15 billion initial investment and a 10 percent return on that investment.

⁴为计算初始的150亿日元投资的等价年成本，我们以10%贴现率的10年年金系数去除：

Equivalent annual cost

参见Section 6.3。

       每年85,000辆的年收入约为319亿日元，你验算一下可以发现这一数字足以弥补变动成本、固定成本和税收，而且还能每年留出24.4亿日元来抵偿150亿日元的初始投资以及该项投资10%的回报率。

Companies that break even on an accounting basis are really making a loss—they are losing the opportunity cost of capital on their investment. Reinhardt has described a dramatic example of this mistake.⁵ In 1971 Lockheed managers found themselves having to give evidence to Congress on the viability of the company’s L-1011 TriStar program. They argued that the program appeared to be commercially attractive and that TriStar sales would eventually exceed the break-even point of about 200 aircraft. But in calculating this break-even point, Lockheed appears to have ignored the opportunity cost of the huge $1 billion capital investment on this project. Had it allowed for this cost, the break-even point would probably have been nearer to 500 aircraft.

       以会计基础来做盈亏平衡分析的公司实际上是亏损的—它们损失了其投资的资本机会成本。Reinhardt描述了这个错误的一个戏剧性的例子⁵。1971年，Lockheed的管理者发现他们不得不就该公司的L-1011 TriStar项目的可行性向国会提交证据。他们强调该项目具有商业吸引力，且TriStar的销售最终会超过200架飞机的盈亏平衡点。但是在计算这个盈亏平衡点的时候，Lockheed忽略了该项目高达10亿美元的资本投资的机会成本。把这一成本放进去，盈亏平衡点差不多会接近500架飞机。

⁵U. E. Reinhardt, “Break-Even Analysis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance 28 (September 1973), pp. 821–838.

⁵U. E. Reinhardt, “Break-Even Analysis for Lockheed’s TriStar: An Application of Financial Theory,” Journal of Finance 28 (September 1973), pp. 821–838.

Break-Even Analysis

盈亏平衡分析

When we undertake a sensitivity analysis of a project or when we look at alternative scenarios, we are asking how serious it would be if sales or costs turned out to be worse than we forecasted. Managers sometimes prefer to rephrase this question and ask how bad sales can get before the project begins to lose money. This exercise is known as break-even analysis.

当我们对一个项目做敏感性分析或者当我们关注各种可能出现的情境的时候，我们所探寻的是如果销售或者成本比我们预期的糟糕的话，情况会有对严重。有时管理者偏好改变这一问题的措辞（rephrase — [transitive] to say or write something again using different words to express what you mean in a way that is clearer or more acceptable），探寻销售多差才会导致项目亏钱。这一过程就称之为盈亏平衡分析。

In the left-hand portion of Table 10.4 we set out the revenues and costs of the electric scooter project under different assumptions about annual sales.² In the right-hand portion of the table we discount these revenues and costs to give the present value of the inflows and the present value of the outflows. Net present value is of course the difference between these numbers.

Table 10.4

NPV of electric scooter project under different assumptions about unit sales (figures in ￥ billions except as noted).

       在表格10.4的左边部分我们列示了在不同年销售数量假设下电动助动车项目的收入和成本²。在表格的右边部分我们贴现了这些收入和成本以给出流入的现值和流出的现值。理所应当地净现值就是这些数字之间的差额。

表格10.4

不同销售数量假设下电动助动车项目的NPV(除注明外金额单位为十亿日元).

²Notice that if the project makes a loss, this loss can be used to reduce the tax bill on the rest of the company’s business. In this case the project produces a tax saving—the tax outflow is negative.

²请注意如果项目造成了损失，这一损失可以被用来抵减公司其他业务利润的税收。这种情况下该项目就制造了一个税收节余—税收的流出为负值。

You can see that NPV is strongly negative if the company does not produce a single scooter. It is just positive if (as expected) the company sells 100,000 scooters and is strongly positive if it sells 200,000. Clearly the zero-NPV point occurs at a little under 100,000 scooters.

       你可以看出如果公司没有生产一辆助动车NPV就负得很厉害。如果（正如预期）公司销售100,000辆，NPV也刚为正值；如果销售200,000辆，NPV就会正得很厉害。很明显零NPV点就发生在100,000辆下一点。

In Figure 10.1 we have plotted the present value of the inflows and outflows under different assumptions about annual sales. The two lines cross when sales are 85,000 scooters. This is the point at which the project has zero NPV. As long as sales are greater than 85,000, the project has a positive NPV.³

       在图示10.1中我们标出了不同年销售额假设下的流入和流出的现值。当销售量为85,000辆时两线相交。在该点时项目的NPV为零。只要销售量大于85,000，这个项目就有正值的NPV。³

³We could also calculate break-even sales by plotting equivalent annual costs and revenues. Of course, the break-even point would be identical at 85,000 scooters.

³我们还可以通过标注等价年成本和收入来计算盈亏平衡销售量。当然，盈亏平衡点还是85,000。

Scenario Analysis

情境分析

If the variables are interrelated, it may help to consider some alternative plausible scenarios. For example, perhaps the company economist is worried about the possibility of another sharp rise in world oil prices. The direct effect of this would be to encourage the use of electrically powered transportation. The popularity of compact cars after the oil price increases in the 1970s leads you to estimate that an immediate 20 percent price rise in oil would enable you to capture an extra 3 percent of the scooter market. On the other hand, the economist also believes that higher oil prices would prompt a world recession and at the same time stimulate inflation. In that case, market size might be in the region of .8 million scooters and both prices and cost might be 15 percent higher than your initial estimates. Table 10.3 shows that this scenario of higher oil prices and recession would on balance help your new venture. Its NPV would increase to ￥6.5 billion.

Table 10.3

How the NPV of the electric scooter project would be affected by higher oil prices and a world recession.

如果这些变量相互关联，那么考虑一些可能出现的情境就是有帮助的。例如，或许公司的经济学家为另一次世界油价的急升的可能而担忧。这一事件的直接效应是会促进电力驱动交通方式的运用。紧凑型汽车在二十世纪七十年代石油价格上升之后的蓬勃发展让你估计石油价格上涨20%会使你能够多取得3%的电动助动车市场。另一方面，这位经济学家还认为更高的油价会导致世界经济的衰退并同时刺激通货膨胀。这种情况下，市场规模也许只有80万辆，而且售价和成本均会较你最初估计的高15%。表格10.3表明了这一高油价和衰退的情境总的来说（on balance— if you think something on balance, you think it after considering all the facts）有助于你的新投资。项目的NPV会增加至65亿日元。

表格10.3

因高油价和世界经济衰退对电动助动车项目的NPV会有何影响

Managers often find scenario analysis helpful. It allows them to look at different but consistent combinations of variables. Forecasters generally prefer to give an estimate of revenues or costs under a particular scenario than to give some absolute optimistic or pessimistic value.

       管理者们常发现情境分析是有帮助的。它允许他们关注不同但是前后一致的各种变量的组合。预测者们通常更偏好在某一特定情境下赋予收入和成本一个预测值而不是给出某些绝对的乐观或悲观值。

Limits to Sensitivity Analysis

敏感性分析的局限

Sensitivity analysis boils down to expressing cash flows in terms of key project variables and then calculating the consequences of misestimating the variables. It forces the manager to identify the underlying variables, indicates where additional information would be most useful, and helps to expose confused or inappropriate forecasts.

敏感性分析可以归结为以各关键项目变量来表示现金流，然后计算错误估计这些变量的后果。它迫使管理者去辨别出关键的变量，指明哪里的新信息会最有用，并有助于暴露那些模糊的和不恰当的预测。

One drawback to sensitivity analysis is that it always gives somewhat ambiguous results. For example, what exactly does optimistic or pessimistic mean? The marketing department may be interpreting the terms in a different way from the production department. Ten years from now, after hundreds of projects, hindsight may show that the marketing department’s pessimistic limit was exceeded twice as often as the production department’s; but what you may discover 10 years hence is no help now. One solution is to ask the two departments for a complete description of the various odds. However, it is far from easy to extract a forecaster’s subjective notion of the complete probability distribution of possible outcomes.¹

       敏感性分析的一个缺点是它总是会给出某种意义上模棱两可的结果。例如，乐观或悲观的确切意味是什么？营销部门也许会以一种与生产部门不同的方式来解释这些名词。从现在往后推十年，在数百个项目之后，事后来看（hindsight — [uncountable] the ability to understand a situation only after it has happened）也许会表明营销部门的悲观预测值会超过生产部门的两倍；但是你十年之后的发现对现在是没有帮助的。一种解决方法是要求这两个部门对各种可能性作一个完整的描述。然而，要提炼出一位预测者对各可能结果的概率分布的主观意见绝非易事。¹

¹If you doubt this, try some simple experiments. Ask the person who repairs your television to state a numerical probability that your set will work for at least one more year. Or construct your own subjective probability distribution of the number of telephone calls you will receive next week. That ought to be easy. Try it.

¹如果你对此有所怀疑，试试一些简单的实验。问问为你修电视机的人，要求他对你的电视机还能至少再工作一年做一个数量概率的预测。或者就下个星期你会接到的电话的数量构建一个你自己的主观概率分布。照理是很简单的，试试看再说。

Another problem with sensitivity analysis is that the underlying variables are likely to be interrelated. What sense does it make to look at the effect in isolation of an increase in market size? If market size exceeds expectations, it is likely that demand will be stronger than you anticipated and unit prices will be higher. And why look in isolation at the effect of an increase in price? If inflation pushes prices to the upper end of your range, it is quite probable that costs will also be inflated.

       敏感性分析的另一个问题是各关键变量可能是互相关联的。单独的观察市场规模增加的效果有什么意义？如果市场规模超过预期，可能需求就会比你预期的更强劲，而单位价格也会更高。还有为什么要单独的观察价格上涨的效果？如果通货膨胀将价格推至你所预测的范围的高端，那么很有可能成本也会被通货膨胀推高。

Sometimes the analyst can get around these problems by defining underlying variables so that they are roughly independent. But you cannot push one-at-a-time sensitivity analysis too far. It is impossible to obtain expected, optimistic, and pessimistic values for total project cash flows from the information in Table 10.2.

       有时分析人员能够通过定义关键变量以使它们大体上独立来回避（get around something — to avoid something that is difficult or causes problems for you）这些问题。但是你无法将这种一次一个的敏感性分析发挥得太过。从表格10.2的信息中不可能获得对项目现金流总额的期望、乐观和悲观值。

10.1 SENSITIVITY ANALYSIS

10.1 敏感性分析

Uncertainty means that more things can happen than will happen. Whenever you are confronted with a cash-flow forecast, you should try to discover what else can happen.

不确定性意味着可能发生的事情要比将发生的事情多。无论何时当你面对现金流预测，你应该尝试去发现还会发生什么。

Put yourself in the well-heeled shoes of the treasurer of the Otobai Company in Osaka, Japan. You are considering the introduction of an electrically powered motor scooter for city use. Your staff members have prepared the cash-flow forecasts shown in Table 10.1. Since NPV is positive at the 10 percent opportunity cost of capital, it appears to be worth going ahead.

	Year 0	Years 1-10
Investment 1.      Revenue 2.      Variable cost 3.      Fixed cost 4.      Depreciation 5.      Pretax profit(1-2-3-4) 6.      Tax 7.      Net profit(5-6) 8.      Operating cash flow(4+7) Net cash flow	15                 -15	37.5 30 3 1.5 3 1.5 1.5 3 +3

TABLE 10.1

Preliminary cash-flow forecasts for Otobai’s electric scooter project (figures in ￥ billions).

Assumptions:

1. Investment is depreciated over 10 years straight-line.

2. Income is taxed at a rate of 50 percent.

       现在把你放到位于日本大阪的Otobai公司，你的职位是收入丰厚（well-heeled— informal rich）的司库。你正在考虑推出一种用于市内通勤的电动助动车（scooter— also motor scooter a type of small, less powerful motorcycle with small wheels）。你的职员已经做好了现金流预测，如表格10.1所示。由于以10%的机会资本成本计算的NPV为正，该项目看来值得推进。

	0年	1-10年
投资额 1.收入 2.变动成本 3.固定成本 4.折旧 5.税前利润(1-2-3-4) 6.税收 7.净利润(5-6) 8.经营现金流量(4+7) 净现金流	15                 -15	37.5 30 3 1.5 3 1.5 1.5 3 +3

表格10.1

Otobai电动助动车项目的初步现金流预测（金额单位：10亿日元）

假定：

1.      投资以10年直线法折旧。

2.      收益税率为50%。

Before you decide, you want to delve into these forecasts and identify the key variables that determine whether the project succeeds or fails. It turns out that the marketing department has estimated revenue as follows:

Unit sales = new product’s share of market × size of scooter market

                             = .1 × 1 million = 100,000 scooters

Revenue = unit sales × price per unit

                                                        = 100,000 × 375,000 = ￥37.5 billion

The production department has estimated variable costs per unit as ￥300,000. Since projected volume is 100,000 scooters per year, total variable cost is ￥30 billion. Fixed costs are ￥3 billion per year. The initial investment can be depreciated on a straight-line basis over the 10-year period, and profits are taxed at a rate of 50 percent.

       在你做出决定之前，你希望深入研究（delve into — to try to find more information about someone or something）这些因素并识别出决定这个项目是成功还是失败的关键变量。研究的结果表明营销部门对收入的估计如下：

Unit sales = new product’s share of market × size of scooter market

                             = .1 × 1 million = 100,000 scooters

Revenue = unit sales × price per unit

                                                        = 100,000 × 375,000 = ￥37.5 billion

生产部门估算单位变动成本为￥300,000。由于预测产量为每年100,000辆，变动成本总额就是300亿日元。固定成本为每年30亿日元。初始投资以10年的直线法计提折旧，利润的税率为50%。

These seem to be the important things you need to know, but look out for unidentified variables. Perhaps there are patent problems, or perhaps you will need to invest in service stations that will recharge the scooter batteries. The greatest dangers often lie in these unknown unknowns, or “unk-unks,” as scientists call them.

       以上这些似乎是你需要知道的重要事项，但是找找未被发现的变量。也许会有专利问题，或者也许你还会需要投资为助动车电池充电的服务站点。最大的危险通常潜伏于这些未知的未知之中（看到这里，想到了美国前防长拉姆斯菲尔德的一段话："Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know."），或者如科学家们称呼其为“unk-unks”。

原帖不知出处，观其行文应为四大职员所做

 

<1>思考任何一件事的合理性

审计界有一句口头禅：“不re”。“不re”，是“not reasonable”的简称，也就是“不合理”，不符合常识。审计师的职责就是检查财务报表的真实性和合理性。为了防止上当受骗，审计师需要仔细推敲公司当局的每一种说法是否合理，这是他们的一种职业习惯。

举一个简单的例子。管理当局会说：“今年收入增长了50％，是因为销售数量增长了50％。”审计师一看报表：“不对啊，成本明明下降了20％啊，期末存货也比上年年底要多。而且也没听说有什么技术进步，能让单位成本大幅下降，所以成本下降只能是因为生产数量在下降。这和销售数量增长不是自相矛盾吗？”

这个例子正印证了一句老话：“说谎话容易，把谎话说圆却很难。”为了把一句谎话编圆，你需要修改很多相关的地方，而且还不一定修改得圆满。审计师就是通过寻找会计资料当中不正常、不合理的蛛丝马迹，从各个角度向公司提出一连串的问题，像猎犬一样刨啊刨，从而把公司隐瞒、编造的事情挖出来。

这年头，不仅公司财务的谎话编得不圆，连骗子的骗术也“不re”。前不久，我收到“淘宝网”发来的一个广告，通知我中了奖。我登陆淘宝网，输入密码，果然有35000元的现金大奖在等着我。在我收到这个广告之前一天，淘宝网的确在搞抽奖，所以我并没意识到这是一个骗局。

我继续读下去，兑奖通知说，税法规定奖不能白拿。只要我邮寄1500元的增值税到某个帐号，他们就会立即把奖金支付给我。我刚要激动地抬屁股去邮局，忽然想起一件事：你直接从我35000元的奖金里扣1500元不就可以了吗，为什么要我去邮局寄钱呢？我又仔细看了看一遍兑奖说明，发现一个新的问题：怎么会让我交增值税呢，增值税一般是在工厂进口原材料的时候才交的。就这样，我识破了一场“不re”的骗局。

审计师喜欢思考事情的合理性，这其实就是日常生活常识的积累。可是，如果审计师把这种职业习惯带到生活当中来，就不那么可爱了。在生活里，人不可能把所有事情都记得很清楚，难免说出一些不太准确的话。而且在夫妻之间，有时也会说一些善意的小谎言，互相哄一哄。如果你的另一半是一个干审计的，那么恭喜你，你的每一句善意的谎话都会引来对方的疑问，你会被打破沙锅问到底，越挖越深，直到谎话彻底败露为之。

所以，敢和审计师结婚的人，一定是个赤诚坦荡的人。


<2>用数字说话

中国人喜欢从表象上，从意识形态上，从趋势上说一些大而化之的话，偏偏懒的拿数字去支持自己的观点，用数字去检验一下是不是这么回事。审计师则不同，他们的很多科目的都需要匡算（Prove in Total）。比如工资费用，审计师会用公司的总人数乘以大致的人均工资，得出一个总数，和报表上的那个数字对比一下，看看相差得大不大。

用数字说话非常重要。因为，有些事情正确与否，并不是从概念上就能看出来的，你得实际计算一下成本、收益分别是多少，才能做出结论。只有数字，才能告诉你答案。

举个例子。很多西方国家发展竞技体育不会动用很多纳税人的钱，而是走市场化、职业化的道路。而在中国，竞技体育基本是靠国家财政支持的。如果你举行一场辩论的话，至少90％的中国人支持用“举国体制”发展竞技体育，恐怕只有不到10％的人反对这么做。到底谁对谁错呢？

我们可以匡算一下，如果让纳税人来赞助的话，一枚奥运会金牌会花费纳税人多少钱。假设1名奥运会冠军，是从1000名运动员里挑选出来的（中国那么大，33个省平均每个省有30个人练习同一个项目，应该不夸张）。光运动员还不够，还得有后勤保障人员，比如教练，领队，队医，厨房师父。就算平均两个运动员有一个后勤人员吧。好了，运动员＋后勤人员，一共1500个人，换一枚奥运金牌。这1500个人是职业性的，假设国家得管他们每个人20年，其中10年训练，10年退休金补贴。每人每月的工资，暂定为1000元。除此之外，运动员还要使用运动器械，要住宿舍，还要出去外地、外国比赛等等开销，每人每月1000元。这样一算，一枚奥运金牌的成本，1500人×20年×12个月×2000元/月＝7.2亿人民币。雅典奥运会上，中国取得了32枚金牌，那么我们在这32枚金牌上花费了7.2亿×30＝230.4亿元人民币。

真是不算不知道，一算吓一条。数字出来以后，双方可以再进行一场辩论，就算仍然谁也说服不了谁，至少，他们会把辩论的焦点从简单的“是”或“否”，转移到对于成本、收益的权衡上来。这场辩论的水平就会上一个层次。

需要说明的是，我上边的这些数字都是自己估算的，而不是从哪个政府预算报告上摘录的。这是一件挺无奈的事情。我从没见政府给出过明细的财政预算。所以我不知道我纳的税有多少用于教育、多少用于竞技体育、多少用于医疗、多少用于公务员工资、多少用于业务招待……不过不要紧，我们每个人都有常识和头脑。就像上边计算奥运会金牌的成本一样，很多事情我们自己就可以依靠现有的知识，大致估算一下。这么做虽然会费点力气，但是总比一无所知要好。

希望每一个人都能够养成用数字说话、向数字索取答案的好习惯。


<3>做事要留证据

在审计工作当中，很重要的一条原则就是：“如果你没有写下来你做了什么，那就等于你没有做。”比如你询问了谁，询问的结果是什么，你查看了什么单据，都要记录在工作底稿里。审计师特别喜欢管客户要资料：合同啦，发票啦，内部文件啦，管理当局的声名啦，都象宝贝似的要过来，把重点标注清楚，归入审计工作底稿里。只有当这些证据齐全了，报表上的数字才有依据。

用书面证据说事，和口头约定相比，无疑是一种进步。只有在每一个环节留下可供查证的证据，才能在发生纠纷的时候有理可说。可惜很多中国的企业总喜欢在合同里说一套，实际当中跟对方口头约定另外一套，不愿意及时更新合同。等发生了纠纷，双方各执一词。我想，随着中国司法制度越来越健全，那些不愿意用合同说事的企业，会越来越吃亏。

其实，审计报告本身就是一种书面证据。会计报表使用者需要看到注册会计师出具的审计报告，以确信会计报表是真实公允的。这年头股民很多，但是会看年报的股民却不多，看年报的时候关注受聘会计师事务所是谁的股民更是寥寥无几。如果你只是“炒股”，而不是“投资”股票的话，审计报告的确是可有可无的东西。

“做事要留证据”——这句话从另外一个角度讲，就是“不该留的证据坚决不留”。比如，审计师发现企业有一些小问题，但是不太严重，并不需要解决。那么，审计师最好就当根本不知道，在工作底稿上提都不提。如果你提了，但是没解决，反而容易被监管机构抓住小辫子。曾经有一种说法：我们做审计的目的，就是在赚到审计费的同时，取得适当的审计证据把责任尽量都推给公司管理层。这话虽然说的有点露骨，但是无疑是句大实话。


<4>简明、清晰地表达观点

“改革开放要坚持，纠正不正之风和打击经济犯罪也要坚持；改革开放要坚决，纠正不正之风和打击经济犯罪也要坚决；改革开放要是一个长期任务，纠正不正之风和打击经济犯罪也是一个长期任务。”——李瑞环，1986年4月3日在中央端正党风座谈会上的发言。

上边这段话，大家可能都读得比较累。如果换成一个审计师，他会怎么表达同样的意思呢？我想，他大概会这么说：“改革开放、纠正不正之风和打击经济犯罪这三件事都是需要长期坚持的任务。而且，我们在执行的时候要坚决。”

这就是商业社会的要求：从阅读者的角度出发，尽量通俗、简明地表达观点。如果阅读者很容易就明白了你的意思，他就有希望变成你的客户，你的表达就是成功的。如果他听不懂，或者听起来很费劲，双方交流的成本很高，你的表达就是失败的。

在我做第一个审计项目的时候，带领我工作的是一个第三年的高级审计员。我记得，她做事情一向很麻利，可是唯独她在往工作底稿上写“注释”的时候，总是磨磨蹭蹭的。每一条注释，她都是写了又写，改了又改，不断试验怎么表达才最清楚、最简明，让经理一眼就能看明白。她在遣词造句上所花费的时间，要远远多于给经理节省的时间。因为她觉得，多考虑一下阅读者的需要，让阅读者能够迅速抓住信息的重点，这样的底稿才是合格的。

在她的影响下，我也学着提高表达的效率，让别人不费脑子就能看明白。如果我想说的事情不太复杂，我就看门见山，第一句话就把结论扔出去，然后再写原因：<1>……,<2>……,<3>……。

如果我想说的事情比较复杂，需要先介绍背景知识，然后进行推理演绎，别人才能看懂，我就由浅入深地写，A，B，C……说清楚一件事，再说下一件事，依次说下去。每一条路如果有多个分支的话，我会加上序号A1，A2，B1，B2，这样读者就心里清楚自己“走”到了哪条路的哪个门牌号。

我看到很多人写长篇大论的时候，总是想到哪就写到哪，相同的意思也不合并一下，序号也不加，把ABCBDAE混成一团写，让人读起来像是在走迷宫。就拿李瑞环的那段话来说吧，第一句话的“要坚持”和第三句的“是一个长期任务”明明说的是同一个意思，他偏偏要拆成两句话到处乱丢。我们自己在写长篇大论的时候，切忌成为这种“乱丢盒子”的悟空啊。

在平时的阅读中，我们经常看到有些文章的作者容易陷入自言自语的梦呓，光顾着自己痛快，光顾着炫耀自己的文采和博学，而不顾文章的条理是否清楚、表达是否简明、别人是否明白。张五常近年来写的文章就是一个典型的例子，半文半白，思维跳跃。一个人的思想高明是一件好事，但是，如果他不善于表达，让读者读得晕头转向、不知所云、忘文兴叹，由于“交易费用高昂，导致交易无法达成”，这实在是一件让人遗憾的事情。


<5>出Q是完善文章的好办法

所谓出Q，就是由一个独立的第三人阅读审计底稿，指出里边有错误、或者是不清楚的地方，然后交给底稿的编制者去修改和完善。

在四大，员工不喜欢经理出Q，经理不喜欢合伙人出Q，审计部不喜欢税务部出Q。没有人喜欢别人给自己Q。但是，他们给别人出Q的时候都毫不留情。

出Q的确是完善文章的好办法。我将这种方法的优点总结如下：

<1>所谓“旁观者清”。有些事情，底稿编制者自己觉得说得很明白了，但是别人可能还是看不懂。让一个独立的第三人看一遍，提出他的疑问，就能够发现哪些地方表达得还不那么清楚。

<2>能够凝聚多个人的智慧。一张好的底稿，需要不断加以完善，充分吸纳不同人的好的思想。经理、合伙人通过出Q，把深层次的问题指出来，等于是将自己在职业生涯中所积累的知识注入到了底稿里。员工通过修改，模仿，下一年再完善，如此循环，底稿的质量就能不断提高。这不仅是工作底稿的进化模式，也是人类文明的进化模式。

<3>避免面对面的接触，从而提高沟通的效率。这个优点说来有点好笑，但是的确是一个事实。每个人都有自尊心和逆反心理的。据我观察，如果你当面指出别人底稿的缺点的话，通常会引起对方的解释、辩护和反驳。争来争去，底稿里问题并没有得到解决。如果是出Q的话，就快了很多。反正问题我已经给你指出来了。有则改之，无则加“注释”在底稿里说清楚，省得别人每次都误会你。

魔鬼存在于细节当中。出Q就是为了把底稿里隐藏着的大大小小的“妖精”挖出来。在四大，好的底稿无一例外都是Q出来的，而且是海量的Q，反复的Q。没有人喜欢别人给自己出Q，但是出Q的确能大大提高底稿的质量。希望你在清Q的时候，能够明白“严师出高徒”这个道理，把心态调整得积极一些。


<6>用二元表格传递大量信息

关于这个问题，happysun写过一篇文章，说的已经很清楚了，我没有什么要补充的。我将他的文章大段引用在下边。

文章写完了，谢谢各位阅读。





用表格来说明问题是一种有条理的思考方法的体现

有这样一个问题，说某家旅馆今天有20个房间有旅客住，其中100元每天的房间有8家，150元每天的房间有7间，200元每天的房间有5间，请问这家旅馆今天的收入是多少？
这是一个很简单的题目。其要点不在于答案，而在于如何表达你的计算过程。我曾经拿着这个问题在近百名大学毕业生的教室里发问，得到的计算过程的表达方式全都是这样的：
100元 x 8 + 150元 x 7 + 200元 x 5 = 2850 元。
这不是一个令人高兴的结果。更好的表达方式是这样的：


房间单价 房间数量    收入
A          B      C=A x B

100元     8         800元
150元     7        1050元
200元     5        1000元

合计               2850元

谁都能看出来，这种表达方式体现了一种数据库结构，而且非常有利于另外一个人来复查整个计算过程。审计师在工作底稿里，要善于使用这样的表达方式。
不过，这也不能怪那些大学生，我随便在互联网上找了一段新闻，是这么写的：
“去年频频出台的宏观政策极大遏制了北京楼市的蹿升式发展，尽管现房和期房的全年供应量都有不同程度的增加，但却明显呈现出求大于供的态势。受此影响，去年本市住宅销售非常火爆，现房销售率以及期房的预售率分别高达97.5%和92.3%。
记者昨天从北京市建委了解到，去年本市商品住宅现房销售面积总计2285.8万平方米，同比增长29.1%。由于供给增长明显小于需求，去年形成的现房市场已基本被消化完毕，销售率高达97.5%，比2003年同期高出12.4个百分点。
本市的期房销售也进入黄金时代。在商品住宅期房批准预售面积仅增长5%的前提下，预售登记同比增长接近60%，预售率为92.3%，比2003年高出30.4个百分点。
建委有关人士表示，上述数据证明目前本市房地产市场的消化吸收能力很强。这种销售、预售双走强的态势在今年还将持续。
《京华时报》(2005年2月18日第B34版) ”
（见http://www.people.com.cn/GB/jingji/1038/3184958.html）
这一段文字，就是典型的可以改造成一个表格的文字叙述。

单位：万平方米    2004年     2003年    增长率/增长百分点
　　　　
现房销售面积     2,285.80   1,770.57    29.1%
现房完工面积     2,344.41   2,080.57    12.7%
现房销售率       97.5%       85.1%      12.4%
　　　
期房预售登记面积   1.57       1.00      57.2%
期房批准预售面积   1.70       1.62       5.4%
期房销售率        92.3%      61.9%     30.4%

我自己试着将上面的文字叙述用表格表达了一下，发现这样做的好处真是多，不仅能够给读者提供更详细更丰富的信息，表达上也更清楚了.

另外，我还发现，从数学上讲，上面那段文字里关于期房销售的数据也很有意思，记者不知道出于什么考虑，并没有给出期房的任何具体数据，只给出了几个百分比，但这几个百分比之间是互相约束并且自恰的。所以，不管我假设期房销售面积是1，还是1000，都无所谓。我因此没有办法推算出面积的任何具体数字。用数学语言说：根据目前的已知条件，期房的面积有无穷多解。

其实不仅仅是中国的记者很少用表格表达这些数字而宁愿用文字叙述，外国的记者也一样。你要是看华尔街日报的第一版，也经常有一大段文字是在讨论某些数字的。甚至连很多企业递交给美国证交会的上市文件里，也时常会用大段文字来描述一些数字。

我猜记者愿意用文字来表达这些数字是为了口头报道的方便。口头报道是一种单一维度的线性的信息输出，很难把一个二维的表格念出来。但写工作底稿和出报纸杂志，信息输出是一种两维的平面方式的，用表格来表达就是一种更清楚也更有效率的方式。

记者当然可以有他们的自由来选择他们喜欢的表达方式，但审计师为了让自己的思路尽量清楚，也为了让自己的工作能够让别人，例如合伙人，审阅起来简单易懂，还是用表格来表述自己的思路为好。

Part III

Chapter Ten A Project is Not a Black Box

第十章 一个项目不是一个黑匣子

 

A BLACK BOX is something that we accept and use but do not understand. For most of us a computer is a black box. We may know what it is supposed to do, but we do not understand how it works and, if something breaks, we cannot fix it.

一个黑匣子是指某样我们接受并且使用但是没有理解的东西。对于我们中的大多数人来说一台电脑就是一个黑匣子。我们也许知道它应该用来做什么，但是我们并不理解它是如何工作的，而且如果某件东西坏了，我们也无法修理它。

We have been treating capital projects as black boxes. In other words, we have talked as if managers are handed unbiased cash-flow forecasts and their only task is to assess risk, choose the right discount rate, and crank out net present value. Actual financial managers won’t rest until they understand what makes the project tick and what could go wrong with it. Remember Murphy’s law, “If anything can go wrong, it will,” and O’Reilly’s corollary, “at the worst possible time.”

       我们一直在将资本项目当成黑匣子来对待。换句话说，我们谈论了似乎管理者会被给予无偏向的现金流预测，而他们唯一的任务就是评估风险，选择正确的贴现率，从而迅速得出（crank something ↔ out — phrasal verb to produce a lot of something very quickly）净现值。实际上财务管理者是不会得到喘息的，直到他们理解是什么使项目与众不同（what makes somebody tick — informal the thoughts, feelings, opinions etc that give someone their character or make them behave in a particular way）以及可能会出什么差错。记住墨菲定律，“凡可出差错者，皆会，”和O’Reilly的推论（corollary — [countable] formal something that is the direct result of something else），“在可能的最坏的时候。”

Even if the project’s risk is wholly diversifiable, you still need to understand why the venture could fail. Once you know that, you can decide whether it is worth trying to resolve the uncertainty. Maybe further expenditure on market research would clear up those doubts about acceptance by consumers, maybe another drill hole would give you a better idea of the size of the ore body, and maybe some further work on the test bed would confirm the durability of those welds. If the project really has a negative NPV, the sooner you can identify it, the better. And even if you decide that it is worth going ahead on the basis of present information, you do not want to be caught by surprise if things subsequently go wrong. You want to know the danger signals and the actions you might take.

       即便一个项目的风险是可以完全分散的，你仍然需要理解为什么这项投资可能失败。一旦你知道了，你就能决定是否值得努力去解决不确定性。也许在市场研究上的更多支出可以消除关于消费者的接受程度的疑虑，也许另一个采掘坑可以使你对矿藏的规模有更好的了解，也许在测试台上多做点工作可以确定那些焊点的耐受性。如果项目确实有负值的NPV，你能越快的发现这一点越好。而即使你决定在现有信息的基础上值得继续前进，如果后来的事情发生了偏差，你也不希望因此而感到意外（take/catch somebody by surprise — to happen unexpectedly）。你希望知道危险的讯号以及你应采取的行动。

We will show you how to use sensitivity analysis, break-even analysis, and Monte Carlo simulation to identify crucial assumptions and to explore what can go wrong. There is no magic in these techniques, just computer-assisted common sense. You don’t need a license to use them.

       我们将会向你展示如何运用敏感性分析、盈亏平衡分析和蒙特卡罗模拟来识别关键的假设和探究什么可能会出错。这些技术方法不是变魔术，而是得到计算机辅助的常识。你不需要一张执照来运用它们。

Discounted-cash-flow analysis commonly assumes that companies hold assets passively, and it ignores the opportunities to expand the project if it is successful or to bail out if it is not. However, wise managers value these opportunities. They look for ways to capitalize on success and to reduce the costs of failure, and they are prepared to pay up for projects that give them this flexibility. Opportunities to modify projects as the future unfolds are known as real options. We describe several important real options, and we show how to use decision trees to set out these options’ attributes and implications.

       贴现现金流分析通常假定公司被动地持有资产，而且它忽略了在项目成功的情况下扩张和失败情况下放弃（bail out — [countable] informal financial help given to a person or a company that is in difficulty）的机会。然而，明智的管理者会评估这些机会。他们寻找使成功资本化和减少失败成本的方法，而且他们准备好为给予他们这种灵活性的项目付款。随着未来展现而出现的修正项目的机会称之为实物期权。我们会描述某些重要的实物期权，我们还会展示如何运用决策树来有条理地解释（set something ↔ out — to explain ideas, facts, or opinions in a clearly organized way, in writing or in a speech）这些期权的属性和影响。

PART TWO的相关网站

Robert Shiller’s home page includes long-term data on U.S. stock and bill returns:

www.aida.econ.yale.edu

Robert Shiller的主页中有美国股票和债券回报率的长期数据：

www.aida.econ.yale.edu

 

Equity betas for individual stocks are found on Yahoo. (Or you can download the stock prices from Yahoo and calculate your own measures):

www.finance.yahoo.com

单支股票的权益beta可以在Yahoo网站中找到。（或者你可以从Yahoo下载股价数据然后计算你自己的尺度）：

www.finance.yahoo.com

 

Aswath Damodoran’s home page contains good long-term data on U.S. equities and average equity and asset betas for U.S. industries:

www.equity.stern.nyu.edu/_adamodar/New_Home_Page

Aswath Damodoran的主页包含了美国权益性证券的可靠的长期数据以及美国各行业的平均权益和资产beta：

www.equity.stern.nyu.edu/_adamodar/New_Home_Page

 

Another useful site is Campbell Harvey’s home page. It contains data on past stock returns and risk, and software to calculate mean-variance efficient frontiers:

www.duke.edu/_charvey

另外一个很有帮助的站点是Campbell Harvey的主页。它包括了过去股票回报率和风险的数据和计算均值—方差有效边界的软件：

www.duke.edu/_charvey

 

Data on the Fama-French factors are published on Ken French’s website:

www.mba.tuck.dartmouth.edu/pages/faculty/ken.french

关于Fama-French各因素的数据发布于Ken French的网站上：

www.mba.tuck.dartmouth.edu/pages/faculty/ken.french

 

ValuePro provides software and data for estimating company cost of capital:

www.valuepro.net

ValuePro提供用以估算公司资本成本的软件和数据：

www.valuepro.net

 

For a collection of recent articles on the cost of capital see:

www.ibbotson.com

近来有关资本成本文章的集合，参见：

www.ibbotson.com

 

Oxford, UK, 17 November 2008 - Elsevier announced today that the paper 'CEVITATM: the valuation and reporting of strategic capabilities', published in Management Accounting Research (http://www.elsevier.com/locate/mar), has received the Management Accounting Section (MAS) of the American Accounting Association (AAA) Greatest Potential Impact on Practice Award.

The article, published in Volume 15, Issue 1, March 2004, was written by Janek Ratnatunga, Norman Gray, and Kashi R. Balachandran. The award is sponsored by the Management Accounting Section (MAS) of the American Accounting Association, the American Institute of Certified Public Accountants (AICPA), the Chartered Institute of Management Accountants (CIMA) and the Certified Management Accountants-Canada (CMA-Canada).

The "new types of measurements" that are needed for both tradable and non-tradable assets in order for organisations to meet the challenges present at the corporate, national and international levels, especially in the areas of strategic decision-making and valuation are explored in this article. The article states that the focus of attention in recent studies has been mainly on the valuation of intangibles, and argues that such a focus misses the point that it is the combination of both tangible and intangible assets that provide an organisation a true 'capability' that ultimately drives its economic value.

The approach proposed is to calculate the Capability Economic Value of Intangible and Tangible Assets (CEVITA) of an organisation, by leveraging its capability enhancing expenses to economic values by using specific Expense Leveraged Value Indexes (ELVIs). The authors illustrate a technique that will not only make these strategic valuations more relevant, but also shows how to report these tangible and intangible asset combinations in an organisation's financial statements.

The Editor of Management Accounting Research, Professor Robert W. Scapens of Manchester Business School, United Kingdom commented "This paper and the award it has received demonstrate the potential for bridging the gap between academic research and professional management accounting practice. I'm delighted Management Accounting Research has published this award winning paper."

CHALLENGE QUESTIONS

挑战性问题

1. Suppose you are valuing a future stream of high-risk (high-beta) cash outflows. High risk means a high discount rate. But the higher the discount rate, the less the present value. This seems to say that the higher the risk of cash outflows, the less you should worry about them! Can that be right? Should the sign of the cash flow affect the appropriate discount rate? Explain.

1. 设你正在对一系列高风险（高beta）的未来现金流出进行估值。高风险就意味高贴现率。但是贴现率越高，现值就越低。这似乎就是说现金流出的风险越高，你就越不需要为它们操心！这是对的吗？现金流的符号应该影响合适的贴现率吗？请解释。

 

2. U.S. pharmaceutical companies have an average beta of about .8. These companies have very little debt financing, so the asset beta is also about .8. Yet a European investor would calculate a beta of much less than .8 relative to returns on European stock markets. (How do you explain this?) Now consider some possible implications.

a. Should German pharmaceutical companies move their R&D and production facilities to the United States?

b. Suppose the German company uses the CAPM to calculate a cost of capital of 9 percent for investments in the United States and 12 percent at home. As a result it plans to invest large amounts of its shareholders’ money in the United States. But its shareholders have already demonstrated their home country bias. Should the German company respect its shareholders’ preferences and also invest mostly at home?

c. The German company can also buy shares of U.S. pharmaceutical companies. Suppose the expected rate of return in these shares is 13 percent, reflecting their beta of about 1.0 with respect to the U.S. market. Should the German company demand a 13 percent rate of return on investments in the United States?

2. 美国医药公司的平均beta约为.8。这些公司的债务融资极少，所以资产beta也约为.8。然而一位欧洲投资者相对欧洲股票市场的回报率会计算出来一个比.8低得多的beta。（你对此有何解释？）现在考虑一些可能的影响。

a. 德国的医药公司应将其R&D（研究与开发）和生产设施转移到美国吗？

b. 设德国公司用CAPM计算出在美国投资的资本成本为9%，在本国为12%。这样带来的一个结果就是其计划将大笔的股东资金投资到美国。但是其股东已经表明了他们的本国偏向性。该德国公司应该尊重其股东的偏好并将资金大部分投于本国吗？

c. 该德国公司还可以购买美国医药公司的股票。设这些股票的期望回报率为13%，反映了它们相对于美国市场约为1.0的beta。该德国公司对美国的投资应该要求13%的回报率吗？

 

3. An oil company executive is considering investing $10 million in one or both of two wells: Well 1 is expected to produce oil worth $3 million a year for 10 years; well 2 is expected to produce $2 million for 15 years. These are real (inflation-adjusted) cash flows.

The beta for producing wells is .9. The market risk premium is 8 percent, the nominal risk-free interest rate is 6 percent, and expected inflation is 4 percent.

The two wells are intended to develop a previously discovered oil field. Unfortunately there is still a 20 percent chance of a dry hole in each case. A dry hole means zero cash flows and a complete loss of the $10 million investment.

Ignore taxes and make further assumptions as necessary.

a. What is the correct real discount rate for cash flows from developed wells?

b. The oil company executive proposes to add 20 percentage points to the real discount rate to offset the risk of a dry hole. Calculate the NPV of each well with this adjusted discount rate.

c. What do you say the NPVs of the two wells are?

d. Is there any single fudge factor that could be added to the discount rate for developed wells that would yield the correct NPV for both wells? Explain.

3. 一位石油公司的执行官正在考虑投资1000万美元于两口油井中的一口或者两口都投：1号井可望在十年中每年产生价值300万美元的石油；2号井可望在十五年中每年产生价值200万美元的石油。这些是真实（通货膨胀调整后）的现金流。

       打井的beta是.9。市场风险溢价为8%，名义无风险利率为6%，期望通货膨胀为4%。

       这两口油井的目的是为了开发一块先前发现的油田。不幸的是，每种情况下仍然有20%的机会会打出一口枯井。一口枯井意味零现金流以及完全损失1000万美元的投资。

       忽略税收并作出所必需的进一步的假设。

a.     打井产生的现金流的正确的真实贴现率是多少？

b.     这位石油公司的执行官提议在真实贴现率上增加20个百分点来抵消打出一口枯井的风险。以这个调整后的贴现率来计算每口油井的NPV。

c.     你说这两口井的NPV是多少？

d.     是否有任何单一的修正因子可以被加到适用于已开发油井的贴现率中来得出这两口井正确的NPV？请解释。

 

4. If you have access to “Data Analysis Tools” in Excel, use the “regression” functions to investigate the reliability of the betas estimated in Practice Questions 3 and 5 and the industry cost of capital calculated in question 6.

a. What are the standard errors of the betas from questions 3(a) and 3(c)? Given the standard errors, do you regard the different beta estimates obtained for each company as signficantly different? (Perhaps the differences are just “noise.”) What would you propose as the most reliable forecast of beta for each company?

b. How reliable are the beta estimates from question 5(a)?

c. Compare the standard error of the industry beta from question 5(b) to the standard errors for individual-company betas. Given these standard errors, would you change or amend your answer to question 6(e)?

4. 如果你进入Excel中的“数据分析工具”，运用“回归”函数来调查习题3和5中估算出来的beta以及习题6中计算出的行业资本成本的可靠性。

a. 习题3(a)和3(c)的beta的标准误是多少？给定该标准误，你会认为所得的每家公司的不同的beta估计是重大差异吗？（也许差异仅是“杂音”）你会提议的对每家公司beta的最可靠的预测是什么？

b. 习题5(a)的beta估算有多可靠？

c. 将习题5(b)的行业beta的标准误和个别公司beta的标准误进行比较。给定这些标准误，你会改变或修正（amend —  If you amend something that has been written such as a law, or something that is said, you change it in order to improve it or make it more accurate.）你对习题6(e)的答案吗？

14. An oil company is drilling a series of new wells on the perimeter of a producing oil field. About 20 percent of the new wells will be dry holes. Even if a new well strikes oil, there is still uncertainty about the amount of oil produced: 40 percent of new wells which strike oil produce only 1,000 barrels a day; 60 percent produce 5,000 barrels per day.

a. Forecast the annual cash revenues from a new perimeter well. Use a future oil price of $15 per barrel.

b. A geologist proposes to discount the cash flows of the new wells at 30 percent to offset the risk of dry holes. The oil company’s normal cost of capital is 10 percent. Does this proposal make sense? Briefly explain why or why not.

14. 一家石油公司正在一块产油的油田周边（perimeter — the border around an enclosed area such as a military camp）钻探新的油井。大约20%的新井会是枯井。即使一口新井打出了油，其石油产量仍然有不确定性：出油的新井中的40%一天仅产油1,000桶；60%每天产油5,000桶。

       a. 预测一块新的周边油井产生的年现金收入。未来油价为每桶$15。

b. 一位地质学家建议用30%来贴现新油井的现金流以抵消枯井的风险。这家石油公司的正常的资本成本为10%。这个建议是否有道理？简单解释为什么有或为什么没有。

 

15. Look back at project A in Section 9.6. Now assume that

a. Expected cash flow is $150 per year for five years.

b. The risk-free rate of interest is 5 percent.

c. The market risk premium is 6 percent.

d. The estimated beta is 1.2.

Recalculate the certainty-equivalent cash flows, and show that the ratio of these certainty-equivalent cash flows to the risky cash flows declines by a constant proportion each year.

15. 再看一下Section 9.6中的项目Ａ。现在假定

a. 期望现金流为每年$150，持续五年

b. 无风险利率为５％

c. 市场风险溢价为６％

d. 估计beta为1.2

重新计算确定等值现金流，并且表明这些确定等值现金流对风险性现金流的比率每年以一个不变的比例下降。

 

16. A project has the following forecasted cash flows: Excel

The estimated project beta is 1.5. The market return r_m is 16 percent, and the risk-free rate r_f is 7 percent.

a. Estimate the opportunity cost of capital and the project’s PV (using the same rate to discount each cash flow).

b. What are the certainty-equivalent cash flows in each year?

c. What is the ratio of the certainty-equivalent cash flow to the expected cash flow in each year?

d. Explain why this ratio declines.

16. 一个项目的预期现金流如下：Excel

估计项目的beta为1.5。市场回报率r_m为16%，无风险利率r_f为7%。

a.     估算机会资本成本和项目的PV（运用相同的利率来贴现每期的现金流）

b.     每年的确定等值现金流是多少？

c.     每年的确定等值现金流对期望现金流的比率是多少？

d.     请解释为什么这个比率会下降。

 

17. The McGregor Whisky Company is proposing to market diet scotch. The product will first be test-marketed for two years in southern California at an initial cost of $500,000. This test launch is not expected to produce any profits but should reveal consumer preferences. There is a 60 percent chance that demand will be satisfactory. In this case McGregor will spend $5 million to launch the scotch nationwide and will receive an expected annual profit of $700,000 in perpetuity. If demand is not satisfactory, diet scotch will be withdrawn.

Once consumer preferences are known, the product will be subject to an average degree of risk, and, therefore, McGregor requires a return of 12 percent on its investment. However, the initial test-market phase is viewed as much riskier, and McGregor demands a return of 40 percent on this initial expenditure.

What is the NPV of the diet scotch project?

17. McGregor威士忌公司准备向市场推广佐餐苏格兰威士忌。该产品首先将在加州南部进行为期两年的测试营销，耗资$500,000。测试营销不会产生任何的利润，但是将揭示消费者的偏好。有60%的机会对该产品的需求将达到令人满意的程度。这种情况下McGregor将投资500万美元在全国推广该产品，预期$700,000的年利润将永久维持。如果需求不让人满意，佐餐苏格兰威士忌就将被取消。

       一旦知晓了消费者偏好，该产品面对的就是一个平均程度的风险，因此，McGregor对其投资要求12%的回报率。然而，初始的测试营销阶段被视为更具风险，McGregor对这初始的支出要求40%的回报率。

       该佐餐苏格兰威士忌项目的NPV是多少？

9. Amalgamated Products has three operating divisions: Excel

To estimate the cost of capital for each division, Amalgamated has identified the following three principal competitors:

	Estimated Equity Beta	Debt/(Debt + Equity)
United Foods General Electronics Associated Chemicals	.8 1.6 1.2	.3 .2 .4

Assume these betas are accurate estimates and that the CAPM is correct.

a. Assuming that the debt of these firms is risk-free, estimate the asset beta for each of Amalgamated’s divisions.

b. Amalgamated’s ratio of debt to debt plus equity is .4. If your estimates of divisional betas are right, what is Amalgamated’s equity beta?

c. Assume that the risk-free interest rate is 7 percent and that the expected return on the market index is 15 percent. Estimate the cost of capital for each of Amalgamated’s divisions.

d. How much would your estimates of each division’s cost of capital change if you assumed that debt has a beta of .2?

9. Amalgamated Products有三个经营部门：Excel

为了估算每个部门的资本成本，Amalgamated识别出了以下三个主要竞争者：

	估计权益Beta	负债/(负债 + 权益)
United Foods General Electronics Associated Chemicals	.8 1.6 1.2	.3 .2 .4

假定这些beta是精确的估计，而且CAPM也是正确的。

a.     假定这些企业的负债是无风险的，估算Amalgamated的每个部门的资产beta。

b.     Amalgamated的负债对负债加权益的比率为.4。如果你对各个部门的beta估算是正确的，Amalgamated的权益beta是多少？

c.     假定无风险利率为7%，市场指数的期望回报率为15%。估算Amalgamated的每个部门的资本成本。

d.     如果你假定负债的beta为.2，你对每个部门的资本成本的估算会发生多大的改变？

 

10. Look at Table 9.2. What would the four countries’ betas be if the correlation coefficient for each was 0.5? Do the calculation and explain.

10. 看一下表格9.2。如果相关系数为0.5，这四个国家的beta将会是多少？做一个计算并解释。

 

11. “Investors’ home country bias is diminishing rapidly. Sooner or later most investors will hold the world market portfolio, or a close approximation to it.” Suppose that statement is correct. What are the implications for evaluating foreign capital investment projects?

11. “投资者的母国偏向正在迅速消失。大多数投资者迟早都会持有世界市场投资组合，或者一个近似的组合。”设这个陈述是正确的。这对于评估国外资本投资项目的影响是什么？

 

12. Consider the beta estimates for the country indexes shown in Table 9.2. Could this information be helpful to a U.S. company considering capital investment projects in these countries? Would a German company find this information useful? Explain.

12. 思考表格9.2所示的对于国家指数的beta估算。对一家考虑在这些国家进行资本投资项目的美国公司来说这一信息有帮助吗？对一家德国公司来说呢？请解释。

 

13. Mom and Pop Groceries has just dispatched a year’s supply of groceries to the government of the Central Antarctic Republic. Payment of $250,000 will be made one year hence after the shipment arrives by snow train. Unfortunately there is a good chance of a coup d’état, in which case the new government will not pay. Mom and Pop’s controller therefore decides to discount the payment at 40 percent, rather than at the company’s 12 percent cost of capital.

a. What’s wrong with using a 40 percent rate to offset political risk?

b. How much is the $250,000 payment really worth if the odds of a coup d’état are 25 percent?

13. Mom and Pop Groceries（老妈老爸杂货公司）刚刚向Central Antarctic Republic（中南极洲共和国）政府输送（dispatch — formal to send someone or something somewhere for a particular purpose）了一年的杂货供应量。$250,000的货款将会在物资通过雪地列车送达的一年之后支付。不幸的是很可能会发生一场政变（coup d’état — a sudden and sometimes violent attempt by citizens or the army to take control of the government ￚsynonym coup d' état），如果这样的话新的政府不会支付这笔货款。所以Mom and Pop的主计长决定以40%来贴现这笔货款，而不是公司的12%的资本成本。

       a. 用40%来抵消政治风险有什么问题？

       b. 如果政变发生的机率为25%，这笔$250,000的货款到底价值多少？