我不知道的……

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.