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。