Two Other Real Options

其他两种实物期权

These are not the only real options. For example, companies with positive-NPV projects are not obliged to undertake them right away. If the outlook is uncertain, you may be able to avoid a costly mistake by waiting a bit. Such options to postpone investment are called timing options.

这些不是仅有的实物期权。例如，有正NPV项目的公司并不是一定要立马就去实施它们。如果前景不明，等待一下也许就能够避免一个代价不菲的错误。这样推迟投资的选择权就被称为时机期权。

When companies undertake new investments, they generally think about the possibility that at a later stage they may wish to modify the project. After all, today everybody may be demanding round pegs, but, who knows, tomorrow square ones could be all the rage. In that case you need a plant that provides the flexibility to produce a variety of peg shapes. In just the same way, it may be worth paying up front for the flexibility to vary the inputs. For example, in Chapter 22 we will describe how electric utilities often build in the option to switch between burning oil to burning natural gas. We refer to these opportunities as productionoptions.

       当公司实施新的投资时，通常它们会考虑在之后的一个阶段希望对项目进行修改的可能性。毕竟，今天每个人也许都想要圆的衣夹（peg — a short piece of wood, metal, or plastic that is attached to a wall or fits into a hole, used especially to hang things on or to fasten things together），但是天晓得，也许明天方的衣夹会铺天盖地（be all the rage — informal to be very popular or fashionable）。这种情况下你需要一家可以提供灵活性来生产各种各样的衣夹样式的工厂。同样的道理，预先耗资于使进料就多样化的灵活性也是值得的。例如，在第22章我们将会描述通常电力事业企业是如何在烧油和烧天然气之间建立转换的选择权。我们把这些机会称为生产期权。

More on Decision Trees

关于决策树的更多

We will return to all these real options in Chapter 22, after we have covered the theory of option valuation in Chapters 20 and 21. But we will close this chapter with a closer look at decision trees.

在第20章和第21章阐述期权估值理论之后，我们会在第22章重返所有这些实物期权。但是我们将以一个对决策树更接近的观察视点来结束本章。

Decision trees are commonly used to describe the real options imbedded in capital investment projects. But decision trees were used in the analysis of projects years before real options were first explicitly identified.¹⁸ Decision trees can help to understand project risk and how future decisions will affect project cash flows. Even if you never learn or use option valuation theory, decision trees belong in your financial toolkit.

       决策树常被用于描述资本投资项目中内含的（imbed — to put something firmly and deeply into something else, or to be put into something in this way）实物期权。但是在实物期权被首次明确辨识之前的年头，决策树就被用于项目的分析¹⁸。决策树可以帮助理解项目风险以及未来的决策将如何影响项目现金流。即便你从未学过或用过期权估值理论，决策树还是可以被纳入你的财物工具箱中。

¹⁸The use of decision trees was first advocated by J. Magee in “How to Use Decision Trees in Capital Investment,” Harvard Business Review 42(September–October 1964), pp. 79–96. Real options were first identified in S. C. Myers, “Determinants of Corporate Borrowing,” Journal of Financial Economics 5 (November 1977), pp. 146–175.

¹⁸决策树的运用首先是由J. Magee在“How to Use Decision Trees in Capital Investment,” Harvard Business Review 42(September–October 1964), pp. 79–96.中倡议的。实物期权最先是由S. C. Myers辨识的“Determinants of Corporate Borrowing,” Journal of Financial Economics 5 (November 1977), pp. 146–175.

The best way to appreciate how decision trees can be used in project analysis is to work through a detailed example.

       理解决策树是如何在项目分析中运用的最好的方法是研究一个详细的例子。

An Example: Magna Charter

一个例子：Magna Charter

Magna Charter is a new corporation formed by Agnes Magna to provide an executive flying service for the southeastern United States. The founder thinks there will be a ready demand from businesses that cannot justify a full-time company plane but nevertheless need one from time to time. However, the venture is not a sure thing. There is a 40 percent chance that demand in the first year will be low. If it is low, there is a 60 percent chance that it will remain low in subsequent years. On the other hand, if the initial demand is high, there is an 80 percent chance that it will stay high.

Magna Charter是一家由Agnes Magna建立的为美国东南部提供行政飞行服务的新公司。创始人认为那些无法承担一架专用全勤公司飞机但有时却需要一架飞机的企业对此会有急切的需求。然而，这项投资不是万无一失的事情。在第一年出现需求低迷的几率为40%。如果这样，在后续年份保持低迷的几率为60%。另一方面，如果初期需求高涨，（在后续年份）维持高涨的几率为80%。

The immediate problem is to decide what kind of plane to buy. A turboprop costs $550,000. A piston-engine plane costs only $250,000 but has less capacity and customer appeal. Moreover, the piston-engine plane is an old design and likely to depreciate rapidly. Ms. Magna thinks that next year secondhand piston aircraft will be available for only $150,000.

       眼前的问题是决定购买何种飞机。一架喷气式耗资$550,000。一架活塞引擎飞机仅耗资$250,000，但是运力和对顾客的吸引力降低。还有，活塞引擎飞机是一种陈旧的设计，可能会迅速贬值。Ms. Magna认为明年二手的活塞飞机将仅需$150,000。

That gives Ms. Magna an idea: Why not start out with one piston plane and buy another if demand is still high? It will cost only $150,000 to expand. If demand is low, Magna Charter can sit tight with one small, relatively inexpensive aircraft.

       这给了Ms. Magna一个主意：为什么不以一架活塞飞机，如果需求仍然高涨就再买一架来开始业务？那将仅耗费$150,000来扩张。如果需求低迷，Magna Charter可以用一架小的、相对不那么昂贵的飞机来维持现状（sit tight — spoken to stay where you are and not move）。

Figure 10.8 displays these choices. The square on the left marks the company’s initial decision to purchase a turboprop for $550,000 or a piston aircraft for $250,000. After the company has made its decision, fate decides on the first year’s demand. You can see in parentheses the probability that demand will be high or low, and you can see the expected cash flow for each combination of aircraft and demand level. At the end of the year the company has a second decision to make if it has a piston-engine aircraft: It can either expand or sit tight. This decision point is marked by the second square. Finally fate takes over again and selects the level of demand for year 2. Again you can see in parentheses the probability of high or low demand. Notice that the probabilities for the second year depend on the first period outcomes. For example, if demand is high in the first period, then there is an 80 percent chance that it will also be high in the second. The chance of high demand in both the first and second periods is .6 × .8 = .48. After the parentheses we again show the profitability of the project for each combination of aircraft and demand level. You can interpret each of these figures as the present value at the end of year 2 of the cash flows for that and all subsequent years.

       图示10.8显示了这些选择。左边的方块标示公司最初的决定，是购买一架$550,000的喷气式还是一架$250,000的活塞式。在公司做出其决策之后，命运会决定第一年的需求。你可以在括号中看到需求高涨或低迷的概率，你还可以看到每一组飞机和需求水平所对应的现金流。如果公司有一架活塞式飞机，到年末公司还要做出第二个决定：它可以扩张或维持现状。这一决定点由第二个方块标示。最后命运会再次接手并选择第2年的需求水平。同样你可以在括号中看到需求高涨或低迷的概率。请注意第2年的概率取决于第一期的结果。例如，如果第一期的需求高涨，那么在第2年还是高涨的几率就是80%。在第一期和第二期的需求均高涨的几率为.6 × .8 = .48。在括号之后我们又显示了每一组飞机和需求水平所对应的项目的盈利能力。你可以把这些数字中的每一个解释为第2年及所有后续年份的现金流在第2年年末的现值。

The problem for Ms. Magna is to decide what to do today. We solve that problem by thinking first what she would do next year. This means that we start at the right side of the tree and work backward to the beginning on the left.

       对Ms. Magna来说问题是决定今天要做什么。我们通过首先思考她在明年会怎么做来解答这个问题。这意味我们从决策树的右边开始，然后反向回到左边起始。

The only decision that Ms. Magna needs to make next year is whether to expand if purchase of a piston-engine plane is succeeded by high demand. If she expands, she invests $150,000 and receives a payoff of $800,000 if demand continues to be high and $100,000 if demand falls. So her expected payoff is

(Probability high demand × payoff with high demand)

+ (Probability low demand × payoff with low demand)

                                                 = (.8 × 800) + (.2 × 100) = +660, or $660,000

If the opportunity cost of capital for this venture is 10 percent,¹⁹ then the net present value of expanding, computed as of year 1, is

If Ms. Magna does not expand, the expected payoff is

(Probability high demand × payoff with high demand)

+ (Probability low demand × payoff with low demand)

                                                 = (.8 × 410) + (.2 × 180) = +364, or $364,000

The net present value of not expanding, computed as of year 1, is

Expansion obviously pays if market demand is high.

       Ms. Magna明年需要做出的唯一的决定是如果购买一架活塞引擎飞机被高涨的需求证明是成功的话，是否应该扩大规模。如果她扩张，她投资$150,000，如果需求持续高涨收益$800,000，而如果需求低迷收益$100,000。所以她的预期收益为

(Probability high demand × payoff with high demand)

+ (Probability low demand × payoff with low demand)

                                                 = (.8 × 800) + (.2 × 100) = +660, or $660,000

如果此项投资的资本机会成本为10%¹⁹，那么计算至第1年末的扩张的净现值就是

如果Ms. Magna没有扩张，预期收益为

(Probability high demand × payoff with high demand)

+ (Probability low demand × payoff with low demand)

                                                 = (.8 × 410) + (.2 × 180) = +364, or $364,000

计算至第1年末的未扩张净现值为

如果市场需求高涨，显然应该扩张。

¹⁹We are guilty here of assuming away one of the most difficult questions. Just as in the Vegetron mop case in Chapter 9, the most risky part of Ms. Magna’s venture is likely to be the initial prototype project. Perhaps we should use a lower discount rate for the second piston-engine plane than for the first.

¹⁹我们很内疚地通过假设回避了最困难的问题之一。正如第9章中的Vegetron助动车案例，Ms. Magna的投资中风险最大的部分可能是最初的原型项目。或许我们应该对第二架活塞引擎飞机运用一个比第一架更低的贴现率。

Now that we know what Magna Charter ought to do if faced with the expansion decision, we can roll back to today’s decision. If the first piston-engine plane is bought, Magna can expect to receive cash worth $550,000 in year 1 if demand is high and cash worth $185,000 if it is low:

The net present value of the investment in the piston-engine plane is therefore $117,000:

       现在我们知道如果面临扩张决定Magna Charter应该怎么做，我们可以回到今天的决策。如果购买了第一架活塞引擎飞机，（那么）如果第1年的需求高涨Magna可望收到现金价值$550,000，需求低迷可望收到$185,000：

所以投资于活塞引擎飞机的净现值为$117,000：

If Magna buys the turboprop, there are no future decisions to analyze, and so there is no need to roll back. We just calculate expected cash flows and discount:

Thus the investment in the piston-engine plane has an NPV of $117,000; the investment in the turboprop has an NPV of $96,000. The piston-engine plane is the better bet. Note, however, that the choice would be different if we forgot to take account of the option to expand. In that case the NPV of the piston-engine plane would drop from $117,000 to $52,000:

The value of the option to expand is, therefore,

117 - 52 =+65, or $65,000

       如果Magna购买喷气式，那就没有更多的决策去分析，所以就不需要回过去。我们只需计算期望现金流并贴现：

因此活塞式引擎飞机的投资NPV为$117,000；喷气式投资的NPV为$96,000。活塞式引擎飞机是更优的选择。然而请注意，如果我们忘记考虑扩张期权的价值，选择就会不同。这种情况下活塞式引擎飞机的NPV将从$117,000降至$52,000：

所以扩张期权的价值就是，

117 - 52 =+65, or $65,000

The decision tree in Figure 10.8 recognizes that, if Ms. Magna buys one piston-engine plane, she is not stuck with that decision. She has the option to expand by buying an additional plane if demand turns out to be unexpectedly high. But Figure 10.8 also assumes that, if Ms. Magna goes for the big time by buying a turboprop, there is nothing that she can do if demand turns out to be unexpectedly low. That is unrealistic. If business in the first year is poor, it may pay for Ms. Magna to sell the turboprop and abandon the venture entirely. In Figure 10.8 we could represent this option to bail out by adding an extra decision point (a further square) if the company buys the turboprop and first-year demand is low. If that happens, Ms. Magna could decide either to sell the plane or to hold on and hope demand recovers. If the abandonment option is sufficiently valuable, it may make sense to take the turboprop and shoot for the big payoff.

       图示10.8的决策树确认如果Magna购买一架活塞式引擎飞机，她不会因该决定而进退两难。如果需求出乎预期的高涨，她有再购买一架飞机来扩大规模的选择权。但是图示10.8还假定如果Ms. Magna决定购买一架喷气式，如果需求出乎预期的低迷，她却无能为力。这不合实际。如果第一年的经营情况糟糕，对Ms. Magna来说可以卖掉这架喷气式并彻底终止此项投资。如果公司购买了喷气式且第一年的需求低迷，我们可以通过在图示10.8中再增加一个额外的决策点（再多一个方块）来表示这一终止的选择权。如果这种情况发生，Ms. Magna可以决定要么就卖掉飞机要么坚持并希望需求反弹。如果废止选择权足够有价值，选择喷气式并期望目标（shoot for/at something — phrasal verb to try to achieve a particular aim, especially one that is very difficult）大收益就是有其道理的。