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。