2004年伯克希尔股东会问答：
AUDIENCE MEMBER: Good morning, gentleman. My name is Tony Ado (PH) and I come from New Jersey.听众：早上好，先生们。我叫托尼·阿多，来自新泽西州。
Mr. Buffett, my question is on business valuation and growth. In one of your letters, you mentioned the discounting formula on earnings divided by the difference between the discount and the growth rate.巴菲特先生，我的问题是关于企业估值和增长。在您的一封信中，您提到了收益除以贴现率和增长率之差的贴现公式。
But if the growth rate is larger than the discount rate and if we use this formula, then we get a negative number. And one way around this — let's call it method A — is to have two growth stages, one with a high growth and the second stage with a low growth.但是，如果增长率大于贴现率，如果我们使用这个公式，就会得到一个负数。解决这个问题的一个方法——我们称之为方法A——就是有两个增长阶段，一个是高增长阶段，另一个是低增长阶段。
And the second way, method B, would be to estimate how much the earnings is on the third year for the company and then multiply this by the average price-to-earning ratio to get the price in the tenth year.第二种方法，即方法B，是估计公司第三年的收益是多少，然后乘以平均市盈率，得出第十年的价格。
I don't know if you use the method A or method B, but if not, I would like to ask, Mr. Buffett, how do you estimate how much a company is worth if the growth rate is larger than the discount rate?我不知道您是否使用方法 A 或方法 B，但如果不用，我想请问巴菲特先生，如果增长率大于贴现率，您如何估算一家公司的价值？
WARREN BUFFETT: Well, you put your finger on an interesting mathematical relationship. Because if you're using a present value discount formula and you put in a growth rate that is higher than the discount rate, as you have postulated, the answer, of course, will be infinity.沃伦·巴菲特：你指出了一个有趣的数学关系。因为如果你使用的是现值贴现公式，而你输入的增长率高于贴现率，正如你所推测的那样，答案当然是无穷大。
And there are a lot of managements around who like to think their stocks are worth infinity, but we — (laughs) — haven't found one yet.周围有很多管理者喜欢认为他们的股票价值无穷大，但我们——（笑）——还没有找到一个。
That precise subject was covered in a paper called "The St. Petersburg Paradox" by a fellow named [David] Durand probably 30 years ago. And somewhere, we probably have a copy at our office. My guess, if you go to Google and you put in the name Durand and you put in St. Petersburg, you may be able to call up that article, although they aren't necessarily terrific on old articles.大概30年前，一位名叫[David] Durand 的研究员在一篇名为“圣彼得堡悖论”的论文中提到了这个确切的主题。在某个地方，我们的办公室里可能有一份复印件。我猜，如果你去谷歌，输入杜兰德这个名字，再输入圣彼得堡，也许就能调出那篇文章，虽然他们不一定对旧文章很在行。
So if you'd like it, we would — if you'll let somebody know in our office, we'll look around a little and see if we can find that.因此，如果您需要，我们会——如果您让我们办公室的人知道，我们会四处找找，看看能不能找到。
It gets very dangerous to project out high growth rates because you get into this paradox. If you say the growth rate of a company is going to be 9 percent between now and judgment day and you use a 7 percent discount rate, it goes off, you know, you get into infinity. And that's where people get in a lot of trouble.预测高增长率非常危险，因为你会陷入这个悖论。如果你说一家公司从现在到判决日之间的增长率将达到9%，而你使用的贴现率是7%，那么就会出现偏差，你知道，你会进入无穷大。这就是人们陷入困境的地方。
The idea of projecting out extremely high growth rates for very long periods of time has caused investors to lose, you know, very, very large sums of money.在很长一段时间内预测极高增长率的想法导致投资者亏损，你知道，亏损额非常非常大。
There aren't many companies — just take a look at the Fortune 500, go back 50 years — they're commemorating that — and look at the companies that were there and how many have really maintained rates much above 10 percent. It's not an easy hurdle. And when you get up to 15, you know, you're in the atmosphere and rarified atmosphere.看看《财富》世界500强企业，回溯 50 年前的情况——他们正在纪念这 50 年——再看看这些企业中，有多少能真正保持远高于 10% 的增长率。这不是一个简单的障碍。而当你达到15%时，你知道，你就进入了一种稀有的氛围。
So that's — there's a real danger in projecting out high growth rates. And Charlie and I will very seldom — virtually never — get up into high digits. You can lose a lot of money doing that.因此，预测高增长率确实很危险。查理和我很少——几乎从来没有——预测到高增长率。这样做会损失很多钱。
You may miss an opportunity some time, but I haven't seen people who have been consistently successful doing that. And you do run into this paradox you mentioned.有的时候你可能会错失良机，但我还没见过有谁能持续成功地做到这一点。你确实会遇到你提到的这个悖论。
查理？
CHARLIE MUNGER: Well, you're obviously right, when you get a mathematical result that is infinity, to back off and realize that can't happen. And, of course, what people do is they project that the growth rate will reduce and, indeed, eventually stop. And then you get more realistic numbers. What else could anyone do?查理·芒格：嗯，你显然是对的，当你得到一个无穷大的数学结果时，你就会退缩，意识到这是不可能发生的。当然，人们的做法是预测增长率会降低，甚至最终停止。然后你就会得到更现实的数字。人们还能做什么呢？
假定我们估值时参考巴菲特，采用10%的贴现率。从数学上就可以知道，任何一家企业都不可能永远保持10%以上的增长率，不然就会陷入悖论，估值的结果是无穷大。事实上，永远保持5%的增长率几乎都不太可能（也许茅台是个例外），因为这意味着合理的估值是20倍市盈率，而巴菲特几乎从没有以这个估值水平买过股票，这里指的是ROE较高的优秀企业，老巴买入喜诗糖果时市盈率约为12、买入可口可乐时市盈率约为15。上面的市盈率标准对应到利润增速上，要求是非常低的。在10%贴现率的基础上，12倍市盈率对应1.67%的增速，15倍市盈率对应3.33%的增速。至于听众所提到的第二种估值方法，即预测三年后的净利润，然后乘以平均市盈率，巴菲特和芒格根本就没有回应，因为他们看企业不会只看三年，他们关心的是10年或是20年后。
![]()
延伸阅读：
戳![]()
关注，右上角菜单栏● ● ●键，设为星标
