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## 公司财务原理，第7版，Chapter 4，4.2 How common stocks are valued

(2006-10-27 19:57:36)

### 杂谈

4.2 HOW COMMON STOCKS ARE VALUED

4.2普通股是如何估值的

Think back to the last chapter, where we described how to value future cash flows. The discounted-cash-flow (DCF) formula for the present value of a stock is just the same as it is for the present value of any other asset. We just discount the cash flows by the return that can be earned in the capital market on securities of comparable risk. Shareholders receive cash from the company in the form of a stream of dividends. So

At first sight this statement may seem surprising. When investors buy stocks, they usually expect to receive a dividend, but they also hope to make a capital gain. Why does our formula for present value say nothing about capital gains? As we now explain, there is no inconsistency.

第一眼看上去这一表述可能会令人感到惊讶。当投资者购买股票时，他们通常期望收到股利，但是他们也希望取得资本利得。为什么我们的现值公式对资本利得只字不提？正如我们现在要解释的，这之间没有不一致。

Todays Price

The cash payoff to owners of common stocks comes in two forms: (1) cash dividends and (2) capital gains or losses. Suppose that the current price of a share is P0, that the expected price at the end of a year is P1, and that the expected dividend per share is DIV1. The rate of return that investors expect from this share over the next year is defined as the expected dividend per share DIV1 plus the expected price appreciation per share P1 - P0, all divided by the price at the start of the year P0:

This expected return is often called the market capitalization rate.

Suppose Fledgling Electronics stock is selling for \$100 a share (P0 = 100). Investors expect a \$5 cash dividend over the next year (DIV1 = 5). They also expect the stock to sell for \$110 a year hence (P1 = 110). Then the expected return to the stockholders is 15 percent:

假设Fledgling Electronics股票以一股\$100出售(P0 = 100)。投资者期望的下一年现金股利是\$5 (DIV1 = 5)。他们还期望一年后股票可以\$110出售(P1 = 110)。则股东的期望回报率就是15%

On the other hand, if you are given investorsforecasts of dividend and price and the expected return offered by other equally risky stocks, you can predict todays price:

For Fledgling Electronics DIV1 = 5 and P1 = 110. If r, the expected return on securities in the same risk class as Fledgling, is 15 percent, then todays price should be \$100:

另一方面，如果给定你投资者预计的其他相同风险的股票提供的股利和价格以及期望回报率，你可以预测今日的价格：

Fledgling Electronics来说，DIV1 = 5P1 = 110。如果r,是与Fledgling相同风险级别的证券的期望回报率，为15%，则今日的价格就应该是\$100:

How do we know that \$100 is the right price? Because no other price could survive in competitive capital markets. What if P0 were above \$100? Then Fledgling stock would offer an expected rate of return that was lower than other securities of equivalent risk. Investors would shift their capital to the other securities and in the process would force down the price of Fledgling stock. If P0 were less than \$100, the process would reverse. Fledglings stock would offer a higher rate of return than comparable securities. In that case, investors would rush to buy, forcing the price up to \$100.

我们如何知道\$100就是正确的价格？因为没有其他的价格能够在竞争性的资本市场中幸存。如果P0超过\$100会如何？那么Fledgling股票将提供一个于其他等价风险的证券的期望回报率。投资者将向其他证券转移他们的资本，而这一过程将迫使Fledgling股票的价格走低。如果P0低于\$100，这一过程就正相反。Fledgling股票将提供一个比可比证券更高的回报率。在那种情况下，投资者将争相购买，迫使股价超过\$100

The general conclusion is that at each point in time all securities in an equivalent risk class are priced to offer the same expected return. This is a condition for equilibriumin well-functioning capital markets. It is also common sense.

总的结论就是在每一个时点上所有处于一个等价风险层级的证券被定价为提供相同的期望回报率。这是运行良好的资本市场均衡equilibrium[singular, uncountable] a balance between different people, groups, or forces that compete with each other, so that none is stronger than the others的一个条件。同时它也是常识。

But What Determines Next Years Price?

We have managed to explain todays stock price P0 in terms of the dividend DIV1 and the expected price next year P1. Future stock prices are not easy things to forecast directly. But think about what determines next years price. If our price formula holds now, it ought to hold then as well:

That is, a year from now investors will be looking out at dividends in year 2 and price at the end of year 2. Thus we can forecast P1 by forecasting DIV2 and P2, and we can express P0 in terms of DIV1, DIV2, and P2:

Take Fledgling Electronics. A plausible explanation why investors expect its stock price to rise by the end of the first year is that they expect higher dividends and still more capital gains in the second. For example, suppose that they are looking today for dividends of \$5.50 in year 2 and a subsequent price of \$121. That would imply a price at the end of year 1 of

Todays price can then be computed either from our original formula

or from our expanded formula

Fledgling Electronics来说。一个看似合理的解释为什么投资者期望股价会在第一年末上涨是（因为）他们期望在第二年有更高的股利和更多的资本利得。例如，假设他们在今日期望在第2年有\$5.50的股利以及一个随后的价格\$121（指第2年的价格）。这将暗示在第1年末的价格为

We have succeeded in relating todays price to the forecasted dividends for two years (DIV1 and DIV2) plus the forecasted price at the end of the second year (P2). You will probably not be surprised to learn that we could go on to replace P2 by (DIV3P3)/(1 + r) and relate todays price to the forecasted dividends for three years (DIV1, DIV2, and DIV3) plus the forecasted price at the end of the third year (P3). In fact we can look as far out into the future as we like, removing Ps as we go. Let us call this final period H. This gives us a general stock price formula:

The expressionsimply means the sum of the discounted dividends from year 1 to year H.

我们已经成功地使今日的价格与两年的预测股利(DIV1DIV2)加上第年末的预计价格(P2)相关。你也许将不会对我们可以继续将P2(DIV3P3)/(1 + r)代替和把今日的价格与三年的预测股利(DIV1, DIV2DIV3)加上第年末的预计价格(P3)相关感到惊讶。事实上我们可以如我们所希望的看到遥远的未来，（只要）我们前进时移除Ps。让我们把这最终期称为H. 这给了我们一个一般股价公式：

Table 4.1 continues the Fledgling Electronics example for various time horizons, assuming that the dividends are expected to increase at a steady 10 percent compound rate. The expected price Ptincreases at the same rate each year. Each line in the table represents an application of our general formula for a different value of H. Figure 4.1 provides a graphical representation of the table. Each column shows the present value of the dividends up to the time horizon and the present value of the price at the horizon. As the horizon recedes, the dividend stream accounts for an increasing proportion of present value, but the total present value of dividends plus terminal price always equals \$100.

表格4.1继续了不同的时间水平线的Fledgling Electronics的例子，假定股利期望可以一个稳定的10%的复利率增长。期望价格Pt 每年也以同样的比率上涨。表格中的每一行代表针对不同的H值的我们的一般公式的一次应用。图表4.1提供了表格的图形化表达。每一栏显示了截止时间水平线的股利的现值和在这一时点的股价的现值。随着水平线的消逝recede[intransitive] if something you can see or hear recedes, it gets further and further away until it disappears，股利流在现值中所占的比例不断增加，但是股利加上终点价格的总的现值一直等于\$100

How far out could we look? In principle the horizon period H could be infinitely distant. Common stocks do not expire of old age. Barring such corporate hazards as bankruptcy or acquisition, they are immortal. As H approaches infinity, the present value of the terminal price ought to approach zero, as it does in the final column of Figure 4.1. We can, therefore, forget about the terminal price entirely and express todays price as the present value of a perpetual stream of cash dividends. This is usually written as

where indicates infinity.

我们可以看到多远？原则上水平线H期可以无限向远方延伸。普通股不会因时间长久而到期expire[intransitive] if an official document expires, it can no longer be legally used。除非（发生）公司灾难如破产或者收购，它们（股票）是不朽的。随着H接近无穷，终点价的现值应该接近于零，正如图表4.1的最后一栏所显示的一样。所以，我们可以完全忘记终点价格并且用一个永续的现金股利流的现值来表示今日的价格。这通常写成

This discounted-cash-flow (DCF) formula for the present value of a stock is just the same as it is for the present value of any other asset. We just discount the cash flowsin this case the dividend streamby the return that can be earned in the capital market on securities of comparable risk. Some find the DCF formula implausible because it seems to ignore capital gains. But we know that the formula was derived from the assumption that price in any period is determined by expected dividends and capital gains over the next period.

这一股票现值的贴现现金流（DCF）公式就与其他任何资产的现值的（计算公式）相同。我们就贴现现金流—在这里是股利流—以资本市场中风险可比的证券赚取的回报。因为它看上去忽略了资本利得，某些人发现DCF公式似乎不合情理。但是我们知道这一公式是从任何一期的价格是由期望股利以及下一期的资本利得决定的假设得来的

Notice that it is not correct to say that the value of a share is equal to the sum of the discounted stream of earnings per share. Earnings are generally larger than dividends because part of those earnings is reinvested in new plant, equipment, and working capital. Discounting earnings would recognize the rewards of that investment (a higher future dividend) but not the sacrifice (a lower dividend today). The correct formulation states that share value is equal to the discounted stream of dividends per share.

注意（如果）说股票的价值等于每股盈利流的贴现额的合计是正确的。因为部分盈利被再投资于新的工厂、设备和营运资本，盈利通常大于股利。贴现盈利会确认投资的报酬（一个更高的未来股利）但没有（确认）牺牲sacrifice[uncountable and countable] when you decide not to have something valuable, in order to get something that is more important（一个更低的今日股利）。正确的公式叙述股票价值等于每股股利流的贴现额（合计）。

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