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同学们大家好
Hello everyone

这一节我将带大家来了解
In this section I introduce the basic formula of

关于收益法的基本公式
the income method

及其一些比较特殊情况的推导
and some derivations of some special cases

以及在收益法这个公式之下
and the solution of some related parameters

我们的一些相关参数的求解
under the formula of income method

现在看到呢就是我们整个收益法折现
What you see now is a rough map

公式的一个大致的图谱
of the entire income method discounted formula

我们说既然这项资产我们愿意为它付出相应的成本
We are willing to pay the corresponding cost for

是因为这项资产
this asset because this asset will bring

能够在未来给我们带来收益
us benefits in the future

那未来的收益我们怎么能够折算成当前
How do we convert future earnings into

我愿意为他支付的成本呢
the current cost of paying for it

这里使用到的方法就被我们称之为收益的折现
The method used here is called discounted income

好 我们假设这项资产能够给我们带来N年的收益
We assume that this asset can bring N-year revenue

那么可想而知从当前开始到明年的这个时候
It can be imagined that from the current beginning

我们称之为一年吧
to the next year, we call it a year,

那么到明年这个时候呢
then by this time next year

我们假设所带来的收益为A1
we assume that the benefit brought by A1

到后年的这个时候为A2
to the next year is A2,

第三年为A3
the third year it’s A3,

一直到第n年结束为An的话
until the end of the nth year is An,

那么这是我们所看到的每年的收益
then this is the annual income we see

如果我们想把这个问题变得更加普遍化
If we want to make this problem more general

我们当然可以想得到 那就是在每年的进行过程中
of course, it has a corresponding discount rate

它会有一个相应的折现率
or a representation of risk

或者说一个风险的表示
in the course of each year

好，那我们需要的是将每一年的
Ok, then what we need is to fold the benefits of

收益都折到当前来
each year to the present

那这个时候我们就可以想
At this time we can think

第一年的收益它所对应的现值等于多少呢
what is the current value of the first year's income

我们需要做的是用A1除以1+r1
We need to divide A1 by 1+r1

这里的1+r1表示的就是
The 1+r1 indicates the increased benefit

在第一年这个时间推进过程中所带来的
or risk change, brought about during

一个收益的增加或者说是一个风险的变动
the first year of advancement

那么第二年结束的时候
What kind of present value does A2

所带来的收益A2又对应我们什么样的一个现值呢
bring to us at the end of the second year

我们转回来
Let's come back

首先是A2，这个收益对应到
First what is the equivalent of A2

第一年结束的时候，等于多少
to the end of the first year

我们按照刚才用A1/(1+r1)的思想
We follow the idea of A1/(1+r1) just now

我们就可以得出它是A2/(1+r2)
we can conclude that it is A2/(1+r2)

可这个时候
But at this time,

我们只是把它折到了第一年的结束
we only folded it to the end of the first year

当前我们需要有A2除以1+r1 同时再除以1+r2
Currently we divide A2 by 1+r1 and divide by 1+r2

所以这个公式我们简单的一个归纳推理
So this formula is a simple inductive reasoning

你就会发现第n年它的收益的现值就应该是
You will find that the present value of its income

An除以1+r1
in the nth year is the division of An by 1+r1

除以1+r2 除以1+rn等等
divided by 1+r2, divided by 1+rn, etc

所以得出来的就是
So what we get is the formula of

我们现在所能看到的收益的公式
the income we can see now

P等于A1/(1+r1)加上A2/(1+r1)/(1+r2)等等它的一个求和
P is equal to the sum of A1/(1+r1) plus A2/(1+r1)/(1+r2)

那么这里当然我们要稍微解释一下了
We have to explain it a bit

A1 A2一直到An是我们每年的纯收益
A1, A2 until An is the annual net income

r1到rn是我们每年的一个折现率
r1 to rn is the annual discount rate

当然你也可以理解为对一些特殊的产品
Of course, you can also understand

或者说资产
the rate of return or principalization of

可以是收益率或者本金化率
some special products or assets

n在我们这里就作为年期出现了
n appears here as a year

这是我们在讲到收益法的时候
This is the most basic formula

一个最基本的公式
when it comes to the income method

那有时候我们在进行评估的时候
Sometimes we may not use such a complicated formula

我们可能不会用这么复杂的公式
when conducting an assessment

因为我们不会假设说每年的折现率都在变动
we don't assume the annual discount rate is changing

甚至有时候我们不会假设
and sometimes we don't assume that

每年的收益在变动
the annual return is changing

所以根据一些不同的情况
So according to some different situations

我们对这个公式会有一些特殊的演进
we will have some special evolution to this formula

好，现在我们就可以看到
Ok, now we can see

在假设所有的折现率
under the assumption that all discount rates

都保持不变的情况下
remain the same situation,

我们都可能会有以下四种情况
we may have the following four situations

第一种，收益保持不变
The first type of income remains unchanged

年期固定
and the term is fixed

那么它就是一个简单的等比数列的求和
Then it is a simple summation of the series

这一块我们由于时间问题
This piece of us does not make a specific expansion

不做具体的展开
due to time issues

我们怎么来理解这个公式？
How do we understand this formula?

我们可以将收益年期推到无限远的时候
When we push the income period to infinity,

就会发现资产的价值其实等于什么呢
we will find out what the value of the asset is equal to

等于收益A除以r
equal to the income A divided by r,

那你会发现它其实就是
then you will find that it is actually

一个收益的本金化
a principal of income

这是我们的一个比较简单的推理
This is a relatively simple reasoning

第二个情况
In the second case,

那就是我们有时候在给出收益的时候
we sometimes don’t ask for it to remain

并不是要求它一直保持不变
the same when giving the return

因为我们可能说靠近我们这个时间点这一段
Because we may close to this point in time

比如说未来的五年
for example, in the next five years ,

我们可能有把握的给出每一年的收益
we may be confident to give the benefits of each year

这个时候它的收益可能不一样
At this time, its income may be different

而再远了之后
And after a long time,

我们会想那么远的事情，谁都不好说
things will not be predicted

那这个时候我可能会稍微的粗略估计一下
At this time, it may be slightly estimated

给出一个恒定不变的值
to give a constant value

比如说A
For example, A,

那这个时候你会发现
you will find that

在我对未来进行折现的时候
when you discount the future,

其实将未来的时间段划分成了两段内容
you will divide the future time period into two paragraphs

第一段我们可以称之为叫做前小n点
The first paragraph we can call it the front small n point

后面我们称为叫做大N减小n
which we call the big N reduction n

这两段内容当中前一段
In the previous paragraph of the two paragraphs,

我们可能每一年给出不同的收益额进行折现
we may discount the amount of income given each year

后面给出一个固定值进行一个折现
followed by a fixed value for a discount

那么这块就会将公式劈成两半来看
Then this will divide the formula into two parts

当然如果说你假设收益是无限远的话
Of course, if you assume that the income is infinite

我们也会将这个公式推成无限年期的形式
we will also push this formula into an indefinite form

这是我们看到的第二类情况
This is the second type of situation we have seen

可有时候我们会想
Sometimes we will think that

我们在对收益额进行估计的时候
when we estimate the amount of income,

可能既不是定值
we may not be a fixed value

也不是一个任意变动值
or an arbitrary change value

而是我们发现了它的收益额
but we may find that

可能存在某种规律
there may be some law in its income

比如说我们常见的等差数列
For example, if we have a common arithmetic progression

或者等比数列
or a series of equal ratios

那么当出现是等差数列的收益额
then when the amount of income that appears

递次增加的时候
to be an arithmetic progression increases in turn,

我们又会发现我们的公式会发生变化
we will find that our formula will change

当然我们在这里同样不会讲
Of course, we will not talk about

这个公式是怎么推导出来的
how this formula is derived here

我们来讲这个公式的理解
When we talk about this formula,

再将这个收益公式
and then turn this income formula

变成无限年期的时候
into an indefinite period

我们会发现它与基本公式之间的
we will find that the difference between it

差别在于哪呢
and the basic formula

基本公式我们说是
The basic formula is that A is divided by r to be

A除以r是对收益的本金化
the principalization of the proceeds

那么有了一个等差数列之后
With an arithmetic progression,

你会发现我们的资产的价值
you will find that the value of

确实有了增加
our assets has indeed increased

它增加了一个B除以r的平方
It adds a B divided by the square of r

相当于在我们的当前资产之上
which is equivalent to a discount on our current assets

又加了一点收益的折现
plus a little gain

我们说可以称之为叫加了个尾项，增加的更多了
we can call it a tail item and add more

这是我们看到的收益
This is the case where we see the increase

以等差数列递增的情况
in earnings in the arithmetic progression

那如果递减呢？
If it is decrementing,

递减我们就将A除以R
we will transform the plus sign between

加上B除以r平方之间这个加号
the A devided by R and B devided by the square of r

变成减号
to become a minus sign,

就相当于我们将收益减少了
which is equivalent to reducing our income

你会发现我们这里其实还是要对A和B做定义了
You will find that we have to define A and B

A是我们的收益，B我们认为是收益的递增
A is our income, B we think is the increase of income

每年递增
increasing every year

这里我们当然要求A是要大于B的
Here requires A to be bigger than B

不然的话我们算出来的就是个笑话
Otherwise, we figured out a joke

第四种情况
In the fourth case,

当我们的收益变成等比数列递增的时候
when our income becomes equal to the number of series

这里当然我们就给出
here we will give the ratio of the

这个等比数列递增的比率
increment of the ratio

我们说比如是S吧
For example, S

那这个时候你会发现我们的折现率
you will find that our discount rate has changed

其实有了变化，反映在我们的折现公式上
reflected in our discount formula

尤其是在年期无限的时候
Especially when the period is infinite,

你会发现所谓的等比数列式的增加
the increase of the so-called proportional ratio

其实是对我们收益所对应的
is actually the reduction of

风险的一个减少
the risk corresponding to the income

所以就变成了P
So it becomes P

我们的价值等于A除以r减s
our value is equal to A divided by r minus s

对风险的减少是个减号
the reduction of risk is a minus sign

那如果说我们的收益是成等比数列的减少
If the income is reduced by a series of equals

那这个时候你会发现我们的分母应该是r加上s
the denominator should be r plus s

仅仅是一个符号的变化
just a change in sign

由此我们就可以发现
From this we can find that

等差数列是
the arithmetic progression is the increase of

收益的尾项增加
the tail term of the income

等比数列相当于
and the equivalence series is equivalent to

是我们对风险的一个调整
our adjustment of the risk

所以这是我们现在看到的
So this is the corresponding meaning of

四种情况下对应的八个公式
the eight formulas corresponding to

它们相应的一个含义
the four cases we are seeing now

这是我们在讲到收益法的时候
This is a series of formulas that

常见的一系列公式
we often talk about when it comes to income law

当然根据不同的情况
Of course, depending on the situation,

我们可能还会有一些其他的变化
we may have some other changes

在这里呢我们也不再做相应的展开
Here, we will not expand accordingly

好，那在了解到这样一些
Well, after learning about the changes

收益法公式的变化之后
in some income method formulas

我们就要想这样一个问题了
we have to think about such a problem,

那就是我们在讲到企业价值的时候
that is, when we talk about corporate value

这里的收益是指什么呢？
what is the income here?

折现率又是指什么呢
What does the discount rate mean

那我们说企业的价值
Then we say that the value of the enterprise

确实会套用收益法的公式
does apply the formula of the income method

那么所谓的收益
So the so-called income,

我们就选择了现金流
we choose the cash flow

企业资本现金流
corporate capital cash flow

所谓的折现率
The so-called discount rate,

我们在这里会做一个相应的处理
we will do a corresponding treatment here

我们在这里看到公司下面呢，它叫做WACC
Here we see the company called WACC,

它所对应的是叫做Weighted Average Cost of Capital
which corresponds to the Weighted Average Cost of Capital,

就是加权平均资本成本
which is the weighted average cost of capital

它所对应的当然是包含着企业所有者权益
It corresponds to the embodiment of

当中所有的一个风险的体现
all the risks involved in the owner’s equity

好，那我们现在就来了解一下这样一些参数
Ok, let's take a look at some of these parameters

它们一个具体的过程是什么
What is their specific process

第一部分
In the first part,

我们说企业的收益到底是用什么来表示
we say what is the company's revenue

我们讲到资产的时候
When we talk about assets,

说他能给我们带来利润是多少
we say that he can bring us profits,

我们直接拿过来
we take them directly

当你讲到企业的时候
When you talk about business,

你会想所谓的收益
you will think about the so-called benefits

其实它有两种表达类型
In fact, it has two types of expression

比如说利润,比如说现金流
such as profit, cash flow,

那么选哪个呢
then which one to choose

我们选现金流
We choose cash flow,

因为现金流真实地反映了
because the cash flow truly reflects

这家企业他的所有的资金往来
all the capital transactions of this company

我们说这是一个不太容易更改的情况
We say this is a situation that is not easy to change

而利润其实是可以通过会计的方法
And the profit can actually be adjusted

来进行一定的调整的
by accounting methods

比如说我们在应收账款的
For example, when we deal with bad debts of

坏账处理的时候
accounts receivable

我们不同的统计口径可能就会对我们的利润带来影响
our different statistical calibers may affect our profits

所以我们为了真实地反映这家企业的价值
So in order to truly reflect the value of this company

我们选用现金流
we choose cash flow

那我们在讲到收益期限的时候
Then, when we talk about the term of income,

也要考虑到
we must also take into account

这家企业的发展特点
the development characteristics of this company

我们将未来的时间段划分成两部分
We divide the future time period into two parts

第一部分我们可以称之为叫做非常增长阶段
The first part, we can call it the very growth stage

第二部分我们可以称之为叫做稳定发展阶段
The second part, we can call a stable development stage

第一部分我们说这家企业
In the first part, we said that this company

可能刚刚开始运营
may just start operating

它的市场占有率在一个我们说
Its market share may increase continuously within

合理经营范围内可能会不断增加
a reasonable business scope and the revenue may increase

收益可能也会增加
So at this time the income is in a changing growth phase

所以这个时候收益处在一个变动的增长阶段
At this time we may need to carry out

那这个时候我们可能需要进行一个不同收益的叠加
a superposition of different benefits

而当这家企业发展稳定之后
When the company develops stably,

它的收益期 我们说假设给一个美好的愿望
we assume a good wish for its income period

到无限远
and the income period is infinite

那这个时候我们在这一段时间内
At this time, we will make a profitable discount

做一个收益不变的折现
in this period of time

这两点我们说
These two points we say that

它都有一个很重要的假设
it has a very important assumption

那就是我们确实是认为
That is, we really think that

这家企业能够持续经营下去
this company can continue to operate

那这个时候你会想了
Then you will think about it at this time,

有什么问题啊？
what is the problem?

我们在使用这个假设的时候
When we use this hypothesis,

第一我们确实没有考虑到
the first we did not consider that

这家企业未来可能会破产
this company may go bankrupt in the future

给他的这个愿望太美好了
This wish is so beautiful

第二点我们对这个收益的预测
Second, our prediction of earnings is

全部是基于过去
based on a basic judgment of the past

乃至当前这家企业的主营业务范围
and even the current business scope of the company

它的发展的策略等等的一个基本判断
and its development strategy

没有考虑到
did not take into account the assumption that

这家企业在未来可能会采取多种经营
the company may adopt diversified operations in the future

乃至改变主营业务的这样一些假设
or even change its main business

我们说已经把这家企业的运营方式限定死了
We said that the company’s operations have been limited

缺少了一定的灵活性
and there is a lack of flexibility

当然这不影响我们使用预期现金流折现的
Of course this does not affect our large premise

这样一个大的前提
of discounting the expected cash flow

所以根据一定的原理和方法
Therefore, according to certain principles and methods

我们对现金流折现法当中的
we can obtain a corresponding reasonable range

第二个参数获利年限
for the profitability of the second parameter

可以给出一个相应的合理范围
in the discounted cash flow method

最后我们还剩一样 那就是折现率
Finally we have a discount rate

因为折现率相对的来说复杂一些
Because the discount rate is relatively more complicated，

我们放在下一节内容来介绍
we put it in the next section to introduce