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股票估价
,
增长率的推导
:
假设你预期下一年
Longs
药店要支付每股
0.56
美元股
利,并在年末股票按每股
45.50
美元交易。如果
与郎石同等
风险投资的期望回报率是
6.80%
,
你今天会为郎石股票最多
支付多少?在这个价格上你
预期的股利收益率和资本利得
率是多少?
解答
应用公式
9.1
,我们有
Div
1
?
P
0.56
?
45.50
1
P
p>
0
?
?
?
43.13
美元
1
p>
?
r
E
1.068
0
在这个价格下,
郎石的股利收益率是
Div
1
/
P
0
?
0.56/
43.13
?
1.30%
。
期望的每
股资本利得是
45.50
美元—
43.
13
美元
=2.37
美元,
资本利得率是
2.37/43.13=5.50%
。因此,在这个价格下郎石
的期望总回报率是
1.30%+5.
50%=6.80%
,这等于其权益资
本成本。
Consolidated Edison
公司是一个管理公共事业的企业,
服务于纽约市地区。假设公司计划在
下一年支付每股
2.3
美
元的股利。如
果其权益资本成本是
7%
,并在未来每年股利
< br>期望增长
2%
,估计股票价值。
解答
如果股利每年期望按
2%
的比例永续地增长,股票的每
股价格:
Div
1
2.30
美元
P
0
?<
/p>
?
?
46.00
美元
r
E
?
g
0.07
?
0.02
Crane
Sporting Goods
预期来年每股收益是
6
美元。公
司计划把所有的收益都作为股利支付。
对于没有增长的预
期,目前每股价格是
60
美元。
假设在可预见的未来,公司可以削减其股利支付率
到
75%
,并且用留存收益开设新商店。这些新商店的投资回报
率预期是
12%
。
假定其权益资本成本不变,
新政策对股价有
什么影响?
p>
现在假设新投资的回报率是
8%
而不是
12%
,又将如何?
解答
首先,
< br>让我们估计科云的权益资本成本。
目前,
科云计划支付等
于其每股收益
6
美元的
股利。给出的每
股价格是
60
美元,科云的股利收益率是
6
美元
/60
美元
< br>=10%
。没有预期增
长(
g<
/p>
?
0
)
,我们可
以运用公式
9.7
来估计
r
E
:
r
E
?
Div
1
?
g
?
10%
?
0%
?
10%
P
0
换句话说,
在目前的政策下调整科云的股票价格,
市场内具有同等风险的其他股票的
期
望回报率一定是
10%
。
其次,我们考虑新政策下的结果。如果科云减少其股利支付率到
75%
,那么从公式
9.8
可知,下一年的股利将下降到
Div
1
?
EPS
1
?
75%
?
6
美元
< br>?
75%
?
4.50
美元
。同时,因
为公司现在要留存其收益的
25%
投资新商店,由公式
9.12
,其增长率将增加到
g
?
留存率
?
新投资回报率
?
25%
?
12%
?
3%
假定科云可
以按这个比率持续增长,我们可以计算在新政策下的每股价格,使用公式
9.6
的稳定股利增长模型:
P
0
?
Div
1
4.5
美元
?
?
< br>64.29
美元
r
E
?
g
0.10
?
0.03
因此,如果科云削减股利来增加投资
和增长,科云的每股价格将从
60
美元增加到
< br>64.29
美
元,意味着投资具有正的
< br>NPV
。
两阶段模型:
持续价值
:
Small
Fry
公司正发明一种薯片,它的外表和口感都像油炸薯条。给出市场对这个产品
的反
应,公司把所有收益进行再投资以扩大经营。
过去的一年收益
是每股
2
美元,并且每年期望增长率是
20%
,直到第
4
年末。在那时,
p>
其他公司可能生产出竞争产品。分析师计划在第
4
< br>年末,将削减投资并开始把
60%
的收益
作为股利支付,其增长将放缓为长期增长率
4%
。如果
权益资本成本是
8%
,今天的每股价
值
是多少?
解答
从第
0
年的
2
美元开始到第
4
年末,
EPS
每年增长
20%
p>
,之后增长放缓为
4%
。股利支付率
在第
4
年之前都是零,当竞争减少了其投资机
会后公司的支付率上升到
60%
。用
E
PS
乘以
股利支付率,我们预计出未来股利,见第
4
行。
从第
4
年往后,股利每年将按期望长期增长率
4%
增长。因此我们可以使用稳定股利增
长模型来预计第
< br>3
年末每股价格。给出其权益资本成本是
8%
,
P
3
?
Div
4
2.49
美元
?
?
62.25<
/p>
美元
r
E
p>
?
g
0.08
?<
/p>
0.04
然后我们把这个最终价值代入,应用股利贴现模型(公式
9.4
)
:
P
0
?
Div
3
P
3
Div
1
Div
2
6
2.25
美元
?
?
?
?
?
49.42
美元
2
3
< br>3
3
1
?
r
E
?
1
?
r
E
?
?
p>
1
?
r
E
?
?
1
?
r
E
?
?
< br>1.08
?
注释:
To be precise, by cash we are referring
to the firm’s cas
h in excess
of its
working capital needs, which is
the
amount of cash it has invested at a
competitive market interest rate.
Solution:
估价乘数:基于可比公司的估价
We can compute a firm’s P/E
ratio by using either
trailing
earnings (earnings over the prior 12
months) or forward
earnings (expected
earnings over the coming 12 months),
with the resulting ratio called the
trailing P/E or forward
P/E,
respectively.
Valuations from
multiples are based on the low, high, and
average values of the comparable firms
from table above.
Red and blue regions
show the variation between the
lowest-
multiple/ worst-case scenario and the
highest-multiple/best-
case
scenario. KCP’s actual share
price of
$$26.75 is indicated by the gray line.
?
信息、竞争与股票
价格
?
竞争与有效市场
The
idea
that
markets
aggregate
the
information
of
many
investors,
and
that
this
information
is
reflected
in
security
prices,
is
a
natural
consequence
of
investor
competition.
If
information
were
available
that
indicated
that
buying
a
stock
had
a
positive
NPV,
investors
with
that
information
would choose to buy the stock; their
attempts to purchase it
would
then
drive
up
the
stock’s
price.
By
a
similar
logic,
investors with information that selling
a stock had a positive
NPV would sell
it and the stock’s price would
fall.
The
idea
that
competition
among
investors
works
to
eliminate
all
positive-NPV trading opportunities is
referred
to
as
the
efficient
markets
hypothesis.
It
implies
that
securities
will
be
fairly
priced,
based
on
their
future
cash
flows, given all information that is
available to investors.
Public, Easily
Interpretable Information
.
Private or Difficult-to-
Interpret Information.
Implications for Corporate
Managers.
If
stocks
are
fairly
valued
according
to
the
models
we
have
described, then the value of the firm
is determined by the cash
flows that it
can pay to its investors. This result has several
key
implications for corporate
managers:
?
Focus on NPV and free cash
flow.
A manager seeking to
boost
the
price
of
her
firm’s
stock
should
make
investments
that
increase the present value of the
firm’s free cash
flow. Thus the
capital budgeting methods are fully
consistent with the objective
of
maximizing the firm’s share price.
?
Avoid accounting
illusions
.
Many managers
make the mistake
of
focusing
on
accounting
earnings
as
opposed
to
free
cash
flows.
With efficient markets, the accounting
consequences of a
decision do not
directly affect the value of the firm and should
not drive decision making.
?
Use financial transactions to support
investment
.
With efficient
markets,
the
firm
can
sell
its
shares
at
a
fair
price
to
new
investors. Thus, the
firm should not be constrained from
raising capital to fund positive NPV
investment opportunities.
The
efficient
markets
hypothesis
is
best
expressed
in
terms
of
returns. It states that securities with
equivalent risk
should
have
the
same
expected
return
.
The
efficient
markets
hypothesis
is
therefore
incomplete
without
a
definition
of
“equivalent
risk.”
Furthermore,
different
investors
may
perceive
risks
and
returns
differently
(based
on
their
information
and
preferences).
There
is
no
reason
to
expect
the
efficient
markets hypothesis
to hold perfectly;
it is
best
viewed as an idealized
approximation for highly competitive
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