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chiara9009 · 2023年08月08日

三阶段模型最后折现，为何都是CF都统一用第一阶段增长率作为折现率，而不是三个阶段分别折现？

NO.PZ2018103102000085

问题如下：

Matt is evaluating the value of Company M by using the dividend discount model. The most recent dividend and the required rate of return are $0.5 per share and 10%, respectively. The company will experience a highly growth of 10% at the first two years, followed by a 5% of growth in another two years. Thereafter, the dividend growth rate would be 3% per year into the indefinite future. What's the value of Company M?

选项：

A.

$8.16

B.

$8.64

C.

$9.67

解释：

考点：Three Stage Model

解析：

$PV_4=\frac{D_4\times\left(1+g_L\right)}{r-g_L}=\frac{0.667\times\left(1+3\%\right)}{10\%-3\%}=\$9.8146$

$P=\frac{0.55}{1.1}+\frac{0.605}{1.1^2}+\frac{0.63525}{1.1^3}+\frac{0.667+9.8146}{1.1^4}=\$8.64$

我的计算过程是用三个阶段的不同增长率分别折现，想请问一下最后为何统一都是用第一阶段增长率10%折现？

具体计算过程如下：

10%

___________

5%

__________

3%

____________

0____1____2____3____4____5____6

Do=0.5

D1=Do*(1+10%)=0.55

D2=D1*(1+10%)=0.605

D3=D2*(1+5%)=0.6353

D4=D3*(1+5%)=0.667

D5=D4*(1+3%)=0.687

TV4=D5/（re-g）=0.687/(10%-3%)

=9.814

CF0=0

CF1=D3=0.6353

CF2=D4+TV4=0.667+9.814=10.481

I/Y=5, CPT NPV=TV2=10.112

TV2=D3/（1+5%）+（D4+TV4）/(1+5%)^2

=0.6353/1.05+10.477/1.1025

=0.605+9.5066=10.112

CF0=0

CF1=D1=0.55

CF2=D2+TV2=0.605+10.112=10.717

I/Y=10, CPT NPV=9.357

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chiara9009 · 2023年08月08日

复盘了一下，应该是折现率应该统一采用Re而非g

1 个答案

已采纳答案

王园圆_品职助教 · 2023年08月08日

是的同学，折现现金流的时候应该用现金流对应的要求回报率，在CFA所有的equity相关的题目中，无论是何时发生的现金流都只会使用统一的要求回报率进行折现，而不会使用不同的折现率的

另外，同学注意把分红增长率g和要求回报率Re进行区分，这类题目就不容易产生疑问了

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