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Catpasta · 2023年08月02日

不明白D5

NO.PZ2018062002000166

问题如下：

Current price per share $20

Current annual dividend per share $2

Annual dividend growth rate for Years 1 – 4: 5%

Annual dividend growth rate for year 5 onwards： 3%

Required rate of return 10%

Based on the above information, calculate the intrinsic value of the stock by using the DDM model. The stock is most likely:

选项：

A.

undervalued.

B.

overvalued.

C.

fairly valued.

解释：

A is correct.

The current price of €20 is less than the intrinsic value of €31.56;therefore, the stock appears to be currently undervalued. According to the two-stage dividend discount model:

$V_0=\sum_{t=1}^n\frac{{\displaystyle D_0(1+g_s)}^t}{{\displaystyle(1+r)}^t}+\frac{V_n}{{(1+r)}^n}$ and $V_n=\frac{D_{n+1}}{r-g_L}$

D₁ = €2 × 1.05 = €2.1

D₂ = €2 × (1.05)² = €2.205

D₃ = €2 × (1.05)³ = €2.31525

D₄ = €2 × (1.05)⁴= €2.431

D₅ = [€2 × (1.05)⁴](1.03) = €2.503

V₄ = €2.503/(0.1 – 0.03) = €35.77

V 0 =31.56(which is greater than the current price of €20)

考点：Multi-stage Model

计算器输入步奏如下：

CF0=0, C01=2.1,F01=1,C02=2.205,F02=1,C03=2.31525,F03=1,C04=2.431+35.77 F04=1 ,CPT--NPV, I=10

我理解到D4就截止了，D5是什么呢

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王园圆_品职助教 · 2023年08月02日

同学你好，题目这里说了“Annual dividend growth rate for year 5 onwards： 3%”，也就是从第5年开始，分红按照更低的增长率3%进行增长，即第五年进入第二阶段增长

本题是一个非常典型的两阶段DDM求解V0的题目，如果不计算D5，那就无法通过GGM公式计算终值V4。只用D1到D4计算公司的V0的话，有很大一块未来现金流的值都会缺失，那肯定是计算不出准确的V0的哦

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