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ZF Everyday · 2023年03月17日

用单阶段模型是否可以

NO.PZ2018103102000105

问题如下：

Matt is evaluating Company M by using the multistage residual income model. He has forecasted that residual income per share will be constant from year 3 into perpetuity and the short-term ROE is higher than the long-term ROE. He has also estimated the earnings and dividends for the following three years in the following table. What`s the intrinsic value of Company M?

选项：

A.

$27.18

B.

$48.91

C.

$55.43

解释：

C is correct.

考点：Multistage Residual Income Valuation

解析：先计算出每一年的BV

BV₁ = BV₀ + EPS - Dividends per share = 28.25 + 6.5 - 1.75 = $33，同理可得BV₂ = $38.19，BV₃ = $43.15

再计算出每一年的RI

RI₁ = EPS₁ – r_e*B₀ = 6.50-10.9%*28.25 = $3.42，同理可得RI₂ = $4.22，RI₃ = $2.77

终值的现值:

$PV=\frac{RI_3}{r\times\left(1+r\right)^3}=\frac{2.77}{0.109\times1.109^3}=18.63$

$V_0=28.25+\frac{3.42}{1.109}+\frac{4.22}{1.109^2}+\frac{2.77}{1.109^3}+18.63=55.43$

1.先求出B3

2.再下面的基本公式计算出来V3，再用V3折现回去到V0，这种方法是否可行呢？感觉更简单，就是结果有偏差，不知道问题出在哪里？

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王园圆_品职助教 · 2023年04月09日

同学你好，因为本题就是一个典型的多阶段模型的题目，多阶段和单阶段，计算出来的结果肯定不一样的

在多阶段下，这里的第二阶段更像是永续年金，用RI3/r（注意这里是r而不是r-g)计算出PVRI2，然后和RI1，RI2一起折现到0时刻，加上BV0来求解V0

而如果用单阶段，相当于是用RI3/(r-g)求PVRI ,结果肯定不一样——请看讲义截图方法中的第一种

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王园圆_品职助教 · 2023年03月17日

同学你好，你这种方法下，RI１和RI２到哪里去了呢？

在第三年的时候，BV３里面并没有反映第一年和第二年公司产生的的residual　income对公司的价值的影响，而是只反映了其账面价值的增加，这样肯定是会低估公司的V０的哦

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yydlut · 2023年04月09日

同样想问这个问题，用上式求出B3,再连同RI1, RI2一起折现，得到结果有偏差，不知道怎么回事

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2024-11-12 18:47 1 · 回答

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