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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 – re*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=RI3r×(1+r)3=2.770.109×1.1093=18.63PV=\frac{RI_3}{r\times\left(1+r\right)^3}=\frac{2.77}{0.109\times1.109^3}=18.63

V0=28.25+3.421.109+4.221.1092+2.771.1093+18.63=55.43V_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?



2 个答案

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





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

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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