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dejiazheng · 2025年06月29日

对第二阶段的理解有差异

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

从字面理解will be constant from year 3 into perpetuity,其实这个表述是从第三年除开始的,所以我一开始切到第二年年末,求出了RI1、RI2和PVRI2折现。看了解释后说到RI3=RI4=...,为考虑到第二阶段的变化所以切到第三年年末?

1 个答案

王园圆_品职助教 · 2025年06月29日

同学你好,首先,RI都是年末的值而不是年初可以得到的值,所以“will be constant from year 3 into perpetuity”准确理解就是从第3年年末的RI开始到永远的RI都是保持不变的

所以基于RI3 = RI4 = RI5 = 。。。。,你其实可以用RI3计算PVRI2 = RI3/ r,然后把RI1,RI2+PVRI2分别折现1年和2年,也是可以算出和答案一样的结果的

当然解析这么算也是可以的,相当于是PVRI3 = RI4/r ,然后RI1,RI2,RI3+PVRI3分别折现1年,2年,3年,从而计算出答案


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