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ZAA · 2023年04月14日

时间点问题

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

from year3 进入永恒

我按照0123那么画时间轴

我切到year2

然后就整整差了一年

我想问问这个时间点怎么区分我分不好

3 个答案
已采纳答案

王园圆_品职助教 · 2023年04月17日

嗨,从没放弃的小努力你好:


不是的同学,本题这种情况属于RI永续不变的情况,但是必须以永续不变那一年的RI作为分子,re作为分母求出的才是正确的PVRI

本题明确说了是从第三年开始公司的RI才保持不变的,并且经过计算RI2和RI3也并不相等,更加证明题目的意思是第三年年末而非第三年年初进入永续不变阶段,那你就必须计算出RI3来算PVRI啊

以下讲义中李老师这个公式一的应用就是助教最开始举例的第二种情况,即如果运用李老师这个公式,就相当于在第三年切一刀,由于RI4=R13,所以落在第三年年末的PVRI3 = RI4/re也同时等于RI3/re

而如果按照一般的永续年金原理的公式,那就是第二年处切一刀,PVRI2 = RI3/re

归根结底,你这个公式的分子必须是永续不变的RI而不可以用还没有进入永续不变的RI2

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加油吧,让我们一起遇见更好的自己!

ZAA · 2023年04月18日

明白了 好的谢谢

王园圆_品职助教 · 2023年04月17日

同学你好, 这里是助教看错你的意思了,我以为你不知道怎么理解从RI3计算PVRI的方式。

你理解切到第二年年末是可以的,此时相当于RI3及RI3以后都是第二阶段(因为PVRI2=RI3/r),所以你依然需要计算出RI3哦

如果只计算到RI2的4.22,那我们是无法推演出RI3的哦

ZAA · 2023年04月17日

就是我那个新评论啊 我想问为啥RIT-1除以Re 不是应该422除以re吗 跟RI3有什么关系

王园圆_品职助教 · 2023年04月14日

嗨,爱思考的PZer你好:


同学你好,其实怎么切时间轴没有那么重要,重要的是你要分清PVRI是折现到哪一年年底的

注意,第三年计算的RI已经进入的永续不变的阶段

也就是说,按照题目解析,其实第一阶段只有两年,第二阶段是RI3和以后的所有年份

所以题目解析中的方法是:RI3/r得到的是第二年年末的PVR I

所以最后的V0 = B0 + RI1折现1年+(RI2+PVRI)折现两年


如果用李老师的方法在第三年切一刀,那相当于默认第四年及未来是永续不变阶段

此时需要注意,第一阶段是三年,相当于PVRI’ = RI4(=RI3)/r——这个PVRI落在第三年的年末

所以最后的V0 = B0+ RI1折现1年+RI2折现2年 + (RI3+PVRI‘)折现三年


你可以验证一下,这两种方法最后算出来的V0一定是相同的

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

ZAA · 2023年04月17日

我没有懂你说的 就是FROM YEAR 3永续,这个YEAR 3是指的第三年对吧 0 1 2 3 4 0是现在 1是第一年 2是 第二年 3 第三年 按照李老师方法 不是切到2时刻吗 我的意思就是已知条件中,就能用到4.22,后面都不需要了 从year3 就开始永续 切到YEAR 2

ZAA · 2023年04月17日

我还有个问题,就是为什么PVRI2不是应该等于RI2除以Re吗 我觉得是4·22除以0,55 我记得公式叫做RIT-1除以Re啊

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