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dejiazheng · 2025年04月16日

PVRI2015得分子为什么不需要乘以持续因子0.7；终值时间段的划分不明确

  1. CFA II
  2. Equity

* 问题详情，请 查看题干

NO.PZ201512300100001207

问题如下：

7. Under Scenario 1, the intrinsic value per share of the equity of Amersheen is closest to:

选项：

A.

R13.29.

B.

R15.57.

C.

R16.31.

解释：

As the multistage residual income model results in an intrinsic value of R16.31.

This variation of the multistage residual income model, in which residual income fades over time, is:

where  is the persistence factor.

The first step is to calculate residual income per share for years 2012 2015:

ROE = earnings / book value

Growth rate = ROE × retention rate

Retention rate = 1  (dividends/earnings)

Book valuet= book valuet 1 + earningst 1  dividendst 1

Residual income per share = EPS  equity charge per share

Equity charge per share = book value per sharet× cost of equity

Using the residual income per share for 2015 of R1.608, the second step is to calculate the present value of the terminal value:

PV of Terminal Value =

R1.6081+0.10-0.70(1.10)3=R3.0203

Then, intrinsic value per share is:

V0=R7.60+R2.52(1.10)+R2.31(1.10)2+R1.98(1.10)3+R3.0203=R16.31

问题一：

问题二：expected ROE in 2015 is 26% but it is assumed that the firm’s ROE will slowly decline towards the cost of equitythereafter

题目说从2015年开始缓慢下降到行业平均，持续因子是否运用在在计算2015年的RI中？求用李老师的方法指教两阶段的划分

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1 个答案

王园圆_品职助教 · 2025年04月17日

同学你好，“PVRI2015得分子为什么不需要乘以持续因子0.7”——

以下是上课的时候带李老师笔记的讲义截图，请看紫色的那一行

具体李老师讲义上的这个PVRI公式——就是分子是RI *w的这个打印版公式，是由右边红色笔记的PVRI公式——就是分子是RI的这个公式的基础上，再向后一期推导出来的

李老师上课的时候推导过，当1+g=w，从PVRIt=RI/（r-g)向后推导一期并且带入g=w-1以后，可以得到PVRI=RI*w/(1+r-w)

而本题的答案，使用的是PVRI=RI/（1+r-w)这个公式计算的，所以这里分子带入的是2015年而非2016年的RI

如果要使用李老师的公式，则需要计算出2016年的RI并用打印版公式计算才可以

问题二，上面的回答中其实已经写了，既然RI是2015年开始缓慢下降的，RI2016 = RI2015*w就完全没有问题了，但是RI2015就不能用RI2014* w来推导得出

用李老师的方法就是PVRI2016=RI2015*w/(1+re-w),其中的RI2016=RI2015*w就是2016年的RI

最后就是V0 = RI2012折现1年+RI2013折现2年，RI2014折现3年，（RI2015+PVRI2016）折现4年

你最后得出的答案和本题结果一定是一样的

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NO.PZ201512300100001207问题如下7. Unr Scenario 1, the intrinsic value per share of the equity of Amersheen is closest to:A.R13.29.B.R15.57.C.R16.31.the multistage resiincome mol results in intrinsic value of R16.31.This variation of the multistage resiincome mol, in whiresiincome fas over time, is: where is the persistenfactor.The first step is to calculate resiincome per share for years 2012 2015:ROE = earnings / book valueGrowth rate = ROE × retention rateRetention rate = 1 (vin/earnings)Book valuet= book valuet 1 + earningst 1 vint 1Resiincome per share = EPS equity charge per shareEquity charge per share = book value per sharet× cost of equityUsing the resiincome per share for 2015 of R1.608, the seconstep is to calculate the present value of the terminvalue:PV of TerminValue =R1.6081+0.10-0.70(1.10)3=R3.0203Then, intrinsic value per share is:V0=R7.60+R2.52(1.10)+R2.31(1.10)2+R1.98(1.10)3+R3.0203=R16.31我详细画图计算了一遍，但是跟答案对不上，没搞明白哪一步错了

2025-04-01 12:00 1 · 回答

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