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Mer · 2021年08月28日

请问是如何计算出的pvri

  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

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


您好，根据公式算出的PVRI2015=RI2015*w/(1+re-w)=1.6018*0.7/0.4=2.81不是3.0203。请问是哪里算错了吗？谢谢！

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王园圆_品职助教 · 2021年08月28日

嗨，努力学习的PZer你好：


同学你好，要注意，讲义上的公式是PVRI(t) = RI(t-1) *w/(1 + re - w)哦~~而书上给的公式是PVRI(t) = RI(t) / (1 + re - w).但是两个公式相同的前提是w = 1+g。本题的问题是g = 9%而pesistent factor = 0.7，两者的对应相等关系并不存在。（按照合理情况，既然RI慢慢下降，g就应该是负数哦）

所以本题中只能用书上给的公式PVRI2015 = RI2015 / (1+re -w) = [1.608 / (1 + 0.1 - 0.7)]/(1.1^3)来计算呢~~

因为这道题比较特殊（g 和 w之间的对应关系不存在，g还大于0），而且涉及RI的计算确实比较复杂，协会的出题风格也比较跳跃，建议同学下次碰到问题的时候，优先使用书上提供的公式计算，可能一次成功的概率更高哦~~

希望我的解答能够有所帮助，如果还有什么不理解的，欢迎同学继续和我们一起探讨哦~~

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ZF Everyday · 2023年03月18日

讲义上的公式是PVRI(t-1) = RI(t-1) *w/(1 + re - w)吧？如果w = 1+g，这位同学的计算是对的吧？老师的解析逻辑看懂了，但是，老师给公司不对，错了一个时间段。PVRI2015=RI2015*w/(1+re-w)=1.6018*0.7/0.4=2.81是对的，请老师确认一下

王园圆_品职助教 · 2023年03月18日

嗨，努力学习的PZer你好：


同学你好，这个回答是助教我早期的回答了，后期其实助教才彻底理清两个公式的关系

首先，PVRI2015 = RI2015 / (1+re -w) = [1.608 / (1 + 0.1 - 0.7)]/(1.1^3)是原版书给出的公式，以下为原版书截图黄色部分

而李老师的讲义上的公式是这个公式向后推导一年得出的，推导的基础就是w=1+g——具体同学可以参考一下基础班讲义列示4个多阶段RI计算公式的后面的那道例题，用到的公式其实也是原版书的公式，而李老师其实特意在这道题目里把他的公式和原版书的公式都解释了一遍的

所以本题其实可以用李老师的公式解题，但是用李老师的公式需要多计算一期多折现一期

也就是PVRI2016=RI2015*w/(1+re-w),得到的RI2016相当于在2015年的年底，

所以最后的V = B0 + RI2012折现1年+RI2013折现2年+ RI2014折现3年+（RI2015+PVRI2016）折现4年


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