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郝王爷 · 2023年05月02日

Pv of terminal value 计算时,为什么分子1.88不需要乘以persistence factor w?

NO.PZ2018103102000064

问题如下:

Jacques prepares to update the valuation of TMT. The company’s expected ROE in 2017 is 34.5% but it is assumed that the firm’s ROE will slowly decline towards the cost of equity thereafter.  As of the beginning of 2015, based upon the information in the below table, use the multistage-stage residual income (RI) model to determine the intrinsic value of the equity of TMT. The intrinsic value per share is closest to:

选项:

A.

22.72.

B.

14.97.

C.

78.81.

解释:

B is correct.

考点:RI

解析:B是正确的。第一步是计算2015 - 2017年的每股剩余收益:

第二步是计算终值的现值:

PV of Terminal Value =1.88/(1+0.08-0.85)(1.08)2=7

那么每股的内在价值就是: V0=5+1.6/(1.080)+1.74/(1.08)2+7=14.97

Pv of terminal value 计算时,为什么分子1.88不需要乘以persistence factor w?

1 个答案

王园圆_品职助教 · 2023年05月02日

同学你好,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)

所以题目这种解法是用了讲义中红色手写公式的解法,分子RI就是2017年的RI,PVRI折现到2016年年底,然后V0 = B0 + RI2015折现一年+RI2016和PVRI一起折现两年

而如果要使用李老师上课的解法也可以,只需要先计算出RI2018 = RI2017*w,然后计算的PVRI‘ 就是折现到2017年年底,然后V0 = B0+RI2015折现一年+RI2016折现2年+RI2017和PVRI’一起折现3年

这两种方法计算的V0都是一样的

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