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rocktomato · 2019年01月30日

问一道题：NO.PZ2018103102000105

  1. CFA II
  2. Equity

问题如下图：

    

选项：

A.

B.

C.

解释：


我不大理解为什么要用永续年金的现值除以(1+r)^3？我反而觉得用永续年金的现值除以(1+r)^2是对的。因为根据题意RI3=2.77，且往后恒为2.77不变。也就是说t=3这个时间点已经产生了永续年金的第一笔现金流2.77，t=3这个时点可以看成永续年金时间轴的T=1时点（为了区别，用大T表示），如果要求永续年金的现值，那么应该是往t=2折现，即题目中的t=2应该是永续年金时间轴的T=0。所以在t=2这个时点会有两笔现金流，一笔是RI2=4.22，另一笔是永续现金流的折现值2.77/0.109=25.41。

即PV=28.2+3.42/1.109+4.22/1.109^2+25.41/1.109^2=55.4.

如果按照答案解析中列示的，用25.41/(1+r)^3，那么这个永续年金实际上是从RI4=2.77开始算永续年金的第一个现金流，缺少了在t=3时点上的现金流RI3往前折现。那就应该在25.41/(1+r)^3前再加上一个7.22/(1+r)^3。所以最终的PV应该为

PV=28.2+3.42/1.109+4.22/1.109^2+2.77/1.109^3+25.41/(1+r)^3=55.4,也是约等于55.4。

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1 个答案

maggie_品职助教 · 2019年02月07日

从第三年开始RI就一直保持不变了，可以看做是计算优先股，你好像把优先股的计算公式记错了，它不是错一位计算，请见讲义77页：


因此，这里是RI3开始保持不变，那么我们计算的价值也是V3.

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2024-11-12 18:47 1 · 回答

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