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cui1130 · 2022年03月17日

没明白啥意思啊，辛苦老师讲解一下

  1. CFA I
  2. Quantitative

NO.PZ2017092702000009

问题如下：

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to:

选项：

A.

$31.

B.

$126.

C.

$133.

解释：

B is correct.

The value of the perpetuity one year from now is calculated as: PV = A/r, where PV is present value, A is annuity, and r is expressed as a quarterly required rate of return because the payments are quarterly. PV = $2.00/(0.06/4) PV = $133.33. The value today is (where FV is future value) PV = FV(1 + r)–N

PV = $133.33(1 + 0.015)–4

PV = $125.62 ≈ $126

没明白啥意思啊，辛苦老师讲解一下

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1 个答案

星星_品职助教 · 2022年03月17日

同学你好，

本题涉及到两步折现。根据题干描述“....makes its first quarterly dividend payment of $2.00 in five quarters”，可知该永续年金的首笔现金流发生在N=5时点，这时候用公式PV = A/r折现得到的现值是在N=4时点。

由于每一期是一个季度，所以r= 6%/4=0.015。N=4时点的PV = $2.00/0.015=133.33

这道题最终要求的是“the stock’s present value”，所以还需要再将这个值折现到0时点。即133.33除以（1+0.015）的四次方，得到0时点的PV=126

时间轴如下，供参考。

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