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ychi5 · 2022年02月10日

第一步的PV是FV4是因为这是第一次分红的原因吗？

  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

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters

请问以下理解对吗：因为第五个quarter分红，又因为这是第一次分红，所以现金流是有1次，故折现到FV4

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2 个答案

星星_品职助教 · 2022年02月10日

@ychi5

学习加油~

星星_品职助教 · 2022年02月10日

同学你好，

是的，关键就在于首笔分红在N=5时刻。

对于正常的永续年金而言，现金流是从1时点开始的，进而1、2、3、4....一直延续下去。折现是折回0时点的。

对于本题而言，第一次分红时点在5时点，进而5、6、7、8.....一直延续下去。所以折现就是折回4时点的。


ychi5 · 2022年02月10日

谢谢老师

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