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hhjinghh · 2024年07月20日

老师，题干的意思是不是前4季度均没有分红，直到第5个季度才分红2？

  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

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老师，题干的意思是不是前4季度均没有分红，直到第5个季度才分红2？

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品职助教_七七 · 2024年07月20日

嗨，从没放弃的小努力你好：


是的。这实际就是一个往后递延的永续年金。

正常的永续年金是第一期开始分红，折现到第0期求现值。这道题的永续年金往后递延到第五期开始分红，折现到第四期求现值。

所以求完133.33后还得再多一步，再从第四期折到第0期。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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