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GS · 2020年07月11日

问一道题：NO.PZ2017092702000009

  1. CFA I
  2. Quantitative

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

没有理解 算完133（是什么值呢）之后，为何还要再折回来。

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3 个答案

星星_品职助教 · 2020年07月14日

@GS

 in FIVE quarters是标准的表示方法，意思是从第五个季度开始付第一笔PMT。这个表述是没有问题的，类似的表达在各个题目里出现过很多次。

没有见到过协会使用in the fifth quarter的这种表述。

 

星星_品职助教 · 2020年07月14日

@GS

 in FIVE quarters是标准的表示方法，意思是从第五个季度开始付第一笔PMT。这个表述是没有问题的，类似的表达在各个题目里出现过很多次。

没有见到过协会使用in the fifth quarter的这种表述。

 

星星_品职助教 · 2020年07月12日

同学你好，

题干中要算的是“perpetual” preferred stock ，所以需要代入永续年金的公式PV=A/r，即PV = 2/(0.06/4) =133.33，

但由于题干提示了“...makes its first quarterly dividend payment of $2.00 in FIVE quarters”，即首笔PMT是在N=5的时候付的，所以以上计算的PV是算到N=4时点的，如果要求0时点的现值，还需要再做一步折现。

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