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Benny™ · 2022年10月29日

这个题目的解析不太理解

  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

看了下其他提问还是不太理解，请问老师PV = A/r 这个公式只能向前折一个时间点吗？怎么判断是要往前折多少个时间点呢？第五个quarter才给的第一笔钱吗？那这个payment不是quarterly dividend的吗？还是说这两块钱是针对前5个quarter的合计应付呢？针对这题能不能有个详细一点的说明和解析呢？

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3 个答案

星星_品职助教 · 2023年08月08日

@iamqing

用“in XX quarters/month/years”来表示就在XX这个时点付款，是协会的固定表述方式。这种表述可以在很多题目中见到。类似的还有诸如starting from year 18，就是在18时间点上付款的意思。主要容易引发歧义的表述就是这两种。

但题目很少会用“ “the fifth quarter"这种带“th”的表述方式。


星星_品职助教 · 2023年07月28日

@咖啡巧克力

... makes its first ...payment...in five quarters....就是首笔付款发生在5时点的意思。如果画时间轴，就是正好画在5这个点上。

这是协会的固定表述方式。和国内习惯的一般表述不大一样，需要掌握一下这种特定说法。

iamqing · 2023年08月07日

谢谢！这个表达真的看不懂，看起来 makes its first payment in five quarters 是五个quarter中第一个quarter付款了的意思，第五个quarter 付款我以为该是makes its first payment in “the fifth quarter"

星星_品职助教 · 2022年10月29日

同学你好，

1） PV = A/r是针对普通的后付永续年金的公式。普通年金的首笔现金流都在第1期产生，折现需要折回第0期。或者将这个公式直接记做PV=D1/r 也可以。

2）“... makes its first quarterly dividend payment of $2.00 in five quarters....”的意思为：①现金流是按季度来支付的，每季度都支付$2.00；②前四个季度不支付现金流，首笔现金流$2.00在5时点产生，所以这道题里的5时点就是上面说的“第1期现金流”，根据上一条的原则，折现就要折到前一期也就是4时点。

咖啡巧克力 · 2023年07月28日

“In five quarters”是不是指度过了5个quarter之后呢？如果是这样，是不是应该折现5次呢？

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