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米其林 · 2023年05月13日

为什么PV不是133

  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

</span>12\frac12

题目问的PV？那算出来的永续年金的PA就是133呀，为什么还要再算一个PV呢

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已采纳答案

星星_品职助教 · 2023年05月15日

同学你好，

PV是计算到0时点的值。本题中，首笔付款在5时点，所以套用永续年金公式得出的133只是在4时点的值，还需要再往前折现4期到0时点才能得到最终的PV值。

王10 · 2023年10月26日

这套题不懂，讲解下

星星_品职助教 · 2023年10月26日

@王10 本题的分析已在原回复和另一个提问中分别讲解，如仍有疑问，请具体说明不理解的地方。

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