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Rachel · 2022年01月13日

为什么算出了perpetuity的pv后，还要再算一次PV呢？

  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

为什么算出了perpetuity的pv $133后，还要再算一次PV呢？

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1 个答案

星星_品职助教 · 2022年01月13日

同学你好，

这道题永续年金的首笔付款是在5时间点的（...makes its first quarterly dividend payment of $2.00 in five quarters）。

所以按照普通永续年金计算现值计算出来的PV是算到4时间点的。

而题目要求的是算到0时点的PV，就需要将这个值再往前折现4期到0时点。

可以参照图像进行理解。

一只🐶哆啦 · 2022年02月24日

看了这么多解答，只有这个看懂了，写的真不错

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