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Jusay · 2021年10月29日

老师能全面通俗的解释下这道题吗？

  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

好像都没怎么看懂

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已采纳答案

星星_品职助教 · 2021年10月30日

同学你好，

这道题的核心是求“perpetual preferred stock”的“present value”。所以本质就是永续年金求现值的问题。先通过公式公式PV = A/r求出永续年金的现值（第一步折现，折现到4时点），然后再将这个现值折现回0时点即可（第二步折现）

时间轴如下：

本题需要注意的点为：

1）“makes its first quarterly dividend payment of $2.00 in five quarters”，所以首笔现金流发生在N=5时点，这时候第一步折现用公式PV = A/r折现得到的现值是在N=4时点

  • “in five quarters”指的就是现金流发生在第5个季度。这是协会的固定表达方式。
  • 首笔现金流发生在5时间点，折现就要折到4时间点，而不是5时间点。这和正常折现时PV需要折到0时间点，而不是首笔现金流发生的1时间点是同样的原理。

2）最终要求的是0时点的现值，所以需要做第二步折现，将上一步算出来现值再往前折四期即可。



Jusay · 2021年10月30日

谢谢 通俗易懂 赞

星星_品职助教 · 2021年10月31日

@Jusay


好的，学习加油~

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