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安在 · 2022年08月24日

题干和解答思路完全不能理解

  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

我理解的题干：收到一个股票第一季度分红2刀，总投资5个4个季度，也就是20个季度，现在年利率6%，求投资现值、

我的解答步骤：计算器做知4求1：N=4*5=20 ;FV=0;PMT=2;I/Y=6/4 得出PV=-34.3372

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1 个答案

星星_品职助教 · 2022年08月25日

同学你好，

A perpetual preferred stock为永续年金，所以N为无穷大，需要代入永续年金的公式计算。

题干中的“...makes its first quarterly dividend payment of $2.00 in five quarters”，指得是从第5个季度开始付股利，每个季度付$2.00，从此无限付下去。

所以首先代入永续年金的公式，得到该永续优先股的现值为2 / 1.5%=133.33。（1.5%为6%/4得到的季度利率）。由于该年金的首笔股利是第5季度开始付的，这个现值就是处于第4时点的现值。

再将这个值折现回0时点。可用计算器第三排按（FV=133.33，I/Y=1.5，PMT=0，N=4），也可直接除以1.015的4次方。得到答案125.62。

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