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𝒜𝒩𝒥𝒜 安雅🎃 · 2021年09月04日

No.PZ2017092702000009 为什么要折现两次？

  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

No.PZ2017092702000009 (选择题)


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:


A.$31

B.$126

C.$133.


解析

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PV=133.33后，还要把它折现到今天？

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星星_品职助教 · 2021年09月04日

同学你好，

通过题干中“......makes its first quarterly dividend payment of $2.00 in five quarters”可知，首笔付款的时间是在5时点。

所以计算出来的133.33是在4时点的值。

如果没具体标明时点，题干要算的是“present value”指得都是今天也就是0时点的值，所以需要再次折现一步。

欢欢 · 2021年11月03日

不太懂，永续年金不是应该每期都有一笔固定payment吗？为什么前四个季度会没有。另外，如果题目没有写“in five quarters”这样的字眼的话，是否就直接用P=A/R就可以了，不用再考虑折现回来的问题？谢谢老师。

星星_品职助教 · 2021年11月03日

@欢欢

①只使用P=A/R和不再进行二次折现的前提是首笔PMT要发生1时间点，此后定期，永续发生；

②本题题干中已经明确的说明了“...makes its first quarterly dividend payment of $2.00 in five quarters”，所以就不是平常所说的从1时点开始逐期支付的永续年金形式了，而是从5时点开始支付的一个递延永续年金的形式；这种情况就需要二次折现，先算永续年金在4时点的现值（首次折现），再折现回0时点（二次折现）

星星_品职助教 · 2021年09月04日

@𝒜𝒩𝒥𝒜 安雅🎃 回复追问：

这句话就是 按照季度付$2.00的股利，首笔付款时间在第5季度 的意思。

要注意“... in five quarters”指的是付款时间就是在5时点。类似这样的“in XX years”的表达有很多，是一种固定的模式，当做规律记一下即可。

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