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过儿 · 2022年05月06日

请问老师

  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

经常看到题目中出现 stated annual rate 6%, compounded semiannually/quarterly等。

出现这样描述的时候，什么时候要折算EAR再计算，什么时候直接用利率，不用折算呢？


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3 个答案

星星_品职助教 · 2022年05月07日

@过儿

做年化的前提是题目问的是和“年”相关的内容，例如题目求的是年度PMT，或要计算N是多少年，这时候I/Y都可以转化为EAR

背后的原理是I/Y和N与PMT三者要一致。如果后两者都是年度的，I/Y也需要是年度的。

如果PMT为0，此时N如果是月、季度、半年，那么I/Y也需要是对应的月、季度、半年。

过儿 · 2022年05月06日

我这样理解可以吗，一般一套题考到年化的最多就1.2道，我正常都按不用转化做，出现月，季，年等提示，且没出现现金流等情况才考虑做年化行吗

星星_品职助教 · 2022年05月06日

同学你好，

这种带着计息频率（coupounding frequency）的描述目的就是要做转化。转化的原则是按照后面的计息频率（coupounding frequency）得到期间利率。

如果题目最后要计算的是多少“年”的情况，此时往往要进一步的将期间利率再转化为EAR。否则直接用期间利率就可以解决问题了。

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