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谢朝木 · 2021年10月12日

永续年金使用的利率问题

  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

这种永续年金使用的利率为什么不用EAR，比如这个题用EAR/4作为季度的利率。以及这种永续年金在题干里面明确了复利到季度的情况，什么时候应该用EAR？希望能系统解释一下

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1 个答案

星星_品职助教 · 2021年10月13日

同学你好，

本题的季度利率需要通过6%/4这种方式进行计算。没有EAR/4这种计算方法。

利率使用的原则是 I/Y，PMT，和N这三者必须一致。以这道题为例，由于确定的是按照季度支付PMT，所以N和I/Y也需要是季度的数值。

同样基于这个原则，当PMT和N都是年度值时，使用EAR。


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