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jzhuangst · 2022年03月16日

为什么不是N=5？

  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

你好，请问这道题说的是第五个quarters，那应该有5个period，N应该等于5呀，为什么N=4？

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1 个答案

星星_品职助教 · 2022年03月16日

同学你好，

先考虑简单的普遍情况，对于一般的后付年金而言，付款是在1时点的，而非0时点。但求现值都是求到0时点。

按照这个逻辑来同理考虑这道题，付款在5时间点，所以此时算第一步永续年金的现值就是算到4时点。

所以第二步再往0时点折现时，就只需要折4期了，即N=4

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