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昕豪 · 2024年03月15日

老师，您好，关于这道题，如果运用推导的公式来看，PVt=Dt/r，按照题中所给条件，D5/(6%/4)=PV5？

  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

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老师，您好，关于这道题，如果运用推导的公式来看，PVt=Dt/r，按照题中所给条件，我知道的是D5的值，和每季度的dividend，即（6%/4），那么，D5/(6%/4)=PV5，那么，求PV0的现值，不还是应该往前折5期吗？

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1 个答案

品职助教_七七 · 2024年03月16日

嗨，努力学习的PZer你好：


PVt=Dt/r实际是PVt=D1/r。由于折现是计算第0期的值，所以相当于要折到首笔现金流D1的前一期（第0期）。

所以，D5/(6%/4)=PV4。否则就变成先付年金了。

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