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nian123 · 2024年07月13日

怎么算的？

  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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1.为什么133.33是fv， 2.既然是永续债券，随便分割付息的时间点不可以吗？就按照5个季度为一个区间，那么d=2,r=6/4*5为什么不行呢

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1 个答案

品职助教_七七 · 2024年07月13日

嗨，爱思考的PZer你好：


1）通过永续年金模型计算出133.33时，这个步骤的结果为PV。由于首笔付款在第五期，所以这个PV是4时点的值。所以，在往0时点继续折现时，133.33在这个新步骤里就变成了FV；

2）不可以随便确定付息时间点。题干里已经说明这是“quarterly dividend payment”和“compounded quarterly”，所以只能以每个季度为一期，不可以5个季度为一期。

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