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胖婷肥周 · 2023年12月28日

能不能我的解题错在哪里了？

  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

</span>12\frac12

因为我的理解是：这个股票是每5个季度发一次分红， 所以用PV=D/r(r是一期的收益率）， 关于r的计算，因为是年利率6%,（1+0.06/4）的5/4次方-1，算出期间收益率 收益率是0.018785 再用2/0.18785=106😂😂😂😂

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1 个答案

品职助教_七七 · 2023年12月29日

嗨，努力学习的PZer你好：


1）该股票为从第五个季度开始发第一次分红，此后永续发放，所以需要使用永续年金的公式PV=D/r，其中r为实际期间利率；

2）r=6%为名义上的报价利率，根据题干中的“compounded quarterly”，可知对应的实际利率为6%/4=1.5%；

3）PV=D/r可以计算此永续优先股的现值，结果为PV=2/1.5%=133.33。但该计算是计算到第四季度的。所以还需要再用133.33往前折现4期，除以（1+1.5%）的四次方，得到最终结果125.62。

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努力的时光都是限量版，加油！

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