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大白 · 2020年11月16日

问一道题：NO.PZ2017092702000009

  1. CFA I
  2. Quantitative

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

算出永续年金的PV = $2.00/(0.06/4) PV = $133.33之后，再带入第一阶段的算PV，

用计算器第三行

FV= $133.33

PMT=2

I/Y=1.5

N=4

得到CPT PV=$133.33，

这个步骤哪里有问题？

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已采纳答案

星星_品职助教 · 2020年11月16日

同学你好，

永续年金的PV没有问题。

第二步的折现中，由于题干中说明“...makes its FIRST quarterly dividend payment of $2.00 in FIVE quarters”，所以可以看出第一笔PMT是N=5的时候支付的。在此之前并没有PMT。所以第二步折现时的PMT应该是0，而不再是2。其余步骤没有问题。

FV= $133.33

PMT=0

I/Y=1.5

N=4

CPT PV=-125.62，四舍五入后选择B选项。

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