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HL · 2021年11月24日

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  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

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. 

这句话该怎么理解？该怎么画时间轴？PV、FV在哪个时间点？

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已采纳答案

星星_品职助教 · 2021年11月24日

同学你好，

“makes its first quarterly dividend payment of $2.00 in five quarters”指的是首笔现金流$2.00发生在N=5时点。隐含的信息是这时候用公式PV = A/r折现得到的现值是在N=4时点。

所以第一步将永续优先股的PV折算到4时点，第二步再将这个值折算到0时点，即可求出最终stock的present value。

时间轴如下图：

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