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小胖嘟 · 2021年01月16日

问一道题：NO.PZ2017092702000009 [ CFA I ]

  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

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1 个答案

星星_品职助教 · 2021年01月17日

同学你好，

这道题的核心是求“perpetual preferred stock”的“present value”。所以是永续年金求现值的问题。

特殊点在于：

1）“makes its first quarterly dividend payment of $2.00 in five quarters”，所以首笔现金流发生在N=5时点，这时候用公式PV = A/r折现得到的现值是在N=4时点

要注意“in X quarters”指的就是现金流发生在第X个季度。

2）最终要求的是0时点的现值，所以需要做第二步折现，将上一步算出来现值再往前折四期即可。

 

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