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叶赫那拉坤坤 · 2020年02月05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

这个题老师能画一下时间轴吗？讲解中的第二步骤不理解，为什么是4？

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2 个答案

星星_品职助教 · 2020年08月13日

@王思祺

同学你好，

n指的是一共有多少“期”，时间轴上的1,2,3,4...每个数字对应的也是“期数”，这道题里是以一个季度为一期的，所以时间轴上数字1,2,3,4指的是4个季度，而不是4年。

这道题首笔现金流发生在第5个季度，也就是第5期（图上的5时间点）。所以step 1是将永续年金折现到第4个季度（4时间点）；step 2是将这笔现金流从4时间点再往前折现4个季度从而折现到0时间点，所以这个时候n就是4。

同样，此时对应的利率也需要是期间利率，也就是季度利率，即6%/4=1.5%。

 

星星_品职助教 · 2020年02月05日

同学您好，

对于后付年金，现金流是从1时刻开始的，而不是0时刻开始的。但如果算现值折现，折现是要折到0时刻的。

所以这道题的永续年金现金流是从5时刻开始的，折现也就是要折到4时刻，而不是5时刻本身。

王思祺 · 2020年08月12日

老师，6%1年计息4次，4年n不是应该等于8吗

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