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绿水精灵 · 2024年09月01日

此题付dividend的时间点如何理解？

  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

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老师，此题困惑的地方是：A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. 并不是表述为make its first quarterly dividend payment of $2 in the fifth quarter. 如何体会是从第五个季度开始付dividend的。

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袁园_品职助教 · 2024年09月02日

嗨，努力学习的PZer你好：


在 “A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters.” 这句话中，“in five quarters” 的意思是在五个季度的时间跨度之后。

我们从时间顺序角度来看，假设从当前这个时间点开始计时，为0时间点，一个季度一个季度地往后推移，那么当到了第五个季度的时候t=5，它就会做出首次每季度 $2.00 的股息支付。

如果表述为 “in the fifth quarter”，这就明确地只限定在第五个季度这一个单独的时间节点进行支付。

而原句中的 “in five quarters” 是一个相对模糊但大致指向从现在开始经历五个季度到达的那个时间段范围。

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努力的时光都是限量版，加油！

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