帮忙解释这道题

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：

$31.

$126.

$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

$< / s p a n > \frac{1}{2}$ $< / s p a n > \frac{1}{2}$

这道题为什么选b不选c

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1 个答案

品职助教_七七 · 2025年02月09日

嗨，努力学习的PZer你好：

本题题目并未说该年金是先付年金，则默认按照后付年金计算。由于这笔永续年金的首笔付款位于第5时点，后付年金的条件下，公式算出的现值应位于4时点。

所以，要计算最终的现值，就还需要将该值133.33再往前折现四期。即解析中的：PV = $133.33 × (1 + 0.015)的-4次方

最终得到C选项的答案。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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