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tinylumpy · 2024年12月17日

PV计算

  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

</span>12\frac12


请问如何理解 The value today is (where FV is future value) PV = FV(1 + r)–N？


这道题的解题思路还是不太明白，请老师把答案逻辑再讲解一下



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1 个答案

品职助教_七七 · 2024年12月18日

嗨，从没放弃的小努力你好：


1）这里的符号是-N次方，相当于公式是PV = FV/(1+r)^N。也就是PV等于FV除以 (1 + r)的N次方。意思是今天的价值PV就相当于未来N期后的价值FV以利率r进行折现。

2）本题的思路为首先将永续优先股按照公式PV=A/r进行折现。由于该永续优先股的首笔付款在第五期，所以折现就要折到第四期。由此得到第四期的现值133.33。然后再将该值折现回0时点，得到最终的现值126即可。

可参考下面的时间轴。

提问请具体说明答案逻辑中是什么地方不明白，解析的哪里需要“再讲解一下”。


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