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嘉轩0903 · 2022年10月22日

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  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

Pv=A/r这个公式不能直接套用吗？为什么这么复杂

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1 个答案

星星_品职助教 · 2022年10月22日

同学你好，

本题第一步折现PV = $2.00/(0.06/4)= $133.33就是Pv=A/r这个公式的直接套用。

根据题干信息，由于首笔现金流是在5时点支付，所以此时133.33是折现到4时点的值，所以还需要再一步折现回到0时点才能解题完毕。

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