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嘉轩0903 · 2022年10月22日

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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

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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