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为了求职冲呀 · 2022年02月20日

PV = $133.33(1 + 0.015)–4

  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

请问为什么在这个方式里面为什么是^-4，为什么是负数呢？

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1 个答案

星星_品职助教 · 2022年02月22日

同学你好，

公式逻辑为：

1）FV=PV×（1+r）^n

2）上式移项后可得PV=FV×（1+r）^ -n，往前折现4期，即为 -4.

第二步折现为4期的原因是：由于首笔现金流在第5期发生，所以第一次折现要将PV1算到N=4的时刻。

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