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庄园monar · 2022年05月02日

不是很理解在PV=A/r的公式

  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，分红除以利率不就是期初的现值，

为什么说永续年金的首笔现金流发生在N=5时点，这时候用公式PV = A/r折现得到的现值是在N=4时点？


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1 个答案

星星_品职助教 · 2022年05月02日

同学你好，

PV = A/r，分红除以利率得到是期初的现值。

当A是从1时点开始时，即可得到期初0时点的现值。

本题A是从5时点开始的，即得到的是“期初”4时点的“现值”。

所以要求0时点时真正的现值，就需要把这个4时点的现值再折现一次回到0时点。

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