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乔。 · 2023年11月28日

PV = FV(1 + r)^–N 这个公式出自那个？

  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

133.3的pv代表的是不是现在股票的价格？

126是季度的价格？



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已采纳答案

品职助教_七七 · 2023年11月29日

嗨，努力学习的PZer你好：


本题的首笔付款在5时点（即第5季度），所以按照公式PV=A/r得到的折现值就应折到4时点。故133.33是位于4时点的值。

由于题目最终要计算的是0时点的值，所以需要将133.33从4时点折现回0时点。126就是第二次折现后折回0时点的最终值。

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由于PV×（1+r）^n=FV，所以已知FV求PV时，可得PV=FV/（1+r）^n，这个式子可以以乘法的形式写成PV=FV×（1+r）^-n。

应用在本题中，就是133.33×（1+0.015）^-4 =125.62


上述时间轴和计算可参照下图：

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