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Yvonne0719 · 2024年09月14日

请问这个两阶段模型，第一阶段是后续永续增长的利息折现到t=5，然后用P5再向前折现对吗？P5向前折现为什么不是5次方呢？

  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

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请问这个两阶段模型，第一阶段是后续永续增长的利息折现到t=5，然后用P5再向前折现对吗？P5向前折现为什么不是5次方呢？

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品职助教_七七 · 2024年09月14日

嗨，从没放弃的小努力你好：


首笔付款在第五时点，由于普通的后付年金都是年末付款， 所以此时折现就应该向前折一期，折到第四时点。

所以计算出来的永续年金现值位于第四时点，二次折现时，需要往前折现的是4期而不是5期，否则就是先付年金了。

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