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Brayden · 2024年03月26日

老师好，请问为什么先用了coupon instrument的公式后再用discount bond的公式再求现值呢？

  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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我已经看完了您对其他同学问题的回答，但还是不太清楚为什么第二步要用PV=FV/(1+t)^t?我对其中逻辑没弄懂，谢谢！

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2 个答案

品职助教_七七 · 2024年05月20日

嗨，爱思考的PZer你好：


@Frank Liu

1）永续优先股第五期付股息为题干设置，想递延多少期付都可以；

2）永续优先股为从首笔付息开始，此后每期永续付息的优先股。现实中有这种产品；

3）In XX quarters为协会对于在第XX期的固定表述方式，没有“No.5 或者 Fifth quater”这种表述方式

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加油吧，让我们一起遇见更好的自己！

品职助教_七七 · 2024年03月27日

嗨，爱思考的PZer你好：


永续年金的公式为PV=每期固定的现金流 / 期间利率。应用在本题的永续优先股上，则是 每期固定的股利 / 期间利率，PV=D/r。

上述公式里的D基于的是首笔付款的股利。常规情况下就是D1，即如果首笔付款在第一期，则该公式可以直接算出位于第0期的现值。

但是，本题首笔付款的股利是在第五期。也就不能直接算出位于第0期的现值，而只能算出该股利前一期的值。所以，基于第五期股利算出来的永续优先股的现值就应该在第四期。即PV = 2.00/(0.06/4)  = 133.33是第四期而不是第0期的值。

而现值是需要算到第0期的，所以就还需要把这个位于第四期的133.33再往前折现四期算到第0期。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Frank Liu · 2024年05月19日

永续优先股为什么要第五期才付股息呢？为什么前四期不付？永续优先股定义是什么？现实中有这个东西吗？按你们的解释的话，这个题的第一句话，英文表述应该有问题，要表达第五期，应该是No.5 或者 Fifth quater，不应该是In five quaters

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