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L · 2023年11月19日

这道题可以用计算器解吗？ 或者别的方式？

  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

</span>12\frac12

PV =A/r 是constant dividends PV = D/r 那个知识点吗？


PV（1+r）^n 这个公式不是求FV的吗？还是要怎么分解？


还有为什么是-4不是4。 我混乱了。


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星星_品职助教 · 2023年11月20日

同学你好，

1）PV =A/r 是constant dividends PV = D/r 那个知识点吗？---------------是，只是代指的字母换了一下；

2）PV×（1+r）^n=FV。所以，PV=FV / （1+r）^n。这个公式也可以以乘法的形式写成 PV=FV ×（1+r）^-n。所以，答案解析中的PV = 133.33(1 + 0.015)^ -4 就是PV =FV / (1 + 0.015)^4，其实就是根据FV折现求PV的过程。

3）这道题一共两个步骤，其中PV =A/r这一步直接按就行。第二步PV = 133.33(1 + 0.015)^-4也可以直接按，也可以用第三排五个键 FV=133.33，PMT=0，I/Y=1.5，N=4，CPT PV=-125.6214。结果都是一样的。

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