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· 2021年08月07日

本题求的Present value 是求1年末的值吗？

  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

本题求的Present value 是求1年末的值吗，往前求现值为什么不用N=5 ？

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1 个答案

星星_品职助教 · 2021年08月07日

同学你好，

本题分成两步折现，第一步是求4时刻的PV，第二步也就是最终求的PV是求0时刻的PV。

计算永续优先股的现值时，由于现金流是从5时刻开始持续存在，所以第一步要把PV算到4时刻。这个道理和正常现金流从1时刻开始，最终算PV要算到0时刻是一样的。

当确定4时刻的值后，再把这个值进行第二步折现算到0时刻，所以N=4.



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