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洪铭泉 · 2024年11月04日

这个公式为什么是-4

  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

The value today is (where FV is future value) PV = FV(1 + r)–N

PV = $133.33(1 + 0.015)–4

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1 个答案

品职助教_七七 · 2024年11月04日

嗨，爱思考的PZer你好：


普通年金的首笔现金流发生在第一年的年末（1时点），现值要计算到0时点。现值不能算到第一年年末（1时点），否则就变成先付年金了。

平移到这道题上，题目没有说这是先付年金。而首笔现金流发生在第5时点，所以现值就应该计算到第4时点。由此，下一步折现回0时点就应该往前折现4期而不是5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！

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