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王10 · 2023年11月13日

年金计算公式。

  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

年金的计算公式：PV=FV/(1+r/m)的mn次方,为什么从5时点算4时点，是直接用2/（0.06/4）

不应该是

2/（1+0.06/4）么

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1 个答案

星星_品职助教 · 2023年11月14日

永续年金的现值为PV = A/r。对于正常的普通年金而言，首笔付款在1时点，现值就应算到0时点。以此类推，本题首笔付款在5时点，现值就应该直接算到4时点。

如果首笔付款在5时点，现值也算到5时点，就是先付年金了。和题干不符。

所以，2/（0.06/4）就是已经算到4时点的该永续年金现值了，不需要再往前折现一期了。


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