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Blue. · 2021年05月13日

关于永续年金的计算

  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

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


为什么PV = $2.00/(0.06/4) PV = $133.33. 这一步所算到的只是N=4时的PV而不是N=0时候的PV？


为什么不可以直接N=5，i/y=6%／4，PMT=2，FV=0代入计算器里计算求PV呢？


感觉很抽象，没有办法理解。

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2 个答案

星星_品职助教 · 2021年05月29日

@yd08qg 学习加油~

星星_品职助教 · 2021年05月13日

同学你好，

“N=5，i/y=6%／4，PMT=2，FV=0”的意思是这个永续年金只有5期。这显然是有问题的，永续年金是无法用计算器来计算的，因为N没法确定。所以只能根据公式PV = A/r 来求解

此外I/Y的输入不能带“%”。

---------------------------

“ 这一步所算到的只是N=4时的PV”是因为“....makes its first quarterly dividend payment of $2.00 in five quarters.”，这句话的意思是这个永续年金的首笔现金流是从N=5的时间点上才开始付，此后永远付下去。所以用“PV = $2.00/(0.06/4) =133.33”，要注意这个PV是算到N=4时间点的。（这和正常折现时PV需要折到0时间点，而不是首笔现金流发生的1时间点是同样的原理），本步骤参照下图的Step 1。

此后再将N=4时间点的这个PV折现回0时点即可。本步骤参照下图的Step 2。

对应时间轴供参考。

yd08qg · 2021年05月29日

谢谢老师 图示很清晰

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