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Zoeyxchen · 2022年02月22日

永续年金PV

题目: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:

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 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:为什么通过公式PV=A/r算得PV后还要除以(1 + 0.015)4  ?


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星星_品职助教 · 2022年02月22日

同学你好,

由于首笔永续年金的现金流是在N=5时间发生的(...makes its first quarterly dividend payment of $2.00 in five quarters),所以此时的PV=A/r是计算到N=4时点的。

以上的原理和正常的永续年金现金流从1时点开始,计算现值计算到0时点是一样的。

所以还需要再将4时点的PV折现到0时点。

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