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Flying马 · 2022年07月13日

关于第一步折现

  1. CFA I
  2. Quantitative

NO.PZ2015120604000013

问题如下：

An annuity of $2,000 per year will be received for twenty years. The first payment is to be received at the end of thirteenth years. Assume the discount rate is 7% over next years, calculate the today's present value of the annuity

选项：

A.

$8,792.

B.

$9,408.

C.

$10,066.

解释：

B is correct.

  1. Calculate the PV of annuity at the end of the twentieth years : N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV = 21,188.03. ;
  2. Calculate the PV today: N = 12; PMT = 0; FV = -21,188.03; I/Y = 7; CPT PV = 9,407.74.

老师  是不是可以这么理解   因为第一步计算里   第13年已经开始收到第一笔pmt2000  n=20 fv=0  说明最后一次收到2000是第32年   所以现值折到第12年   否则第13年的第一笔2000就是没参与折现

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星星_品职助教 · 2022年07月13日

同学你好，

这类两次折现的题目的第一步折现按照正常后付年金的思路去理解就可以了，不需要考虑的很复杂。

回忆一下上课时讲过的普通后付年金，现金流是从1时点开始的，但折现是折到0时点（与此对比，先付年金的现金流是从0时点开始的，折现也是折到0时点）

把上面这个逻辑套用到第一步折现上，此时现金流是从13时点开始的（相当于上面例子中的“1时点”），所以折现就要折现到12时点（相当于上面例子中的“0时点”）。

此后第二步折现再把12时点的值折现回0时点就可以了。

星星_品职助教 · 2022年07月13日

@Flying马

好的，学习加油~

Flying马 · 2022年07月13日

好的懂了谢谢您

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