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政昭 · 2023年04月18日

第二步折现中，N的取值

  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.

第二步折现中为什么N是12不是13？

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已采纳答案

星星_品职助教 · 2023年04月19日

同学你好，

根据首笔现金流是在13时点收到，可知第一步折现要折现到12时点。

以上原理同正常后付年金的首笔现金流在1时点收到，折现需要折到0时点。

所以第二步折现时，从12时点折回到0时点是12期。

Zack · 2023年04月27日

1时末收到代表0-1坐标的第1年，13时末收到代表12-13坐标的第13年。应该是折现折了13次，为什么是12？

Zack · 2023年04月27日

是12 知道了。

米其林 · 2023年05月13日

还是没有搞懂为什么是折现12期，第一笔是在13时末收到的，往前数就是n=13呀

星星_品职助教 · 2023年05月15日

@米其林

参见原回复：“正常后付年金的首笔现金流在1时点收到，折现需要折到0时点。

就相当于正常的后付年金往后递延了12期，即正常后付年金的1时点=本题第13时点，正常后付年金的0时点=本题的12时点。


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