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十个馒头 · 2022年07月09日

这是一道后付年金还是先付年金的题目 这两者怎么判断呢

  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.

这是一道后付年金还是先付年金的题目 这两者怎么判断呢

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1 个答案

星星_品职助教 · 2022年07月10日

同学你好，

这道题的题型是两次折现，这类题型统一的解题思路是根据第一笔现金流发生的时间，用后付年金的方法得到第一个折现值；然后再把这个值二次折现到0时点。

以本题为例，根据The first payment is to be received at the end of thirteenth years和....for twenty years，可知这是从12时间点开始的，首笔现金流发生在13时间点的，一共有20期的后付年金。

这里12时间点就相当于此后付年金的“0时间点”，13时间点（即首笔现金流发生的时间点）就相当于此后付年金的“1时间点”。

所以此时第一次折现需要折到12时间点，然后再将这个算出来的折现值二次折现到0时间点。


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