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xiao15 · 2021年11月06日

老师这个题没明白能画个图解释一下吗

  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.

老师这个题没明白能画个图解释一下吗

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1 个答案

星星_品职助教 · 2021年11月06日

同学你好，

本题核心有两点：

1. An annuity of $2,000 per year WILL be received for twenty years。有一笔持续20年的年金“即将”被收到

2. The first payment is to be received at the end of thirteenth years。这笔“即将”发生的年金的首笔现金流发生在第13年末（即N=13时间点）

所以是从N=13这个时间点开始有连续20笔的现金流。涉及到两步折现，首先计算年金的现值（折现到N=12时间点，即答案解析中的第一步），再将年金现值折现回0时间点（答案解析中的第二步）即可。

要注意的是首笔现金流发生在13时间点说明折现就要折到12时间点，而不是13时间点本身。

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。

 

 

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