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phoebeqp · 2023年05月27日

No.PZ2015120604000013 类似题干的问题

  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.

之前也有一个说first payment in 5 quarters. 这道题是 first payment will happen at the end of 13th year,都是求PV。 所以怎么理解这个first payment与present的关系，这个first payment都是未来发生的情况？


这道题里面，如果first payment是在第十三年发生， 那么之前是没有现金流入的呀。at the beginning of the 13th year应该是时点零，算这个时点的PV的话，N等于8， I/Y=7，PMT=-20000，FV=0。然后这个PV等于十二年后的FV，再折现得到现在的PV？如果按照答案解析里面，开始算PV就是N=20，那等于说在开始12年都是有payment的，跟题干要求不一致呢，怎么理解呢？

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1 个答案

星星_品职助教 · 2023年05月27日

同学你好，

“... will be received for twenty years”指的是这是一笔20年期的年金。“The first payment is to be received at the end of thirteenth years”指的是这笔20年期的年金从13时点开始首笔付款。

所以，本题的现金流为：13时点前没有现金流流入，从13时点第一笔起，连续流入20笔。

换个角度讲，这就是正常的普通后付年金递延了12期。原来的0时点变成了现在的12时点，原来的1时点变成了现在的13时点。

故需折现两次。首次是计算这笔20年期年金的现值，由于是普通后付年金，所以首笔现金流发生在13时间点意味着现值要折现到12时间点。

然后再把这个值往前再折现12期到0时点，得到最终的现值。


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