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VincentShell · 2022年11月23日

如题,请老师解答一下。

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.

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.


题目中说The first payment is to be received at the end of thirteenth years. 的意思不是说是在13年结束时会收到。那不就是说明13年结束是在14年年初。为什么用的是N=12? 不需要用到BGN吗?为什么不能先算出第12年的,然后再算出后面的然后再加在一起?


1 个答案

星星_品职助教 · 2022年11月24日

同学你好,

“The first payment is to be received at the end of thirteenth years”指的是首笔付款发生在13这个时间点上,理解成13年末也可以。这就相当于一笔递延的普通年金(首笔现金流发生在1时间点上)。所以折现也需要同样的递延,普通年金折现到0时点,该笔年金就需要折现到12时间点。

所以二次折现的时候还需要往前再折现12期。

以上是需要掌握的常规解题思路,不需要使用BGN模式,按照最简单的普通年金计算即可。

---------

下面为了解即可的内容:

如果认为首笔付款处于14年年初,想使用先付年金,则此时相当于认定13时点是新的“0时点”,此时的计算为BGN模式, N = 20; I/Y = 7; PMT = -2,000; FV = 0; CPT PV =22,671.1905。此时这个值是在13时点的值,所以需要再折现13期到0时点,即除以1.07的13次方,得到相同的答案为9,407.7380.

上述方法容易出错,从考试的角度来讲就是一种错误的方法。

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