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雷雷12322 · 2023年02月11日

还是没看明白答案解释

  1. CFA I
  2. Quantitative

NO.PZ2018062016000014

问题如下：

Tom has twin daughters Lucy and Lily at 12 years old. Six years later, both will study in a famous university in California for four years with a tuition fee of $6,000 paid at the beginning of each year per person. Assume the annual discount rate is 5%, today Tom should prepare:

选项：

A.

$16,670

B.

$33,340

C.

$31,753

解释：

B is correct. Six years later, Tom will pay tuition fee of $12,000 each year and last for 4 years, as he has two daughters. The payment is paid in the front, therefore set the calculator at BGN mode and input: N=4, I/Y=5%, PMT=12,000, FV=0, then PV=44678.98. The value of tuition fund at year 6 is $44,678.98, so the present value is $44,678.98/(1+5%)6=$33,340.

6年后为什么不是19那个点开始第一笔现金流到22节点呢？这种题目一直分不清这中间的节点和具体N是怎么算出来的，一次都没做对过，有没有容易理解的方法

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1 个答案

星星_品职助教 · 2023年02月12日

同学你好，

本题的时间点没有固定的描述规律。但题目很直白，相当于目前是0时点，6年后就是6时点付首笔现金流（也可以理解为现在是12时点，6年后是18时点，不影响解题）

CFA题目的时点都很简单，不需要很复杂的分析，简单加减就可以。几乎不会涉及年初或年末等数字游戏。

------

确定首笔付款在6时点后，有两种解题思路：

1）按照题干说的BGN模式，将四笔学费现金流折现到6时点，再往前折6期，得到现值；

2）不需要去管是什么年金，反正首笔现金流在6时点，四笔现金流已经确定为了6、7、8、9四个时点。直接将这四笔现金流折现到5时点就可以，然后再往前折现5期。

可以两种方式都尝试一下，结果一定是一样的。大部分人会因为题干的描述而选择做法一，但实际上做法二更为简单和常用。

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如前所述，本题的时间点没有固定的描述规律。但很多题目有如下的规律可记忆：

1）....make the first payment in six years。这个描述指得就是首笔现金流在6时点发生；

2）....starting from 6 years.这个描述同样也是指首笔现金流在6时点发生


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