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安在 · 2022年08月22日

时间节点不清楚

  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年后的年初需要交资金，那么在时间轴上体现为：17岁末18岁初？ 折算到12岁（today）是指12岁初还是末呢 这个题意现金流怎么把控，（此外延伸问一下其他CFA考试中涉及的现金流末尾一般是）

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星星_品职助教 · 2022年08月22日

同学你好，

“at 12 years old”指的就是时间轴上的12时间点本身。“Six years later”指的就是时间轴上的12+6=18时间点本身。

即此时学费是从18这个时间点开始付第一笔。

在这背景下，无论学费是什么年金，此时四笔现金流的时间点都已经确定了就是18,19,20,21。

之后可以根据四笔现金流的时点去灵活处理，例如可以按后付的方式折现到17时间点。然后再折现到12时点，此时N=5；

也可以按照先付年金的模式，将四笔学费现金流折现到18时间点本身，然后再折到12时间点，此时N=6。两种方法的结果是一样的。

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CFA题目中，如果题干明确标明了是先付，才按照先付处理。否则都按照后付处理。

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