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JustinSun · 2022年07月14日

如何求出第17年的PV

  1. CFA I
  2. Quantitative

NO.PZ2017092702000014

问题如下：

Grandparents are funding a newborn’s future university tuition costs, estimated at $50,000/year for four years, with the first payment due as a lump sum in 18 years. Assuming a 6% effective annual rate, the required deposit today is closest to:

选项：

A.

$60,699.

B.

$64,341.

C.

$68,201.

解释：

B is correct.

First, find the present value (PV) of an ordinary annuity in Year 17 that represents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack} = $50,000 × 3.4651 = $173,255.28. Then, find the PV of the annuity in today’s dollars (where FV is future value):

PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}

PV0 = $64,340.85 ≈ $64,341.

老师能解释一下吗，答案没看懂

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2 个答案

星星_品职助教 · 2022年12月01日

@zhouanne

1）这类题目的常规做法都是后付年金，不需要使用BGN计算；

2）如果后四年用BGN模式算，则计算出的是18时点的PV。第二步折现就变成FV=-183,650.5975，PMT=0，N=18，I/Y=6，CPT PV=64,340.8466

星星_品职助教 · 2022年07月14日

同学你好，

本题为两步折现的题型。

1）第一步折现

根据“ the first payment due as a lump sum in 18 years”可知这是首笔付款在18时间点的4年期年金。所以第一步折现时，现值是算到第17时间点的。

这就和正常的后付年金现金流从1时间点开始，但折现是折到0时间点是一样的。

正常按照4年期年金的做法按计算器：

PMT=50,000，N=4，I/Y=6，FV=0，CPT PV=-173,255.2806，这是在N=17时间点的PV。

2）第二步折现

第二步再把这个值折现回0时点计算PV，此刻这个值就是17时间点的FV了。计算器按法为FV=-173,255.2806，PMT=0，N=17，I/Y=6，CPT PV=64,340.8466

示意图如下，所有的二次折现问题都可以按照这个思路去做。

zhouanne · 2022年11月30日

老师，如果后四年的是用bgn模式计算的话 算出的pv是不是也是17时刻的pv啊 也就是前面18年的fv

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NO.PZ2017092702000014 问题如下 Granarents are funng a newborn’s future university tuition costs, estimate$50,000/yefor four years, with the first payment e a lump sum in 18 years. Assuming a 6% effective annurate, the requireposit toy is closest to: A.$60,699. B.$64,341. C.$68,201. B is correct. First, finthe present value (PV) of ornary annuity in Ye17 threpresents the tuition costs: 50,000[1−1(1+0.06)40.06]50,000{\lbrack\frac{1-\frac1{{(1+0.06)}^4}}{0.06}\rbrack}50,000[0.061−(1+0.06)41​​] = $50,000 × 3.4651 = $173,255.28. Then, finthe PV of the annuity in toy’s llars (where FV is future value):PV0=FV(1+0.06)17=173,255.28(1+0.06)17PV_0=\frac{FV}{{(1+0.06)}^{17}}=\frac{173,255.28}{{(1+0.06)}^{17}}PV0​=(1+0.06)17FV​=(1+0.06)17173,255.28​PV0 = $64,340.85 ≈ $64,341. 173255.28我能算出来 但为什么下一步时间是17 不是18

2023-09-23 20:31 1 · 回答

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2023-09-19 22:24 1 · 回答

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2023-08-21 16:57 1 · 回答

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2023-05-22 14:50 1 · 回答

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2023-05-21 17:37 1 · 回答