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欢欢 · 2021年11月03日

对比前面有一题，这题不是说了in one month吗？那算出来的400不需要在按T=1时的FV折回去么？

  1. CFA I
  2. Quantitative

NO.PZ2017092702000012

问题如下：

A sweepstakes winner may select either a perpetuity of £2,000 a month beginning with the first payment in one month or an immediate lump sum payment of £350,000. If the annual discount rate is 6% compounded monthly, the present value of the perpetuity is:

选项：

A.

less than the lump sum.

B.

equal to the lump sum.

C.

greater than the lump sum.

解释：

C is correct.

As shown below, the present value (PV) of a £2,000 per month perpetuity is worth approximately £400,000 at a 6% annual rate compounded monthly. Thus, the present value of the annuity (A) is worth more than the lump sum offer. A = £2,000 r = (6%/12) = 0.005 PV = (A/r) PV = (£2,000/0.005) PV = £400,000

the present value of the“perpetuity”--永续年金，带入永续年金的公式 PV=A/r即可：

A=2,000， r=(6%/12)=0.005， PV=A/r=400,000

如题。。。。。。。。。

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1 个答案

星星_品职助教 · 2021年11月04日

同学你好，

对于普通的永续年金而言，现金流是从1时点开始永续进行。求现值即折回0时点。

本题的“...with the first payment in one month”即指的是现金流从1时点开始进行，所以使用P=A/r的公式得到的现值也就是在0时点的，并非在1时点，也不需要再二次折现。

需要注意的是这种描述即说明了是以月度为期间，所以对应的r也需要是月利率，即6%/12.

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