level 1 Quantitative的题 - 13年practice exam上的 exam1 morning session#20 investor, practice, successful, 题, 的

katheee

13年practice exam上的 exam1 morning session#20
TVM好像很简单 。。 大家不要笑我啊
这题我怎么没看懂 是不是永久以$25000给scholarship.. 不会算 看了答案也不太懂 ='( 杯具了！！！！

求助

题如下

A successful investor has decided to set up a scholarship fund for deserving students at her alma mater. Her plan is for the fund to be capable of awarding $25,000 annually in perpetuity. The first scholarship is to be awarded and paid out exactly four years from today. The funs will be deposited into an account immediately and will grow at a rate of 4%, compounded semiannually, for the foreseeable future. How much money must the investor donate today to fund the scholarship?

答案是：

先算了 EAR, 就是把r=4% 换成 annualized 4.04% 这个能懂，

问题来了， 之后用25000/4.04%=618811.88 这个我就开始不懂为啥呢。 是不是所有 perpetuity都这么算PV的？直接拿每期的pmt除以年利率？

之后就是把这个数当fv再用计算器discount到今天。这个ok懂。

hacklu

回复 1# katheee


其实这是dividen的preferred stock valuation model的一个应用, 把这里无限期的奖学金作当做从第4年开始每年一次的dividen就可以套用了。

P = D/k. 参见 Book 4 329页的公式表。