问题如下图：
选项：
A. 
B. 
C. 
解释：
请问老师，如果是后付年金的模式，那么应该是第五季度末付款，算出来PV应该是第五季初也就是第四季末的PV，答案公式应该改为PV=133.33*(1+0.015)的负五次方，和答案不符。
星星_品职助教 · 2019年09月26日
同学你好，
这道题是后付年金的模式，也是N=5的时候付第一笔年金，这些你理解的都没问题。但需要注意的是，计算永续年金的时候，PV是算到前一期也就是N=4时期的。也就是计算出来的133.33的时间点是N=4.
这里面涉及到一个非常之重要的概念，就是永续年金折现的时候，虽然公式的形式是P=D/r，但是这个D实际上是D1的概念。只是因为所有的D都相同，才不显示角标。
换句话说，后续永续年金的第一笔现金流发生在N=5，那么这个N=5的Dividend就相当于刚刚上面提到的“D1”，折现算出来的PV是折到N=4时刻的，所以继续往前折现的时候才是-4次方。
所以就这道题本身而言，需要掌握的就是永续年金的折现时间点，及实际公式其实是P或PV=D1/r。
但这个理念其实应用更多的是在权益里面，往往会给你current dividend也就是D0的概念，但是实际上真正折现时候要用的是D1，也就是forecasted dividend。无论是永续年金，还是DDM模型都是如此，所以这个折现用的是D1而不是D0的理念非常重要，需要掌握。
加油
NO.PZ2017092702000009 问题如下 A perpetupreferrestomakes its first quarterly vinpayment of $2.00 in five quarters. If the requireannurate of return is 6% compounquarterly, the stock’s present value is closest to: A.$31. B.$126. C.$133. B is correct. The value of the perpetuity one yefrom now is calculateas: PV = A/r, where PV is present value, A is annuity, anr is expressea quarterly requirerate of return because the payments are quarterly. PV = $2.00/(0.06/4) PV = $133.33. The value toy is (where FV is future value) PV = FV(1 + r)–NPV = $133.33(1 + 0.015)–4 PV = $125.62 ≈ $126 /sp12 /sp\frac12 /sp21 The value toy is (where FV is future value) PV = FV(1 + r)–NPV = $133.33(1 + 0.015)–4
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