PV = FV(1 + r)^–N 这个公式出自那个？

NO.PZ2017092702000009

问题如下：

A perpetual preferred stock makes its first quarterly dividend payment of $2.00 in five quarters. If the required annual rate of return is 6% compounded quarterly, the stock’s present value is closest to:

选项：

$31.

$126.

$133.

解释：

B is correct.

The value of the perpetuity one year from now is calculated as: PV = A/r, where PV is present value, A is annuity, and r is expressed as a quarterly required rate of return because the payments are quarterly.

PV = $2.00/(0.06/4) PV = $133.33.

The value today is (where FV is future value) PV = FV(1 + r)^–^N

PV = $133.33(1 + 0.015)^–⁴

PV = $125.62 ≈ $126

$< / s p a n > \frac{1}{2}$ $< / s p a n > \frac{1}{2}$

133.3的pv代表的是不是现在股票的价格？

126是季度的价格？

添加评论

1 个答案

已采纳答案

品职助教_七七 · 2023年11月29日

嗨，努力学习的PZer你好：

本题的首笔付款在5时点（即第5季度），所以按照公式PV=A/r得到的折现值就应折到4时点。故133.33是位于4时点的值。

由于题目最终要计算的是0时点的值，所以需要将133.33从4时点折现回0时点。126就是第二次折现后折回0时点的最终值。

-------

由于PV×（1+r）^n=FV，所以已知FV求PV时，可得PV=FV/（1+r）^n，这个式子可以以乘法的形式写成PV=FV×（1+r）^-n。

应用在本题中，就是133.33×（1+0.015）^-4 =125.62

上述时间轴和计算可参照下图：

----------------------------------------------
加油吧，让我们一起遇见更好的自己！

添加评论

1
回答
0
关注
170
浏览

我要回答关注问题

相关问题

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 请问这个两阶段模型，第一阶段是后续永续增长的利息折现到t=5，然后用P5再向前折现对吗？P5向前折现为什么不是5次方呢？

2024-09-14 20:00 1 · 回答

2024-09-05 20:17 1 · 回答

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 老师，此题困惑的地方是A perpetupreferrestomakes its first quarterly vinpayment of $2.00 in five quarters. 并不是表述为make its first quarterly vinpayment of $2 in the fifth quarter. 如何体会是从第五个季度开始付vin。

2024-09-01 10:00 1 · 回答

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 老师，题干的意思是不是前4季度均没有分红，直到第5个季度才分红2？

2024-07-20 10:49 1 · 回答

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 这里是写错了吗？算出的PV=133 下面继续算的时候133就成了FV?

2024-07-14 19:27 1 · 回答