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Stella · 2021年04月17日

为何不是在0时刻分两种情况看

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NO.PZ201601200500000804

问题如下:

4. What is the NPV (C$ millions) of the optimal set of investment decisions for Society Services including the expansion option?

选项:

A.

6.34.

B.

12.68.

C.

31.03.

解释:

B is correct.

Assume we are at time = 1. The NPV of the expansion (at time 1) if demand is "high" is

NPV=190+t=19401.10t=C$40.361millionNPV=-190+\sum_{t=1}^9\frac{40}{1.10^t}=C\$40.361million

The NPV of the expansion (at time 1) if demand is "low" is

NPV=190+t=19201.10t=C$74.820millionNPV=-190+\sum_{t=1}^9\frac{20}{1.10^t}=‐C\$74.820million

The optimal decision is to expand if demand is "high" and not expand if "low."

Because the expansion option is exercised only when its value is positive, which happens 50 percent of the time, the expected value of the expansion project, at time zero, is

NPV=11.100.50(40.361)=C$18.346millionNPV=\frac1{1.10}0.50(40.361)=C\$18.346million

The total NPV of the initial project and the expansion project is

NPV = –C$5.663 million + C$18.346 million = C$12.683 million

The optional expansion project, handled optimally, adds sufficient value to make this a positive NPV project.

为何不是在0时刻看,有两种情况
  1. 需求低,只投了190,不追加投资,npv为负
  2. 追加投资190,需求高,npv为正
然后将两种情况各0.5加权求和?现在答案只考虑了第二种情况加权0.5,为何不第一种情况也加权0.5加在一起呢
1 个答案

王琛_品职助教 · 2021年04月18日

嗨,努力学习的PZer你好:


你说的方法是可以的,但是解析提供的算法,并不是你说的算法中的第二种情况,解析的算法是先单独计算不考虑期权时的 NPV,然后单独计算期权价值,两个加总,就是考虑期权时的 NPV

我把你说的情况的现金流和计算器按法附在下面,你会发现和解析不是一种算法


第一种情况,计算器按法

CF0 = -190

C01 = 20,F01 = 10

I = 10

NPV(需求低) = -67.108658


第二种情况,计算器按法

CF0 = -190

C01 = -190+40=-150,F01 = 1

C02 = 40+40=80,F02 = 9

I = 10

NPV(需求高) = 92.474459


所以,考虑期权的 NPV = 0.5 x (-67.108658 + 92.474459) = 12.682901


这道题还有一种做法,就是如果考虑期权,先把未来现金流确认好。这里的现金流,是指同时考虑原有现金流,和扩张现金流之后的现金流。相当于把你前面考虑的两种情况,综合考虑计算:

CF0 = -190 (t=0 时刻,原有现金流的期初投入)

C01 = 30+(-190/2)= -65 (原有期间现金流 30+扩张现金流的期初投入)

F01 = 1 (t=1 时刻)

C02 = 30+(40/2)= 50 (原有期间现金流30+扩张期间现金流20)

F02 = 9 (t=2 至 t=10,共 9 期现金流)

I = 10

NPV = 12.682901


不管用什么方法,核心都是要确认好各期现金流。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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NO.PZ201601200500000804 请问行权的时候不就是最优价值了吗?为什么最后还要加上没有option的原始NPV呢?谢谢!

2021-10-23 10:56 1 · 回答

NO.PZ201601200500000804 12.68. 31.03. B is correct. Assume we are time = 1. The NPV of the expansion (time 1) if manis \"high\" is NPV=−190+∑t=19401.10t=C$40.361millionNPV=-190+\sum_{t=1}^9\frac{40}{1.10^t}=C\$40.361millionNPV=−190+∑t=19​1.10t40​=C$40.361million The NPV of the expansion (time 1) if manis \"low\" is NPV=−190+∑t=19201.10t=‐C$74.820millionNPV=-190+\sum_{t=1}^9\frac{20}{1.10^t}=‐C\$74.820millionNPV=−190+∑t=19​1.10t20​=‐C$74.820million The optimcision is to expanif manis \"high\" annot expanif \"low.\" Because the expansion option is exerciseonly when its value is positive, whihappens 50 percent of the time, the expectevalue of the expansion project, time zero, is NPV=11.100.50(40.361)=C$18.346millionNPV=\frac1{1.10}0.50(40.361)=C\$18.346millionNPV=1.101​0.50(40.361)=C$18.346million The totNPV of the initiprojeanthe expansion projeis NPV = –C$5.663 million + C$18.346 million = C$12.683 million The optionexpansion project, haneoptimally, as sufficient value to make this a positive NPV project.请问老师,40/1.1^t t=9,这个计算器怎么按啊?还是要一个一个按,按9个?

2021-07-29 16:45 2 · 回答

为什么现金流要乘以0.5呢?即使PROBABILITY是50%,但是这个不是应该假设已经是OPTIMAL了吗,为什么还需要考虑概率。谢谢!

2020-06-04 11:09 1 · 回答

12.68. 31.03. B is correct. Assume we are time = 1. The NPV of the expansion (time 1) if manis \"high\" is NPV=−190+∑t=19401.10t=C$40.361millionNPV=-190+\sum_{t=1}^9\frac{40}{1.10^t}=C\$40.361millionNPV=−190+∑t=19​1.10t40​=C$40.361million The NPV of the expansion (time 1) if manis \"low\" is NPV=−190+∑t=19201.10t=‐C$74.820millionNPV=-190+\sum_{t=1}^9\frac{20}{1.10^t}=‐C\$74.820millionNPV=−190+∑t=19​1.10t20​=‐C$74.820million The optimcision is to expanif manis \"high\" annot expanif \"low.\" Because the expansion option is exerciseonly when its value is positive, whihappens 50 percent of the time, the expectevalue of the expansion project, time zero, is NPV=11.100.50(40.361)=C$18.346millionNPV=\frac1{1.10}0.50(40.361)=C\$18.346millionNPV=1.101​0.50(40.361)=C$18.346million The totNPV of the initiprojeanthe expansion projeis NPV = –C$5.663 million + C$18.346 million = C$12.683 million The optionexpansion project, haneoptimally, as sufficient value to make this a positive NPV project.扩张项目的PVCF1已经得出,为什么折现一期的PV就是NPV?能不能用老师说的画图作差法再一下?

2020-03-30 06:03 1 · 回答