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Basel Zhang · 2022年03月12日

做差出来的是option value吧，这题问的是NPV of project including the expansion option呀。

  1. CFA II
  2. Corporate Issuers

NO.PZ2018101501000018

问题如下：

Company M has a four-year project with an expansion option, which depends on the demand at the end of the 1st year. Whether demand is -high- or -low- in Years 1–4 will be determined during the first year. The probabilities of -high- or -low- demand are equal. The cost of capital is 12%. We should notice that the expansion option will not exist if the initial investment is not made. The detailed information of the project is given in the following tables.

The initial project:

Additional cash flows with the optional expansion project:

The NPV of the initial project without the real option is given to be -13.32, what’s the NPV of project including the expansion option?

选项：

A.

-$6.11 million

B.

$6.37 million

C.

$19.69 million

解释：

B is correct.

考点：Evaluating Projects with Real Options

解析：t=1时，如果是高需求，NPVexpansion = -100 + ∑t=13601.12t\sum_{t=1}^3\frac{60}{1.12^t}= $44.11 million，此时扩张期权会执行。如果是低需求，NPVexpansion = -100 +∑t=13301.12t\sum_{t=1}^3\frac{30}{1.12^t} = -$27.95 million，此时扩张期权不会执行。

t=0时，Expected NPVexpansion = 0.5*44.11/1.12 = $19.69 million

因此在考虑了扩张期权之后的NPV = -13.32 + 19.69 = $6.37 million

问题求NPV of project including the expansion option，而不是option value，为什么要做差呢？

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王琛_品职助教 · 2022年03月13日

嗨，从没放弃的小努力你好：


没有做差呀。。

解析最后一行的含义是：含权项目的 NPV = 不含权项目的 NPV + 期权价值

只不过不含权项目的 NPV 为负数 -13.32，期权价值为 19.69，所以二者相加为 6.37

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NO.PZ2018101501000018 问题如下 Company M ha four-yeprojewith expansion option, whipen on the manthe enof the 1st year. Whether manis -high- or -low- in Years 1–4 will terminering the first year. The probabilities of -high- or -low- manare equal. The cost of capitis 12%. We shoulnotiththe expansion option will not exist if the initiinvestment is not ma. The taileinformation of the projeis given in the following tables.The initiproject: Aitioncash flows with the optionexpansion project: The NPV of the initiprojewithout the reoption is given to -13.32, what’s the NPV of projeinclung the expansion option? A.-$6.11 million B.$6.37 million C.$19.69 million B is correct.考点Evaluating Projects with ReOptions解析t=1时，如果是高需求，NPVexpansion = -100 + ∑t=13601.12t\sum_{t=1}^3\frac{60}{1.12^t}∑t=13​1.12t60​= $44.11 million，此时扩张期权会执行。如果是低需求，NPVexpansion = -100 +∑t=13301.12t\sum_{t=1}^3\frac{30}{1.12^t}∑t=13​1.12t30​ = -$27.95 million，此时扩张期权不会执行。t=0时，ExpecteNPVexpansion = 0.5*44.11/1.12 = $19.69 million因此在考虑了扩张期权之后的NPV = -13.32 + 19.69 = $6.37 million 第一年可以确定高需求，要expan话，原项目的现金流也应该确定为60吧。这样原项目的NPV会不会因此而改变？然后再加expansion project的NPV。

2022-08-28 11:04 1 · 回答

NO.PZ2018101501000018 李老师上课是直接计算npv不要折现 cf0=0 cf1=-100 cf2-4=60 这样计算出来是-832.4 的npv 哪里计算错误？ 计算出来在乘以prob才是最终的option vlaue

2022-02-05 13:20 2 · 回答

NO.PZ2018101501000018 $6.37 million $19.69 million B is correct. 考点Evaluating Projects with ReOptions 解析t=1时，如果是高需求，NPVexpansion = -100 + ∑t=13601.12t\sum_{t=1}^3\frac{60}{1.12^t}∑t=13​1.12t60​= $44.11 million，此时扩张期权会执行。如果是低需求，NPVexpansion = -100 + ∑t=13301.12t\sum_{t=1}^3\frac{30}{1.12^t}∑t=13​1.12t30​ = -$27.95 million，此时扩张期权不会执行。 t=0时，ExpecteNPVexpansion = 0.5*44.11/1.12 = $19.69 million 因此在考虑了扩张期权之后的NPV = -13.32 + 19.69 = $6.37 million 既然在year1就已经知道现金流是60还是30了，为什么算期权价值还要乘0.5呢,直接按60算npv不可以吗？

2022-01-26 12:44 1 · 回答

NO.PZ2018101501000018 老师，在t1的时候进行比较，看NPV大于0的话，那我们就会行权，那么我们这时候只有在60的时候会行权，在30的时候就不行权了。 那为什么不就是把在60的t1=44.11/1.12，折现到0时间点，再加上原来的NPV就好了，而是还要再乘以0.5呢？ 这个0.5我不是很理解，麻烦老师一下。谢谢！

2021-10-04 20:03 1 · 回答