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Spencer · 2020年03月14日

问一道题：NO.PZ2018101501000018

  1. CFA II
  2. Corporate Issuers

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

老师请问，19.69 million，-13.32million, 这里的两个数值19.69和-13.32 如果带入讲义的公式Project NPV=NPV(based on DCF alone)-Cost of options+Value of options应该如何带入呢？Cost of options应该是0吧？

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1 个答案

Debrah_品职答疑助手 · 2020年03月15日

同学你好。这道题目的期权价值value of option=19.69，也就是因为扩张期权给整个项目带来增加了的NPV；-13.32就是原有旧项目的NPV，cost of option=0.

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

2022-03-12 19:56 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