问题如下图：
选项：
A. 
B. 
C. 
解释：
maggie_品职助教 · 2018年01月10日
1.答案里面第二个公式应该等于-74.28
2.扩张项目：该扩张项目是否进行取决于第一笔投资在第一年的demand是否是“high”，那么该扩张项目发生的概率只有0.5. 如果发生，那么t=1再投资190，t=2才获得第一笔现金流，因此到第10年一共9笔现金流。
3.如果还有不明白的地方，建议再听下基础课
regina929 · 2018年01月10日
非常感谢助教快速的回答，但是对于答案中，在T=1时刻，为何会有190的outlay 则仍然没能理解，继续请教，谢谢！
lulu · 2018年03月27日
因为是扩张项目，所以要继续像在0时刻一样 重新投资
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!
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=191.10t40=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=191.10t20=‐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=1.1010.50(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？
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=191.10t40=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=191.10t20=‐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=1.1010.50(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.为何不是在0时刻看，有两种情况 需求低，只投了190，不追加投资，npv为负 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
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！
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=191.10t40=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=191.10t20=‐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=1.1010.50(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？