问题如下图：
选项：
A. 
B. 
C. 
解释：
可否理解为这题算74.82并没有什么实际的意义，真正考试只算行权时候的npv就好？
maggie_品职助教 · 2019年02月04日
是的，这里只是用于比较（但万一问到，你也要会算）。应该是-74.82。我们会尽快修改后台数据。
新年快乐~
我想静静 · 2019年03月28日
老师为什么我可以理解这里是一个call option所以只有正的npv的时候行权，那么讲义P42上那个abandonment option里为什么要算两种可能性的平均数呢？望解惑，谢谢
maggie_品职助教 · 2019年03月29日
这里也是两种情况啊，也需要平均啊，只不过需求低，就不扩张，不扩张也就没有现金流，所以只有需求高的一笔再乘0.5. 而放弃项目那道题，放弃或不放弃都有现金流产生。
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？