为何不是在0时刻分两种情况看

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=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？

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=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？