Question $5$ You are considering setting up a firm to produce electric cars. The cost of the project is $\backslash (\backslash$$ $30\backslash$mathrm$\{$M$\}\backslash )$ today. The demand for widgets is uncertain. It can be either high or low with equal probability. When the demand is high, cash flows in $\backslash ($ t$=1\backslash )$ are $\backslash (\backslash$$ $66\backslash$mathrm$\{$M$\}\backslash )$ and when the demand is low, cash flows in $\backslash (\backslash$mathrm$\{$t$\}=1\backslash )$ are $\backslash (\backslash$$ $34\backslash$mathrm$\{$M$\}\backslash ).$ The discount rate is $\backslash (10\backslash \%\backslash ).$ a$)$ What is the NPV of the project? b$)$ Suppose you can commission a study that tells you whether the demand for widgets will be high or low. The study takes one year to complete. That is$,$ if you commission the study you must decide in $\backslash ($ t$=1\backslash )$ whether to invest. If you invest, the cash flows will arrive in $\backslash ($ t$=2\backslash ).$ What is the maximum amount you are willing to pay for the study today?