Singh Development Co$.$ is deciding whether to proceed with Project X$.$ The after$-$tax cost would be $$11$ million in Year $0.$ There is a $50\%$ chance that X would be hugely successful and would generate annual after$-$tax cash flows of $$7$ million per year during Years $1,2,$ and $3.$ However, there is a $50\%$ chance that X would be less successful and would generate after$-$tax cash flows of only $$1$ million per year for the $3$ years. If Project X is hugely successful, it would open the door to another investment, Project Y$,$ which would require an after$-$tax outlay of $$8$ million at the end of Year $2.$ Project Y would then be sold to another company netting $$16$ million after taxes at the end of Year $3.$ Singhs WACC is $9\%.$

a$.$ If the company does not consider real options, what is Project Xs expected NPV$?$

b$.$ What is Xs expected NPV with the growth option?

c$.$ What is the value of the growth option?