A project with an up$-$front cost at t $=0$ of $$1500$ is being considered by a cloud computing firm $$ Upath Corporation. $($All dollars in this problem are in thousands.$)$ The project's subsequent cash flows are critically dependent on costumers$$ demand. There is a $70\%$ chance that the demand will be high, in which case Upath's expected cash flows will be $$500$ at the end of each of the next seven years $($t $=1$ to $7).$ There is a $30\%$ that the demand will be low, in which case the expected cash flows will be only $$25$ at the end of each of the next seven years $($t $=1$ to $7).$ Upath will know for sure one year from today about the customers$$ demand.

Upath$$s weighted average cost of capital is $10\%.$ The risk free rate is $6\%.$

What is the project$$s expected net present value?

Upath is considering whether to make the investment today or to wait a year to find out about the customers$$ demand. If it waits a year, the project's up$-$front cost at t $=1$ will remain at $$1,500,$ the subsequent cash flows will remain at $$500$ per year if the demand is high and $$25$ per year if the demand is low. However, if Upath decides to wait, the subsequent cash flows will be received only for six years $($t $=2...7).$

Use decision$-$tree analysis to determine whether Upath should proceed with the project today or wait a year before deciding. What is the value of this option to delay if any? $$discount the cost of the project at risk$-$free rate when applicable$)$

The CFO wants to use the Black$-$Scholes model to estimate the value of the option to delay. Specify the value of X and T in the Black$-$Sholes formula.

What would be the value of P in the Black$-$sholes formula?

Estimate the variance sigma squared in the Black$-$Sholes formula.