Randall and Arts Inc. is looking at investing in a production facility that will require an initial investment of $$500,000.$ The facility will have a three$-$year useful life, and it will not have any salvage value at the end of the project$$s life. If demand is strong, the facility will be able to generate annual cash flows of $$260,000,$ but if demand turns out to be weak, the facility will generate annual cash flows of only $$135,000.$ Randall and Arts Inc. thinks that there is a $50\%$ chance that demand will be strong and a $50\%$ chance that demand will be weak.

If the company uses a project cost of capital of $12\%,$ what will be the expected net present value $($NPV$)$ of this project?

$-$$$16,665$

$-$$$14,101$

$-$$$25,638$

$-$$$26,920$

Randall and Arts Inc. could spend $$510,000$ to build the facility. Spending the additional $$10,000$ on the facility will allow the company to switch the products they produce in the facility after the first year of operations if demand turns out to be weak in year $1.$ If the company switches product lines because of low demand, it will be able to generate cash flows of $$255,000$ in years $2$ and $3$ of the project.

What is the expected NPV of this project if Randall and Arts Inc. decides to invest the additional $$10,000$ to give themselves a flexibility option? $($Note: Do not round your intermediate calculations.$)$

$$32,215$

$$54,900$

$$80,538$

$$49,410$

What will be the value of Randall and Arts Inc.$$s flexibility option?