Dernham 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 $$255,000,$ but if demand turns out to be weak, the facility will generate annual cash flows of only $$130,000.$ Dernham 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 $13\%,$ what will be the expected net present value $($NPV$)$ of this project?

$-$$$47,752$

$-$$$34,108$

$-$$$45,478$

$-$$$31,835$

Dernham 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 $$250,000$ in years $2$ and $3$ of the project.

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

$$31,429$

$$29,785$

$$33,094$

$$78,572$

What will be the value of Dernham Inc.$$s flexibility option?