The Z$90$ project being considered by Steppingstone Incorporated $($SI$)$ has an up$-$front cost of $$250,000.$ The project's subsequent cash flows are critically dependent on whether another of its products, Z$45,$ becomes an industry standard. There is a $50\%$ chance that the Z$45$ will become the industry standard, in which case the Z$90\text{'}$s expected cash flows will be $$110,000$ at the end of each of the next $5$ years. There is a $50\%$ chance that the Z$45$ will not become the industry standard, in which case the Z$90\text{'}$s expected cash flows will be $$25,000$ at the end of each of the next $5$ years. Assume that the cost of capital is $12\%.$

Refer to data for Steppingstone Incorporated. Based on the above information, what is the Z$90\text{'}$s expected net present value?

a$.$ $$45,965$

b$.$ $$20,004$

c$.$ $$15,303$

d$.$$$6,678$

e$.$$$3,251$