Hermon Co$.$ is considering a four$-$year project that will require an initial investment of $$12,000.$ The base$-$case cash flows for this project are projected to be $$12,000$ per year. The best$-$case cash flows are projected to be $$19,000$ per year, and the worst$-$case cash flows are projected to be $$$$3,000$ per year. The company$$s analysts have estimated that there is a $50\%$ probability that the project will generate the base$-$case cash flows. The analysts also think that there is a $25\%$ probability of the project generating the best$-$case cash flows and a $25\%$ probability of the project generating the worst$-$case cash flows.

What would be the expected net present value $($NPV$)$ of this project if the project$$s cost of capital is $10\%?$

$$22,653$

$$19,698$

$$16,743$

$$21,668$