$15.$ ZED Inc. is evaluating a new machine. The machine requires an initial cash outlay of $$20,000$ and will generate the following after$-$tax cash inflows over the

next four years:

Cash Flows

Year $1$ $$6,000$

Year $2$ $$7,000$

Year $3$ $$8,000$

Year $4$ $$9,000$

The machine will have a salvage value of $$4,000.$ If the machine is sold at the end of Year $4,$ calculate its NPV$.$ ZED$$s cost of capital is $10\%.$