A company is considering a $$161,000$ investment in machinery with the following net cash flows. The company requires a $10\%$ return on its investments. $($PV of $$1,$ FV of $$1,$ PVA of $$1,$ and FVA of $$1)$

Note: Use appropriate factor$($s$)$ from the tables provided.

Year $1$ Year $2$ Year $3$ Year $4$ Year $5$

Net Cash Flow $$10,000$ $$27,000$ $$53,000$ $$40,000$ $$108,000$

$($a$)$ Compute the net present value of this investment.

$($b$)$ Should the machinery be purchased?