$($Engineering Economics$)$

O$\backslash$&A Manufacturing plans on purchasing a new machine for $\backslash (\backslash$$ $100,000\backslash )$ to automate one of its current manufacturing operations. It will cost an additional $\backslash (\backslash$$ $15,000\backslash )$ to have the new machine installed. With the new machine, O$\backslash$&A expects to save $\backslash (\backslash$$ $25,000\backslash )$ in annual operating and maintenance costs. The machine will last ten years with an expected salvage value of $\backslash (\backslash$$ $10,000\backslash ).$

$($a$)$ Draw the cash flow series for this investment plan.

$($b$)$ Using the conventional payback method, how long will it take to recover the investment $($plus installation cost$)?$

$($c$)$ If O$\backslash$&A$\text{'}$s interest rate is known to be $\backslash (17\backslash \%\backslash ),$ determine the discounted payback period.