Ivanhoe Inc. wants to purchase a new machine for $$48,200,$ excluding $$1,500$ of installation costs. The old machine was purchased $5$ years ago and had an expected economic life of $10$ years with no salvage value. The old machine has a book value of $$2,000,$ and Ivanhoe Inc. expects to sell it for that amount. The new machine will decrease operating costs by $$10,000$ each year of its economic life. The straight$-$line depreciation method will be used for the new machine for a $6-$year period with no salvage value.

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$($a$)$

Determine the cash payback period. $($Round cash payback period to $2$ decimal places, e$.$g$.10\mathrm{.}53.)$

Cash payback period years

$($b$)$

Determine the approximate internal rate of return. $($Round answer to $0$ decimal places, e$.$g$.13\%.$ For calculation purposes, use $5$ decimal places as displayed in the factor table provided.$)$

Internal rate of return

$\%$