Splish Auto Care is considering the purchase of a new tow truck. The garage currently has no tow truck, and the $$59,990$ price tag for

a new truck would be a major expenditure for it$.$ Carol Lewis, owner of the garage, has compiled the following estimates in trying to

determine whether she should purchase the tow truck:

Carol's good friend, Steven Lee, stopped by$.$ He is trying to convince Carol that the tow truck will have other benefits that Carol has

not even considered. First, he says, cars that need towing need to be fixed. Thus, when Carol tows them to her facility, her repair

revenues will increase. Second, he notes that the tow truck could have a plow mounted on it$,$ thus saving Carol the cost of plowing her

parking lot. $($Steven will give her a used plow blade for free if Carol will plow Steven's driveway.$)$ Third, he notes that the truck will

generate goodwill; that is$,$ people who are rescued by Carol and her tow truck will feel grateful and might be more inclined to use her

service station in the future or buy gas there. Fourth, the tow truck will have "Splish Auto Care" on its doors, hood, and back tailgate$-$a

form of free advertising wherever the tow truck goes.

Steven estimates that, at a minimum, these benefits would be worth the following:

Additional annual net cash flows from repair work

$$3,010$

Annual savings from plowing

$490$

Additional annual net cash flows from customer goodwill $970$

Additional annual net cash flows resulting from free advertising $,510$

The company's cost of capital is $9\%.$

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$($a$)$

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Calculate the net present value, ignoring the additional benefits described by Steven. $($If the net present value is negative, use either $a$

negative sign preceding the number e$.$g$.-45$ or parentheses e$.$g$.(45).$ For calculation purposes, use $5$ decimal places as displayed in the

factor table provided, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.5,275.)$

Net present value $

Should Carol purchase the tow truck?

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$($b$)$

Calculate the net present value, including the additional benefits suggested by Steven. $($If the net present value is negative, use either

a negative sign preceding the number e$.$g$.-45$ or parentheses eg$.(45).$ For calculation purposes, use $5$ decimal places as displayed in the

factor table provided, e$.$g$.1\mathrm{.}25124$ and final answer to $0$ decimal places, e$.$g$.5,275.)$

Net present value $

Should Carol purchase the tow truck?