Sheffield Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck $($not the least of which is that it runs$).$ The new truck would cost $$57,270.$ Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $$8,300.$ At the end of eight years, the company will sell the truck for an estimated $$28,200.$ Traditionally, the company has used a general rule that it should not accept a proposal unless it has a payback period that is less than $50\%$ of the asset's estimated useful life. Chris Jackson, a new manager, has suggested that the company should not rely only on the payback approach but should also use the net present value method when evaluating new projects. The company's cost of capital is $8\%.$

$($a$)$

Calculate the cash payback period and net present value of the proposed investment. $($If the net present value is negative, use either a negative sign preceding the number e$.$g$.-45$ or parentheses e$.$g$.(45).$ Round cash payback period to $2$ decimal place, e$.$g$.12\mathrm{.}51.$ For calculation purposes, use $5$ decimal places as displayed in the factor table provided, e$.$g$.1\mathrm{.}25124$ and net present value to $0$ decimal places, e$.$g$.5,275.)$

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Cash payback period years

Net present value $