Splish 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 $$57,024.$ Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $$8,800.$ At the end of eight years, the company will sell the truck for an estimated $$27,700.$ 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. Steven Lewis, a new manager, has suggested that the company should not rely only on the payback approach but shouid 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. l