Orange Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck. The new truck would cost $$137,200.$ Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $$19,700.$ At the end of $8$ years, the company will sell the truck for an estimated $$42,600.$ Traditionally, the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than $50\%$ of the asset's estimated useful life. John Doe, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company's cost of capital is $8\%.$

Present value factor of cash inflows for $8$ years is $5\mathrm{.}747.$ Present value factor of cash inflow for salvage value at year $8$ is $0\mathrm{.}540.$

Round payback period to $1$ decimal place such as $1\mathrm{.}2.$

Round net present value to $0$ decimal place such as $20.$

For any negative net present value, use either a negative sign preceding the number as $-30$ or parentheses as $(30).$

Do NOT enter a dollar sign. For example, if you are typing $$10,000$ as your answer, answer should be typed as $10,000$ without any dollar sign.

$($a$)$ Compute the cash payback period and net present value of the proposed investment.