splish Inc. wants to replace its current equipment with new high$-$tech equipment. The existing equipment was purchased five years ago at a cost of $$126,000.$ At that time, the equipment had an expected life of $10$ years, with no expected salvage value. The equipment is being depreciated on a straight$-$line basis. Currently, the market value of the old equipment is $$44,200.$

The new equipment can be bought for $$174,010,$ including installation. Over its $10-$year life, it will reduce operating expenses from $$192,300$ to $$146,600$ for the first six years, and from $$204,900$ to $$193,500$ for the last four years. Net work ng capital requirements will also increase by $$21,000$ at the time of replacement.

It is estimated that the company can sell the new equipment for $$24,400$ at the end of its life. Since the new equipment$$s cash flows are relatively certain, the project$$s cost of capital is set at $10\%,$ compared with $15\%$ for an average$-$risk project. The firm$$s maximum acceptable payback period is five years.

$($a$)$Calculate the initial investment amount.

$($b$)$ Calculate the project$$s cash payback period.

$($c$)$ Calculate the project$$s net present value.

$($d$)$ State whether or not the company should replace its current equipment with the new high$-$tech equipment.