Cummins Co$.$ is working on the launch of a new product. A marketing and economic analysis has been performed to study the market reaction to this new product and, as a result, a report has been elaborated. An extract of the report is provided below.

$"$As a consequence of the new product launch, Cummins $Co.$ is likely to get an immediate cash inflow of $$50,000.$ The company's cash flows are then likely to experience a constant growth of $2\%$ yearly for the subsequent $2$ years. We expect customer loyalty to increase and industry market competition to weaken sensibly$,$ and, as a result of this, the company should be able to get a perpetual cash inflow of $$300,000,$ starting from Year $3,$ and growing at the rate of $3\%$ yearly for all subsequent years. The appropriate discount rate is estimated to be $4\%."$

Construct the PV of the Cummins Co$.\text{'}$s cash flows as of time $O$ based on the extract reported above. Show all your calculations.