The director of RCM Inc. is considering launching a new product. The initial investment in equipment and other facilities is $$800,000.$ The management has been thinking about launching this new product for a while. They have made several trips to different cities to understand the potential demand, and have finally decided to launch this product. These trips have cost the company about $$50,000$ so far. The project is expected to have a lifespan of $5$ years. The revenue for the first year is expected to be $$600,000,$ and the revenue is expected to remain the same for the duration of the project. The operating costs of the project are estimated at $$200,000$ per year. If the project is undertaken, the total investment in net working capital will increase by $$100,000$ at the start of the project, but the company will recover $50\%$ of its investment in net working capital at the end of the $5$th year. The tax rate is $30\%,$ and the depreciation rate on capital cost is $20\%.$ The equipment can be sold at the end of the project for $$150,000.$ The appropriate discount rate for the project is $9\%.$ Calculate the NPV to see if the company should undertake this project or not.

$(((!!!$ provide all the necessary information for this exercise step by step $!!!$ DO not use ai$,$ i need clear explanation for each steps taken do not let me assume how the results was found it needs to be proven, literally please, than you in advance$)))$

min$=$ minimum

Ps: This formula is used to calculate the tax savings related to depreciation : $(($ C$*$dTc$/$k$+$d $)*(1+1\mathrm{.}5$k$)/(1+$k $))-($min$($C$,$ S$)$dTc $/$ k$+$d$)*(1/(1+$k$)^$n$))$

$($C$)$ is the total capital cost of the asset

$($d$)$ is the CCA rate for this asset category

$($Tc$)$ is the company$$s marginal tax rate

$($k$)$ is the discount rate

$($S$)$ is the salvage value

$($n$)$ is the asset$$s lifespan in years