The director of RCM Inc. is considering launching a new product. The initial investment in equipment and other facilities is $$800,000.$ The project is expected to have a lifespan of $5$ years. First$-$year revenue is projected to be $$600,000,$ and the revenue is expected to remain the same throughout the project's duration. Operating costs for 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 beginning 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 cost of capital depreciation rate 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 determine whether the company should undertake this project or not. give me have i mistake a tihonk becouse you take $2$ time the operation cost $(200000)$

Let's go through each step:

$1$: Calculate Annual Cash Flows

Revenue per year: $$600000$

Operating costs per year: $$200000$

Net revenue per yea $=$ Revenue $-$ Operating Costs

$=$$$600,000-$$$200,000$

$=$$$400,000$

The net revenue remains constant throughout the project's lifespan.

$2$: Discount Rate and Depreciation

Discount Rate $(r)=9\%$

Depreciation Rate $=20\%$

$3$: Calculate Depreciation and Taxable Income

$1.$ Depreciation per year $"2.$ Taxable Income per year $=$ Net Revenue $-$ Depreciation

$=$$$400,000-$$$160,000$

$=$$$240,000$

$4$: Calculate Taxes

$1.$ Tax per year $\{\begin{array}{ccc}\text{:}[=& \text{T}\text{a}\text{x}\text{R}\text{a}\text{t}\text{e}**\text{T}\text{a}\text{x}\text{a}\text{b}\text{l}\text{e}\text{I}\text{n}\text{c}\text{o}\text{m}\text{e}& ]\\ =30\%\text{\$}240,& 000\\ =\text{\$}72,& 000\mathrm{.}00\end{array}$

$5$: Calculate Net Cash Flows

Net Cash Flow per year $=$ Net Revenue $-$ Operating Costs $-$ Taxes

$=$$$400,000-$$$200,000-$$$72,000$

$=$$$128,000$

$6$: Include Initial Investment and Salvage Value

Initial Investment: $$800000$

Salvage Value $($at the end of $5$ th year$)$: $$150000"$