Ruby is considering opening a new business for a long$-$term care facility. The initial investment for the business is $$650,000,$ which includes constructing the housing unit and purchasing other assets. For tax purposes, the projected salvage value of all the assets is $$82,000.$ The government requires depreciating the assets using the straight$-$line method over the business's life of $15$ years. Ruby is trying to estimate the net cashflows after tax for this business. She has already figured out that the business will generate an annual after$-$tax cash inflow of $$85,000$ from the operation. She now needs your help to estimate the net cash inflow that she will receive from selling the facility's assets at the end of $15$ years. Ruby's required return is $8\%.$

Required:

$(1)$ Ruby estimates that, if the economic is booming at the end of the $15$ years, she can sell the assets for $$120,000.$ Assuming the tax rate of $30\%,$ what is the net after$-$tax cashflow Ruby will receive from selling her assets at the end of $15$ years? $($Please round your answer to the nearest dollar.$)$ $

$(2)$ If Ruby is able to sell her assets for $$120,000,$ as mentioned in $(1)$ above, what is the Internal Rate of Return $($IRR$)$ for Ruby's business? $($Please round your answer to two decimal points, i$.$e$.,$ XX$.$XX$\%)\%$

$(3)$ Ruby estimates that, if the economy is in recess at the end of the $15$ years, she can sell the assets for $$52,000.$ Assuming the tax rate of $30\%,$ what is the net after$-$tax cashflow Ruby will receive from selling her assets at the end of $15$ years? $($Please round your answer to the nearest dollar.$)$ $

$(4)$ If Ruby is able to sell her assets for $$52,000,$ as mentioned in $(3)$ above, what is the Net Present Value $($NPV$)$ for Ruby's business? $($Please round your answer to two decimal points$)$ $