$(20$ points$)$ Your firm is considering a new project of manufacturing healthy chocolate bars, the details of information are given below:

A new machine costing $$5$ million is required $($at $t=0).$ In addition, the company needs to invest $$10$ million to build a new manufacturing plant $($at $t=0).$

The project requires an initial investment $($at $t=0)$ into net working capital equal to $10\%$ of predicted first$-$year sales, Subsequently, net working capital is $10\%$ of the predicted sales over the following years, and can be fully recovered at the end of the project $($end of year $4).$

The machine is being depreciated to zeno for tax purposes using the $5-$year straight$-$line method. The machine can be sold at the end of the project $($end of year $4)$ for $$800,000.$

The plant is being depreciated to zero for tax purposes using the $20-$year straightline method. The plant can be sold at the end of the project $($end of year $4)$ for $$8\mathrm{.}5$ million.

Sales of chocolate bars arc expected to be $$50$ million per year for the next four years. The company expects total manufacturing costs to be $40\%$ of sales each year, and the employec annual costs $($salary and related costs$)$ for this project to be $$10$ million. In addition, the annual advertising costs of the company will increase from $$9\mathrm{.}6$ million to $$16$ million.

The corporate tax rate is $35\%.$

The company has a target debt$-$cquity ratio of $0\mathrm{.}5,$ its cost of equity is $15\%,$ and its cost of debt is $8\%.$

$(1)$ What is the after$-$tax salvage value of plant and machine, respectively?

$(2)$ Estimate the annual free cash flow from this project

$(3)$ This new project is somewhat riskier than a typical project for the company Management uses the subjective approach and applies an adjustment factor of $+2\%$ to account for this increased riskiness. Calculate the appropriate discount rate to use when evaluating the new project.

$(4)$ Estimate the NPV of this project