Brougham Packaging is considering expanding its production capacity by purchasing a new machine, the XDC$-450.$ The firm has just spent $$50,000$ on a feasibility study to analyse the decision to buy the XDC$-450.$ The cost of this new machine is $$3\mathrm{.}5$ million and installation will cost a further $$0\mathrm{.}5$ million. The technology in the industry is changing rapidly and machines typically have a short life. The machine is expected to have a working life of $5$ years. The initial cost of the machine and the installation cost will be depreciated using the straight$-$line method over the expected life of the machine to a residual value of $$0.$

The consultants estimate that the XDC$-450$ will produce $20$ million units annually that can be sold for $$0\mathrm{.}50$ each. Raw material costs are estimated at $$0\mathrm{.}20$ per unit, energy costs at $$0\mathrm{.}05$ per unit and labour cost at $$0\mathrm{.}10$ per unit. Administration costs are estimated at $$1$ million annually. The expansion will also require additional inventory to be held, equivalent to $10\%$ of annual raw material costs. The consultants have also estimated additional accounts receivable equivalent to $15\%$ of sales revenue will need to be held. Any inventory and accounts receivable held at the end of year four will be recovered in the final year of the project. The resale value of the machine is expected to be $$100000$ at the end of year $5.$ What is the NPV of the project if Brougham$$s cost of capital is $10\%$ and the corporate tax rate is $30\%?$