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 analyze 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 consultant 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 $$0\mathrm{.}05$ per unit and labour cost at $S0\mathrm{.}10$ per unit. Administration costs are estimated at $S1$ million annually. The expansion will also require additional inventory to be held, equivalent to $10\%$ of annual raw material costs. The consultants have also estimated additional and accounts receivable equivalent to $15\%$ of sales revenue will need to be held. Any inventory and accounts receivable held at the end of year four will be recovered in the final y ear of the project. The resale value of the machine is expected to be $$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 $30\%?$