$4.$ A business is evaluating a project for which the following information is relevant:

I. Sales will be $$100,000$ in the first year and are expected to increase by $5\%$ per year.

II$.$ Costs will be $$50,000$ and are expected to increase by $7\%$ per year.

III. Capital investment will be $$200,000$ and attracts tax allowable depreciation of the full value of the investment over the $5$ year length of the project.

IV$.$ The tax rate is $30\%$ and tax is payable in the following year.

V$.$ Working Capital invested will be $20\%$ of projected sales for the following year.

VI$.$ General inflation is expected to be $3\%$ over the course of the project and the business uses a real discount rate of $9\%.$

Calculate the NPV for the project.