Scenario $3$: A project requires an initial outlay of $$200,000.$ It will generate $$50,000$ in the first year and is expected to increase by $5\%$ annually for the next four years. Additionally, at the end of the fifth year, the project will be sold for a terminal value of $$100,000.$ The discount rate for this project is $12\%.$ Calculate the NPV of the investment.