A new project is expected to cost $$100,000.$ in the first year the gross profits would be $$20,000.$ In consecutive years, the profit is expected to go up by $$5,000$ from the previous year until year $6.$ a$)$ What is the payback period? b$)$ What is the net present worth of this project, if the company used a $15\%$ rate of return? c$)$ If the company expects the probability of commercial success to be $80\%,$ what is the most initial investment that can be spent of the project?