Construction Project Case Study: A construction company is planning to invest in a new project with an estimated cost of $$750,000.$ The project is expected to generate a steady income of $$120,000$ per year for $15$ years. To finance part of the project, the company takes a loan of $$300,000$ with an annual interest rate of $7\%,$ to be repaid over $15$ years in equal annual payments. The company also plans to set up an annuity sinking fund with an annual return of $5\%$ to accumelate $$200,000$ for future expansion at the end of the $15-$year period.

a$)$ what's the present value of the income generated by the project, and how does it compare to the initial investment, considering the company's discount rate of $6\%?$

b$)$ what's the annual payment for the loan, and how much will the company need to contribute to the sinking fund to reach its $$200,000$ goal?