Drawing a timeline will help solve this problem. Investing in a troubles business. You are buying a business that has been losing money. Next year (at t = 1) you will need to invest $100 into the business (to cover losses). You will be making contributions at t = 2, t = 3, t = 4, t = 5. The contributions are declining at 20% from year to year (for example, your contribution at t = 2 is $100*(1-0.2) = $80). At t = 6 the business will have zero profits (your cash flow at t = 6 is zero). At t = 7 you will receive first profits of $90. Profits will be paid forever and will grow at an annual rate of 7%. The discount rate is 12% per year.

Stage one. What is the Present Value (at t = 0) of all your investments during the first stage? (You are calculating the present value of payments made at t = 1, 2, 3, 4, 5).

Stage two. What is the Present Value (at t = 0) of all your profits. (You are calculating the present value of payments received, which are profits, from t =6 to infinity).

Total. What is the value of this business at t = 0?