What is the minimum contract period which will be acceptable for the private sector partner?

For the renewal of the urban water system the city is looking to establish a PPP with the following terms:

Water Rate should not exceed $3/m³ allowing for an inflation rate of 2% (to account for inflation rate: )

Expected consumption of 500,000 m³/day for a population of 2 million

The private sector partner will be in charge of project financing, renewal, operation and transfer of the renewed infrastructure system at the end of contract period to the city government.

Renewal capital cost of P = $5B USD; for the project financing the private sector partner will have to take a loan with an interest rate of 5% (to calculate future values of capital investment refer to time conversion below)

Agreed benefits for the private sector partner 7%.

F=P(1 + i)n