A local investor plans to build a new production factory in your hometown of $2,000$ households. The investors initial investment is $2,500,000$ and the expected infinite cashflow stream from the investment is $150,000$ p$.$a$.$ The investors risk$-$adequate discount rate is $5\%$ p$.$a$.$ However, the production factory is expected to cause large quantities of toxic wastewater which is released directly into the local sewage system. Because the local purification plant must be expanded the local waste management fees are expected to increase by $20$ p$.$a$.$ per household as from t $=1.$ Assume the households have discount rate of $7\%$ p$.$a$.$ on average.a$)$ Calculate by which amount the project changes the local investors wealth, and by which amount it changes the overall wealth of your hometown.b$)$ To internalize the negative externality from the toxic wastewater, the local administration decides that the investor must purify the wastewater before releasing it into the local sewage system. This increases the initial investment by $200,000.$ Up until which annual maintenance costs for the firms purification plant would the investor still go ahead with the project?