$3.$ Pilot Plus Pens is considering when to replace its old machine. The replacement costs $$3$ million now and requires maintenance costs of $$500,000$ at the end of each year during the economic life of five years. At the end of the years the new machine would have a salvage value of $$500,000.$ It will be fully depreciated by the straight$-$line method. The corporate tax rate is $34$ percent and the appropriate discount rate is $12$ percent. Maintenance cost, salvage Evalue, depreciation and book value of the existing machine are given as follows.

Year $0$:maintenance $$400000,$Salvage$$2000000,$depreciation $$200000,$book value$($end of year$)$ $$1000000$

Year$1$:maintenance $$1500000,$Salvage$$1200000,$depreciation $$200000,$book value$($end of year$)$ $$800000$

year $2$:maintenance $$1500000,$Salvage$$800000,$depreciation $$200000,$book value$($end of year$)$ $$600000$

year$3$:maintenance $$2000000,$Salvage$$600000,$depreciation $$200000,$book value$($end of year$)$ $$400000$ year$4$: maintenance $$200000,$Salvage$$400000,$depreciation $$200000,$book value$($end of year$)$ $$200000$

The company is assumed to ear a sufficient amount of revenues to generate tax shield? from depreciation. When should the company replace the machine?