In an unrelated analysis, you have the opportunity to choose between the follow$-$ing two mutually exclusive projects, Project T $($which lasts for $2$ years$)$ and Project F $($which lasts for $4$ years$)$:

Expected Net Cash Flows

followingYear $01234$

Project T $$$$100,00060,00060,000--$

Project F $$$$100,00033,50033,50033,50033,500.$ The projects provide a necessary service, so whichever one is selected is expected to be repeated into the foreseeable future. Both projects have a $10\%$ cost of capital. $(1)$ What is each project$$s initial NPV without replication? $(2)$ What is each project$$s equivalent annual annuity? $(3)$ Apply the replacement chain approach to determine the projects$$ extended NPVs$.$ Which project should be chosen?

$(4)$ Assume that the cost to replicate Project T in $2$ years will increase to $$105,000$ due to inflation. How should the analysis be handled now, and which project should be chosen? Give specific formulas