Google is considering a project to move a fraction of its workforce out of Silicon Valley to a cheaper, more efficient location. There are two alternatives.

Project $1$: the initial move costs $$45$ million in year zero and generates costs savings of $$32$ million per year in each of the following three years $($years $1,2,$ and $3).$

Project $2$: the move costs $$30$ million in year zero and generates costs savings of $$24$ million per year in each of the following three years $($years $1,2,$ and $3).$

Suppose Google's cost of capital is $15\%$ per year.

$($a$)$ What is the NPV of Project $1?$

$($b$)$ What is the IRR of Project $1?$

$($c$)$ Suppose Google can only choose to do one of the two projects a single time. Which project $($if either$)$ should it undertake? Explain why.

$($d$)$ Suppose instead that Google can do either project multiple times until it spends $$180$ million in year zero. Which project$($s$)$ should it do now? Explain why.