Uncharacteristically, I'll begin by answering your question:
No, I would not embrace hosted applications wholeheartedly. I'd ask a bunch of questions first to determine whether that was the right approach, or whether starting with small, incremental steps yielded greater long-term business value.
Here are some questions you might consider asking to determine whether hosted CRM is the right answer:
I'd also want to re-examine the breadth, depth, and reach of the parent company's existing IT infrastructure and understand whether there are components that are leverage-able, either from a platform standpoint or a licensing standpoint. Will the operational systems (e.g., general ledger system) also be built from scratch? (Seems a shame to start from scratch when the company is a subsidiary and could take advantage of the cost advantages and economies of scale.)
Where I'm going with all this is that the company has an exciting and rare opportunity to create a business-driven IT infrastructure, just not the time. Assuming that you're time and resource bound -- a very good argument for hosted CRM indeed -- I'd suggest beginning with hosted CRM for operational CRM functionality while building out the analytical CRM infrastructure in-house. That way, the data generated by the hosted CRM applications and operational sources can be institutionalized for a range of more strategic purposes across business functions. The company will outsource the processing, but own the customer data.
And yes, 120 days isn't a lot of time, but with the hybrid and incremental approach described above, there's a compelling business case for moving forward and entrenching a customer focus into the company's culture in the seminal stages.
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