In addition to its data centre in Texas, BitTech currently has $1,000$ servers located in Singapore. These are deployed for cloud services. With the advent of AI technologies such as Google Bard, OpenAI chatGPT and Microsoft coPilot, BitTech is thinking about pivoting from cloud services to AI services. It is evaluating whether it should pivot $500$ servers to the new AI services. These $500$ servers have a remaining shelf$-$life of $7$ years. At the end of this period, all these servers will be written$-$off with zero book value.

Presently in Singapore, monthly sales per server are $$24,000.$ Operating costs per server are $$5,000$ a month. It expects sales of cloud services to decline by $5\%$ each year. Costs per server $($for cloud services$)$ are expected to increase by a gradual $3\%$ per year.

On the other hand, monthly sales per server for AI services are estimated to be $$36,000.$ However, operating costs per server are higher at $$10,000$ per month. Sales of AI services are expected to increase by a hefty $15\%$ each year. The costs of operating such servers will also increase by $12\%$ per year.

For all its projects, BitTech uses a minimum ROI target of $18\%.$

$($i$)$ Create an appropriate NPV$-$based model to analyse whether BitTech should pivot to AI services for $500$ of its existing cloud servers. State any two $(2)$ assumption$($s$)$ used by your model.