Question: Let's say I'm in an area of a business that is a cost sink: something like customer support. In this support realm there's a KPI that's based on Net Promoter Score. NPS is more or less used in industry to drive growth. Does it make sense to want to use a KPI to drive growth for a cost-sink end of the business? Is there any relevant literature on the subject?

Likewise, this is my first post here. Is this a relevant question to ask?

Answer: 
> 
> Does it make sense to want to use a KPI to drive growth for a
>  cost-sink end of the business?
> 
> 
> 

If you are a believer in KPIs and metrics like Net Promoter Score, then certainly you see value in improving them.

And even if you view customer support as a "cost sink", you might concede that customer support is a cost of doing business and growing customer support might be a cost of doing business well.

Given the above it makes perfect sense to improve your KPIs by growing this cost sink up to the point where the marginal value of further improvement is outweighed by the cost of attaining it.

While I'm not a fan of metrics, I have used similar arguments to get by-in for growing many teams that might fall into what you view as a "cost sink", and what some might view as "making our customers happy".
> 
> Does it make sense to grow a cost-sink?
> 
> 
> 

Sometimes it does, it depends what it is. Services which don't make a visible profit, or actually look like a loss can be essential to a business and give it an edge over competitors. Or they can provide rarely needed redundancy which saves a huge amount in disaster recovery situation. Two examples would be network redundancy and expanded support.

In the first I have seen one of my clients experience a power issue that took out 3/4's of their core hardware on a Saturday (servers, switches, backup units), and had them business-as-usual by 6AM Monday morning, most staff didn't even know anything had happened. I have also seen an office burn down and the next week the owners were advertising in the local newspaper that if anyone owed them money, please come forwards (they'd lost all their hard copy and digital records and had no current offsite backup).

In the second example some invest heavily in support so that clients have a minimum of frustration when they have issues. This can be THE major selling point for them in terms of customer relations and reputation.