If this is a 'random sample' system, it's only purpose would be to monitor agent quality. This is something that ROI calculations don't factor into really well, unless you have significant agent turnover in your call center.
If you're constantly hiring agents, then it has some value in shortening training cycles, and early identification of agents who might not fit well in their role. But that's about it. Since you have to spend the money to hire and train agents anyway (and most call centers can't afford to be picky about who applies) it really doesn't reduce or eliminate any expenses.
If your call center makes money on every call, and sales are an objective, you might have the single argument of reduced learning curve for agents. (And therefore speedier returns and more profits.) It's a stretch to make that argument sometimes.
If this is a 'record every call' system to allow a record of the conversation (which is sometimes required by agencies like the SEC) then it's easy. Just create a liablity argument. How much could you stand to lose if a caller were to challenge the outcome of a call. The system simply becomes an insurance policy with a one time fixed cost.
In my opinion, most agent monitoring systems like these have little or no value to a call center that is properly managed. Those that have calls where a fixed scripted text must be followed have little to evaluate except 'did vs didn't' follow the script, and those that have random calls that are all different with different outcomes, are really only evaluating the outcome based on a subjective opinion. (Not a good measure.)
If agents have clear directions, and good assistance when they need it, then call centers who implement such systems rarely see much benefit.
If you find yourself seaching for justification to buy any system, then you probably don't need it. Systems should fulfill something that you clearly lack in your organization. You should never have to 'create' a need for them to exist.
Unless someone in your organization is coming to you requesting the system, I'd forget it. Spend the money on pizza and training sessions for the call center once a month... you'll get more goodwill, happier, more well-adjusted, and better trained agents out of that than any agent monitoring system could produce.
Carpe dialem! (Seize the line!)