How do I build a business case for new software?

A compelling software business case: quantify the current cost of the problem (time wasted, errors, missed deals), estimate the value of the solution (hours saved × hourly rate, increased conversion, reduced errors), calculate payback period, and identify risks. Decision-makers respond to numbers — "this saves 10 hours/week at $75/hour = $39,000/year for a $15,000 tool" is more persuasive than feature lists.