I\'m currently working with a fairly old product that\'s been saddled with a lot of technical debt from poor programmers and poor development practices in the past. We are star
+1 for jldupont's focus on lost business opportunities.
I suggest thinking about those opportunities as perceived by management. What do they think affects revenue growth -- new features, time to market, product quality? Relating debt paydown to those drivers will help management understand the gains.
Focusing on management perceptions will help you avoid false numeration. ROI is an estimate, and it is no better than the assumptions made in its estimation. Management will suspect solely quantitative arguments because they know there's some qualitative in there somewhere. For example, over the short term the real cost of your debt paydown is the other work the programmers aren't doing, rather than the cash cost of those programmers, because I doubt you're going to hire and train new staff just for this. Are the improvements in future development time or quality more important than features these programmers would otherwise be adding?
Also, make sure you understand the horizon for which the product is managed. If management isn't thinking about two years from now, they won't care about benefits that won't appear for 18 months.
Finally, reflect on the fact that management perceptions have allowed this product to get to this state in the first place. What has changed that would make the company more attentive to technical debt? If the difference is you -- you're a better manager than your predecessors -- bear in mind that your management team isn't used to thinking about this stuff. You have to find their appetite for it, and focus on those items that will deliver results they care about. If you do that, you'll gain credibility, which you can use to get them thinking about further changes. But appreciation of the gains might be a while in growing.