It is hard to show a causal relationship between investment in knowledge management and increased returns. That said, there are some ways that you can demonstrate positive contribution to business results. First, you have to understand the performance that needs to be changed in order to demonstrate a return. In fact, you will need to know the metrics that the business uses to measure results in the business process.
Say, for example, the business wants to improve sales performance and the key metric is win rate. Knowledge management can have a profound impact on win rate by helping the sales people understand their clients and sales prospects better and by helping them prepare for sales calls. The KM function can help the sales person understand what the customer has bought in the past and what other analogous solutions other companies in the same industry are buying. The KM function may be able to find information on the customer buying team and specific individuals in the company. If expertise in the company is mapped and searchable, the sales team can access subject matter specialists in the company to help with proposals. If you have a shared bookmarking capability in the company, the sales team can research sites that have been useful to others in the past. To make sales easier, there may be boiler plate language or certain valuable slides that are put in every sales presentation and the KM function can make this content visible to the entire sales community. So you can see there are many interventions that you can make to improve win rate.
Armed with the facts and the details about what the KM function did specifically to enable the sales process you can demonstrate the causal relationship between specific actions and increased sales performance. It is likely that you can even show that teams that took advantage of KM resources were more successful than teams that did not.
To make the business case for knowledge management and to demonstrate a return on investment, this type of detailed analysis is required. The depth of your analysis and your passion can be very convincing to management.