Implementing an enterprise architecture (EA) project might not always be a success due to uncertainty and unavailability of resources. Hitherto, we have proposed a new metaphor -Enterprise Architecture Debt (EAD)-, which makes bad habits within EAs explicit. We anticipate that the accumulation of EAD will negatively influence EA quality, also expose the business into risk. Recognizing the importance of business-IT alignment in enterprise architecture context, this paper proposes an application of portfolio-based thinking and utility theory for EAD prioritization. For proof-of-concept purpose, we develop synthetic data using coarse-grained estimates to demonstrate the application of the proposed portfolio-based approach which helps to determine the optimum selection of EAD to be resolved. The results show that our approach can help EA practitioners and management to reason their EA investment decisions based on the EAD concept, with adjustable enterprises risk tolerance level. Copyright © 2019 for this paper by its authors.