In IT service delivery and support, the cloud paradigm has introduced the problem of resource over-provisioning through rapid automation (or orchestration) of manual IT operations. Due to the elastic nature of cloud computing, this shortcoming ends up significantly reducing the real benefit, viz., the cost-effectiveness of cloud adoption for Cloud Service Consumers (CSC). Similarly, detecting and eliminating such over-provisioning of cloud resources without affecting the quality of service (QoS) is extremely difficult for Cloud Service Providers (CSPs) since they have visibility only into the state of the IT services (cloud resources) but none into the actual performance of business services. In this paper, we propose T-BICA (Tier-centric Business Impact and Cost Analysis), a tier-centric optimal resource allocation algorithm, to address the problem of rapid provisioning of IT resources in modern enterprise cloud environments, through extensive data gathering and performance analyses of business services in a simulated environment emulating a mature cloud service provider. We have derived improved analytics to address the issues and to accelerate real cloud adoption for large enterprises within the context of meeting (or exceeding) business service level objectives (SLOs) and minimizing the cloud subscription cost (OpEx) for the business. While investigating the problem, we consider the time and the cost of delivering business service in medium- to large-size enterprise environments, quantifying the negative impact of IT resource over-provisioning (due to highly mature IT services centric orchestration capabilities) on the business, and indicate how the suggested cloud analytics could assist in reducing total cost of ownership (TCO) of the business service. From our analysis of the test data, we have observed that our suggested approach and analytic reduces the cost of delivering business services by 65.19%, and improves the performance (total time to deliver) by 74.18% when compared to the existing modern cloud management and resource provisioning approach. Using T-BICA also dramatically reduces upfront costs (CapEx) for CSPs (from the capacity procurement and management points of view) through efficient on-demand resource de-provisioning, without affecting business SLOs and IT service level agreements (SLAs). The improved dynamic allocation of resources also makes for better efficiency of utilization, which in turn has desirable consequences for sustainability, and makes this an approach for ``Green'' IT.