In this study, the real scheduling problem of a construction company is considered. And the problem is recognized as the Resource Constrained Project Scheduling Problem with Discounted Cash Flows (RCPSPDC). This problem involves scheduling the project activities with cash inflows and outflows, in such a way the net present value of the cash flows is maximized subject to resource and precedence constraints. The modified EH procedure was proposed as a heuristic solution technique for this problem. This procedure improves the net present value by moving the activities with positive cash flow to the left and negative cash flow to the right. In this problem, it is not important to minimize the makespan. The effectiveness of the proposed heuristic rule is evaluated by comparing it with the solution of real company’s method. And we also compare it with 1300 different feasible solutions generated randomly. EH algorithm successfully produced near-optimal solutions with reasonable computational effort.