TITLE:
An S-Shaped Curve and Efficient Frontier Model for Income Projection in New Business Projects
AUTHORS:
Fadzilah Salim, Nur Azman Abu, Satrya Fajri Pratama
KEYWORDS:
Efficient Frontier, Income Projection, Project Management, S-Shaped Curve
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.9,
September
22,
2026
ABSTRACT: Income projection is a fundamental component of a business project, particularly in supporting management decisions on investment, resource allocation, and expected financial returns. Conventional income projection approaches commonly assume a constant or continuously increasing income pattern and may not adequately represent the different stages that a new business project experiences before reaching maturity. This study proposes a conceptual S-shaped curve model for projecting projected revenue throughout the lifecycle of a new business project. The proposed model represents the progression of income through four phases, namely the initial development phase, rapid growth phase, saturation phase, and maturity phase. An efficient frontier concept is subsequently introduced to represent alternative income growth trajectories resulting from different levels of managerial intervention and resource allocation. The inflection point of the S-shaped curve is used to identify the transition between the growth and saturation phases and to provide an indication of the stage at which additional investment may produce diminishing income growth. The proposed model provides a graphical and mathematical framework for analysing income growth dynamically rather than assuming a uniform growth pattern throughout the project lifecycle. The model is intended to assist project managers and senior management in evaluating alternative income projections, identifying appropriate intervention points, and supporting investment and resource allocation decisions for new business projects.