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The Takahashi and Alexander (TA) model is a widely used framework for simulating private equity cash flows. However, its core shape parameter b, which governs the distribution timing, lacks a direct connection to investor-relevant metrics such as internal rate of return (IRR) and total value to paid-in capital (TVPI). This article introduces a reformulation of the TA model that replaces the opaque b-parameter with a more intuitive and analytically derived function of the investor’s performance goals. We define a dimensionless quantity d=log(M)/(G*L) where M is the desired TVPI, G the target IRR, and L, the fund’s life. We then derive the relationship b=exp(pi*d)/sqrt(2) offering a closed-form link between fund performance objectives and the TA model’s cash flow shape. This formulation simplifies calibration, enhances interpretability, and enables goal-driven simulation of capital calls and distributions. Numerical validation confirms the robustness of the approximation across a wide range of practical scenarios, making the TA model significantly more accessible and aligned with real-world decision-making.