The BSM Formula can be derived according to various generic approaches, including a simple binary taxonomy (T) regarding use and not of the BSM Equation as a partial differential equation (PDE) as an intermediate step. Namely, (T1) using the PDE and (T2) not using the PDE. While Wurts (2020 BSM, 2021 DM) focused on the T1 part of the taxonomy, this paper adds more regarding the T2 part of the taxonomy, illustrated by an example as one of seven BSM Formula derivations that appear in the seminal Black and Scholes (1973) and Merton (1973) papers. Wurts (2020 DM) also (1) introduced a variety of derivations that provided adequate coverage of T1 derivations, yet it left out four named herein (i.e., BSDS, MDS, ME, and SS); and (2) introduced a cafeteria of derivation elements that led to the same logic Watershed of the BSM Equation, yet it did not elaborate upon T2 derivations and how T2 expands the Watershed of the BSM Formula yet, ultimately, provides only equivalent information as the T1 Watershed (ultimately, since the BSM Formula Watershed was never escaped, despite a fundamentally different derivation approach with T2). Hence, illustrating both the diversity and robustness of the BSM Formula Watershed as well as the still restrictive nature of such a diversity of apparently equivalent information. T2 ultimately provides not only insight into T1, T2 serves as a categorization beyond the simple example provided within Merton (1973) where a T2 example is found, even toward including a mathematics and approach (i.e., an Equivalent Martingale Measure approach) that has often replaced the Merton (1973) mathematical approach that had already replaced the Black and Scholes (1973) mathematical approach, even beyond the original and explicit hedging approaches utilized in the two seminal papers. Yet that extension of T2 is beyond the scope of this paper, which provides only a narrow retrospect of the simple Merton (1973) example (as ME), and its role in extending beyond T1 derivations. Such a narrow extension still provides four important points regarding the general use of the BSM Formula: the need to distinguish between pricing and valuation, the need to identify and verify both input numerical values and application that are consistent with derivation, how various combinations of cafeteria fare effectively convey equivalent information in a logic Watershed as well as provide insight for escaping a logic Watershed, and a specific identification of the discount rate to utilize when discounting future cashflow to the present
