Quantify build-vs-buy training decision

Your company plans a new employee training program and must choose among: (1) External vendor—Standard package: fastest to implement, not customizable, training data stored in the vendor’s database; (2) External vendor—Premium package: customizable, higher data security controls, longer to implement; (3) Internal build: fully tailored, longest to implement. Propose a quantitative decision framework that: a) defines the core KPIs (e.g., completion rate, performance uplift) and how you would causally estimate the incremental impact of training versus baseline (describe an experiment or quasi-experiment with success metrics and power considerations); b) constructs a risk‑adjusted NPV model over horizon H with variables for implementation time T, upfront cost C0, annual run cost Ct, annual benefit Vt, breach probability p and loss L, and a discount rate r. Write the exact decision rule/inequality that chooses among the three options, explicitly modeling the value lost while implementation is in progress; c) specifies a sensitivity analysis (which parameters, ranges, and stopping rules) and a pilot plan to update priors for Vt and p; d) given only ordinal information that Standard < Premium < Internal on customization and that Standard is fastest, defend which option you’d select and what observable threshold would cause you to switch.