CapEx ROI

Initial cash flow = −capital cost −disruption cost. Full-year baseline B = full-year incremental revenue −full-year incremental operating expense. Year 1 operating cash flow = B × ramp-up fraction. For year t ≥ 2, operating cash flow = B × (1 + growth rate)^{t − 1}.

Ramp-up scales the net operating benefit and assumes proportional realization of revenue and expenses. Later years grow from the full-year baseline, not the reduced Year 1 amount. Growth includes inflation and other expected growth and is applied once starting in Year 2. Ramp-up does not reduce capital, disruption, or residual value. Disruption is already included in initial outlay: do not deduct the same loss again through revenue, expenses, or ramp-up.

Operating cash flows occur at each year-end. Residual value is added only in the final year. NPV discounts each year-end cash flow by (1 + discount rate)^year and adds the time-zero cash flow. Unlevered yield on cost uses the full-year baseline B divided by initial outlay, including disruption, before financing and income taxes.

Cash payback is the first year-end when cumulative undiscounted cash flow is nonnegative. There is no within-year interpolation. This does not guarantee that later negative cash flows will remain recovered.

Financing, taxes, depreciation, equity returns, and IRR are outside this version. Use a nominal, unlevered required project return consistent with the nominal cash-flow assumptions, including inflation only once.