FIN.9:4.2 - Compare value under interactions and dated constraints

Bring values to one date, currency, claimant and compatible tax and risk grounds. Different components may properly have different required returns. Value them on their supported bases before combining present values; forcing their cash differences through one convenient rate can change the economics. If selecting the combination changes financing terms or risk treatment, recalculate those affected values through FIN.5.

For a proposed combination, project whole incremental cash against the common baseline. Compare it with the sum of the individual incremental cash accounts. Their difference is the interaction to be valued: shared setup savings, lost customers, capacity congestion, duplicated costs or another actual effect. It can be positive or negative and can arise at several dates. Explain the operating cause so that it can be revised when the combination changes.

Map the resource use and money needed when each constraint binds. Include initial commitments, later investment, collateral, working capital, operating capacity and financing access. A project with a modest initial outlay can absorb the capital needed by another one next year. A positive annual ending balance can conceal an earlier shortage. FIN.2 supplies the dated cash requirement; operating practice supplies the capacity account.

For a small set, enumeration is often enough. Include the empty choice when feasible, singles and combinations; remove only those excluded on established grounds; compare the whole values of those remaining. A useful dominance conclusion requires one alternative to be no worse on every relevant consequence and constraint and better on at least one, under the stated conditions. A higher NPV alone does not dominate a lower-NPV alternative that uses less scarce capital.

A larger problem can use a constrained optimization model. Let a binary selection variable represent an indivisible project. A mutual exclusion restricts two selections to at most one; a prerequisite requires the dependent selection to imply the prerequisite. Resource constraints use the actual dates and amounts. Interaction terms or scenario-dependent choices need their own representation. Inspect what the objective and constraints mean before accepting the computed optimum; a solver cannot find an alternative omitted from the model.

For divisible independent investments with one initial capital limit, linear scalable values and no other constraints, ranking value per unit of capital can construct an allocation. State the chosen profitability-index definition; conventional PV-of-receipts divided by initial outlay and NPV divided by initial outlay differ by one for that simple flow pattern. Indivisibility, minimum scale, interactions or future funding constraints can defeat the ranking. A large ratio is not evidence that the leftover budget can be usefully deployed.