Separable Components

Sometimes a project consists of several interrelated subprojects or components.

When the components are independent, each component must be

treated as if it were a separate project. The analyst then must determine

whether each component increases or decreases the project’s total NPV.

Any component with negative NPV should be dropped, even if the total

NPV of all the components is positive. Each separable component must

justify itself as a marginal part of the overall project.

Suppose a project provides three benefits: hydroelectric power, irrigation

water, and recreational facilities. If the benefits and costs of each component

are independent of each other, then the components are separable and can

be treated as independent projects. In this case, the decision to include each

component in the final design will depend solely on whether the NPV of the component is positive. But if the water is needed early in the year for irrigation

and only later in the year to meet peak demand for electricity, and if the

tourist season occurs at the end of the year, the three uses might conflict. For

example, maximizing the use for electricity generation might result in an

empty reservoir when the tourist season begins. If maximizing the NPV of

the whole package entails reducing the efficiency of one component, then

dropping one or more components might result in an overall package with a

higher NPV. In this case, the components are not mutually exclusive and,

hence, not separable.

Appraising such a project requires three steps:

• The analyst must appraise each component independently.

• The analyst must appraise each possible combination of components.

• The analyst must appraise the entire project, including all the components, as a package.

Thus, the analyst must appraise the hydroelectric component separately,

considering the most appropriate technology for generating electricity and

disregarding its uses for irrigation or recreation. Similarly, the analyst must

appraise the irrigation component as an irrigation project, choosing the

most appropriate design for irrigation and disregarding its potential use

for electricity generation or recreation. Finally, the analyst must appraise

the recreation component independently using the same general approach.

The second step would involve appraising three combinations, hydroirrigation,

hydro-recreation, and irrigation-recreation. In each case, the most

appropriate technology for the combination would be used, and the NPV

of each combination would be assessed.

The final step would be to evaluate the design that combines all three

components. This design would also be predicated on a technology that

maximizes the NPV from the combined facilities. We would thus have seven

alternatives: hydroelectricity, irrigation, recreation, hydro-irrigation, hydrorecreation,

irrigation-recreation, and hydro-irrigation-recreation. The preferred

alternative would be the one that yields the highest NPV without

exceeding the budget.

If the components are separable, then the NPV of the combinations is

equal to the sum of the NPVs of each separable component. If the components

are not separable, then the NPV of the combinations is not equal to

the sum of the NPVs of each component. In this table the NPVs of the

combinations are greater than the NPVs of the sums of the individual components.

This, however, does not need to be the case. If the components

are not separable, then choosing the combination with the highest NPV

entails assessing the NPV of each combination and choosing the one with

the highest NPV.