The discussion of how to calculate asset value has thus far focused on how to perform the calculation for a single asset or asset component. This section addresses the question of how to perform the calculation for groups of assets. The following subsections provide an overview of the calculation process and key issues, and recommended calculation steps.

The steps detailed in Chapter 3 to 6 detail all of the building blocks of the asset value calculation. The only remaining step to calculate the value of a given asset or component at time *t* is to subtract depreciation from the initial asset value :

\begin{equation*} V(t) = V(t_0) - D(t) \end{equation*}

In practice, however, the calculation does not stop there. For most applications one seeks to calculate the value for multiple assets and asset classes, requiring some form of aggregation. Also, one should ideally account for the fact that there is inherent uncertainty in the calculations of asset value, particularly if they are prospective (predictions of future value) rather than retrospective. Additional analysis may be required to address these and other issues.

Note that depreciation should never exceed the initial value of the asset or component. This and other calculation issues may arise depending on the level of detail at which calculations are performed, determination of how different treatments are incorporated in the calculations, and approach used for componentization (discussed in Chapter 3).

### Asset Aggregation

Aggregating asset value calculations can be accomplished in two basic ways: either the asset value calculation is performed for individual assets or components and then the results are aggregated, or assets are grouped together for analysis first and the calculation of value is performed at an aggregate level.

Performing calculations on aggregated data is preferable, as doing so saves effort. However, it is important not to introduce errors in the calculation process by over-aggregating. When data are aggregated one relies on averaging to obtain an aggregate result. Provided the groups of assets are homogenous in their characteristics and all of the underlying relationships being modeled are linear, then one can aggregate prior to calculating value. However, if there is a lack of homogeneity or non-linear effects then aggregating can introduce errors. Examples of situations where aggregation may not be appropriate include:

- Initial costs are calculated using a more complex method than a simple unit cost;
- Initial costs are calculated using a simple unit cost, but this unit costs varies for different assets in the group;
- Useful lives vary for different assets in the group;
- Depreciation is non-linear;
- An asset consists of multiple components with different ages and useful lives, but is being valued at the asset level rather than component level; and/or
- One or more assets or components are fully depreciated.

Table 7-1 illustrates the issue. Here value is calculated using age-based depreciation for assets A and B. The calculation is performed separately for both, and then at an aggregate level combining the two assets. The table shows the initial value of each asset, and the accumulated depreciation. It also shows the current value, which is the initial value less depreciation. When the calculation is performed separately for each asset the total current value is calculated as $8.2 million. However, when A and B are treated as a single asset, the value calculated is $4.2 million – substantially less!

The culprit responsible for the error in this case is the treatment of depreciation. Asset B is older than the useful life of 50 years, and thus fully depreciated. Once an asset is fully depreciated its value is assumed to be equal to its residual value and not allowed to become negative. This effect is correctly accounted for when the calculations are performed by asset, but ignored in the aggregate calculation in which the average age is used.

## Table 7-1. Approaches for Calculating Depreciation

Measure | A | B | Total if Calculated by Asset | Total if Assets are Aggregated |
---|---|---|---|---|

Initial Value ($ million) | 11.0 | 22.0 | 33.0 | 33.0 |

Residual Value | 1.0 | 2.0 | 3.0 | 3.0 |

Age (years) | 24 | 60 | N/A | 48 |

Useful Life (years) | 50 | 50 | N/A | 50 |

Depreciation ($ million) | 4.8 | 20.0 | 24.8 | 28.8 |

Current Value ($ million) | 6.2 | 2.0 | 8.2 | 4.2 |

Ultimately, establishing the correct level of aggregation requires careful consideration of the approach and experienced judgement to determine the appropriate level of detail based on the approach and the asset characteristics.

### Treatment of Uncertainty

The quantitative approaches described in this guide are deterministic – they assume that calculation parameters are known with certainty. In reality key parameters are subject to uncertainty and error, particularly when an analysis is performed at an aggregate level. For example:

- Treatment costs and effects can be highly variable and depending on a large number of factors.
- Future asset deterioration is uncertain, and subject to changes as a result of changing technology, the changing climate, and myriad other factors.
- Future traffic/level of use will drive the benefits obtained from an asset and also depend on economic and demographic factors well outside of the control of an asset manager.
- Economic parameters such as inflation, the discount rate, and the value of time are subject to uncertainty and may be computed differently depending on one’s assumptions.

In certain respects, calculating asset value at an aggregate level can help address some of the inherent uncertainties underlying the calculations given parameters such as treatment costs and treatment effects are often derived at this level. Asset level calculations may be more precise – but no more accurate – if they rely on highly variable parameters derived through observations of large populations of assets.

A number of approaches have been developed for handling uncertainty in numeric calculations. Uncertainty is inevitable in calculations of asset value; the question for the analyst is whether the level of uncertainty is tolerable given the manner in which the results of the calculation will be used. The approach recommended here is to acknowledge where uncertainty exists, and – if sufficient time and resources are available – perform sensitivity analyses to show the degree to which changes in key parameters would impact the results of the analysis. For calculations of current value, the analysis may, at a minimum, include testing the impact of changes in asset useful life. For predictions of future value an accompanying sensitivity analysis should also address changes in treatment costs and any economic parameters used in the calculation approach (e.g., the discount rate, if applicable).

The following steps are recommended for calculating current asset value for one or more asset classes and components. These build on the results of prior steps for establishing the scope of the analysis, selecting the initial value calculation approach, identifying treatments, and selecting the depreciation approach.

- Step 1 – Review the Level of Detail in the Calculations:
Review the decisions made on the level of detail in the asset value calculation made in Step 1. Combine assets to perform a more aggregated analysis if feasible without significantly impacting the results. Disaggregate the analysis further if key parameters such as costs and useful lives are found to vary within subgroups of assets.

- Step 2 – Calculate Initial Value:
Apply the approach selected previously to calculate initial value for each asset group, asset or component. Note that in cases where treatments besides initial purchase/construction are included in the analysis and depreciation is based in part or entirely on age, the initial value should be calculated as of the time of the most recent treatment. (but may not be the same as that of a “like new” asset unless the most recent treatment was replacement or reconstruction).

- Step 3 – Calculate Depreciation:
Apply the selected approach to calculate depreciation for each asset group, asset or component.

- Step 4 – Calculate Asset Value:
Calculate value as the difference between initial value and accumulated depreciation. Sum the results across components, assets and/or asset classes to obtain total asset value.

- Step 5 – Conduct Sensitivity Analysis:
Document the impact of changes to key parameters on the calculations of asset value.