This section describes the specific steps involved using the three different depreciation approaches addressed in this chapter: linear depreciation based on actual age (“age-based”); a linear-based depreciation using a condition-based approach (“condition-based”); and non-linear depreciation established through analysis of the pattern of benefit consumption (“non-linear”).

Note that the steps presented here describe the case in which depreciation is calculated for an individual asset or component since the point at which the initial value was calculated as described in Chapter 4, or since the last treatment, if a treatment was performed more recently than the time of the initial value calculation. However, depreciation can be calculated for other contexts using the same basic steps. For instance, one can use the steps described here to calculate the cumulative depreciation of an asset looking back in time prior to a recent valuation, predict future depreciation when testing different scenarios or treatment assumptions, or calculate depreciation for an inventory rather than an individual asset.

The steps for calculating depreciation using an age-based approach are described below. The steps describe the case where depreciation is calculated relative to the last treatment, or relative to the calculation of initial value described in Chapter 4 – whichever is later. If the only treatment being considered in the analysis is the construction or reconstruction of an asset, then depreciation is calculated since the asset was first purchased, constructed or reconstructed. If additional treatments are included, then depreciation is calculated from the time of asset purchase or construction until a treatment occurs. Overall asset value is a function of the initial asset value, value added through treatments, and value lost from depreciation. The overall calculation process is discussed further in Chapter 7.

Note that depreciation can never be greater than asset value, or an asset’s value would be deemed to be negative, and thus the asset would become a liability.

- Step 1 – Compile Data:
For each asset class and type of component being valued, compile the available data on the asset inventory and its age. Also compile the key parameters established through prior steps, such as useful life and residual value. If treatments other than asset purchase, construction/reconstruction are included, compile the available data on asset treatment history. The assumptions developed previously regarding the level of detail in the analysis and treatments to include may need to be revisited based on what data are available.

- Step 2 – Determine Asset Age:
Specify age at the level of detail established for the calculation – e.g., by individual asset or as a distribution of ages for the inventory. Refer to Chapter 13 of

*Measuring Capital (11)*for guidance on estimating age distributions based on useful life if age data are unavailable. - Step 3 – Calculate Depreciation:
Use the following equation to calculate depreciation D at time t:

\begin{align*} D(t) &= \frac{(V(t_0)-RV) * (A(t) - A(t_0))}{UL - A(t_0)} \end{align*}

where:

V(t_0) =value at time t_0;RV =residual value;UL =useful life;A(t) =asset age at time t;A(t_0) =asset age at time t_0;Note that when the initial value is based on current replacement cost and residual value is 0 this simplifies to the following:

\begin{align*} D(t) &= \frac{Replacement Cost * A(t)}{UL} \end{align*}

Generally the steps followed using a condition-based approach are similar to those described above for an age-based approach, with two important differences. That is, the determination of asset age is more involved in this case. The condition may be used as the sole determinant of effective age, or as a factor that modifies the effective age. Further, in the event that effective age is based strictly upon an asset’s condition then historic asset data is technically not needed in this case (though presumably would be used to established technical parameters such as unit costs and useful lives).

- Step 1 – Map Asset Condition to Effective Age:
For each asset class and type of component being valued, determine how asset condition relates to age. If condition is the best predictor of remaining life, then a simple function or lookup table can be defined to predict effective age for each feasible condition value. Alternatively, one may predict effective age based on condition, actual age and/or other variables. Refer to NCHRP Report 713 (18) for detailed guidance on modeling asset life.

- Step 2 – Compile Data:
For each asset class and type of component being valued, compile the available data on the asset inventory and its condition. If the calculation of effective age requires knowledge of actual age, also compile data on asset age and prior treatments that impact age. Also compile the key parameters established through prior steps, such as useful life and residual value. The assumptions developed previously regarding the level of detail in the analysis and treatments to include may need to be revisited based on what data are available.

- Step 3 – Determine Asset Age:
Specify effective age at the level of detail established for the calculation using the approach established in Step 1.

- Step 4 – Calculate Depreciation:
Use the following equation to calculate depreciation D at time t:

\begin{align*} D(t) &= \frac{(V(t_0)-RV) * (E(t) - E(t_0))}{UL - E(t_0)} \end{align*}

where:

V(t_0) =value at time t_0;RV =residual value;UL =useful life;E(t) =asset age at time t;E(t_0) =asset age at time t_0;Note that when the initial value is based on current replacement cost and residual value is 0 this simplifies to the following:

\begin{align*} D(t) &= \frac{Replacement Cost * E(t)}{UL} \end{align*}

The final option for calculating depreciation is the most complicated of the three. With this approach, one must understand how the benefits of an asset are actually being consumed over time, and structure the depreciation function accordingly.

For this approach it is necessary to define what the benefits of an asset are, and then establish a function for predicting how these benefits are consumed. Factors to consider in establishing asset benefits are:

- Level of use – traffic volume or ridership patterns over time. As described above, for highway assets often traffic is assumed to increase over time, which tends to result in accelerating depreciation. On the other hand, if an asset is utilized less as it ages then depreciation may decelerate over time.
- Travel time, operating and social costs – generally the benefit of a transportation asset is that it supports mobility. Thus, in many cases the basic benefit an asset provides can be measured in terms of the savings in travel time, operating and social costs experienced if the asset is in service in good condition relative to the case where the asset is allowed to deteriorate. For instance, as a road deteriorates its surface roughness increases, potentially increasing traffic congestion – and thus user travel time and social costs of transportation – and increasing vehicle operating costs.
- Asset failure – as an asset deteriorates it is more likely that the asset will fail in some manner, requiring emergency repairs, as well as temporary or complete closure. Where the likelihood of asset failure can be related to asset condition these costs tend to increase over time.

Once the benefits of an asset are established, it is necessary to define a function for representing how benefits are consumed over time. There is no single functional form that can be used for this step, though exponential and logistic curves provide flexibility for capturing a range of different depreciation patterns. A common approach is to use “declining balance depreciation,” in which an asset loses a specified percentage each year. Various other approaches have been defined in the accounting literature, most of which result in accelerated depreciation early in an asset’s life, such as double declining balance and sum of year’s digit’s appreciation. The following steps describe a basic approach to establishing the depreciation relationship considering a non-linear depreciation pattern.

- Step 1 – Quantify Asset Benefits:
For each asset class and type of component being valued, establish what benefits the asset yields, and how these vary over the life of an asset. Consider agency, user and social costs and benefits, and how these vary over time, as well as based on an asset’s condition.

- Step 2 – Establish the Depreciation Curve:
Determine the functional form of the depreciation curve based on the results of Step 1. If the pattern of benefit consumption can be approximated using a linear relationship, then revert to using a linear model. Otherwise, determine whether the depreciation pattern is accelerated or decelerated relative to linear depreciation.

If the depreciation pattern is accelerated, evaluate whether a fixed depreciation rate can be used, resulting in use of an exponential curve as described in Section 6.1. If the depreciation pattern is decelerated related to linear depreciation, evaluate whether a logistic (s-shaped) curve can be used as described in Section 6.1. Otherwise develop a customized depreciation function.

- Step 3 – Compile Data:
For each asset class and type of component being valued, compile the available data on the asset inventory and other data required to support the depreciation calculation approach defined in Step 2. The assumptions developed previously regarding the level of detail in the analysis and treatments to include may need to be revisited based on what data are available.

- Step 4 – Calculate Depreciation:
Calculate depreciation using the relationship determined in Step 2 with the data compiled in Step 3.