The calculation of annualized costs was carried out using an Microsoft Excel©-based computational model. The computational model represents the core of the study because it links extensive arrays of input data with the end result: estimated annualized full cost of road infrastructure by representative road classes (per one kilometre of a single traffic lane).
The functional capabilities of the model include the following features:
• Automated linkage between input values and calculated results. For example, it is possible to change a unit construction cost for a specific part of the road infrastructure and the change is automatically reflected in the end result.
• Suitability for sensitivity analysis. For example, it is possible to change key input data in the Universal Input Sheet to carry out sensitivity analysis in terms of the discount rate.
• Aggregation of results. The model enables to aggregate annualized costs and road inventory data across the entire road network or part of the network.
• Modular design. The key input unit cost and quantity data are grouped in specific worksheets for clarity and ease of future modifications.
Description of the Computational Model
The model was created in Excel© because of its versatile nature and its ability to facilitate the investigation of the “what if” situations associated with this project. The model allows for the input values to be easily changed with the annualized costs automatically recalculating.
Due to the large number of input parameters associated with the cost of roadway infrastructure, the computational model incorporates a series of workbooks representing the different components of roadway inventory. Each workbook is then subdivided into a series of worksheets that contain the input values, the intermediate calculations, and the required output values.
The main parts of the computational model are shown in the model flowchart in Figure 4. Table 52 outlines the workbooks and worksheets that constitute the computational model. A complete set of input and output tables for the computational model is given in Appendix D.
How to use the Model
The computational model used to estimate the representative annualized road costs was developed as a suite of linked Excel© worksheets. Changes in one worksheet are automatically propagated throughout the suite. Thus, changing input data in one worksheet automatically changes the results.
Workbook Linkage
As can be seen in the upper left hand corner of Figure 4, the Main.xls workbook is used to contain not only the universal inputs, but also the summary of the entire roadway infrastructure. This workbook is the central link combining all of the other workbooks.
When opening any of the workbooks, Microsoft© Excel will verify that the user wants to maintain the linkage between the various workbooks. The screen capture from Excel© 2003, given in Figure 5, shows the dialog box used to update workbook connectivity. To work with the computational model, the user should click on the button labelled ‘Update’ (Figure 5).
Universal Inputs
Table 52. Description of Computational Model Files
Main.xls Input This worksheet contains the universal inputs that affect the annualized costs.
Age This worksheet contains the average age of the infrastructure components.
Raw Summary This worksheet is used to summarize the annualized costs of all roadway infrastructure components provided in the various other workbooks, in terms of a 2-Lane km roadway.
Summary This worksheet is used to summarize the deteriorated, adjusted, annualized costs of all roadway
They show the annualized roadway costs per lane km of roadway.
Bridges.xls Quantities This worksheet contains the values that show the average number of square metres of bridge deck per 2-lane km of roadway.
Unit Costs This worksheet contains the initial construction cost, the maintenance and rehabilitation costs, and the frequency of the maintenance.
New Costs This worksheet uses the quantities and unit costs to calculate the cost of new bridges per 2-lane km.
New Costs – Annualized
This worksheet contains the new costs calculated in the previous sheet as an annualized value over the analysis period at the discount rate.
Unit Costs This worksheet contains the unit costs of the key items representing all other road infrastructure.
Quantities This worksheet contains information on the quantity of the various items on the different road categories.
Service Lives This worksheet contains the expected service lives of the other road infrastructure items. These represent the age at which these items need to be replaced.
Allowances This worksheet contains the mark up rate that will be used to account for all other road infrastructure components that are not specifically listed.
Workbook name
Worksheet name
Worksheet description
New Costs This worksheet has the cost of all key items per 2-lane km.
New Costs – Annualized
This worksheet contains the new costs calculated in the previous sheet as an annualized value over the analysis period at the discount rate.
M&R Costs - Annualized
This worksheet contains the annualized costs (per 2-lane km) of the maintenance and rehabilitation of the key items within the analysis period annualized over
Unit Costs This worksheet contains the unit cost of all roadway materials and construction activities. construction and M&R costs for all of the categories within the province. operating costs (per lane km) based on the annualized cost and expected frequency of initial construction activities.
Comparison This worksheet calculates the expected total capital and operating costs based on estimates of network length and compares the prediction to values reported by the provincial and municipal agencies.
.
Figure 5. Dialog Box to Update Workbook Connectivity
The computational model is designed to read the worksheets located within the same directory as the Main.xls file. To verify the location of the linked workbooks, a list of the linked workbooks can be found by clicking the ‘Links’ item under the Edit menu.
The easiest way to work with the model and keep all values current in all worksheets is to open the Main.xls workbook first. As values are updated in the linked sheets, they will then automatic update in the Main.xls summaries as well.
Excel will not recalculate values in worksheets that are not currently open. This means that in order to completely recalculate the model after a change in a universal input, such as the discount rate, it is necessary to open all of the pertinent workbooks. Consequently, it is recommended to have all of the workbooks open simultaneously when updating universal inputs.
Protection of Formulas
The computational model contains a large quantity of both model inputs, as well as calculated values. To prevent accidentally over-writing calculated values, the workbooks have all values, except for the model inputs, locked so they cannot be edited.
It is possible to unlock the worksheets within Excel by using the ‘Protection’ option under the ‘Tools’
menu. No password has been set-up to further protect the formulas from accidental changes.
In order to simplify long and complicated Excel functions and to make the model easier to trace, custom functions were developed to calculate the EUAC, the present worth, and EUAC of regularly occurring payments. The custom formulas were created with Visual Basic for Applications and are stored within each of the workbooks. The equations for these formulas can be found in Chapter 6. The custom formulas should not be changed.
Layout of Data
Each of the workbooks contains a series of worksheets that represent the various steps in the
computational model. The general format of the each work book is that the worksheets flow from left to right in the sequence of unit costs, quantities, service life (if applicable), annualized initial road
infrastructure costs, and annualized maintenance and rehabilitation costs.
The summary listing of workbooks and their worksheets, and the description of worksheets, can be found in Table 52. Workbooks deal with major computational blocks such as main infrastructure components (e.g., bridges, or pavements) or with main cost types (e.g., routine and winter maintenance). Worksheets within the workbooks deal with specific parameters such as unit costs. Worksheet tables contain the data for all road infrastructure categories established in Chapter 3. Consequently, all unit costs and quantities
are provided for all the 14 geographical regions and for all 14 possible combinations of geographical regions, jurisdiction, rural-urban alignment, and functional class.
Each workbook starts with a worksheet named Introduction. The Introduction worksheet contains a brief description of the purpose and the structure of the workbook and provides a brief description of all the worksheets contained in the workbook. The objective of the Introduction worksheets is to ensure that the computational model is user-friendly12.
When applicable, the input data, calculations, and summary results are stored in 14 by 14 tables
throughout the computational model. The 14 by 14 tables also contain the unit costs, quantities, service lives, and calculations for the various infrastructure components. Some unit costs were not expected to vary based on the functional class of road and hence are presented in a manner more applicable to the data.
A reporting format was developed in order to facilitate printing the final results of the model. The reporting format consists of one page of results per geographical region and contains the costs for each of the road infrastructure items as well as the total cost. The estimated annualized roadway infrastructure costs are found in the Cost Reporting Sheets in Main.xls file.
12 The Introduction worksheets were added to all workbooks of the revised computational model. The computational model that accompanied Final Report of March 31, 2006, does not contain the Introduction worksheets.