Business Logistics 420Public Transportation

Lecture 19:Cost Models for Public Transportation

Lecture Objectives

• To understand the role of cost estimation and cost allocation in transit planning and operations

• To understand the differences between alternate operating cost models

• To understand and be able to use the unit cost model

Operating Cost Models

• Purpose of cost models: Estimate operating expenses (not capital) for a system or individual route or service.

Typical Uses of Cost Models

• Evaluate new service proposals– For example, how much will it cost to add service to a

new apartment complex?– One important issue -- what is your definition of cost --

incremental cost or fully allocated?

• Determine the cost of a route as part of a system performance evaluation– Helps answer the questions such as what is the cost per

passenger, or the ratio of revenue to expenses for a specific route

Typical Uses of Cost Models

• Allocate costs for subsidy purposes– The local share of transit operating subsidies is

usually shared by a number of local government units (CATA is funded by 7)

– One way to divide this subsidy obligation is to estimate the revenue and cost of service provided to each unit of government

Typical Uses of Cost Models

• Evaluate competitive bids for service– Need fair way to compare cost of a public

agency providing services v s. a private contractor

– Issue of fully allocated vs. incremental costs– Public agency actually experiences incremental

changes, but fully-allocated costs the “best” way for a fair comparison.

Types of Cost Models• Regression where Annual Cost = f(miles, hours, vehicles)• Engineering/Accounting whereby costs are estimated

by calculating units consumed and the cost of the units. For example, you estimate total cost by figuring out what it will take to provide the service – so many hours of labor time the labor and fringe rate, so many gallons of fuel times the number of gallons to be consumed, etc.

• Unit Cost Model or Fully Allocated Cost model – the preferred way

Types of Cost Models (Continued)

• Unit Cost Model or Fully Allocated Cost model – the preferred way Annual Cost for System or Route = a x miles + b x hours = c x peak vehicles

• Where: a = unit cost of mileage-related expenses b = unit cost of hours-related expenses c = unit cost of peak vehicle-related expenses

Steps Required to Apply the Unit Cost Model

• Determine allocation variables – decide what factors you will use to allocate costs. Most common factors are vehicle miles, vehicle hours, and peak vehicles

• Determine for each cost item for a transit system budget (or actual expense report) which of the allocation variables best explains the variation in the cost item. For example, fuel and maintenance costs are most closely related to distance traveled (vehicle miles), driver wages and fringe costs are most closely tied to vehicle hours driven, and overhead costs such as administrative salaries and other administrative expenses are allocated based on peak vehicles.

Assign Expenses to Categories

Expense Item Miles-Related

Hours-Related

Peak Veh.Related

Driver Labor& Fringe

X

Fuel X

MaintenanceParts

X

MaintenanceLabor/Fringe

X

Insurance X

AdministrativeLabor/Fringe

X

Steps Required to Apply the Unit Cost Model

• Assign each budget or actual expense item to one of the three cost variables and then total the costs for each of the three categories

• Divide the total cost for say vehicle miles, by the number of miles traveled in order to obtain the unit cost for each variable.

Example Expense Assignment to Categories

Expense Item Miles-

RelatedHours-Related

Peak Veh.Related

Driver Labor& Fringe

$400,000

Fuel $60,000

MaintenanceParts

$100,000

MaintenanceLabor/Fringe

$ 90,000

Insurance $ 100,000

AdministrativeExpenses

$200,000

Total $250,000 $400,000 $300,000

System Units (Input)

• System Variables– Annual Vehicle Miles = 250,000– Annual Vehicle Hours = 16,000– Peak Vehicles = 8

Calculate Unit Cost Factors

• Miles Related Expenses

$250,000 / 250,000 miles = $1.00

• Hours-Related Expenses

$400,000 / 16,000 hours = $25.00

Calculate Unit Cost Factors

• Peak Vehicle Related Expenses

$300,000 / 8 vehicles = $37,500

The Unit Cost Model for this Example

• Total expense =

$1.00 x vehicle miles +

$25.00 x vehicle hours +

$37,500 x peak vehicles

Application of Model to Determine Route Expense

• Given route data - 1 bus, 35,000 miles per year, 3,000 vehicle hours

• Total expense for route =

$1.00 x 35,000 vehicle miles = $35,000 +$25.00 x 3,000 vehicle hours = $75,000 +$33,125 x 1 peak vehicle = $37,500 =

Total Cost $147,500

Use for Calculating Performance Measures

• For the sample route, say you know that ridership is 75,000 riders per year and revenue is $75,000

• Revenue/Expense Ratio $75,000/$147,500 = 50.8%

• Expense per Passenger $147,500/75,000 = $1.97

Fully Allocated vs. Incremental Cost

• The $147,500 figure is the fully allocated cost and includes a portion of costs that would not likely change with small changes in service provided, e.g., administrative salaries

• To determine incremental cost, omit administrative salaries and recalculate formula. In the example, incremental cost would be $147,500 - $25,000 = $122,500

Study Questions• What are the uses of operating cost models?

• What is the best model to use in most situations?

• How do you develop the unit costs for a unit cost model?

• What is the appropriate cost to use (fully allocated vs.. incremental) when:– doing a service evaluation– determining the cost of a new service– comparing competitive bids to provide service