Using Spreadsheet Models for Using Spreadsheet Models for

Toll Revenue ForecastingToll Revenue Forecasting

Don Hubbard, PE, AICPDon Hubbard, PE, AICP Senior Supervising Planner Senior Supervising Planner

PBPB

Topics CoveredTopics Covered

Why Are New Methodologies Needed?Why Are New Methodologies Needed?

Description of Spreadsheet ModelsDescription of Spreadsheet Models

Advantages & DisadvantagesAdvantages & Disadvantages

A Sample ApplicationA Sample Application

ConclusionsConclusions

Why Are New Methodologies Why Are New Methodologies

Needed?Needed?

Travel is a derived demand …Travel is a derived demand …

so is travel demand forecastingso is travel demand forecasting

The trouble with traffic models …The trouble with traffic models …

Post-project studies have found that traditional Post-project studies have found that traditional 4-step models have a poor record for accuracy 4-step models have a poor record for accuracy for toll roadsfor toll roads

… … and accuracy has not improved over the last and accuracy has not improved over the last thirty yearsthirty years

Models are slow, noisy, cumbersome, opaqueModels are slow, noisy, cumbersome, opaque

Output not focused on issues of highest Output not focused on issues of highest concern to clients (terms of the agreement)concern to clients (terms of the agreement)

Private investors are used to a different kind of analysis tool Private investors are used to a different kind of analysis tool and are less tolerant of 4-Step models than DOTs have beenand are less tolerant of 4-Step models than DOTs have been

What Do Investors Want?What Do Investors Want?

Ability to Ability to test variationstest variations of the things that they have of the things that they have some influence over (toll structure, number of lanes, some influence over (toll structure, number of lanes, duration of contract, exempt classes of vehicles)duration of contract, exempt classes of vehicles)

Ability to perform Ability to perform sensitivity testssensitivity tests of the things they of the things they cannot control cannot control

TransparentTransparent & easy to check & easy to check

FastFast (able to test options during negotiations) (able to test options during negotiations)

Seamless Seamless connection to financialconnection to financial post-processors post-processors

This describes a spreadsheet, This describes a spreadsheet,

not a traditional 4-step modelnot a traditional 4-step model

Description ofDescription of

Spreadsheet ModelsSpreadsheet Models

StructureStructure

Mimics a traditional Mimics a traditional modelmodel

But with simplified But with simplified trips generation & trips generation & distributiondistribution

Primary focus is on Primary focus is on traffic assignment traffic assignment and post-processingand post-processing

Trip Generation & Distribution

Traffic Assignment

Post-Processing

Trip Generation & DistributionTrip Generation & Distribution

Traffic counts are Traffic counts are done for different done for different periods of different periods of different types of daystypes of days

User groups split User groups split out to extent data out to extent data allowsallows

Traffic Counts24-hr 365 days

Off Peak

Mid-Day&Shoulders

PM Peak

# of AM Peak Hours/Day (existing)

Group 3

Group 2

Daily Origin-Destination

Demand User Group 1 (Existing)

Group 3

Group 2

Growth Rate for User Group 1

Group 3

Group 2

Daily O-D Demand for User Group 1 for

Future Study Year

1

2

34

5

6

Off Peak

# of Mid-Day & Shoulder Hours/Day

(existing)

WeekdaysWeekends & Holidays

Off Peak

Mid-Day&Shoulders

PM Peak

Initial Volumes & Numbers of AM Peak

Hours/day (study year)

One set for Weekdaysand a second set for Weekends & Holidays

Growth factors based on population & Growth factors based on population & employment forecasts by catchment areaemployment forecasts by catchment area

Peak SpreadingPeak Spreading

Excess peak period traffic Excess peak period traffic results in longer peakresults in longer peak

Revised traffic then goes Revised traffic then goes to diversion modelto diversion model

Traffic DiversionModel

Peak Spreading Algorithm

6

78

9

10

Off Peak

Mid-Day&Shoulders

PM Peak

Initial Volumes & Numbers of AM Peak

Hours/day (study year)

One set for Weekdaysand a second set for Weekends & Holidays

Off Peak

Mid-Day & Shoulders

PM Peak

Revised Volumes & Numbers of AM Peak

Hours/day

Corridor Capacity

TrafficAssignmentModel

Traffic Profile for AM Peak Period

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

5:30 6:00 6:30 7:00 7:30 8:00 8:30 9:00 9:30 10:00

Time of Day

Tra

ffic

Vo

lum

e p

er H

alf-

Ho

ur

Ajusted Future

Unadjusted Future

Existing

Traffic DiversionTraffic Diversion

Split between tollway & Split between tollway & non-tolled alternative non-tolled alternative based on ratio of costsbased on ratio of costs

Group 3

Group 3

Assume 80:20 Splitin Traffic between

Tollroad & Free Road

Travel Times for each Section

Group 3

Final Traffic Volumesby Section for

Period in Question

Spreadsheet Methodology for Traffic Assignment andRevenue Forecasting for a Single Time Period

Group 2

Origin-Destination Data for User

Group 1

Group 2

SectionalDemand Group 1

New Volumes by Section

Group 2

Toll Costs for Group 1 (minutes)

Group 3

Group 2

DiversionCurve Group 1

Speed-Volume Relationship

Feedback until stable

Tollroad Revenues for Period in Question

Group 3

Group 2

Value of Time for Group 1

Group 3

Group 2

Toll for Group 1

1

2

3

4

6

5

7 8

9

10

11

13

12

Key

Input

Intermediate Step

Output

Free-Flow Speed

Capacity of Competing Routes by Sections

Length of Competing Routes by Sections

Speed - Volume Relationship

0.010.020.030.040.050.060.070.080.0

0 400 800 1200 1600 2000 2400 2800

Traffic Volume

Sp

ee

d

Diversion Curves

0%

20%

40%

60%

80%

100%

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Difference in Travel Time

% U

sin

g T

ollw

ay

Starts with a seed value Starts with a seed value for the split, then for the split, then iterates assignment to iterates assignment to produce a stable resultproduce a stable result

Post-ProcessingPost-Processing

Outputs from the diversion model are traffic volumes and Outputs from the diversion model are traffic volumes and revenues for each periodrevenues for each period

Off Peak

Study Year Revenues

Midday & Shoulders

PM Peak

AM Peak Period Revenues

Traffic DiversionModel

Off Peak

Midday & Shoulders

PM Peak

# of AM Peak Hours/Year

Number of Weekdays,

Weekend Days & Holidays per Year

12

13

14

15

Off Peak

Midday & Shoulders

PM Peak

AM Peak Period Traffic Volumes

11

LOS Analysis

Capacity Improvement Plans

16

17

The volumes can be fed into The volumes can be fed into LOS analysis and used to LOS analysis and used to forecast when capacity forecast when capacity improvements will be neededimprovements will be needed

Revenues can be Revenues can be aggregated to annual aggregated to annual levels for use in financial levels for use in financial analysesanalyses

Sample SheetSample Sheetfor Single Periodfor Single Period

High Income Cars Low Income Cars Trucks with More Than 2 Axles

Toll = Toll = Toll =

Value of Time = Value of Time = Value of Time =

Demand (vehicle-trips per hour) Demand (vehicle-trips per hour) Demand (vehicle-trips per hour)Free Tollway

1 4 2 3.5 A B C D E F A B C D E F A B C D E F2 4 2 2.0 A - 250 525 416 250 2,500 A - 500 1,050 833 500 5,000 A - 25 53 42 25 2503 4 2 2.5 B - - 59 25 13 488 B - - 118 50 25 975 B - - 6 3 1 494 4 2 2.5 C - - - 59 29 579 C - - - 118 58 1,158 C - - - 6 3 585 4 2 2.5 D - - - - 46 870 D - - - - 93 1,740 D - - - - 5 87

E - - - - - 1,250 E - - - - - 2,500 E - - - - - 125Capacity per Lane = 2,000 F - - - - - - F - - - - - - F - - - - - -Truck PCU Factor = 2.0

Percent of This Group's Demand that Uses Tollway Percent of This Group's Demand that Uses Tollway Percent of This Group's Demand that Uses Tollway

A B C D E F A B C D E F A B C D E FFree Tollway A - 0% 19% 26% 28% 50% A - 0% 6% 12% 15% 35% A - 0% 13% 20% 23% 45%

1 7,574 3,250 30% B - - 3% 13% 19% 49% B - - 0% 3% 8% 30% B - - 1% 8% 14% 42%2 7,991 3,750 32% C - - - 4% 12% 47% C - - - 0% 4% 26% C - - - 2% 8% 39%3 7,833 4,134 35% D - - - - 3% 48% D - - - - 0% 21% D - - - - 2% 37%4 8,447 4,663 36% E - - - - - 0% E - - - - - 0% E - - - - - 0%5 11,099 4,517 29% F - - - - - - F - - - - - - F - - - - - -

Number of Tollway Users from This Group Number of Tollway Users from This Group Number of Tollway Users from This Group

A B C D E F A B C D E F A B C D E FFree Tollway A - 0 102 107 70 1,254 A - 0 64 97 77 1,751 A - 0 7 8 6 112

1 68 69 B - - 2 3 2 237 B - - 0 2 2 292 B - - 0 0 0 202 66 68 C - - - 2 3 275 C - - - 1 2 300 C - - - 0 0 233 67 65 D - - - - 2 419 D - - - - 0 360 D - - - - 0 324 64 59 E - - - - - 0 E - - - - - 0 E - - - - - 05 40 61 F - - - - - - F - - - - - - F - - - - - -

Study Year:Number of Tollway Users Period: Overall Percent Using Tollway Direction:Total Hourly Revenues $1,461$620

2,947

$73734% 25%

Orig

ins

1 2

$105

User Group

Destinations

Orig

ins

$0.50

$18.00

All TripsDestinations

2004

Destinations

AM Peak

$0.25

$12.00

$0.25

$6.00

2,478 209

Destinations

Southbound

All TripsDestinations

Orig

ins

All TripsDestinations Destinations

Orig

ins

All Trips

Orig

ins

Section Length

Orig

ins

All Trips

Orig

ins

Traffic VolumesAll Trips

# of Lanes onDestinations

All Trips

Total

20% 28%

5,635

Section

Orig

ins

Orig

ins

3

SectionSpeed

% Using Tollway

All TripsDestinations

All Trips

Area A

B

C

D

Section1

E

Area F

Inputs for Road Supply

Inputs for Corridor Demand

ResultsSection

2

Section3

Section4

Section5

Free Tollway1 4 2 3.52 4 2 2.03 4 2 2.54 4 2 2.55 4 2 2.5

Capacity per Lane = 2,000Truck PCU Factor = 2.0

Section Length# of Lanes on

Inputs for Road Supply

High Income Cars

Toll =

Value of Time =

Demand (vehicle-trips per hour)

A B C D E FA - 250 525 416 250 2,500B - - 59 25 13 488C - - - 59 29 579D - - - - 46 870E - - - - - 1,250F - - - - - -

$0.25

$12.00

DestinationsAll Trips

Orig

ins

Percent of This Group's Demand that Uses Tollway

A B C D E FA - 0% 19% 26% 28% 50%B - - 3% 13% 19% 49%C - - - 4% 12% 47%D - - - - 3% 48%E - - - - - 0%F - - - - - -

Orig

ins

All TripsDestinations

Free Tollway1 7,574 3,250 30%2 7,991 3,750 32%3 7,833 4,134 35%4 8,447 4,663 36%5 11,099 4,517 29%

Traffic VolumesSection

% Using TollwayFree Tollway

1 68 692 66 683 67 654 64 595 40 61

SectionSpeed

Number of Tollway Users

Overall Percent Using TollwayTotal Hourly Revenues $1,461$620

2,947

$73734% 25%

1 2

$105

User Group

2,478 209

Total

20% 28%

5,635

3

From Master Input Sheet

Assumed Capacity Per Lane 2,000 SECTIONAL VOLUMES AND LOS

Southbound Northbound

Tollway Other Tollway Other Tollway Other Tollway Other Tollway Other Tollway Other2 4 2 4 2 4 2 4 2 4 2 4

Free 3,863 5,593 41% 4,317 7,087 38% 4,699 8,263 36% Free 1,932 2,284 46% 2,324 2,751 46% 2,623 3,110 46%$0.045 2,359 7,098 25% 3,310 8,094 29% 4,100 8,861 32% $0.045 894 3,321 21% 1,076 3,999 21% 1,220 4,513 21%$0.089 1,439 8,018 15% 2,457 8,947 22% 3,494 9,467 27% $0.089 423 3,792 10% 511 4,564 10% 584 5,149 10%$0.134 923 8,534 10% 1,902 9,502 17% 3,008 9,953 23% $0.134 212 4,004 5% 256 4,819 5% 296 5,437 5%$0.150 792 8,664 8% 1,752 9,652 15% 2,867 10,094 22% $0.150 168 4,048 4% 203 4,872 4% 235 5,498 4%

Tollway Other Tollway Other Tollway Other Tollway Other Tollway Other Tollway Other2 4 2 4 2 4 2 4 2 4 2 4

Free 4,141 6,407 39% 4,577 8,042 36% 4,963 9,333 35% Free 2,183 2,930 43% 2,618 3,499 43% 2,937 3,913 43%$0.045 2,556 7,993 24% 3,552 9,067 28% 4,381 9,914 31% $0.045 1,010 4,103 20% 1,212 4,905 20% 1,368 5,483 20%$0.089 1,573 8,975 15% 2,667 9,952 21% 3,775 10,520 26% $0.089 478 4,634 9% 576 5,542 9% 656 6,194 10%$0.134 1,018 9,531 10% 2,086 10,533 17% 3,286 11,009 23% $0.134 239 4,874 5% 289 5,829 5% 332 6,518 5%$0.150 876 9,672 8% 1,929 10,690 15% 3,145 11,150 22% $0.150 190 4,923 4% 229 5,888 4% 265 6,586 4%

Tollway Other Tollway Other Tollway Other Tollway Other Tollway Other Tollway OtherLanes 2 4 2 4 2 4 2 4 2 4 2 4Free 4,246 6,343 40% 4,645 7,795 37% 5,002 8,912 36% Free 2,278 2,874 44% 2,734 3,465 44% 3,067 3,896 44%

$0.045 2,663 7,926 25% 3,660 8,779 29% 4,468 9,447 32% $0.045 1,054 4,098 20% 1,266 4,933 20% 1,430 5,533 21%$0.089 1,659 8,929 16% 2,785 9,654 22% 3,892 10,023 28% $0.089 499 4,653 10% 602 5,598 10% 687 6,276 10%$0.134 1,087 9,501 10% 2,206 10,234 18% 3,420 10,494 25% $0.134 250 4,903 5% 302 5,897 5% 349 6,614 5%$0.150 940 9,648 9% 2,049 10,391 16% 3,283 10,632 24% $0.150 198 4,954 4% 240 5,959 4% 278 6,685 4%

2010 2020 2030Tollway

as %

Tollway as %

Tollway as %

2010

Tollway as %

2020 2030

Tollway as %

Tollway as %

Tollway as %

Tollway as %

2020 2030

Tollway as %

2010 2020 2030

20302010

AM Peak Hour

Tollway as %

Tollway as %

Tollway as %

Tollway as %

Tollway as %

2020

Tollway as %

2010 2020 2030 2010Tollway

as %Tollway

as %Tollway

as %

Section1

Section2

Section3

Section4

Section5

Sample VolumeSample Volume& LOS Output & LOS Output

Color Code Level of Service A, B, or C Level of Service D or E Level of Service F

Tollway Other2 4

Free 4,141 6,407 39%$0.045 2,556 7,993 24%$0.089 1,573 8,975 15%$0.134 1,018 9,531 10%$0.150 876 9,672 8%

2010Tollway

as %SchematicSchematic

Southbound NorthboundSouthbound Northbound

Managing the ProcessManaging the Process

All scenario inputs are All scenario inputs are entered into a single pageentered into a single page

Macros then open other Macros then open other workbooks, process data, workbooks, process data, and closeand close

Summary results then Summary results then copied into master filecopied into master file

Fast, compact resultsFast, compact results

Master FileInputs & Outputs

Traffic Assignment

Traffic Assignment

Traffic Assignment

Traffic Assignment

Traffic Assignment

Traffic Assignment

Traffic Assignment

Traffic Assignment

Model for Each Period, Day, & Year Combo

Traffic Assignment

Post-Processed Results for Each

Study Year

Advantages &Advantages &

DisadvantagesDisadvantages

AdvantagesAdvantages

Often quicker & easier to createOften quicker & easier to create They force you to examine your assumptions, so may They force you to examine your assumptions, so may

be more rigorousbe more rigorous Less noise than traditional models, so more accurate Less noise than traditional models, so more accurate

for small changesfor small changes Can feed directly to/from other models (land use, Can feed directly to/from other models (land use,

financial models) financial models) Better control over the process (for the same reasons Better control over the process (for the same reasons

that airplanes are more maneuverable when not using that airplanes are more maneuverable when not using auto-pilot)auto-pilot)

DisadvantagesDisadvantages

Limited to well-defined corridors with only a few Limited to well-defined corridors with only a few realistic alternative routesrealistic alternative routes

Single-purpose models; cannot replace 4-step Single-purpose models; cannot replace 4-step models for general modeling usemodels for general modeling use

Agencies may be reluctant to accept alternatives Agencies may be reluctant to accept alternatives to a regional model if one existsto a regional model if one exists

Sample Application:Sample Application:

North Luzon ExpresswayNorth Luzon Expressway

Project BackgroundProject Background

Old tollway extending Old tollway extending northwards from Metro northwards from Metro Manila Manila

Leased to private company Leased to private company under an upgrade-operate-under an upgrade-operate-transfer agreementtransfer agreement

Varies from 8-lane freeway Varies from 8-lane freeway in south to 4-lane in south to 4-lane expressway in northexpressway in north

Alternate route is 2-to-4 Alternate route is 2-to-4 lane undivided highwaylane undivided highway

Source: PB AsiaSource: PB AsiaManila

(12 Million)

San Fernando (500,000)

Angeles City (500,000)

Key FeaturesKey Features

50 miles of freeway50 miles of freeway16 interchanges16 interchanges$377 million cost$377 million cost

Need to keep costs down; Need to keep costs down; toll increase politically toll increase politically sensitivesensitive

Needed detailed volume Needed detailed volume forecasts for each ramp to forecasts for each ramp to do “just enough” and do “just enough” and “just in time” upgrading“just in time” upgrading

Urban SectionUrban Section

Rural SectionRural Section

Model RequirementsModel Requirements

Also needed detailed cost Also needed detailed cost and revenue projections to and revenue projections to arrange for various loan arrange for various loan packages packages

Banks required that all Banks required that all assumptions be open to assumptions be open to scrutinyscrutiny

Model must be able to Model must be able to predict, on the spot, the predict, on the spot, the effect of changes in effect of changes in assumptions assumptions

Costs Revenue

$

Background for the NLE Background for the NLE ModelModel

Existing regional lacked Existing regional lacked detail in study corridor detail in study corridor

Ramp volumes varied Ramp volumes varied erratically for different erratically for different study yearsstudy years

Investors unwilling to Investors unwilling to take risks on unreliable take risks on unreliable forecastsforecasts

New Approach - SpreadsheetNew Approach - Spreadsheet

9 months spent trying to fix regional model, 9 months spent trying to fix regional model, only 3 months remained before firm forecasts only 3 months remained before firm forecasts were neededwere needed

Determined that the regional model was unlikely Determined that the regional model was unlikely to produce the needed accuracy within the time to produce the needed accuracy within the time availableavailable

Decided to replace the regional model with a Decided to replace the regional model with a spreadsheet modelspreadsheet model

Trip Generation Trip Generation

O-D table taken from O-D table taken from toll receipts from toll receipts from previous 5 yearsprevious 5 years

Growth rates for Growth rates for each O-D pair were each O-D pair were based on the based on the expected population expected population and employment and employment growth at each endgrowth at each end

Growth of O-D TableGrowth of O-D Table

The existing volumes at The existing volumes at each ramp were then each ramp were then factored up, based on factored up, based on future volumes of the O-D future volumes of the O-D pairs served, to make pairs served, to make “Base Demand”“Base Demand”

Existing

2010

2020

2030

Other Input AssumptionsOther Input Assumptions

0

2 0000

4 0000

6 0000

8 0000

1 E +05

1 E +05

1 E +05

2 E +05

2 E +05

2 E +05

0 0.5 1 1 .5 2 2 .5 3 3 .5 4

Toll

Tra

ffic

Next added:Next added:

- Assumed tolls- Assumed tolls

- Toll sensitivity- Toll sensitivity

- Income assumptions- Income assumptions

Income GrowthIncome Growth

0.1

0.1 2

0.1 4

0.1 6

0.1 8

0.2

0.2 2

0.2 4

0.2 6

1 2 3 4 5 6 7 8 9 1 0

YearIn

com

e

Diversion CurveDiversion Curve

Capacity ConstraintsCapacity Constraints

Explicit capacity constraints Explicit capacity constraints were made for:were made for:

- Receiving capacity of- Receiving capacity of local roads local roads

- Toll plaza capacity- Toll plaza capacity

- Mainline capacity- Mainline capacity

Peak SpreadingPeak Spreading

Separate sheets were done Separate sheets were done for each peak period and for each peak period and for the off-peak period, for the off-peak period, with spillover (peak with spillover (peak spreading) based on spreading) based on conditions during the peak conditions during the peak hourhour

Peak

Off-Peak

Spill-Spill-OverOver

Schedule for UpgradingSchedule for Upgrading

Ramp volumes were Ramp volumes were automatically compared to automatically compared to service thresholdsservice thresholds

Produced an upgrading Produced an upgrading schedule for each of 40+ schedule for each of 40+ rampsramps

RampVolumes

Year UpgradeNeeded

LOS LOS ThresholdThreshold

Financial ResultsFinancial Results

The resulting volumes for The resulting volumes for each ramp-to-ramp pair, each ramp-to-ramp pair, for each vehicle class, for each vehicle class, were converted into annual were converted into annual revenuesrevenues

These were automatically These were automatically fed into the financial fed into the financial spreadsheetsspreadsheets

Volume

Revenue

Annuali-Annuali-zation zation FactorFactor

Application During NegotiationsApplication During Negotiations

The model was able to quickly answer questions like, The model was able to quickly answer questions like, “What happens if the government refuses to approve “What happens if the government refuses to approve toll increases after the first 5 years?”toll increases after the first 5 years?”

?- Traffic increases- Traffic increases- Upgrading needed sooner- Upgrading needed sooner- Revenue/veh decreases- Revenue/veh decreases- Rate of return declines- Rate of return declines

Results of the NLE ModelResults of the NLE Model

The methodology was The methodology was robust and defendablerobust and defendable

The resulting forecasts The resulting forecasts were reasonablewere reasonable 0

50

100

150

200

250

Year

Av

era

ge

Da

ily T

raff

ic (

bo

th d

ire

cti

on

s)

1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 2015

The client was able to get financing; upgrading now The client was able to get financing; upgrading now underwayunderway

“Asia-Pacific Transport Project of the Year”“Asia-Pacific Transport Project of the Year”Project Finance Magazine Project Finance Magazine (London)(London)

Past Future

ConclusionsConclusions

ConclusionsConclusions

Model types should be considered tools in a toolbox; Model types should be considered tools in a toolbox; different types are needed for different tasksdifferent types are needed for different tasks

There are circumstances where spreadsheet models There are circumstances where spreadsheet models are likely to produce better results than traditional are likely to produce better results than traditional modelsmodels

– Well-defined corridor with limited routesWell-defined corridor with limited routes

– Uncertainties about input assumptions more likely Uncertainties about input assumptions more likely source of error than computational mechanicssource of error than computational mechanics

Don HubbardDon Hubbard

Senior Supervising PlannerSenior Supervising PlannerPBPB

Tel. (916) 567-2555Tel. (916) 567-2555hubbardd@pbworld.comhubbardd@pbworld.com