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Rapid Flood CBA Formula

Rapid Flood CBA Formula. Final Formula. Components of Equation. Total Diverting Costs Waiting Costs Not Travelling Costs If a diversion route does not exist, PCostDiv should be replaced with Min(MaxCostNT, ADC×Costperhr).

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Rapid Flood CBA Formula

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  1. Rapid Flood CBA Formula

  2. Final Formula

  3. Components of Equation Total Diverting Costs Waiting Costs Not Travelling Costs If a diversion route does not exist, PCostDiv should be replaced with Min(MaxCostNT, ADC×Costperhr). Accident and externality costs have been excluded from rapid formula for simplicity

  4. Components of Equation Benefit Cost Ratio BCR = Discounted Benefits / Discounted Costs Average Exceedance Probability (approximation) AEP = AATOC / ADC AATOC = Average Annual Time of Closure ADC = Average Duration of Closure

  5. Cost of Diverting Formula: total diverting costs (TDC) Calculated using Figure A Where: BC = perceived costs AB = accident and externality costs CD = duration of closure – equilibrium waiting time DE = number of road users diverting per hour Figure A

  6. Total Waiting Costs Figure B Formula: total waiting costs Calculated using Figure B and Figure D Where: GF = perceived costs FH = equilibrium waiting time FI = number of road users diverting per hour MN = perceived costs NO = equilibrium waiting time OP = number of road users not travelling per hour Figure D

  7. Costs of Not Travelling Figure C Formula: total not travelling costs (NTC) Calculated using Figure C and Figure D Where: JK = perceived costs XL = duration of closure - equilibrium waiting time KX = number of road users not travelling per hour MN = perceived costs NO = equilibrium waiting time OP = number of road users not travelling per hour Figure D

  8. Perceived Costs As expressed in the formula: PCostDiv=CPI×K1×Min(K2×DSL,K3,ADC×K4) • K1 is an adjustment factor for isolation costs and other flood associated costs not included in the model e.g. accident and externality costs • K2 is a constant value derived for VOC and TTC per kilometre of an average vehicle based on a typical rural used for a diversion • K3 is a constant value assigned to the maximum cost of not travelling • K4 is a constant value representing costs per hour of travel of an average vehicle type • CPI represents the change in prices since 2007

  9. Equilibrium Waiting Costs As expressed in the formula: WTE=min(K2×DSL/K4,K3/K4,ADC)

  10. Percentage vehicles not travelling As expressed in the formula: NT=min((K2×DSL/K3),(ADC×K4×CPI /K3),1)

  11. Benefit Cost Ratio BCR = Discounted Benefits / Discounted Costs As expressed in the formula: K = Capital Costs R = Residual Value NDRRA = Future NDRRA costs r = Discount Rate 15 and 16 are the median years of evaluation 30 years of benefits 1.5 is included to account for the growth rate in traffic over the life of the project

  12. Upper and Lower Bounds Since the formula is imprecise and a number of assumptions have been made, a lower and upper bound BCR has been calculated. Parameters applied to lower and upper bounds

  13. Calculation of K2 and K4

  14. RC = RMUC × RSCMRF OC = ((DTOPCF × PDIES + (1 - PDIES)) × OILCON(J,K) × GEAR) × Oil CostperL Austroads Formula (VOC) FC = Fuel Costs OC = Oil Costs TWC = Tyre Wear Costs RC = Repair and Maintenance Costs DC = Depreciation and Interest Costs DTOPCF = Petrol powered to diesel vehicle conversion ratio (model variable = 1.5) PDIES = Proportion of vehicles which are diesel powered OILCON(J,K) = Basic engine oil consumption speed relationship for petrol powered vehicle type J at speed K (Model variable, J by K array) GEAR = Factor relating total oil consumption to engine oil use (allows for gear box and differential oil use) (Model variable = 1.1) DSTDEP = Basic Distance Depreciation (cents/km) DEPSRF = Factor relating distance depreciation to road surface type TDPINT = Marginal time depreciation and interest SPEEDJ = Speed of new vehicle type J BTW = Basic Tyre Speed Relationship BF/SR = Basic Fuel/Speed Relationship GradAdj = Gradient Adjustment CurvAdj = Curvature Adjustment RoughAdj = Road Roughness Adjustment CongAdj = Traffic Congestion Adjustment RMUC = Basic repair and servicing costs for good condition sealed pavement RSCMRF = Factor reflecting the effect of pavement condition and surface category.

  15. VTVEHR (VT) = TT_VALUE (VT) x OCCUPANCY (VT) + FREIGHT (VT) Where: VTVEHR (VT) = Travel time cost per vehicle type TT_VALUE = Travel time cost per person per vehicle type OCCUPANCY = Average occupancy per vehicle FREIGHT (VT) = Travel time cost of freight per vehicle type Where: SPVVCR1 = Speed when VCR is equal to 1 VCRSPL = The VCR at which speed begins to drop below free speed due to congestion VCR = Actual Volume Capacity Ratio Queuing Speed = 30km/h VCRQ = The Volume Capacity Ratio once Queuing Speed has been reached (1.25) Austroads Formula (TTC) Where: PGRAD = Proportion of road section in each category FSA(MRS,KURV,IG) = Element of Free Speed Array (FSA) defined by Model Road State (MRS), Curvature (KURV) and grade (IG) IG = Grade Category: IG=1, grade = flat, IG=2, grade = 4%, IG=3, grade = 6%, IG=4, grade = 8%, IG=5, grade = 10% KURV = KURV = 1 when AHSPD≥ 95km/h KURV = 2 when 75km/h ≤AHSPD< 95km/h KURV = 3 when AHSPD< 75km/h AHSPD = Average Highway Speed

  16. Limitations of Rapid Model Formula • Approximations are made for VOC and TTC • Accident and externality costs are excluded from both base and project cases (inclusion of K1) • Median discount year is applied rather than discounting individual years (the impact of discounting is reduced) • Arbitrary value assigned to maximum cost of not travelling (inclusion of K3) • Demand functions are linear • Additional benefits of projects not relating to flooding cannot be included • Benefits of model are likely to be understated due to exclusions of data

  17. Limitations of Methodology • Network impacts are excluded • Impacts of interrelated projects are excluded • Impacts of varying severity of floods are excluded • Flood related accidents are not included • Wider economic benefits are not included • The level of anticipation of flooding is not included, e.g. flash flooding is not distinguished from seasonal flooding • Destinations of traffic are also not included or accounted for in the current model

  18. Conclusion • The model enables a very quick comparison of flood immunity and flood resiliency projects • Very strong projects can be identified very quickly using the model • The model identifies very quickly projects are not likely to be economically viable • The amount of time and data required to conduct an evaluation is greatly reduced • Borderline projects can be identified for a detailed evaluation

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