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Cost-Benefit Analysis for Dummies

Written by Carl Alsabrook

Law enforcement agencies use basic police vehicle cost analysis, i.e., lifecycle cost analysis (LCA), in examining acquisition costs of vehicles and equipment, as well as operating expenses associated with maintaining vehicles. The LCA measures all associated costs of vehicles over their entire service lives, from acquisition to disposition. It is used to select among alternative vehicle choices and to determine the best vehicle replacement policy.

A more advanced decision tool is cost-benefit analysis (CBA). A CBA not only measures the costs but also the benefits of the underlying project, such as a specific police vehicle program. It compares the advantages and disadvantages and weighs the benefits of a purchase or program with the costs such a purchase or program generates over its expected lifetime.

A common example is the decision-making process of an agency deciding whether to implement a specialty police vehicle program, such as the purchase of a squad for a selective traffic enforcement program (STEP). A lifecycle cost analysis can assist in choosing a particular make and model for such a program. However, only a CBA can tell agency administrators and fleet managers whether the program itself makes economic sense. A CBA shows whether the program is efficient and does not constitute a waste of valuable agency resources and taxpayers’ money.

Rockwall’s STEP program

The Rockwall, TX Police Department (RPD) is a mid-size agency employing 55 full-time sworn officers. RPD has successfully operated a one-vehicle STEP program since the mid- 1980s. The STEP vehicle is only used for the program and for special events such as parades, cruises, crime prevention fairs, neighborhood events, and school events. Its main purpose is to enforce traffic laws in areas experiencing above-average traffic violations and areas with statistically significant accident rates. The STEP vehicle is not used for general patrol or traffic enforcement duties during officers’ regular shifts.

The RPD was considering adding a second special service vehicle to its STEP program. In order to decide whether the purchase of a second STEP vehicle would be an efficient use of departmental resources, RPD had to look at its past STEP experiences and project future costs and benefits of a second STEP vehicle.

RPD’s STEP vehicle at the time was a 1997 special service package Chevrolet Camaro, and the department was considering adding a second such Camaro to its STEP program. Given the deployment as overtime vehicles only, RPD’s STEP vehicles traditionally see less use both in hours and in odometer mileage compared with regular patrol and traffic enforcement squads. Based on past experiences, we assumed that the second STEP Camaro would only accumulate a maximum of 7,000 miles a year and stay in service for seven years.

Just like in a LCA, costs are analyzed in periodic time intervals in a CBA such as on an annual basis. However, a basic CBA encompasses more data than a basic LCA. Whereas a basic LCA merely covers actual vehicle cost data, a basic CBA introduces some overhead cost such as officers’ overtime expenses like in RPD’s STEP program’s case. Also important is that a CBA covers the benefit side of a program, as well. In our case, this would be ticket revenue.

Therefore, the minimum data required for a basic CBA such as in RPD’s example are: vehicle acquisition price, emergency equipment cost, insurance cost if applicable, fuel cost, maintenance and repair expenses, officer labor cost, and benefit items such as revenue from various traffic citations. Other data required are numbers for the cost escalation and discount rates without which a CBA would not be valid.

Escalation and Discount Rates

The cost escalation rate is an approximate measure for future cost of living/cost of doing business increases. We set the escalation rate at 5%. Figures for the escalation rate can be derived from past consumer price index (CPI) numbers or future forecasts. Changes in the CPI represent a commonly employed measure for the inflation rate.

The discount rate is an approximate measure to determine today’s value of an expense or benefit to be paid or received in the future. The process of determining this value is called discounting. We set the discount rate at 6%. Figures for the discount rate can be derived from government bond interest rates or commercial loan rates as published in the financial section of newspapers.

Costs

For Rockwall PD’s CBA purposes, we distinguished between variable vehicle costs, officer overtime costs, and fixed vehicle costs for the 2002 Camaro. Variable vehicle costs vary with the amount of use a vehicle experiences. These constitute operating costs and are fuel, maintenance, and repair expenditures.

We assumed $1.60 as the average price of fuel for the first year of service for the Camaro. Of course, this example comes from 2002. We took 18 miles per gallon as the average fuel efficiency figure for the Camaro. This is based on the manufacturer provided EPA city/highway (18/25) fuel economy ratings, past STEP Camaro service experiences, and RPD’s suburban enforcement environment encompassing an interstate highway, a couple of state highways, and various city and neighborhood streets.

Dividing the annual miles driven of 7,000 by the 18 miles per gallon results in an annual gasoline consumption of 389 gallons. Multiplying this figure by the assumed average price of fuel of $1.60 produces an annual fuel expenditure of $622 for the Camaro. This number is entered in Row 2 of our CBA table (seen on page 68).

Maintenance expenses comprise fluid changes and other minor regularly scheduled service items, including car washes. Repair expenses typically cover more costly items such as brakes and tires in addition to items addressed because of impending or actual failure such as transmission, engine, electrical, and suspension work. To keep the analysis simple, we subsumed both maintenance and repair expenses under the same heading.

We further incorporated the purchase of a General Motors GMPP 5- year/100,000 mile extended warranty into our analysis. This allowed us to keep projections for repair expenses at a minimum because the extended warranty would presumably cover most potential repairs. The annual maintenance and repair expenses for the years 2002 through 2008 are displayed in Row 3 of our CBA table. They were set after careful review of RPD’s STEP vehicle service history and the manufacturer’s severe service maintenance schedule.

Next, officer overtime cost was calculated to be about $20,000 a year as shown in Row 4 of the CBA table. This dollar figure was derived by analyzing STEP vehicle use patterns of officers. Averaging the various overtime pay rates of officers and supervisors, according to their different pay steps, resulted in an overtime pay rate of $40 an hour. The use pattern analysis also revealed that the Camaro would be used about 500 overtime hours a year for STEP program purposes. Multiplying these 500 overtime hours by the average overtime pay rate of $40 an hour results in the above mentioned annual $20,000 labor expense.

Finally, fixed vehicle costs are incurred once as set up expenses. They comprise the Camaro’s acquisition price, cost of the emergency equipment installed, and insurance cost. RPD is self-insured. Therefore, there is no insurance cost for which to account.

The 2002 B4C Camaro’s bid price was $22,911. We added the cost of the GMPP extended warranty of $1,800 to this bid price resulting in a purchase price of $24,711. RPD traditionally buys its squads outright. Therefore, there were no financing or leasing costs to consider.

We expect the Camaro’s residual in 2008 to be $9,000 or about 36%. The reason for this high expected residual is the Camaro’s relative low mileage at the end of its service life, as well as the expected demand for such a last model year B4C special service Camaro in the enthusiast market.

Subtracting this $9,000 residual from the purchase price of $24,711 gives us the total vehicle depreciation of $15,711. This total depreciation is measured annually for CBA purposes. Used vehicle market research has shown that new vehicles depreciate the most during their first year of use. To be realistic yet keep the analysis still simple we assumed an initial depreciation of $4,713 (a 30% first year depreciation) and a straightline annual depreciation of $1,833 thereafter. These figures are reflected in Row 8 of the CBA table.

RPD’s STEP vehicles are equipped with a radio, siren, speaker, graphics, VHS camera, radar, and interior emergency lighting. We assumed that the STEP Camaro would be a slick top vehicle with an interior LED light package. We set the total cost of the emergency equipment installed at $10,150. STEP vehicle equipment is traditionally purchased new and not transferred to other vehicles at rotation.

For simplicity’s sake, we assumed that the equipment has only scrap value after its service life of seven years. Therefore, it has no residual. The total depreciation is equal to the total equipment cost of $10,150. Dividing this figure by seven years for a simple straightline depreciation results in an annual emergency equipment depreciation of $1,450, as shown in Row 9 of the CBA table.

Benefits

A main source of potential benefits of RPD’s STEP program is revenues from traffic citations. We investigated RPD’s past STEP vehicle logs and traffic citation records in order to determine the statistical composition of the various traffic tickets issued. We found that on average, 74 speeding tickets were issued a month on STEP duty. RPD’s scheduled fine for 18 over the speed limit is $180. We contacted Rockwall’s municipal court in order to analyze the final disposition of STEP issued citations. We discovered that 40% of cited drivers take defensive driving courses and pay the state mandated fee and court costs. RPD does not derive any revenue from these proceedings.

However, half of the other 60% of drivers take deferred adjudication and pay the fine in full, whereas the remaining half simply pay the full fine amount without further court proceedings. Court data also showed that about $85 of the $180 fine remains for Rockwall after deductions for state mandated fees and court costs. Therefore, we took 60% (44 citations) of the average number of monthly STEP speeding tickets (74 citations) and multiplied this number with $85 to get the amount of the monthly revenue ($3,750) that RPD’s STEP Camaro is projected to derive from speeding citations. For CBA purposes we multiplied this figure by 12 to get the annual revenue amount of $44,880, which is exactly the figure entered into Row 14 of the CBA table.

Cost-Benefit Analysis Calculation

Begin by entering annual estimates for operating expenses before summing them up. Next, apply the cost escalation rate by multiplying the respective factor with the sum of the annual operating costs to derive the sum of escalated annual operating costs as displayed in Row 7 of the CBA table.

Escalation rate factors can be found in publications such as J. Price Gittinger’s “Compounding and Discounting Tables for Project Analysis”; under the formula command of spreadsheet software; through the use of calculators containing financial functions; or simply through hand calculation by making use of the cost escalation formula of (1 + escalation rate)number of service years. For example, the escalation rate factor for the seventh and last service year of the Camaro using this formula and assuming an escalation rate of 5% is (1 + 0.05)7 equaling 1.407. This is indeed the factor entered into the table for 2008.

It is important to realize that the factor is 1.407, meaning 40.7%, and not simply 1.35, meaning 35%, i.e., seven years times 5%. This difference is due to the escalating effect of inflation. The above formula takes into account that annual cost increases are not only applied to the original price of fuel, parts, and labor in a vehicle’s first year of service but are also applied to the portion of the price of fuel, parts, and labor that has increased in latter years.

Next, list your annual vehicle depreciation and equipment depreciation estimates, as well as the sum of these fixed costs in separate rows. Then add the sum of operating costs and the sum of fixed costs in a new row labeled “total costs” as shown in Row 11 of the CBA table.

Apply the discount rate by multiplying the annual total cost estimates with the discount rate factor to get the discounted total cost (Row 13). You can get this factor through the same sources listed above for the escalation rate factor. Alternatively, you can use the discounting formula of 1 / (1 + discount rate)number of service years. For example, the factor for the fifth service year of the Camaro assuming a rate of 6% is 1 / (1 + 0.06)5 equaling 0.747. This is the discount rate factor given for 2006 in Row 12 of the CBA table.

List your benefits in a new row as we did in Row 14 by entering the annual speeding ticket revenue estimates. Note that we assumed annual revenues to stay the same throughout the service life of the Camaro for simplicity’s sake. Apply the discount rate here the same way as above for the cost side to derive the discounted total benefit shown in Row 16. The final step is to subtract the discounted total cost estimates from the discounted total benefit estimates to get the net present value figures as illustrated in Row 17. The annual net present value (NPV) estimates indicate the net cash flow of RPD’s second STEP vehicle program.

Cost-Benefit Analysis Interpretation


The most critical aspect of a CBA is to correctly interpret the estimates. The goal of a basic CBA is to determine whether a program makes efficient use of scarce budget resources. To determine this you can use two alternative but related measures: the NPV mentioned above and the benefit-cost ratio.

To employ the NPV you must add all the estimates in Row 17 to derive an overall NPV. This is relevant because some projects have negative net cash flows in their earlier years before rendering positive net cash flows. If this overall NPV is equal to 0 or a positive number, then your proposed program is efficient at the chosen discount rate. However, if your overall NPV is negative, your proposed project would be inefficient and waste your agency’s resources.

For example, the overall NPV for RPD’s STEP Camaro is $83,469. Therefore, the program was deemed efficient. It is important to point out that the amount of the overall NPV has no bearing whatsoever on how efficient a program is. You cannot compare two programs both with positive NPVs and pick the one with the higher NPV. The NPV merely tells you whether a program itself is efficient or inefficient. It is not a measure for ranking various programs. Other measures exist for this purpose in more advanced CBAs.

The benefit-cost ratio (BC) is an efficiency measure. To determine the BC ratio, add the annual estimates of the discounted total benefit in Row 16 and divide this number by the sum of the annual estimates of the discounted total cost in Row 13. In RPD’s STEP Camaro case this amounts to $250,519 / $167,050, which is equal to a BC ratio of 1.5.

A BC ratio of 1.0 or greater means that the analyzed program is efficient at the chosen discount rate. A BC ratio of less than 1.0 indicates that a proposed project would make inefficient use of resources. The BC ratio also is not an appropriate measure for ranking different programs even though some analysts have misappropriated it for such a purpose in the past.

The second B4C Camaro was purchased. Since 2002, RPD’s STEP program has successfully operated with two specialty squads. You can also use the information for any other program under consideration for which you are able to list cost and benefits in a coherent manner.

Set your assumptions based on your own experiences and circumstances, and see whether your program would make efficient use of funds. It does not hurt to demonstrate to your city’s or county’s management, council, or commissioner’s court not only the bottom line of your program but also your ability to stay on top of things financially.

Lieutenant Carl L. Alsabrook commands the Administrative Services Division of the city of Rockwall, TX Police Department. In that function he serves as the fleet manager for Rockwall P.D. He can be reached at calsabrook@rockwall.com.

Giant A. Aryani, School of Social Sciences, University of Texas at Dallas, is a law enforcement economics researcher. He specializes in police vehicle procurement research. He can be reached at cowboys@utdallas.edu.

Published in Police Fleet Manager, Jul/Aug 2006

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