Report to Congress 

on the 

Depreciation of Business-Use Light Trucks 

Department of the Treasury 

September i991 
DEPARTMENT OF THE TREASURY 

WASHINGTON 

ASSISTANT SECRETARY September 1991 

The Honorable Dan Rostenkowski 

Chairman 

Committee on Ways and Means 

U.S. House of Representatives

Washington, D.C. 20515 

Dear Mr. Chairman: 

Section 7612(f) of Public Law 101-239, the Omnibus 

Budget Reconciliation Act of 1989, directs the Secretary of the 

Treasury or his delegate to conduct a study of the proper class 

life for cars and light trucks and submit a report to the 

Congress within one year of enactment. The Omnibus Budget Reconciliation Act of 1990 extended the date for submission of 

the report to April 15, 1991. 

Pursuant to those directives, a study entitled "Report

to Congress on the Depreciation of Business-Use Passenger Cars" 

was submitted to Congress in April. In completion of this 

mandate, I hereby submit the companion study "Report to Congress 

on the Depreciation of Business-Use Light Trucks.Il 

I am sending a similar letter to Representative

Bill Archer. 

Sincerely, 

Kenneth W. Gideon 

Assistant Secretary

(Tax Policy) 

Enclosure 
DEPARTMENT OF THE TREASURY 

WASHINGTON 

ASSISTANT SECRETARY September 1991 

The Honorable Lloyd Bentsen 

Chairman 

Committee on Finance 

United States Senate 

Washington, D.C. 20510 

Dear Mr. Chairman: 

Section 7612(f) of Public Law 101-239, the Omnibus 

Budget Reconciliation Act of 1989, directs the Secretary of the 

Treasury or his delegate to conduct a study of the proper class 

life for cars and light trucks and submit a report to the 

Congress within one year of enactment. The Omnibus Budget

Reconciliation Act of 1990 extended the date for submission of 

the report to April 15, 1991. 

Pursuant to those directives, a study entitled IIReport 

to Congress on the Depreciation of Business-Use Passenger Cars" 

was submitted to Congress in April. In completion of this 

mandate, I hereby submit the companion study IIReport to Congress 

on the Depreciation of Business-Use Light Trucks.11 

I am sending a similar letter to Senator Bob Packwood. 

Sincerely, 

kenneth W. Gideon 

Assistant Secretary

(Tax Policy) 

Enc1osure 
Table of Contents 

Chapter I. Introduction and Principal Findings ................................................................ 1 

A. Mandate for This Study ......................................................................................... 1 

B. Methodology and ClassificationIssues ................................................................. 1 

C. Principal Findings and Recommendation .............................................................. 4 

Chapter IT. Industry Background ...................................................................................... 5 

Chapter El. Data Collection and Estimation Methods ..................................................... 9 

A. Public meetings ..................................................................................................... 9 

B. Description of the Data .......................................................................................... 9 

C. Structuring the Data ............................................................................................... 11 

D. Equivalent Economic Lives ................................................................................... 13 

Chapter Tv. Results of the Analysis ................................................................................. 15 

Chapter V. Conclusions and Recommendation ................................................................ 21 

Appendix A. The Mandate for Depreciation Studies ....................................................... 23 

Appendix B. Determination of Equivalent Economic Lives ............................................ 25 

References ......................................................................................................................... 37 

Acknowledgments ............................................................................................................. 37 

-V. 
Table of Fig 

Figure 1. Age-price profile and straight-line depreciation schedule for trucks with a 

GVWR of 6,000 pounds or less (Class 1) .................................................... 15 

Figure 2. Disposition probabilities (retirements and sales to households), by age of 

truck, for trucks with a GVWR of 6,000 pounds or less (Class 1) .............. 16 

Figure 3. Fraction of initial investment in trucks that remains in business use, by 

age of truck, for trucks with a G'VWR of 6,000 pounds or less (Class 1) ... 17 

Figure 4. Unrecovered investment value as a fraction of the original investment, by 

age of truck, based on economic depreciation and on straight-line depreciation, for trucks with a GVWR of 6,000 pounds or less (Class 1) .............. 18 

Table of Tables 

Table 1. Investment in Business-Use Trucks By GVWR Class, 1989 ...................... 5 

Table 2. Distribution of Data ObservationsBy Type of Firm and Analytical 

Purpose ......................................................................................................... 10 

Table 3. Equivalent Economic Lives and Useful Lives for Trucks By GVWR 

Class ............................................................................................................. 19 

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Chapter I. Introduction and Principal Findings 

A. Mandate for This Study 

This study of the depreciation of business-use light trucks has been prepared by the Office 

of Tax Analysis (OTA) in response to a Congressional mandate in the Omnibus Budget ReconciliationAct of 1989(P.L. 101-239). Section7612(f) of the Act, which became effective December 

19, 1989, directed Treasury to conduct a study on the proper class life for cars and light general 

purpose trucks and to report its findings to the Congress within one year. The Omnibus Budget 

Reconciliation Act of 1990 extended the due date for the report to April 15,1991. A report on the 

depreciation of business-use passenger cars was submitted to Congress in April 1991; this report 

completes the task requested in P.L. 101-239. 

QTA conducts studies of the depreciationof assets, including assets not expressly requested 

for study by the Congress, as part of its general mandate under Section 168(i)(1)@) of the Internal 

Revenue Code, as modified by the Tax Reform Act of 1986. (See Exhibit 1 of Appendix A.) This 

Code provision directed the Treasury to "monitor and analyze actual experience with respect to all 

depreciable assets", and granted Treasury explicit authority to change the classification and class 

lives of assets. The Technical and Miscellaneous Revenue Act of 1988 (TAMRA) repealed 

Treasury's authority to alter asset classes or class lives, but the revised Section 168(i) continued 

Treasury's responsibility to "monitor and analyze actual experience with respect to alldepreciable 

assets." (See Exhibit 2 of Appendix A.) 

B. Methodology and ClassificationIssues 

The General Explanation of the Tax Reform Act of 1986 indicates that the determination of 

the class lives of depreciable assets should be based on their anticipated useful lives and the 

anticipated declineintheir value overtime, after adjusnnentforinflation. (SeeExhibit 3 of Appendix 

A.) IJnder current law, the useful life of an asset is taken to be its entire economic life span over 

all (business) users combined, and not just the period it is retained by a single owner. The General 

Explanation also indicates that, if the class life of an asset is derived from the decline with age of 

its market value, such life (which, to avoid confusion, is hereafter referred to as its "equivalent 

economiclife")should be set sothat thepresent valueof straight-linedepreciation overthe equivalent 

economic life equals the present value of the decline in value of the asset (both discounted at an 

appropriate rate of interest). 

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In its study of the depreciation of business-usepassenger cars, OTA accounted for not only 

the decline in the vehicles' market values with age, but also for their conversion from business to 

non-business use and the tax gains and losses that arise from their sale at different ages. "his 

treatmentwas necessarybecauseof apmicular characteristicof business-use passenger cars. Unlike 

most other business equipment, passenger cars are typically sold before the end of their useful life 

as vehicles. Moreover, unlike a number of other business assets for which an established resale 

market exists, used passenger cars are nearly always acquired for household or other non-business 

use. 

Like passenger cars, business-uselight trucks are also frequently sold before the end of their 

useful life as vehicles. However, in contrast to passenger cars, business-use light trucks are often 

sold to other businesses. This feature of the business-uselight truckmarket requiredOTA to mow 

the methodologyused for passenger cars to account for business-uselight trucksthat are capitalized 

and depreciated for tax purposes by more than one owner. Moreover, because the period of time 

light trucks are held by business owners (eitherthe initial owners or subsequentpurchasers) can be 

comparableto their total useful life, it was also necessary to take account of the retirement pattem 

with age of light trucks, a factor which was not as important for passenger cars. 

Revenue Procedure 87-56, which lists the depreciable asset classes and their corresponding 

class lives, indicatesthat "light general purpose trucks" have an actual unloaded weight of less than 

13,000pounds, and are to be distinguishedfrom automobiles,buses, heavy generalpurpose trucks 

(with an actual unloaded weight of 13,000pounds or more), over-the-road tractorunits, and trailers 

and trailer-mounted containers. Under current law, light general purpose trucks are assigned to 

Asset Class 00.241, and have a class life of four years, regardless of whetherthey are owned,leased, 

or rented by their business users. Under section 168(e)(3)(B)(i) of the Internal Revenue Code, 

however, light general purpose trucks are expressly assigned to the (modified) accelerated cost 

recovery system's five-year property recovery class, regardless of their class life. Likewise,under 

section 168(g)(3)(D),the alternative depreciation system recovery period for light trucks is five 

years, independent of their current class life. 

Trucks arenot generallyclassifiedaccordingto their unloaded weight for otherlegalpurposes, 

including aspects of tax law, motor vehicle safety standards, and fuel economy standards. Classificationis commonlybased on the vehicle's gross vehicleweightrating (GVWR) and otherfactors. 

The GV"WR is the value specified by the manufacturer as the vehicle's maximum design loaded 
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weight; a GVWR must be assigned to each domesticallyproduced truck.' Two vehicles possessing 

similar empty weights may have dramatically different GVWRs. This is because the GVWR 

depends upon the vehicle's specific characteristics: suspension system, shock absorbers, axle 

strength,transmission, tires, seating capacity,etc. These characteristicsdetermine,in part, a truck's 

intended use, and therefore can play an importantrole in establishing the truck's expectedeconomic 

life. Moreover, each vehicle's GVWR class is incorporated in the vehicle's identificationnumber 

(VIN),which is often included in the data used in this study; the unloaded vehicle weights are not 

so readily available. For these reasons, trucks were classified in this study by their GVWR, rather 

than by their unloaded weight. 

More specifically, "light general purpose trucks" are defined in this report as those trucks 

having a GVWR of less than 33,000 pounds. The trucks examined are classified into four weight 

classes: trucks with a GVWR of 6,000 pounds or less (referred to in this report as Class 1 trucks); 

trucks with a GVWR in the range of 6,001 to 10,000 pounds (Class 2); trucks having a GVWR in 

the range of 10,001 to 19,500 pounds (Class 3); and trucks with a GVWR of more than 19,500 

pounds but less than or equal to 33,000 pounds (Class 4). 

An investigation was conducted into the relationship between unloaded truck weights and 

loaded weight measures. Using the Census' 1987 Truck Inventory and Use Survey, it was found 

that over 98 percent of business-use trucks with a reported empty weight of less than 13,000pounds 

also reported an average loaded weight of 33,000 pounds or less. Thus, virtually all available 

observations on "light general purpose trucks" as defined by Asset Class 00.241 were included in 

the analysis. Of those business-use trucks with a reported empty weight of 13,000pounds or more, 

55 percent reported an average loaded weight of more than 33,000 pounds, while 38 percent had 

an average loaded weight of 19,500 to 33,000 pounds, and 7 percent had an average loaded weight 

of under 19,500pounds, Trucks with an empty weight of 13,000pounds or more constituted about 

7 percent of the total number of business-use trucks in Class 3 and about 33 percent of business-use 

1

In submitting information to the National Highway and Traffic Safety Administration ("SA), 

manufacturers must use the following GVWR classes: Class A: 3,000 pounds or less; Classes B 

through H: 3,001 to 10,000pounds, at 1,000pound increments; Class 3: 10,001to 14,000pounds; 

Class 4: 14,001 to 16,000pounds; Class 5: 16,001 to 19,500pounds; Class 6: 19,501 to 26,000 

pounds; Class 7: 26,001 to 33,000 pounds; Class 8: 33,001 pounds and over. The U.S. Bureau of 

the Census, in its Truck Inventory and Use Survey, classifies trucks into either four or fourteen 

weight categories for reporting purposes. These categories are groupings of the NHTSA classes, 

although they refer to average loaded weights as reported by survey respondents rather than the 

assigned GVWRs. 
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trucks in Class 4. A sigmficant probability thus exists that some "heavy general purpose trucks" 

belonging to Asset Class 00.242 were also included in the data examined in this study, particularly 

trucks with a GVWR above 19,500pounds.2 

dings and Reco 

'The principal findings of this study are that trucks with a GVWR of 6,000 pounds or less 

have an equivalent economic life of 4.1 years and a useful life of 7.1 years. Trucks with a GVTWR 

of 6,001 to 10,000pounds have an equivalent economic life of 4.4 years and a useful life of 10.9 

years. Trucks with a GVWR of 10,001 to 19,500 pounds have an equivalent economic life of 4.8 

years and a useful life of 16.5 years. Trucks with a GVWR of 19,501to 33,000 pounds have an 

equivalenteconomiclife of 6.6 years and ausefullife of 16.5years. As stated above,these categories 

cover virtually all trucks included in Asset Class 00.241. Based on the adjusted relative annual 

investment in trucks in each weight class,an overall equivalent economic life for alltrucks in Asset 

Class 00.241 is estimated to be 4.6 years, with a useful life of 9.4 years. If Congress wishes to 

retain the existing definition of light general purpose trucks, it is recommended that the class life 

for Asset Class 00.241 be changed from 4 years to 4.5 years. 

Buses, heavy general purpose trucks with an unloaded weight of more than 13,000pounds, 

tractor units, trailers and trailer-mounted containers, (Le., vehicles defined in Asset Classes 00.23, 

00.242,00.26, and 00.27) were not expressly examined in this study, and no inference can be made 

of their equivalent economic lives from the findings of this report. 

2 This fact was taken into account by adjusting the investment weights used to generate a single

overall economic equivalent life for "light general purpose trucks" in Asset Class 00.241. The 

possible inclusion of heavy trucks belonging to Asset Class 00.242 in the analysis of Classes 3 and 

4, however, was unavoidable. 
Chapter II. Industry Background 

Tmcks are importantbusiness assets. Accordingto the Bureau of EconomicAnalysis (BEA), 

in 1989U.S.business spent $36.5 billion on the purchase of new trucks, trailers, and buses. While 

BEA does not identify trucks separately from buses and trailers, OTA estimates that nearly 80 

percent of the BEA total ($28.9 billion) was spent on trucks alone (including tractor-trailer 

combinations). Slightly more than half (52.2 percent) of this latter figure was spent on trucks with 

a gross vehicle weight of 10,000pounds or less. Business new truck purchases accounted for nearly 

one-half of total domestic new private truck sales, and about seven percent of total business 

investmentin new equipment. Table 1 shows 1989investment in new business-usetrucks by gross 

vehicle weight class. 

II 1 

Table 1. Investment in Business-Use Trucks by GVWR Class, 1989 

(Weight in Pounds, lJnits in Thousands, Dollars in Billions) 

GVWR Class 

6,000 or less 

6,001-10,000 

10,001-19,500 

19301-33,000 

More than 33,000 

Total 

Percentage

Distribution 

Number of 

Vehicles 

Acquisition

Cost Number cost 

693 10.3 48.3 35.6 

436 4.8 30.4 16.6 

51 0.7 3.6 2.4 

123 4.5 8.6 15.6 

130 8.6 9.1 29.9 

1,434 28.9 100.0 100.0 

Sources: OTA estimates based on data from Bureau of Economic Analysis, Motor Vehicle 

Manufacturers Association, and U.S. Bureau of the Census. 

As noted in Table 1,trucks with a GVWR of 10,000pounds or less dominate the number of 

business purchases of new trucks. Within this weight class are a wide variety of body styles that 

are designedfor carryingpassengers,cargo, or both. Such vehicles include four-wheeldrive utilities 

(eg., Ford Bronco, Chevrolet Blazer, etc.), vans, mini-vans, station wagons built on a truck chassis 

(e.g., GMC Suburban, Jeep Wagoneer, etc.), compact and conventional pick-up trucks, and other 

light-dutytrucks. Most of these truck types are used by both households and businesses. According 

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to the Census Bureau's 1987Truck Inventory and Use Survey (1987 TIUS), in terms of aggregate 

mileage driven, utility vehicles, vans, and pick-up trucks as a group were used about one-third for 

business purposes and about two-thirds for household purposes. 

In OTA's study of the depreciation of business-use passenger cars, a sigmficant difference 

in economic lives was found among cars held in fleets of 10 or more and all other ("non-fleet") 

business-usepassenger cars. This differencewas attributedprimarily to differencesin intensity of 

use, sincefleet cars appearedto be drivenon averagenearlytwice asmany milesper year as non-fleet 

passenger cars.' While evidence from the 1987 TIUS suggests that business-use light trucks in 

fleets are driven somewhat more intensively than non-fleet trucks, the difference does not appear 

to be as si~cantas for passenger cars.' Thus, no distinction was made in this study between 

fleet and non-fleet status. 

Trucks are distinguishedfrom automobilesin this studyprimarily on the basis of information 

conrained in vehicle identification numbers (VINs). In general, any vehicle identified in its VIN 

as a truck (whethercompleteor incomplete)or a multipurposevehicle is regarded as a "truck." This 

definition generally includes sport utility vehicles and mini-vans, which are consideredby some to 

be more similarin functionto passenger automobilesthan to trucks. These vehicles constituteabout 

10percent of the business-usetrucks in Classes 1and 2, althoughtheir shares of current investment 

may be higher? 

Under safety standard regulations issued by the National Highway and Traffic Safety 

Administration (NHTSA), "multipurposepassenger vehicles" are distinguished from "passenger 

cars" by being constructedeither on a truck chassis or with special features for occasionaloff-road 

operation. "Trucks" are defined as being designed for the transportation of property or special 

purpose equipment (49 CFR, sec. 571.3). Most passenger vans and sport utility vehicles would be 

considered as "passenger automobiles" under NmSA's fuel economy standards regulations. 

It was found that fleet vehicles (passenger cars held by owners of 10 or more cars) were driven 

on averageabout25,000 milesper year, while non-fleetvehicleswere drivenon averageonly 15,000 

miles per year. 

According to the 1987 TIUS, business-use trucks in Classes 1 and 2 held in fleets of 20 or more 

were driven on average about 16,000miles per year; those held by businesses owning less than 20 

trucks were driven on average 13,000miles per year. 

2 

Vans (excludingmini-vans and multi-stop or step vans) and pick-up trucks constituteroughly 80 

percent of business-usetrucks having a GVWR of 10,000poundsor less. Pickups,vans, mini-vans, 

station wagons on a truck chassis, and sport utility vehicles constitute almost 97 percent of Class 

1 business-usetrucks. These data come from an analysis of the 1987 Census Truck Inventory and 

Use Survey. 

1 
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However, those regulations cover most pick-up trucks as well. "Listed property" under section 

280F and "passengervehicles" subject to the luxury tax under section4001 of the Intemal Revenue 

Code generally include trucks, vans, and utility vehicles, as long as they have a gross vehicle weight 

of 6,000pounds or less and aremanufacturedprimarilyfor use onpublic streets,roads, and highways. 

Regulationsproposed under section 4001 explicitly state that the term "truck or van" includes sport 

utility vehicles and mini-vans. The section 4064 gas "guzzler tax" does not cover sport utility 

vehicles and pick-up trucks, but does cover ''passenger automobiles" as defined under the NHTSA 

fuel economy standards regulations. 
Chapter III. Data Collection and Estimation Methods 

A. Public meetings 

Public meetings were held at the Treasury Department in January and March of 1990 to 

determine the scope of the passenger car and light truck study, discuss the study design and general 

methodology, and describe the kind of data needed for the study. The first public meeting was 

announced in the Federal Register on December 21, 1989, and invitations were extended to each 

of the major trade associations representing different sectors of the business-use car and light truck 

industry. Invitations were also sent to executives of the largest leasing and rental firms in the United 

States. 

At these meetings, it was determinedthat the scope of the study should include allautomobiles 

and light- and medium-duty trucks designed for use over-the-road and used in a trade or business. 

This coverage was generally understood by Treasury and industry participants to include both fleet 

and non-fleet vehicles, and vehicles that are either leased or owned by their users. Although no 

attempt was made to formally define "light trucks", data collection for trucks was limited to all 

those with a GVWR of 33,000pounds or less. 

Unlike many of the previousdepreciationstudiesconductedby OTA,no survey of the industry 

was conducted or proposed. Instead, data were solicited directly from a limited number of owners 

of business-use vehicles based on vehicle specificationsthat were proposed and developed at the 

public meetings. This procedure was adopted because of the relatively short time frame granted 

by the Congress for completion of this study, and because of the availability of machine-readable 

data from several of the firms that agreed to participate in the study. 

B. Description of the Data 

Firms participating in the study were asked to provide OTA with detailed data on certain 

characteristics of cars and light general purpose trucks either disposed of during the last few years 

or remaining in their inventory at the time the data were provided. Each observation in each data 

set was to include, at a minimum, the vehicle's Vehicle Identification Number (VIN), original 

acquisition cost, the month and year of acquisition, and, in the case of dispositions, the proceeds 

(net of refurbishing costs), and the month and year of disposition. Some data sets also included the 

type of disposition and the mileage of the vehicles at disposition. All of the data were received by 

OTA from May through August of 1990. 

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Table 2. Distribution of Data Observations 

By Type of Firm and Analytical Purpose 

Analytical Purpose 

Estimation of Estimation of 

Type of Firm Age-Price Profile Sales Distribution 

Leasing Firms 97.2% 97.3% 

Private Fleets 2.7% 2.7% 

Non-Fleet Trucks 0.1% 0.0% 

Total Observations 33,470 189,283 

Data for light general purpose trucks were received from five leasing firms and four truck 

fleet owners.' A data set covering a small number of independent owner-operators was also made 

available to OTA. In addition, a few observations were also obtained from an analysis of a small 

sample of IRS returns covering non-fleet truck dispositions. Truck data from three of the leasing 

firms, from two of the private fleets, and from the non-fleet sources were used? In total, there were 

about 112,000total usable observations. Table 2 shows the distribution of observations by type of 

firm and analyticalpurpose. It is apparent that data from the leasing companies dominatethe usable 

data, and thus sigruficantly influence the results presented. Nevertheless, the available data do not 

1 Except for three of the leasing firms and one fleet owner who provided data directly to OTA, the 

data were first collected from the participating firms and examined by Price Waterhouse,which in 

turnprovided the data, together with a paper summarizing the results of their preliminary andysis, 

to OTA. This mechanism was chosen by the industry in order to maintain the confidentiality of 

several of the companies participating in the study, which were not revealed to OTA. 

2 Data provided by one of the leasing firms and one of the private fleet firms were not analyzed

because the data were incomplete. However, due to the large sample of complete data, these firms 

were not asked to resubmit their information. 
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provide any strong evidence in favor of the view that leasing firm data differ in a systematicmanner 

from the data obtained fkom non-leasing firms. Table 2 also shows that estimates based on data 

from non-leasing firms would reflect almost exclusivelytheprices and retirements from truck fleet^.^ 

C. Structuring the Data 

Although the depreciation of trucks may vary by vehicle type and whether the vehicle is 

designed for passengers or cargo, preliminary analysis of the data suggested that aggregation of the 

data into four GVWR classes would make the analysis more manageable, and yet capture the more 

sigmficant differences in intensity of usage. Trucks were classified to the following categories: 

Class 1 - trucks having a GVWR less than or equal to 6,000 pounds; Class 2 - trucks with a GTrWR 

of more than 6,000 but less than or equal to 10,000pounds; Class 3 - trucks with a GVWR of more 

than 10,000 pounds but less than or equal to 19,500 pounds; and Class 4- trucks with a GVWR of 

more than 19,500 pounds but less than 33,000 pounds. 

Equivalent economic lives, taking into account truck prices, retirements, and sales by age, 

were derived (as described below and in Appendix B) for trucks in each weight class. A light truck 

retirement probability distribution was obtained from a previous study of vehicle scrappage rates 

observed over the period 1978 to 1988.4 These rates were available through age 25. At that age, 

about 22 percent of trucks were still registered. For the purpose of this study, all of those remaining 

trucks were assumed to be retired in year 26. This truncation of the retirement curve does not affect 

the final estimate of equivalent life, because of the additional assumption that the value of those 

remaining trucks reaches zero at 26 years of age. The retirement curve used indicates a median 

retirement age of 16.0 years and a mean age at retirement of 16.5 years.5 

3 According to the 1987 'ITUS, less than three percent of trucks in business use with a GVWR of 

33,000pounds or less are operated in fleets of more than 100trucks. About 10percent are operated

in fleets of more than 20 trucks, while one-half of business-use trucks are operated in small fleets 

containing between 2 and 19trucks. About 39 percent belong to firms operating only a singletruck. 

Fleets of ten ormoretrucks, however,account for about 5Opercentof new investment in business-use 

light trucks. 

Scrappagerates by age were produced by Shaw-Pin Miaou, "Study of Vehicle ScrappageRates," 

Oak Ridge National Laboratory, Oak Ridge, TN, August 1990. These rates were reported in Stacy

C. Davis and Patricia S. Hu, Transportation Energy Data Book: Edition I I, Oak Ridge National 

Laboratory, Oak Ridge TN, January 1991. 

4 

5 The estimate of mean age at retirement is affected by the assumption that all trucks are retired at 

age 26. The median retirement age, however, is independent of that assumption. 
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Observations from all data sources were pooled in order to estimate the age-price curve and 

age-sales probability curve for each weight category. Data forthese curveswere generally available 

to about age ten for each GVWR class. Only observationsrepresentingbona fide arms-length sales 

were used to produce estimates of the age-price curves. Sales to lessees or trade-in prices were 

disregarded. The price curves were obtained by first adjusting observed prices for the effects of 

inflation; the overall consumer price index for urban workers was used in this regard. Sales prices 

were then expressed as ratios of the original acquisition costs, and these normalized prices were 

averaged at each age to obtain a curve showing the mean relative price as a function of age. These 

mean prices were extrapolated in a linear fashionfor ages where price observationswere insufficient, 

reaching zero (by assumption) at age 26.6 The arbitrary nature of this extrapolationis not important, 

however, due to the discounting and the small value changes involved at ages above ten years7 

Allsales data were used in estimating the probability of truck sales at each age. This curve 

was obtained by dividing the number of sales at each age by the number of assets in the sample 

examined that had remained in business use to at least that age. The probability of truck sales was 

set equal to zero for the years where fewer than five observations were available. No further 

smoothing of either the price curve or sales distribution curve was employed. 

All sales of trucks in Classes 3 and 4 were assumed to be to other businesses. For trucks in 

Class 2,75 percent of sales were assumed to be to other businesses, while 25 percent of sales were 

assumed to be to households. For trucks in Class 1,50percent of sales were assumed to be to other 

businesses and 50 percent to households. These repurchase percentages were assumed to be 

independent of the age of the truck.8 

6

For each truck class at each age, the observed mean price was adopted as long as long as at least 

five observations were available at that age. This criterion generally could not be met for ages

beyond ten or eleven years. Normally, the standard deviations of the mean price estimates were 

well under one percent, although higher values were often experiencedat age one and at ages above 

eight years. 

Assurning that prices trail off to a five percent minimum salvage value, instead of a zero value, 

increases the estimatedequivalent economic life for all light trucks by less than one-tenth of a year. 

Analysis indicated that the estimates of equivalent economic lives are only mildly sensitive to 

these assumptions. For example, raising the percentage of sales assumed to be made to other 

businesses from 50 percent to 75 percent for Class 1trucks, or from 75 percent to 100percent for 

Class 2 trucks, increasesthe estimated equivalenteconomiclives for these trucksby about one-tenth 

of a year. Assuming that dltruck salesin thesetwo classes areto householdsdecreasesthe estimated 

equivalent economic life for Class 1by one-tenth of a year but leaves the equivalent economic life 

for Class 2 trucks unchanged. However, assuming that no Class 1trucks are sold to households 

increases the estimated equivalent economic life by four-tenths of a year (to 4.5 years) for Class 1 

trucks. 

8 

7 
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A single weighted average equivalent economic life for all light general purpose trucks was 

obtained by weighting the observed characteristics (price-age and sales-age distributions and the 

probability of business-to-business sales) for each weight class with the observed share of 1989 

investment in new general purpose light trucks for the class. The observed investment shares were 

adjusted to reflect the fact that some trucks in classes 3 and 4were possibly heavy general purpose 

trucks with empty weights in excess of 13,000pounds. The weighted-averagecharacteristicswere 

then used to obtain an overall equivalent economic life for trucks in Asset Class 00,241.' 

D. Equivalent Economic Lives 

As suggested in the General Explanation of the Tax Reform Act of 1986,the class life of an 

asset is to be determinedfrom the declinein its value with age. This life (which for clarity has been 

referred to as the asset's equivalent economic life) can be either longer or shorter than its useful 

life &e., the period over which the asset provides service to business users). 

For each weight category, an equivalent economic life was derived by equating the present 

value of the average loss in economic value over time for those trucks that remain in business use 

with the present value of tax deductions for those trucks in business use. The loss in economic 

value includesboth the declinein the value of assets which remain in businessuse and the economic 

losses that are incurredupon the retirementof trucks from businessuse. The relevant tax deductions 

taken into account include both the depreciation allowances available to taxpayers, as determined 

by applying a straight-line schedule over the equivalent economic life, and the recognized losses 

resulting from sales of trucks in business use and from retirements of trucks from business use. 

Gains on sales and retirements are treated as negative losses." Both change-in-value curves are 

discounted at a four percent annual discount rate." 

9 These average characteristics are shown in Appendix �3, where they are used to illustrate the 

methods employed to compute equivalent economic lives. 

10In the analysis, salvage values available upon the retirement of trucks are assumed to be zero. 

This assumptionis immaterial. Salvagevalue affectsthe recovery of capitalequallyunder economic 

depreciation accounting and under tax accounting. It therefore has no direct impact on the value 

of the estimatedequivalenteconomiclife. Salvage can have an indirectimpact through an influence 

on used asset prices, however. 

11The estimated equivalent economiclives are only mildly dependentupon the actual discount rate 

chosen. For example, halving the discount rate to two percent raises the estimated equivalent

economic life for all trucks by less than one-tenth of a year. Doubling the rate to eight percent

lowers the estimated equivalent economic life by two-tenths of a year. 
- 14-

The straight-line tax depreciation allowances are calculated over a recovery period equal to 

the equivalent economic life, starting with the year of acquisition, with the same recovery period 

for both new and used trucks. However, both straight-line and economicdepreciation are considered 

only up to the truck’s date of sale or retirement. See Appendix B for a more detailed description 

of the analysis. 
Chapter IV. Results of the Analysis 

This chapter presents the results of applying the methods described in Chapter IDto obtain 

equivalenteconomic lives for trucks in each of the four weight categories and the economiclife for 

all trucks in Asset Class 00.241. In addition, the estimated average useful life of trucks in each 

weight category and the method of depreciation used for financial accounting purposes by the 

participating firms are noted. 

lzm I 

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

Age in Years 

+Value of Truck 

-+-Straight-Line Depreciation Schedule 

Figure 1. Age-price profile and straight-line depreciation schedule 

for trucks with a GVWR of 6,000 pounds or less (Class 1). 

Figure 1 illustrates the relationship between the observed age-priceprofile and the adjusted 

basis obtained from the use of a straight-line depreciation schedule with a recovery period of 4.1 

years (the estimated equivalent economic life) for trucks with a GVWR of 6,000 pounds or less. 

The age-price profile drops rapidly over the first year of service, and then at successively slower 

rates over ages two through eight. A small increase in the average price occurs between ages eight 

-15-
- 16-

and ten, but the absolute amount of economic depreciation is constant thereafter by assumption.' 

The straight-line depreciation schedule underlying the tax basis curve in Figure 1 allows for a 

half-year allowance in the first taxable year, and reaches zero during the fifth taxable year. 

0 2 4 6 E 10 12 14 16 18 20 22 24 26 

Age in Years 

Retirements Sales to Households 

Figure 2. Disposition probabilities (retirements and sales to households), by age of truck, for trucks with a GVWR of 6,000 pounds or 

less (Class 1). 

The depreciation of trucks remaining in business use does not reflect the total source of 

economic loss; losses incurred upon retirement of trucks in business use must also be considered 

in determiningthe equivalent economic life. Also, since sales of trucks also trigger the recognition 

of tax losses or gains, these must also be taken into account.' 

1 Price observationswere either few or nonexistent for ages above ten years for trucks in this weight

class. 

2 Because the adjusted economic basis equals the market value when economic depreciationis used, 

under this method of accounting no gains or losses are realized when trucks are sold. 
- 17-

0 2 4 6 8 10 12 14 16 I8 20 22 W 26 

Age in Years 

Figure 3. Fraction of initial investment in trucks that remains in 

business use, by age of truck,for trucks with a GVWR of 6,000pounds 

or less (Class 1). 

The estimated disposition frequencies (the fraction of remaining business-use Class 1 trucks 

at each age that are either retired or sold to households) are shown in Figure 2.3 As described in 

Chapter 3, no sales are assumed to occur after age 10 (the oldest age at which the number of 

observations was five or more), and all trucks remaining in business use at age 25 were assumed 

for convenience to be retired at age 26. The resulting fraction of trucks with a GVWR of 6,000 

pounds or less remaining in business use at each age are shown in Figure 3. 

As is discussed more fully in Appendix B, investment may be recovered in several ways in 

addition to depreciation allowances. These include losses upon retirement of business-use trucks, 

gain or loss realized when trucks are sold, salvage value received upon the retirement of trucks, 

and payments received from the sale of trucks to households. Figure 4 shows the unrecovered 

3 Since one-half of business sales of Class 1 trucks are assumed to be to households, the values in 

Figure 2 for sales to households merely need to be doubled in order to obtain the probability of total 

truck sales at each age. 
- 18-

0% 

0 1 2 3 4 5 6 7 8 9 10 11 12 13 

Age in Years 

+Economic Depreciation 

+Straight-Line Depreciation 

Figure 4. Unrecovered investment value as a fraction of the original

investment,by age of truck, based on economic depreciation and on 

straight-line depreciation, for trucks with a GVWR of 6,000 pounds 

or less (Class 1). 

investment, measured as a fraction of the original investment in new trucks, by age of truck, based 

on the use of economic depreciation and straight-line depreciation (and the recognition of losses 

and gains) for trucks in this weight category. The two curves coincide at zero at age 26, when the 

last trucks are assumed to be retired. The equivalent economic life is determined by equating the 

present values (discounted at a 4 percent rate) of the annual increase in recovered investment under 

the two methods shown in Figure 4. 

Table 3 lists the estimated equivalent economic lives by weight class, as well as the overall 

equivalenteconomiclife fortrucks in Asset Class 00.241. These results show apositive relationship 

between the estimatedequivalent economiclives and gross vehicleweight;the equivalent economic 

lives range from 4.1 years for Class 1 trucks to 6.6 years for Class 4trucks. This is partly due to 

differences in price profiles and sales distributions and partly due to the fact that lighter trucks are 
- 19 -

Table 3. Equivalent Economic Lives and Useful Lives 

For Trucks By GVWR Class 

(Weight in Pounds, Lives in Years) 

GVWR Class 

6,000 or less 

6,OO1-10,000 

10,001-19,500 

19,501-33,000 

Asset Class 00.241 

Economic Average

Equivalent Useful 

Life Life 

4.1 7.1 

4.4 10.9 

4.8 16.5 

6.6 16.5 

4.6 9.4 

also sold to households. It may also reflect the fact that observationsused for analyzing Classes 3 

and 4 may include some heavy general purpose truck^.^ An overall equivalent economic life for 

trucks in Asset Class 00.241 was estimated to be 4.6 years. 

In addition to the equivalenteconomic lives, Congress has expressed an interest in the useful 

lives of the assets studied. If the useful life is taken to be the period the trucks are used for business 

purposes (regardless of the number of owners), the answer obtained is somewhat dependent upon 

the assumed fraction of trucks sold that are purchased by households. It also is somewhat sensitive 

to the assumption that all trucks remaining in use at age 25 are retired during the following year. 

Based on the values of the repurchase percentages assumed for each weight class, useful lives for 

trucks in each weight class, as well as an overall weighted average useful life for trucks in Asset 

Class 00.241, may be obtained. These useful lives are noted in Table 3.5 Sinceno sales for personal 

use are presumed to occur for trucks with a GVWR greater than 10,000 pounds, the useful life 

equals the mean retirement age for trucks in Classes 3 and 4. 

4 In additionto the categoriesshowninTable 3, an equivalenteconomiclife was computedseparately

for multipurpose vehicles with a GVWR of less than 6,000 pounds. These vehicles are comprised

mainly of sport utility vehicles and mini-vans; they constitute about 51 percent of the sarnple of 

Class 1 trucks. Their equivalent economic life was estimated to be 4.1 years, indicating little 

difference between multipurposevehicles and light pickups and vans. 

5 The useful life for Class 1multipurpose vehicles was estimated to be 6.3 years. 
- 20 -

Congress was also interested in the method used to depreciate the assets for financial 

accounting purposes. All of the companies which reported their methods of accounting for trucks 

used the straight-linemethod of depreciation. The recoveryperiods ranged from 3 to 8 years, with 

an investment-weightedaverage recovery period of 4.4years. 
Chapter V. Conclusions and Recommendation 

The principal findings of this study are that trucks with a G W of 6,000 pounds or less 

have an equivalent economic life of 4.1 years, while trucks with a G W of between 6,000 and 

10,000pounds have an equivalenteconomic life of 4.4 years. Trucks with a GVWR between 10,000 

and 19,500 pounds have an equivalent economic life of 4.8 years, and those with a GVWR of 

between 19,500and 33,000 pounds have an equivalenteconomiclife of 6.6 years. These categories 

cover virtually all vehicles included in Asset Class 00.241 (trucks having an unloaded weight of 

less than 13,000 pounds). The values for truck classes 3 and 4may also reflect the influence of 

some heavy general purpose trucks with an unloaded weight of 13,000pounds or more, which are 

currently classified to Asset Class 00.242. The useful lives of the trucks ranged from 7.1 years (for 

Class 1trucks) to 16.5 years (for Class 3 and Class 4 trucks). The overall useful life for light general 

purpose trucks is 9.4 years. 

When the estimated equivalent economic lives for each weight class are combined by 

weighting the results for each class by the adjusted share of business investment in new trucks in 

that class, a single overall equivalent economic life of 4.6 years is obtained. Treasury thus recomends that, if the current definition of light general purpose trucks is retained, the class life for 

Asset Class 00.241 be changed from 4 years to 4.5 years. Tractor units, trailers, trailer-mounted 

containers, tractor-trailercombinations, and heavy generalpurpose trucks with an unloaded weight 

of more than 13,000 pounds (i.e., trucks in Asset Classes 00.242, 00.26, and 00.27) were not 

expressly examined in this study, and no recommendation is thus made in this report regarding the 

appropriate class life for such trucks. 

Under current law, this recommendation, if adopted,would have no effect on the depreciation 

deductions claimed by taxpayers for light general purpose trucks. Section 168(e)(3)@)(i)assigns 

automobiles and light general purpose trucks to the-five-yearproperty recovery class,regardless of 

their class lives. If this provision were repealed, light trucks would be assigned to the WCRS 

three-year property recovery class if the recommended change in the class life were not enacted, 

and to the IvIACRS five-year property recovery class if the recommendation were enacted.* 

Likewise, under Section 168(g)(3)@), the alternative depreciation system recovery period for 

automobiles and light general purpose trucks is currently five years, regardless of their class lives. 

1 The three-year property recovery class generally includes property with a class life of four years 

or less. The five-year property recovery class includes property with a class life of greater than 

four years but less than ten years. 

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- 22 -

If this provision were repealed, taxpayersusing the alternativedepreciationsystemcould depreciate 

their light trucks over four years (based on the current law class life) or over 4.5years (based on 

the recommended class life). 
Appendix A. The Mandate for Depreciation Studies 

Exhibit 1. 

Section 168(i)(1)(B)of the Internal Revenue Code as Revised by the Tax Reform Act of 1986 

(i) Definitions and Special Rules. 

For purposes of this section-­

(1) Class Life. 

(�3) Secretarial authority. The Secretary, through an office established in the 

Treasury-­

(i) shall monitor and analyze actual experience with respect to alldepreciable 

assets, and 

(ii) except in the case of residential rental property or nonresidential real 

property-­

(I) may prescribe a new class life for any property, 

(TI) in the case of assigned property, may mode any assigned item, or 

(EI) may prescribe a class life for any property which does not have a class 

life within the meaning of subparagraph (A). 

Any class life or assigned item prescribed or modified under the preceding sentence shall 

reasonably reflect the anticipateduseful life, and the anticipated decline in value over time, 

of the propeay to the industry or other group. 

Section 168(i)(l)of the Internal Revenue Code as Revised by the Technical and Miscellaneous 

Revenue Act of 1988 and the Revenue Reconciliation Act of 1990. 

Definitions and Special Rules. 

For purposes of this section-­

(1) Class Life. Except as provided in this section,the term "class life" means the class 

life (if any) which would be applicable with respect to any property as of January 

1,1986, under subsection (m) of section 167 (determined without regard to paragraph (4)and as if the taxpayer had made an election under such subsection). The 

Secretary,through an office established in the Treasury, shall monitor and analyze

actual experience with respect to all depreciable assets. The reference in this 

paragraph to subsection (m) of section 167 shall be treated as a reference to such 

subsection as in effect an the day before the date of the enactment of the Revenue 

ReconciliationAct of 1990 [11/5/90]. 

-23-
- 24 -

Exhibit 3. 

Provisions for Changes in Classification from the General Explanation of the Tax Reform 

Act of 1986 (pp. 103-104) 

The Secretary, through an office established in the Treasury Department is authorized to 

monitor and analyze actual experience with all tangible depreciable assets, to prescribe a new class 

life for any property or class of property (other than real property) when appropriate, and toprescribe 

a class life for any property that does not have a class life. If the Secretary prescribes a new class 

life forproperty,such life will be used in determiningthe classificationof property. Theprescription

of a new class life for property will not change the ACRS class structure, but will affect the ACRS 

class in which the property falls. Any classification or reclassification would be prospective. 

Any class life prescribed under the Secretary's authority must reflect the anticipated useful 

life, and the anticipated decline in value over time, of an asset to the industry or other group. Useful 

life means the economic life span of property over all users combined and not, as under prior law, 

the typical period over which a taxpayer holds the property. Evidence indicative of the useful life 

of property, which the Secretary is expected to take into account in prescribing a class life, includes 

the depreciation practices followed by taxpayers for book purposes with respect to the property,

and useful lives experiencedby taxpayers, accordingto their reports. It further includesindependent

evidence of minimal useful life -- the terms for which new property is leased, used under a service 

contract, or financed -- and independent evidence of the decline in value of an asset over time, such 

as is afforded by resale price data. If resale price data is used to prescribe class lives, such resale 

price data shouldbe adjusteddownward to remove the effects of historicalinflation. This adjustment

provides a larger measure of depreciation than in the absence of such an adjustment. Class lives 

using this data would be determined such that the present value of straight-line depreciation

deductionsover the class life, discounted at an appropriate real rate of interest,is equal to the present

value of what the estimated decline in value of the asset would be in the absence of inflation. 

Initial studies are expected to concentrate on property that now has no ADR midpoint.

Additionally,clothing held for rental and scientFficinstruments(especiallythose used in connection 

with a computer) should be studied to determine whether a change in class life is appropriate. 

Certain other assets specifically assigned arecovery period (includinghorses in the three-year

class, qualified technological equipment, computer-based central office switching equipment, 

research and experimentation property, certain renewable energy and biomass properties, semiconductor manufacturing equipment, railroad track, single-purpose agricultural or horticultural 

structures,telephonedistributionplantand comparable equipment,municipalwaste-watertreatment 

plants, and municipal sewers) may not be assigned a longer class life by the Treasury Department

if placed in service before January 1,1992. Additionally, automobiles and light trucks may not be 

reclassified by the Treasury Department during this five-year period. Such property placed in 

service after December 31, 1991, and before July 1, 1992, may be prescribed a different class life 

if the Secretary has notified the Committee on Ways and Means of the House of Representatives

and the Committee on Finance of the Senate of the proposed change at least 6 months before the 

date on which such change is to take effect. 
Appendix B. Determination of Equivalent Economic Lives 

This appendix describesthe calculationsused in this studyto estimate an equivalenteconomic 

life for light general purpose trucks. As an aid to the reader, the set of data used to determine the 

overall equivalent economic life for light trucks has been presented here in order to illustrate the 

more formal algebra. Results of the calculations using these data are reported in the tables at the 

end of this appendix. 

The computations described assume the availability of certain data. These data include the 

expected relative prices for trucks remaining in business use by age (the age-price profile), the 

expected salvagevalues of retired trucks by age, the probability of retirementof business-usetrucks 

by age (the retirement distribution), the probability of business-use truck sales by age (the gross 

sales distribution), and the probability that business-use trucks sold will be purchased for business 

purposes (the repurchase percentage). In this study, the age-priceprofile and the gross sales distribution are obtained from data provided by the participating firms. The retirement probability is 

taken from Davis and Hu (199l),while a zero salvagevalue and fixedrepurchasepercentage (which 

vary by weight class) are assumed. In keeping with the dictates of the General Explanation of the 

Tax Reform Act of 1986,the observed truck prices are adjusted for general inflation prior to their 

incorporation into the analysis. 

The analysisof the depreciationof passenger cars focused on the relativenumber and relative 

value of business-use passenger cars as continuous functions of a single variable -- the age of the 

cars. Because used trucks as well as new trucks are acquired by businesses, in this study a second 

variable -- the age of the truck at acquisition -- is needed. For convenience, a discrete rather than 

continuoustime frameworkis used. Thus, the analysisin this study utilizes matriceswhich specify, 

among other things, the number of trucks remaining in business use, business-usetruck retirements, 

and business-use truck sales for trucks of a given age that were acquired at the same or an earlier 

age. 

OTA has interpretedthe General Explanationas defining the equivalenteconomiclife as that 

life which, when used as the recovery period for depreciation purposes (in association with the 

straight-linedepreciationmethod, a half-year depreciationtiming convention,and other applicable 

tax rules), equatesthe present value of the tax deductions associatedwith the businessuse of a group 

of assets with the present value of the loss in the group’s economic value while in business use. 

This definitiontakes as given the currentlaw treatment of asset retirements and sales; in particular, 

it relies on the principle that tangible asset sales and retirements are recognized as taxable events, 

-25-
- 26 -

and that any gains or losses associated with these taxable events enter together with depreciation 

allowances into the taxable income of the asset owner.' It also relies on the principle that a truck 

sold from one business to another does not carry over its adjusted tax basis. Instead,the new owner 

adopts his or her own cost as the new depreciable basis of the truck; the depreciation schedule for 

the used truck is the same as that for new trucks. Thus, a truck that is sold once or twice during its 

lifetime will have a different pattem of tax deductions associated with it than would an identical 

truck that has been held entirely by a single owner. 

Constructing the Data Matrices 

The number of trucks in business use at the beginning of an accounting period is designated 

asN(t,v), where t refers to the actual physical age of the trucks in the account, and v refers to the 

age at which the trucks were most recently acquired.' Thus, N(0,O)refers to an initial investment 

in new trucks at the beginning of some given time period. N( 1,O) refers to those trucks purchased 

as new assets in the prior period that were neither retired from use nor sold before the end of that 

period. N(1,l) refers to one-period old trucks that were sold at the end of the initial period and 

purchased by another business. 

W,O) N(1, 1) 0 ... 

N(2,O) N(2,l) N(2,2) ... 

N(t,v) = 

1 This assumes that taxpayers account separately for each truck, rather than use general asset 

accounts. 

2 Trucks are assumed to be placed in service in the middle of the taxable year. Accounting periods

for the analysis, therefore, run from the middle of each taxable year to the middle of the following

taxable year. Economic depreciation, sales, and retirements are assumed to occur uniformly over 

each accounting year. Tax depreciation allowances were are assumed to occur uniformly over each 

taxable year. 
- 27 -

The passage of time implies a movement from one row to the next in N(t,v). Movement 

down a particular column traces the number of trucks held in established depreciation accounts. 

The transfer of a truck from one owner to another means a shift of a truck to the diagonal element 

lying in a column to the right. For example,the sale of a truck from cell N( 1,0)implies that N(2,O) 

will be at least one less than N(1,Q) and that N(2,2) will be increased by one. In this matrix, m 

designates the maximum age that a business-use truck may reach. Consequently, the order of the 

matrix is (m + 1x m + 1). The last row (and column) of this matrix will be comprised of all zeros. 

Given the diagonal elements of N(t,v), the probabilities of truck retirements and sales will 

determine the values taken by the lower left-hand off-diagonal element^.^ Let R(t,v) and S(t,v) 

designate the number of trucks expected to be retired and sold, respectively, during the t 'th period 

and which were most recently acquired at age v. Then, 

N(t,v) =N(t -1,v)-R(t,v) -S(t,v), t > v. 

The incidence of truck retirements and sales are assumed to be a function solely of their age. 

I& r(t)be the probability that a truck of age t - 1 will be retired before reaching age t. Then, 

R(t,v) = r(t)xN(t-l,V), t>V 

= 0, tlv 

Similarly,let s(t)represent the probability that an asset of age t - 1 which is not retired before 

age t will be sold during the following period. Then, 

S(t,V) = s(t)x [l -r(t)] xN(t -l,V), t>V 

= 0, t <v. 

It follows that 

N(t,v) = [l -s(t)] x [l-r(t)] xN(t -l,v), t > v. 

3 The matrix elements above the diagonal are zero by definition. 
- 28 -

The diagonal elements, N(t,t),are determined by the probabilities associated with the purchase of used trucks by business. The analysis assumes that (i) used trucks purchased for business 

purposes are bought only from other businesses, and (ii)the probability of a business-to-business 

sale is dependent only upon the age of the truck! Let the fraction of trucks sold that are purchased 

for business use be represented by b(t). Then, 

N(t,t)=b(t)xS(t), 

where S(t)is the total number of sales of trucks of age t (i.e., the sum over v of S(t,v) for v < t). 

Thus, given the initial number of new trucks, N(O,O), and the distributions,r(t),s(t),and b(t),the 

complete N(t,v), R(t,v), and S(t,v) matrices can be computed. 

'be number of trucks remaining in business use at each age, N(t),may be obtained by calculating the row sums of N(t,v), i.e., by taking the sum over v of N(t,v). Similarly,the number 

ofbusiness truckretirements by age,R(t),and of gross businesstruck salesby age, S(t),are obtained 

from the row sums of R(t,v) and S(t,v),respectively. Used truck purchases by age, U(t),are zero 

for t = 0 and equal to the diagonal elements,N(t,t), for t > 0, while net truck sales to households, 

H(t), are equal to the difference between S(t) and U(t). The first column of N(t, v) represents the 

number of remaining trucks that werepurchased asnew trucks,whilethe number of trucksremaining 

at each age that were purchased used, W(t),can be obtained by subtracting N(t,0) from N(t). 

The data used here to constructN (t,v ),R (t,v ), andS(t,v ) are displayedin columns (2)through 

(4) of Table A-1. The percentages shown are r(t),s(t),and [l-b(t)] xs(t), respectively. The 

maximum age is assumed to be 26, so that r(26) equals 100 percent. Table A-2 shows a number 

of the results referred to in the previous paragraph. All numbers have been rounded to the nearest 

integer for easier reading. 

Calculation of Economic Loss 

The calculationof the loss in economic value requires knowledge of the number of remaining 

trucks at each age, N(t),and the number of retirements at each age, R(t). Since no gains or losses 

are incurred on a truck sale when economic depreciation is used, sales are important in calculating 

the economic loss only insofar as they determine the number of used trucks of the given vintage 

that remain in business use. The calculation of economic loss also requires knowledge of the 

expectedpriceof remainingbusiness assets,P(t),and of the salvage value, V(t),that can be expected 

4 A constant repurchase percentage is actually used in the analysis for this report. 
- 29 -

to be received from a truck retirement. The hypothetical end-of-year values used in the numerical 

example for these variables are shown in calums (5) and (6) of Table A-1. These prices have been 

normalized so that the price of a new truck is unity. 

The total loss in economic value is the sum of the loss in value that occurs while a truck is 

employedin a trade or business (economicdepreciation)and the loss invalue occurringwhen trucks 

are retired from business use. Economic depreciation,EDP(t),is a straightforwardfunction of the 

average number of trucks that are in business use during the prior period, times the depreciation 

for a representative truck: 

EDP(t) = [Nt -1)+Wl -[P(t-1)-P(t)],t = l...m 

= 0, t =O. 

Economic loss on retirement,EL& (t),is the product of the number of truck retirements during 

each period and the difference between the average expected price of trucks remaining in use and 

the average expected truck salvagevalue at that time: 

where, 

P(t)+P(t - 1 ) P,,(t)= 2 

and 

V(t)+V(t- 1) V,(t>= 2 

Total loss in economicvalue, ELV(t),is simply EDP(t)+EL& (t). Its present value, PVELV, 

can be calculated directly as 

PVELV = 2 P(t)ELV(t), I =O 
- 30 -

where P(t) is the relevant discountfactor? Note that the loss in economicvalue at time zero,ELV(O), 

is equal to zero and that the loss in value occurring at the beginning of period one, ELV(l), is 

discounted by a single period discount factor. 

Values of economicdepreciation,losses upon retirement, and total losses in value for the data 

set are shown in columns (2) through (4) of Table A-3. PVELV is shown at the bottom of column 

(4)in the row labeled ttPV.t'6The final column of that table displays the remaining economic value 

at each age, REV(t). This value declines to $148, rather than zero, and represents the revenues 

obtained through sales to non-business en ti tie^.^ Since there are 594 such sales, these sales have 

an averageprice equal to about 25 percent of the initial investmentvalue. The average age of trucks 

sold at the time of such sales is 5.3 years. 

Calculation of Tax Deductions and the Eauivalent Economic Life 

With the present value of the loss in economicvalue calculated,the equivalent economic life 

can be computed through an iterativeprocedure. In this procedure, a trial value is chosen, and the 

total tax deductions associated with the use of that life for depreciation purposes are calculated. 

The present value of those tax deductions is computed and compared to the present value of the 

loss in econoInicvalue that was previously calculated. The initial trial value is then adjusted, based 

on the algebraicsign of the differencein the two presentvalues. The iterationends when the absolute 

value of this difference fails to exceed some small preset tolerance value. 

The first step in deriving the tax deductions associated with any given trial equivalent economic life is the calculation of the tax depreciation schedule, A(t). In this regard, a half-year 

convention is employed; thus, the initial taxable year's deductionper dollar of investment,A (0),is 

5 A four percent annual discount rate was employed in the example. The resulting discounting 

function, P(t),is shown in the last column of Table A-1. 

6 The present values shown in Tables A-3 and A-4 are expressed on a per asset basis; that is, they 

have been divided by the initial investment value, N(0,O). 

7 If positive salvage values were assumed in the analysis, this would be another source of capital 

cost recovery. 
-31 -

held to be 0.5/1;, where L; is the class life. Scheduled allowances for subsequent taxable years are 

set at 1/L per dollar of investment, and the final nonzero scheduled deduction is established so as 

to make the sum of the A(t) equal unity.8 

Theresulting schedule is applied separately to each column ofN(t, v), weightedby the average 

price element, P,(t). The initial deduction is available to taxpayers with respect to the initial 

investment in new sucks and with respect to each subsequent investment in used trucks. Thus, the 

diagonal elements, P,(t)N(t,t), are each multiplied by A,(O), whereas the elements one period 

removed from the diagonal,P,(t)N(t + 1,t),are each multiplied by Au(l),the second element from 

the averaged depreciationschedule. The remaining off-diagonal elements are similarly constructed. 

The depreciation allowances are represented by the elements of the tax depreciationmatrix,D (t,v). 

The sum over v of the elements of this matrix provide the total depreciation allowances available 

by age, TDP(t). 

Losses or gains on sales are computed fromthe basis matrix,Z(t,v) (whose elements indicate 

the remaining tax basis), the previously computed sales matrix, S(t,v), and the retirements matrix, 

R(t,v), along with the price function,P (t),and the salvagevalue function, V(t).These calculations 

take into account the following facts: (i)the basis of each asset differs accordingto when the asset 

was last placed in service, and (ii) since a truck’s tax basis does not, in general, equal its market 

value, asset sales as well as retirements result in the recognition of loss or gain for tax purposes. 

To compute the remaining tax basis for each truck category,the depreciationmatrix, D (t,v), 

is divided element-by-elementby the asset matrix, N(t,v). This result expresses the depreciation 

allowances on a per asset basis. Cumulative sums for each column of this result are computed and 

then subtracted from the column’s applicable per asset average cost, P,(v),resulting in a matrix 

showing the beginning-of-period-basisper truck, Z(t,v). In algebraic form, Z(t,v) is equal to 

8 The tax basis curve shown in Figure 1 of the main text shows values at the end of each taxable or 

calendar year. However, tax depreciation allowances are averaged in order to correspond to the 

accounting periods used in the analysis. Thus, for example, the initial accounting year’s tax 

depreciation per dollar of investment consists of the first taxable year’s depreciation allowance 

(equal to OSL, where L is the equivalent economic life) plus one-half of the second taxable year’s

allowance (0.5x 1/L)for total depreciation in the first accounting year of UL. This averagingeffect 

is not reflected in the tax basis curve shown in Figure 1. The averaged depreciation allowances are 

referred to as A,(t) 
- 32 -

Z(t,v)=P,(v)- 7-1D(i,v) ~

i=,.N(i,v)' 

Inthisexpression,Tis theminimumoft and2,wherezisthesmallestvalueoft forwhichN(t,v)= 0. 

The tax loss (gain) matrix, TLG(t,v), is calculated as 

TLG(r,v) = [Z(t,v)-P,(t)] xS(t,v)+[Z(t,v)-VJt)] xR(t,v). 

Sums over the columns of this matrix yield the total net tax loss (gain) by age, TLG(t). Sdg 

TDP(t) and TLG(t) yields total tax deductions by age, TDD(t). The present value, PVTDD, is 

calculated with a formula identical to that used in calculating PVELV. 

The final results from the iterative procedure for the numerical example are shown in Table 

A-4. The life which yields a PWDD of equal value to PVELV is 4.6 years.' The straight-line 

depreciation schedule associated with this life is shown in column (2)of Table A-4." The depreciation allowances, loss deductions, and total deductions are shown in columns (3)-(5). 

Column (6)reports the remaining tax basis, RTB (t),associated with the initial investment of 

$1,000. As with the remaining economic value column in Table A-3, this series ends with $148 of 

remaining value. This value represents capital investment that is recovered not through tax 

deductions, but through sales to non-business truck users." The remaining tax basis is initially 

above the remaining economic value curve, but drops below it by year four. This implies that, after 

that point, truck sales will generate reportable taxable gains.I2 

9 The average period of business use for a truck in the example is 9.4 years, while the average

retirement age for a truck is 16.5 years. Use of either the average holding period or the average

retirement age as a useful life for straight-line depreciation purposes would yield a present value 

of tax deductions that differs, perhaps substantially, from PVELV. 

"The present value of the depreciation schedule is 0.8980,well above 0.7796, the present value of 

the total economic loss in value. However, these values are not comparable. Only about 85 percent

of the original investment outlay in the example is recovered in the form of tax deductions, and 

reported taxable gains offset a good portion of the depreciation deductions. 

1 1The unrecovered investmentvalues shown in Figure 4 in the main text reach zero at age twenty-six. 

Those curves were obtained by subtracting the proceeds from sales of trucks to households from 

the remaining values shown in the final columns of Tables A-3 and A-4. 

12In the early years, the remaining tax basis exceeds the remaining economic value of the original

investment. In this period, a sale generates a tax loss. It is assumed that transaction costs are 

significant enough to inhibit tax-motivated wash sales in tangible depreciable assets, so that the 

probability of sales remains unchanged. 
- 33 -

Table A- 1 

Truck Prices and Retirement and Sale Probabilities by Age 

Initial Investment: $1,000 

Period Discount Rate: 4.0 percent 

Probability Distributions Prices 

(Percent) (Normalized) 

RetireAge 

t 

ments 

r(t> 

Gross Sales 

s(t) 

Net Sales 

[1 -b(as(t) 

Assets 

p (0 

Salvage 

V(t> 

Factors 

P(t> 

(1) (2) (3) (4) (5) (6) (7) 

0 0.0 0.0 0.0 1.ooo 0.000 1.000 

1 0.2 1.o 0.3 0.655 0.000 0.98 1 

2 0.4 10.3 3.5 0.467 0.000 0.943 

3 0.6 21.5 7.3 0.344 0.000 0.907 

4 0.9 26.5 9.0 0.280 0.000 0.872 

5 1.3 41.5 14.0 0.241 0.000 0.838 

6 1.9 43.0 14.5 0.172 0.000 0.806 

7 2.6 36.5 12.3 0.1 18 0.000 0.775 

8 3.5 25.6 8.7 0.106 0.000 0.745 

9 4.5 28.4 9.6 0.109 0.000 0.717 

10 5.4 33.7 11.4 0.103 0.000 0.689 

11 6.3 15.4 5.2 0.093 0.000 0.662 

12 7.O 0.0 0.0 0.087 0.000 0.637 

13 7.6 0.0 0.0 0.08 1 0.000 0.612 

14 8.O 0.0 0.0 0.075 0.000 0.589 

15 8.3 0.0 0.0 0.068 0.000 0.566 

16 8.4 0.0 0.0 0.062 0.000 0.544 

17 8.6 0.0 0.0 0.056 0.000 0.524 

18 8.7 0.0 0.0 0.050 0.000 0503 

19 8.7 0.0 0.0 0.044 0.000 0.484 

20 8.7 0.0 0.0 0.037 0.000 0.465 

21 8.8 0.0 0.0 0.03 1 0.000 0.448 

22 8.8 0.0 0.0 0.025 0.000 0.430 

23 8.8 0.0 0.0 0.019 0.000 0.414 

24 8.8 0.0 0.0 0.012 0.000 0.398 

25 8.8 0.0 0.0 0.006 0.000 0.383 

26 100.0 0.0 0.0 0.000 0.000 0.368 

Remaining Discount 
- 34 -

Table A-2 

Retirements, Sales, and Assets Remaining in Business Use by Age of Trucks 

Remaining Business 

Assets 

Total Used 

Age Assets Assets 

t N(t> w(t> 

0 1000 0 

1 994 7 

2 956 74 

3 88 1 193 

4 795 294 

5 675 385 

6 566 404 

7 483 383 

8 426 354 

9 368 319 

10 308 277 

11 274 249 

12 255 232 

13 235 214 

14 217 197 

15 199 181 

16 182 166 

17 166 152 

18 152 138 

19 139 126 

20 127 115 

21 116 105 

22 105 96 

23 96 88 

24 88 80 

25 80 73 

26 0 0 

Sum - -

Business Asset Sales 

Business 

Asset Gross Household Business 

Retirements Sales Purchases Purchases 

R (t> s(t> H (t> u(0 

0 0 0 0 

2 10 3 7 

4 102 35 68 

6 204 69 135 

8 232 78 153 

10 326 110 216 

13 285 96 188 

15 201 68 133 

17 119 40 79 

19 115 39 76 

20 117 40 78 

19 44 15 29 

19 0 0 0 

19 0 0 0 

19 0 0 0 

18 0 0 0 

17 0 0 0 

16 0 0 0 

14 0 0 0 

13 0 0 0 

12 0 0 0 

11 0 0 0 

10 0 0 0 

9 0 0 0 

8 0 0 0 

8 0 0 0 

80 0 0 0 

406 1756 594 1162 
3 

- 35 -

Table A-3 

Loss in Economic Value by Age of Trucks 

Economic 

Economic Losses on 

Age Depreciation Retirements 

t EDP (t) Em (t) 

0 0 0 

1 344 2 

2 183 2 

3 113 2 

4 54 2 

5 29 3 

6 43 

7 29 2 

8 5 2 

9 -1 2 

10 2 2 

11 3 2 

12 2 2 

13 2 2 

14 1 1 

15 1 1 

16 1 1 

17 1 1 

18 1 1 

19 1 1 

20 1 0 

21 1 0 

22 1 0 

23 1 0 

24 1 0 

25 1 0 

26 0 0 

Sum 817 36 

PV 0.7536 0.0260 

Total Loss in 

Economic Value 

EI,V(t) 

0 

346 

185 

115 

56 

31 

45 

31 

7 

1 

4 

5 

3 

3 

3 

3 

2 

2 

2 

2 

1 

1 

1 

1 

1 

1 

0 

852 

0.7796 

Remaining

Economic 

Value 

REV(t) 

1000 

654 

468 

354 

297 

266 

221 

190 

183 

182 

178 

173 

170 

167 

164 

161 

159 

157 

155 

154 

152 

151 

150 

149 

149 

148 

148 
- 36 -

Table A-4 

Tax Deductions and the Resulting Equivalent Economic Life 

~~ 

Equivalent Economic Life: 4.6 years 

Depreciation Depreciation Loss Total Tax Remaining 

Age Schedule Allowances Deductions Deductions Tax Basis 

t A (t) TDP(t) TLG (t) TDD (t) RTB (t) 

0 0.0 0 0 0 1000 

1 10.9 218 1 219 78 1 

2 21.8 216 3 219 562 

3 21.8 201 -9 193 369 

4 21.8 169 -32 137 232 

5 21.8 84 -54 30 202 

6 2.0 29 -28 1 201 

7 0.0 22 -8 14 187 

8 0.0 17 -3 14 173 

9 0.0 13 -5 7 166 

10 0.0 9 -7 2 164 

11 0.0 6 -2 4 160 

12 0.0 4 1 5 155 

13 0.0 3 0 3 151 

14 0.0 2 0 2 149 

15 0.0 1 0 1 148 

16 0.0 0 0 0 148 

17 0.0 0 0 0 148 

18 0.0 0 0 0 148 

19 0.0 0 0 0 148 

20 0.0 0 0 0 148 

21 0.0 0 0 0 148 

22 0.0 0 0 0 148 

23 0.0 0 0 0 148 

24 0.0 0 0 0 148 

25 0.0 0 0 0 148 

26 0.0 0 0 0 148 

Sum 100.0 995 -143 852 

PV 0.8980 0.8969 -0.1 173 0.7796 
References 

Miaou, Shaw-Pin,"Study of Vehicle ScrappageRates," Oak Ridge National Laboratory,Oak Ridge,

TN, August 1990,cited in Davis, Stacy C. and Hu, Patricia S., TransportationEnergy Data Book: 

Edition 11,Oak Ridge National Laboratory, Oak Ridge TN, January 1991. 

1J.S. Department of Commerce, Bureau of Economic Analysis, unpublished business fixed 

investment worksheets, 1990. 

U.S. Department of Commerce, Bureau of the Census, 1987 Census of Transportation: Truck 

Inventory and Use Survey, United States. U.S. Govement Printing Office, Washington, DC, 

August, 1990. 

Acknowledgments 

The analysis in this report was conducted by David W. Brazell. Robert E. Yuskavage and Lowell 

Dworin provided editorial assistance. 

-37-