Statistical Considerations and Graphical Presentation of the
Residual Value of Heavy Construction Equipment
By Gunnar Lucko1, John C. Hildreth2, and Michael C. Vorster3
1
Assistant Professor of Civil Engineering and Director, Construction Engineering
and Management Program, Department of Civil Engineering, G-17 Pangborn Hall,
The Catholic University of America, Washington, DC 20064, email: lucko@cua.edu.
2
Senior Research Associate, Vecellio Construction Engineering and Management
Program, The Charles E. Via, Jr. Department of Civil and Environmental
Engineering, 200 Patton Hall, Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061, email: hildreth@vt.edu.
3
David H. Burrows Professor of Construction Engineering and Management,
Vecellio Construction Engineering and Management Program, The Charles E. Via, Jr.
Department of Civil and Environmental Engineering, 200 Patton Hall, Virginia
Polytechnic Institute and State University, Blacksburg, VA 24061, email:
mikev@vt.edu.
Abstract
Hourly equipment cost rates are vital to the long-term profitability of a
company. Hourly rates are based on the forecasted owning and operating costs. The
residual value is the most elusive element of owning and operating costs. It differs
from book value, which is typically calculated for taxation purposes using a
depreciation model. The residual value of heavy construction equipment is defined as
the monetary value that can be anticipated to be actually realized in an open market
transaction. Forecasting it statistically allows for an integrated cost model for heavy
construction equipment.
A comprehensive study of auction records for various equipment types,
makes, and sizes resulted in a statistical model of residual value. Quality of the
model was ensured through hypothesis testing and coefficient validation. Residual
value grids are intuitive graphical tools used to present the underlying datasets and
quickly and accurately forecast residual value with reliability.
Introduction
Equipment economics is the art and science of financially managing
construction equipment. Key decisions made by equipment managers all relate to
minimizing the owning and operating costs over a certain period of time to ensure
profitability. They include decisions such as whether to purchase, lease, or rent,
acceptability of pricing and financing options, assessing machine value at any point in
time, and determining the optimum duration of owning the equipment, i.e., the
economic life (Vorster 2004b). The components of equipment costs vary over time
1
and the value of money itself changes with time due to inflation. Thus, financial
management of construction equipment can be a daunting task.
The residual value of a machine is a component of owning costs and has
proven to be the most elusive. A statistical model of residual value was developed
based on auction records. Residual value grids are used to graphically represent the
data on which the analysis is based and provide insight regarding the relationship
between residual value and equipment age.
Equipment Costs
Equipment costs are categorized as either owning or operating costs. Owning
costs are connected to ownership of a machine and accrue regardless of whether the
machine is actually utilized on a construction project or not. Ownership costs are
typically comprised of purchase price, loan payments, insurance premiums, and
property taxes (Lucko and Vorster 2003). Operating costs are only incurred when the
machine is working and are directly dependent on the hours of use. They include all
consumables (fuel, oil, and grease), wear items in the traction system (tires or tracks),
attachments of the machine (cutting edge or bucket teeth), labor and parts costs from
maintenance and repairs (Mitchell 1998), and wages and fringe benefits for the
operator (Lucko and Vorster 2003).
Equipment managers must control each cost element relative to the hourly rate
charged for the machine to ensure a profitable operation. However, the ability to
predict each owning and operating cost element differs. The purchase price and
associated fees for the machine are known, while interest and principal payments can
be calculated. These cash outflows are offset by the residual value, which provides
cash inflow upon sell of the machine at the end of the owning period. True residual
value depends on many factors and is unknown until the machine is sold; it is the
value of a machine when sold at any point in its life (Vorster 2004a). Machine
factors influence residual value, including type, make, model, age, condition, and the
degree to which its technology is current (Grinyer 1973). External factors also
influencing residual value may be global, such as the overall state of the economy, or
regional, such as volume of work, climate, and soils conditions
Residual Value Definition
Residual value is the price for which a piece of used equipment may be sold in
the market at a particular time in a fair transaction between an equally informed buyer
and seller. Its importance for owning and operating cost calculations is well
established (Cross and Perry 1995, Cross and Perry 1996, Unterschultz and Mumey
1996).
Residual value differs fundamentally from depreciation, which is used in cost
accounting to determine the book value of an asset for administrative and taxation
purposes based on a prescribed model. The residual value is realized in the market
place through actual transactions, i.e., “evidences of value” (Cowles and Elfar 1978),
whereas a depreciated value remains an artificial estimate (Vorster 2003).
Current Practice
Residual value is often assumed equal to depreciated value, which is
commonly zero. However, this assumption of zero value is overly conservative
(Grinyer 1973), since as a minimum there is scrap value of the metal. Equipment
2
manufacturers Caterpillar (2001) and Deere (2002) recommend a non-zero residual
value. Equipment managers use rules-of-thumb (Cubbage et al. 1991) to estimate
residual value as a percentage of the initial value for different equipment types,
makes, and models. Slight adjustments may be made to account for unusual types,
setups, or utilization (Lucko et al. 2007). This approach simplifies the influence of a
complex combination of factors on residual value by selecting an isolated point on the
curve of residual value over time and neglecting any potential variability.
Data for Residual Value Forecasts
The best data for forecasting residual value are company records. Any piece
of used equipment that a company has bought or sold provides a measure of residual
value. However, the volume of data required to adequately forecast residual value is
likely unavailable unless a large fleet is owned and operated. Data can also be
extracted from auction sales records (Koger and Dubois 1999), which are the best
source from which a realistic model for residual value can be developed. Auction
data is commercially available for construction equipment and contain a large
selection of equipment types, makes, and models. Such data sources include serial
number, year of manufacture, a brief description, condition rating, auction firm,
location, date, and price. The auction data should be augmented by size categories
(bucket size or horsepower) to better describe the machines, list prices from
manufacturers (including costs for non-standard options), and equipment age in
calendar years.
Statistical Model of Residual Value
Making accurate forecasts of the residual value requires that its behavior and
dependency on various factors is extracted from real-world data. Statistical models of
different equipment types and sizes were developed to predict residual value as a
percentage of list prices.
List prices, or manufacturer suggested retail prices
(MSRP), do not reflect actual economic value, but rather recommend where to begin
price negotiations. Moreover, construction equipment is typically sold at discounts
off the MSRP depending on the business relationship between distributors and
equipment owners. Simply said, a price offer only becomes an economic value once
another party has been found that is willing to pay it. List prices, however, can serve
well as baselines for calculating residual value percentages (Cross and Perry 1995).
A carefully maintained database of actual purchase and sales prices for machines
reflect the circumstances under which a particular company operates.
Inflation Adjustment
The initial purchase and resale of machines typically occur several years
apart. Therefore, the effect of inflation on monetary value should be considered. All
cost values in the database were adjusted to a common base year to account for
inflation. Only auction prices and list prices that have been corrected for inflation
should be used together in the same owning and operating cost calculation.
Measures of inflation for various industry applications are published by the
Bureau of Labor Statistics (BLS). The Bureau of Economic Analysis (BEA) of the
U.S. Department of Commerce provides additional macroeconomic data. The
producer price index (PPI) for finished manufacturer goods reported monthly by BLS
3
comes was considered applicable to construction equipment. Cross and Perry (1995,
1996) have successfully used it to adjust residual values for inflation.
Normalization for Comparisons
In practice, the residual value is expressed in dollars. It may, however, be
useful to normalize the residual value by dividing its dollar value by the list price
(Cross and Perry 1995). This normalization to residual value percent (RVP) allows
different types, makes, and models to be directly compared (Cubbage et al. 1991,
Perry et al. 1990, Cross and Perry 1996). Normalization results in a small change to
the amount of information that is contained in a dataset, where the residual value and
list price data are replaced by a single residual value percent. This in turn causes
small changes in the statistical parameters that describe the dataset (Lucko et al.
2006). However, the extent of this effect is typically negligible.
Outliers
Displaying the relationship of residual value with time graphically in a
scatterplot will aid in identifying any outlying data. Outliers are extreme
observations that are inconsistent with the basic relationship or differ significantly in
sign or magnitude from other data points. Closer investigation of the database may
reveal whether outliers should be considered valid entries or were caused by errors in
measuring or recording and should be purged.
Regression Analysis
Common statistical approaches of modeling data are simple linear regression
(SLR) analysis and multiple linear regression (MLR) analysis. Simple and multiple
in this context mean that either one or several influential factors, respectively, are
included in the model. Linear regression signifies that the individual terms in the
regression equation are additive; they may be of higher order and more complex with
respect to the coefficients and variables that they contain to replicate the behavior of
the dataset (Lucko 2003). Mitchell (1998) used MLR to model repair costs. Nonlinear regression (NLR) models are theoretically more powerful than SLR and MLR,
but are cumbersome and have not been found necessary for equipment cost
calculations.
In a typical regression analysis, various models are created and tested for best
fit with the data. Measures of the goodness-of-fit are the coefficient of determination
(R2) and the adjusted coefficient of determination (R2adjusted). R2 describes how much
variability in the data is captured by the model as opposed to how much remains
unexplained, while R2adjusted includes a correction that makes it independent of the
actual sample size and resistant to including unnecessary extra factors in the model. .
Large coefficients of determination indicate good fits.
Newer data points for additional equipment sales should be added to the
database as soon as they become available and the statistical analysis should be re-run
with the same basic model to keep its forecasting capabilities current. In the long run,
forecasting the residual value could thus become an ongoing endeavor (Cubbage et al.
1991) that always includes the latest market data to provide the most current tool to
support decision making.
4
Functional Form
Evaluation of the data revealed that the general assumptions underlying
regression analysis were satisfied by each of the datasets for 28 different types and
size classes of equipment (Lucko 2003). A second-order polynomial function of
equipment age in calendar years with added terms for manufacturer, condition, and
regions was ultimately chosen based on the coefficient of determination. In some
versions macroeconomic measures were also included. Equipment age was
consistently found to be the most influential factor for residual value. The stability
and consistency of the regression model, as well as the sign and magnitude of
coefficients were validated.
Table 1 shows the basic functional expressions for residual value percent
(RVP) derived for two classes of common equipment types and sizes: wheel loaders
and track dozers. The coefficients m1, m2, m3, and c1, c2, and c3, and r1, r2, r3 are
triplets of binary indicator variables encoding the manufacturer, condition rating, and
regions, respectively.
Table 1: Regression Equations for Common Equipment Types and Sizes
Type
Wheel
loaders
Track
dozers
Size
Equation
RVP = 0.73678 + 0.00243 ⋅ age2
- 0.06494 ⋅ age - 0.13094 ⋅ m1 2-4 cy
0.09149 ⋅ m2 - 0.08869 ⋅ m3 +
bucket
0.02927 ⋅ c1 - 0.02013 ⋅ c2 +
size
0.02033 ⋅ c3 + 0.00681 ⋅ r1 +
0.00816 ⋅ r2 + 0.02213 ⋅ r3
RVP = 0.66202 + 0.0031 ⋅ age2
- 0.07476 ⋅ age + 0.0 ⋅ m1 100-200
0.10034 m2 - 0.02558 ⋅ m3 +
HP (net
0.04668 ⋅ c1 - 0.02164 ⋅ c2 +
flywheel)
0.01716 ⋅ c3 + 0.02785 ⋅ r1 +
0.01804 ⋅ r2 + 0.02694 ⋅ r3
Data
Points
R2
R2adjusted
3,857
0.747
0.746
4,594
0.806
0.805
Residual Value Grids
The residual value grid is comparable to the bird’s eye view of a terrain map
that charts the topography of a landscape with its valleys and ridges. The grids
innovatively extend traditional histograms to three dimensions and present the
number of transactions for each combination of machine age and inflation-corrected
residual value. Separate grids are used to present the dataset for each category of
equipment type and size. It should be noted that all machine makes, models, and
conditions are included for a given machine type and size.
Evident from each grid are the most common values at which machines are
sold for any age and the variability in selling values. This knowledge allows a
manager to quickly estimate the range of values at which a machine may sell and
gauge the change in value over time. This is valuable information in determining if
and/or when to sell.
5
Sample Application
The data for the two types and size classes of heavy construction equipment
listed in Table 1, wheel loaders and track dozers, are plotted as residual value grids in
Figures 1 and 2. All values are inflation-corrected actual dollars. The resolution of
the contour lines has been adjusted to reflect the number of data points in each
category and to limit the number of categories to retain the clarity of the diagram and
not artificially introduce a higher resolution.
Figure 1 shows the 3,857 observations for wheel loaders with bucket size
between 2 and 4 cy. The highest peak occurs at about 4 years with sales prices
between $60,000 and $70,000. The sales are overall solid throughout the entire range
of ages, with a decline between 8 and 10 years and another secondary peak after 11
years of age for about $30,000. It would be interesting to analyze whether the
difference between these two groups of machines lies in their manufacturer or
condition rating as possible influential factors.
Figure 2 shows the 4,594 observations for track dozers between 100 and 200
net flywheel HP. Track dozers exhibit a rather steep initial value loss from
approximately $150,000 at 2 years to $50,000 at 6 years and a noticeably lower slope
afterwards to between $30,000 and $20,000 at 15 years. Interestingly, track dozers
seem not to be sold in significant numbers before they have attained 2 years of age,
but are sold solidly until 15 years of age and possibly beyond. The primary peak is
found doubly at $80,000 and 3 years and $60,000 and 4 years with between 140 and
160 machines each. Also, the secondary peak is found doubly at $30,000 between 10
and 11 years and at 13 years.
For forecasting a particular residual value of a machine of known age, the
equipment manager should stay as close as possible to the ridgeline of the residual
value grid. For example, a track dozer of 3.5 years of age should be expected to sell
on average for approximately $70,000 in an auction. The innovative topographic
feature of residual value grids allows the equipment manager at the same time to
place high confidence in this estimate, as the residual value grid shows that a large
amount of machines have been sold at this value in the past. Price offers in the
private market can be gauged against this value. The equipment manager can use this
forecasted value as a basis that may be adjusted additionally using professional
experience and any available knowledge about the individual strengths and
weaknesses of the machine of interest to come up with a very accurate and reliable
customized forecast for the residual value.
Conclusions
Residual value is a central consideration within owning costs of used heavy
construction equipment. However, until recent research, it has remained clouded in
uncertainty and equipment managers relied on very broad rules of thumb. Statistical
models of residual value were developed from large datasets of different types and
sizes of construction equipment. Equipment managers are now better able to predict
residual value, more accurately determine owning and operating costs, and contribute
to the profitability of their companies. To facilitate the practical implementation of
the results, residual value grids are innovative and intuitive graphical presentations of
the large datasets. The grids aid managers in quickly estimating the range of selling
values for a machine.
6
References
Caterpillar (2001). Caterpillar Performance Handbook. 32nd Edition, Caterpillar,
Inc., Peoria, IL.
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Cross, T. L., Perry, G. M. (1995). “Depreciation Patterns for Agricultural
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Cross, T. L., Perry, G. M. (1996). “Remaining Value Functions for Farm
Equipment.” Applied Engineering in Agriculture 12(5), 547-553.
Cubbage, F. W., Burgess, J. A., Stokes, B. J. (1991). “Cross-sectional estimates of
logging equipment resale values.” Forest Products Journal 41(10), 16-22.
Deere (2002).
Deere Performance Handbook: 2002 Edition. Worldwide
Construction & Forestry Division, Deere & Company, Moline, IL.
Grinyer, P. H. (1973). “The Effects of Technological Change on the Economic Life
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reverse capital budgeting techniques.” Forest Products Journal 49(6), 35-38.
Lucko, G. (2003). “A Statistical Analysis and Model of the Residual Value of
Different Types of Heavy Construction Equipment.” Ph.D. Dissertation,
Virginia Polytechnic Institute and State University, Blacksburg, VA.
Lucko, G., Vorster, M. C. (2003). “Predicting the Residual Value of Heavy
Construction Equipment.” Proceedings of the 4th Joint International
Symposium on Information Technology in Civil Engineering, Nashville, TN,
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Mitchell, Z. W. (1998). “A Statistical Analysis of Construction Equipment Repair
Costs Using Field Data & The Cumulative Cost Model.” Ph.D. Dissertation,
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Perry, G. M., Bayaner, A., Nixon, C. J. (1990). “The Effect of Usage and Size on
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107(7), 50.
7
$120,000
$100,000
$90,000
$80,000
$70,000
$60,000
$50,000
$40,000
$30,000
Inflation Corrected Residual Value
$110,000
Number of
Transactions
120-140
100-120
80-100
60-80
40-60
20-40
0-20
$20,000
$10,000
0
1
2
3
4
5 6 7 8 9 10 11 12 13 14 15
Age in Calendar Years
Figure 1: Wheel Loaders 2-4 cy General Purpose Bucket Size
$160,000
$150,000
$140,000
$120,000
$110,000
$100,000
$90,000
$80,000
$70,000
$60,000
$50,000
Inflation Corrected Residual Value
$130,000
$40,000
$30,000
$20,000
$10,000
0
1
2
3
4
5 6 7 8 9 10 11 12 13 14 15
Age in Calendar Years
Figure 2: Track Dozers 100-200 hp (Net Flywheel)
8
Number of
Transactions
140-160
120-140
100-120
80-100
60-80
40-60
20-40
0-20