Final report

4.15 
REFERENCES 
̄ APPENDIX 4-C 
̄ 
1.  
http://media.cygnus.com/files/cygnus/document/AUTM/2011/AUG/1839_soivendingrep 
ortemf_10343108.pdf
, “2011 State of the Vending Industry Report,” Automatic 
Merchandiser, VendingMachineWatch.com, pp. 18–30, December 2011. 
2.  
http://www.coinnews.net/2011/12/14/production-of-circulating-presidential-1-coins­
halted/
, Darrin Lee Unser, “Production of Circulating Presidential $1 Coins Halted,” 
CoinNews.net, December 14, 2011. 
3.  
http://online.wsj.com/article/SB10001424052970203914304576627252381486880.html? 
mod=e2tw
, Greg Bensinger, “A Future in Pay Phones?  One Firm Answers the Call,” The 
Wall Street Journal, October 13, 2011. 
4.   Craig A. Hesch, “Statement of the National Automatic Merchandising Association,” to 
the House Subcommittee on Domestic Monetary Policy and Technology of the U.S. 
House of Representatives Committee on Financial Services, July 20, 2010. 
5.  
http://www.ibisworld.com/industry/default.aspx?indid=1647
, Arcade, Food & 
Entertainment Complexes in the US, U.S. Industry Report, IBIS World Industry Report, 
February 2012. 
6.  
http://www.transitchicago.com/about/facts.aspx
, “CTA Facts at a Glance,” Chicago 
Transit Authority Web site, February 2012. 
7.  
http://www.ny.com/transportation/buses/
, “New York City Bus System,” ny.com, July 2, 
2012. 
8.  
http://www.selfserviceworld.com/article/160994/New-study-says-self-checkout­
terminals-to-quadruple-by-2014
, Caroline Cooper, “New study says self-checkout 
terminals to quadruple by 2014,” February 23, 2012.  
9.  
http://www.vending-cama.com/INDUSTRY/industry-Jan13-2012.asp
, “New steel 
loonies, toonies to be released,” The Canadian Press, January 13, 2012.  
284  

4.15.1  Appendix 4-D:  Estimate of the Number  of US Coins in Cir culation 
4.15.1.1  Method # 1:  Use of Estimated Total Value of Coins in Circulation 
This method of estimating the number of coins in circulation assumes that the current 
distribution of coins in circulation is identical to the distribution in the number of coins minted 
by the United States Mint between the years 2000 and 2010.  As reported on the United States 
Mint Web site, the United States Mint production of coins is shown in Table 4-D-1. 
Table 4-D-1.  Circulating Coin Production from the United States Mint 
Year 
Annual Production (number of coins of given denomination) 
One-Cent 
5-Cent 
Dime 
Quarter Dollar 
Half Dollar 
Dollar 
2000 
14,277,420,000 
2,355,760,000 
3,661,200,000 
6,470,940,000 
42,070,000 
1,286,060,000 
2001 
10,334,590,000 
1,303,380,000 
2,782,390,000 
4,806,980,000 
40,700,000 
133,410,000 
2002 
7,288,860,000 
1,230,480,000 
2,567,000,000 
3,313,700,000 
5,600,000 
7,600,000 
2003 
6,848,000,000 
824,880,000 
2,072,000,000 
2,280,400,000 
5,000,000 
6,160,000 
2004 
6,836,000,000 
1,445,040,000 
2,487,500,000 
2,401,600,000 
5,800,000 
5,320,000 
2005 
7,700,050,000 
1,741,200,000 
2,835,500,000 
3,013,600,000 
7,300,000 
5,040,000 
2006 
8,234,000,000 
1,502,400,000 
2,828,000,000 
2,941,000,000 
4,400,000 
7,700,000 
2007 
7,401,200,000 
1,197,840,000 
2,089,500,000 
2,796,640,000 
6,500,000 
950,670,000 
2008 
5,419,200,000 
640,600,000 
1,050,500,000 
2,538,800,000 
3,400,000 
489,120,000 
2009 
2,354,000,000 
86,640,000 
146,000,000 
533,920,000 
3,800,000 
423,640,000 
2010 
4,010,830,000 
490,560,000 
1,119,000,000 
347,000,000 
3,500,000 
402,220,000 
TOTAL 
80,704,150,000 
12,818,780,000 
23,638,590,000 
31,444,580,000 
128,070,000 
3,716,940,000 
Percent 
of Total 
52.94 
8.41 
15.51 
20.63 
0.08 
2.44 
Based upon the total estimated dollar value of US circulating coins currently in circulation from 
data prepared by the Financial Management Service of the United States Department of the 
Treasury,
126 
the estimated dollar value of US circulating coins on June 30, 2011 was 
$36,361,263,077.  In words, the total value of coins in circulation can be described as follows: 
Total value of circulating coins = SUM (Total number of coins in circulation X 
percentage of this denomination in circulation X value of this denomination).  In 
mathematical terms, this can be expressed as: 
where, 
= total value of US circulating coins 
j = one of the US coin denominations 
126 
Ref.:  September 2011 U.S. Currency and Coin Outstanding and in Circulation. 
285  

= total number of US coins in circulation 
= percentage of denomination j of the total number of coins in circulation 
= value of denomination j. 
Since the total number of US circulating coins is a constant in the above equation, it can be 
factored out of the summation and the equation solved for the total number of US circulating 
coins as follows. 
From the percentages listed at the bottom of Table 4-D-1 and the estimated values of US coins in 
circulation, the estimated number of coins can be computed from this equation.  The estimated 
number of coins of any given denomination in circulation can be estimated by multiplying the 
percentage of the denomination (  ) by the total number of circulating coins (  ).  The estimated 
numbers of US coins in circulation by denomination are shown in Table 4-D-2. 
Table 4-D-2.  Estimated Number of US Coins in Circulation – Based Upon Method # 1 
Number of Coins (in billions) 
One Cent 
5 Cent 
Dime 
Quarter Dollar 
Half Dollar 
Dollar 
TOTAL 
189.88 
30.16 
55.62 
74.00 
0.30 
8.75 
358.68 
4.15.1.2  Method # 2:  Scaling from Sample Set of Coins to Total Number of Coins in 
Circulation 
The second analysis method used relies upon sorting a large sample of coins by year, and 
counting the number of coins in the sample for each of the years.  The sample fraction by year is 
then projected to the whole population of circulating coins.  For a perfect sample, the sample 
fraction for any given year is identical to the population fraction for that same year.  Therefore, 
the only characteristic that remains (once the year-by-year fractions of the sample population are 
known) is the multiplication factor needed to scale from the sample size to the total population 
size.  The method of determining this multiplication factor is discussed below. 
The number of coins of a given denomination counted from the sample for a given year ( ) is 
and the total number of coins in the sample set is  .  In a similar definition, 
represents the 
number of coins in circulation for year  and  represents the total number of coins of a given 
denomination that is in circulation.  Assuming that the sample distribution is identical to the 
distribution of coins in circulation, then the coin fraction by year is identical for each year. 
Solving for 
yields. 
286  

The actual number of coins in circulation during any given year can also be expressed as 
where, 
= scaling factor, fraction of coins still in circulation relative to the total minted in year
= total number of coins minted in year  . 
At this point the values for 
are not known; however, the maximum value for any 
is 1.0. 
From the last two equations, the follow can be defined. 
Solving for n yields the following. 
This last formula can be used to compute an estimate of the total number of coins in circulation 
for the given denomination.  By computing an estimate for each year ( 
), the actual number of 
coins in circulation is the minimum of these year-by-year estimates.  This conclusion falls out 
since the scaling factors that yield larger total number of coins, must actually be less than 1.0.  
The actual fraction of coins in circulation for the year corresponding to the lowest value of 
, 
is assigned a value of 1.0 (or less) and the corrected scaling factors (  ) for all other years can 
then be determined by the following equation. 
This computed scaling factor can then be used to determine the number of coins in circulation for 
any given year by multiplying it by the number of coins minted in that year.  This method was 
followed by CTC using a large sample of coins for each of the following denominations:  one-
cent, 5-cent, dime and quarter dollar coins. 
The sampling completed by CTC included 2536 one-cent coins, 2219 5-cent coins, 1288 dime 
coins and 1745 quarter dollar coins.  The following curves show the fraction of coins in 
circulation after one additional factor is applied to the above method:  reducing the value of the 
maximum value of 
by an engineering estimate of the actual anticipated maximum number of 
coins for that year.  This estimate was arbitrarily made based upon the year in which the peak 
value of 
was observed for any given denomination and based upon how far above the 
neighboring years any given maximum value of 
was found to be.  Values of 0.9, 1.0, 0.9 and 
1.0 were selected for the one-cent, 5-cent, dime and quarter dollar coins, respectively.  Figures 4­
D-1 through 4-D-4 show the estimated fraction of coins in circulation by year since 1960 using 
this method. 
287  

Figure 4-D-1.  Estimated number of US one-cent coins in circulation. 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
1950 1960 1970 1980 1990 2000 2010 2020 
Fr
action in 
Cir
culation 
Year Minted 
Figure 4-D-2.  Estimated number of US 5-cent coins in circulation. 
0 
1950 1960 1970 1980 1990 2000 2010 2020 
Year Minted 
1.2 
1 
Fr
ac
ti
o
n
 in 
C
ir
cu
lat
io
n 
0.8 
0.6 
0.4 
0.2 
288  

Figure 4-D-3.  Estimated number of US dime coins in circulation. 
0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
0.9 
1 
1950 1960 1970 1980 1990 2000 2010 2020 
Fr
action in 
Cir
culation 
Year Minted 
Figure 4-D-4.  Estimated number of US quarter dollar coins in circulation. 
1.2 
1 
Fr
ac
ti
o
n
 in 
C
ir
cu
lat
io
n 
0.8 
0.6 
0.4 
0.2 
0 
1950 1960 1970 1980 1990 2000 2010 2020 
Year Minted 
Half dollar and dollar coins were not passed through this method, since these coins are in such 
low demand and CTC did not have confidence that they could get a representative sample of 
either of these coins.  An additional factor was considered to account for US circulating coins 
that were minted prior to 1960, Canadian coins and mutilated coins.  In these cases, the fraction 
of each of these coin types was computed relative to the total number of coins evaluated.  This 
fraction was then multiplied by the total number of coins predicted to be in circulation from 1960 
and beyond.  This provided an estimate of these other coin types that also appear in circulation in 
the US. 
289  

Based upon the counted coins from the samples mentioned above, the total number of coins in 
circulation in the US is estimated by the above method as: 
One-Cent:  240 billion  
5-Cent:  29 billion  
Dime:  44 billion  
Quarter Dollar:  43 billion  
Half Dollar:  0.3 billion (from Method # 1 above)  
Dollar:  9 billion (from Method # 1 above)  
Total:  366 billion .  
Many of these coins are not in active circulation on a daily basis.  Many US citizens hoard coins 
in storage containers in their homes, automobiles, office desk drawers and other locations.  
Although no known data exist about the percentage of the above estimated 366B coins that are 
currently being hoarded, a study 
127 
completed for the Reserve Bank of New Zealand concluded 
that approximately 84% of all circulating New Zealand coins are in some type of storage.  It is 
speculated that a similar fraction of US coins are being hoarded at any given time. 
4.15.1.3  Conclusions – Appendix 4-D 
The total coin count resulting from both methods is close to each other (< 2% difference). 
Based upon the results of the above methods, the total number of US coins in circulation is 
estimated to be between 355 billion and 370 billion. 
4.15.1.4  Improvements to the Implementation of Method # 2 
A method to evaluate the sample size required to assure accuracy in a sample can be computed 
from the following equation:
128 
where, 
R 
= sample size required 
D 
= number of elements in the population (here, the total number of circulating coins of a given 
denomination) 
c 
= estimated fraction of population, as a decimal (here, the fraction of circulating coins of a 
given year) 
= precision desired, expressed as a decimal (value chosen here was 10% = 0.10) 
127 
Antoinette Hastings, Alan Anderson and Josie Askin, “New Coin Requirements,” Report prepared for the 
Reserve Bank of New Zealand, Reference Number O141300022, AC Nielsen, March 2006.
128 
How to Determine a Sample Size,” Penn State Cooperative Extension, Program Evaluation, Tipsheet # 60, 
extension.psu.edu/evaluation/pdf/TS60.pdf.  
290  

= number of standard deviations required to reach desired confidence level (here, 1.96 was 
selected to achieve a 95% confidence level) 
= estimated response rate, expressed as a decimal (here, 100% [= 1.0] was selected). 
Given the typical fraction of coins for any given year and a desire to assure an accuracy of ±10% 
of the actual number of coins in circulation for any given year, this above equation was applied 
to the values found for each year and for each denomination from Method # 2.  Ignoring the 
outliers in the list of values, the typical number of coins was computed to be 20,000 for each 
denomination to assure sound values at a 95% confidence level for each denomination and for 
each year.  In other words, more accuracy and a higher level of statistical confidence in the 
results could be obtained in the CTC methodology if 20,000 randomly selected coins of any 
given denomination were sorted (by year), counted and the Method # 2 process applied to 
estimate the total number of coins in circulation in the US.  Future estimates of the number of 
coins in circulation should rely upon 20,000 randomly selected coins of each denomination to 
obtain a more robust and accurate number of coins than the sample sizes used in the limited-
effort CTC assessment discussed above. 
Some other factors that should be used to improve on the implementation of the CTC method 
would be to pull all samples on the same date from a widely dispersed geographic location 
(preferably at least 10 sites throughout the US).  In addition, some automated methods for 
determining the date of each coin would be useful to reduce the labor involved and the associated 
eye strain caused by reading 7500 coins twice (once to catalogue by year and a second time to 
confirm each selection). 
291  

5.0 
PRODUCTION EFFICIENCY 
5.1 
INTRODUCTION 
The Coin Modernization, Oversight, and Continuity Act of 2010 (Public Law 111-302), 
authorized the Secretary of the Treasury to review, research and develop new materials of 
construction for, improve the production efficiency of and report on the associated finding for 
production and use of current and alternative metallic material of construction for United States 
(US) circulating coinage.  This chapter of the first biennial report to the United States Congress 
focuses on the findings from Concurrent Technologies Corporation (CTC) related to improving 
the production efficiency of circulating coins.  The goal of the production efficiency efforts is 
well described by Section 3(c) of the language of the Act: 
Improved Production Efficiency.--In preparing and submitting the 
reports required under subsection (a), the Secretary of the Treasury 
shall include recommendations for changes in the methods of 
producing coins that would further reduce the costs to produce 
circulating coins, and include notes on the legislative changes that are 
necessary to achieve such goals. 
The first part of this production efficiency effort involved investigating whether changes in 
production technology, in the machinery and methods used to produce patterned metal discs, 
could be expected to achieve cost savings.  The United States Mint currently uses conventional 
stamping machinery to produce precisely detailed metal surfaces, with very tight quality control 
of each coin’s diameter, edge thickness and weight.  The United States Mint has shipped 5 to 14 
billion (B) coins annually in the past five years. 
Other industrial-scale metal shaping processes were evaluated to determine their capability to 
produce a metal piece with similar accuracy as that of current United States Mint production 
methods.
129 
Each process was evaluated for its ability to reproduce surface details, hold 
dimensional tolerances and ultimately produce cost savings to the United States Mint. 
In addition, surveys were taken of other producers of similar objects, including other mints 
around the world, and token and medal manufacturers, to see if production techniques were in 
use elsewhere that did not rely on traditional methods for producing circulating coins.  Neither of 
these investigations revealed any superior production technology currently in use. 
The second part of this production efficiency evaluation was a detailed study of circulating coin 
production by the United States Mints in Philadelphia and Denver.  Differences in production 
practices between the two mints were investigated.  In addition, scrap rates for coins, die life and 
production scheduling were studied.  Meetings with relevant experts from the United States Mint 
were held to discuss production issues and explore possible means of facilitating production 
improvements.  Several recommendations are discussed that are expected to improve the 
efficiency of the current production practices. 
129 
Processes that are used for non-metallic materials were not considered, since the Coin Modernization, Oversight, 
and Continuity Act of 2010, Public Law 111-302 specifically limits consideration of potential coinage materials to 
metallic materials. 
292  

5.2 
PRODUCTION TECHNOLOGY  
5.2.1  Conventional Coining 
The means of producing coins for circulation have not seen substantial changes since the 
introduction of steam-powered presses in 1788 [1] and knuckle or toggle presses, which replaced 
the slower screw presses beginning in the 1830s [2].  A knuckle press converts the continuous 
rotary motion of a flywheel into a back-and-forth linear motion, which is used to press the dies 
together on either sides of a piece of metal using a two-piece linkage that retracts and extends 
like a finger when the knuckle is bent or flattened, respectively.  The continuing evolution of 
machine design has increased the speed and reliability of operations at mints, but the basic 
process steps are still used today for bulk production of coinage:  rolling metal to a thin sheet, 
blanking
130 
discs from the sheets, annealing the discs to soften the metal, cleaning the surfaces of 
the blanks, upsetting
131 
the blank edges and coining between steel dies in a knuckle press. 
5.2.2  New Technologies 
The United States Mint facilities use presses that are capable of producing 750 coins per minute.  
The surface finish of newly produced circulating coins is very smooth, reproducing the finely 
polished surfaces of the coining dies.  Meeting or exceeding these two criteria, relative to current 
circulating coin standards, represents a significant hurdle to overcome in order to successfully 
introduce any new process. 
Various methods for creating finely-detailed metal surfaces were studied with the view of 
potentially replacing the traditional coin production processes in use today.  A great deal of 
development has recently occurred in net and near-net-shape
132 
production of metal objects. 
Alternative manufacturing processes were assessed in the present study based upon two principal 
criteria:  1) economics of producing coins at high rates of speed and 2) quality of resulting 
surface finish. 
There are several casting technologies that have evolved over many years to produce accurately 
shaped small parts with fine details.  In addition, there has been rapid development of new 
manufacturing techniques for producing net or near-net-shape, small, metal parts over the last 
several decades.  Many of these techniques rely on computer controls to carefully manage the 
processes to ensure the production of consistency, high-quality parts.  A discussion of each 
process capable of producing coin-sized objects follows. 
5.2.3  Investment Casting 
Investment casting is used to produce high-quality metallic parts.  Based on the ancient lost wax 
process, investment molds are formed using liquid slurries of ceramic materials poured around 
patterns made of low-temperature-melting materials (such as wax or plastics) made in the shape 
of the desired object.  Once the mold has dried, the wax/plastic is melted and drained out and the 
resulting mold is fired, like pottery, to harden it.  The resulting mold has a precision cavity for 
molten metal to fill.  After molten metal is poured into the mold and has cooled and solidified, 
130 
Blanking is the process of mechanically punching small disks from flat sheet.  
131 
Upsetting permanently deforms the edge of the blanks to gather metal near the rim for use in effectively filling  
the die during subsequent striking of the piece into a finished coin.
132 
Near-net-shape refers to processes that yield metal parts needing minimal machining after initial formation.  
293  

the mold is broken away to retrieve the finished metal casting.  While this process can produce 
quite detailed parts, the surface finish is not comparable to fine machining; further finishing steps 
such as grinding, polishing or burnishing are usually required to obtain the highest quality 
surface finish.  In addition, shrinkage of the hot metal reduces the dimensions of the cooled 
object and dimensional consistency similar to that of circulating coins is difficult to achieve on a 
consistent basis.  The normal tolerance for dimensional stability is quoted at ± 0.010 inch per 
linear inch of material.  With special care this can be improved to ± 0.005 inch per linear inch. 
This tolerance is larger than what is currently allowed (typically ± 0.1 mm [0.004 inch]) for US 
circulating coinage.  A wide range of materials can be processed using this technique, especially 
if casting is conducted in a vacuum to avoid oxidation.  However, due to the time and effort 
required to create the single-use molds, this is an expensive process for production of circulating 
coins.