Case Study 32
Taylor Borden, Sean Croley, Gavin McCluskie
Abstract
The purpose of this study is to determine a
new van replacement schedule that
minimizes costs while maximizing the
amount of available vans for use. This study
utilizes Equivalent Uniform Annual Worth
analysis. It also analyzes the projected
maintenance and operating costs for the vans
to help determine which factors are the most
important to the van replacement schedule.
It also contains the proposed changes to the
van replacement schedule. The final results
indicate that the ideal time to replace a van
would be after 6 years of use taking into
account practicality, tax, and monetary
factors.
Introduction
Mr. Speedy is an HVAC company
owned by George Moustakis that has a fleet
of 24 vans. 20 of the vans are used by the
company, while four of the vans are reserved
as backup vans for when the regular vans
break down or need routine maintenance.
Mr. Moustakis wants to determine what
changes, if any, need to be made to the
current van replacement schedule to
minimize costs.
As van operation, maintenance, and
replacement is an ongoing process lasting
theoretically indefinitely, we felt that
condensing all of these processes into a
single uniform annual expense using EUAC
analysis was most appropriate. With analysis
proceeding as such, it would be possible to
determine the uniform annual cost for van
operation assuming van replacement at each
year in the analysis range, and select the
option with the lowest annual cost.
Currently, vans are retired after seven
years or six if a major repair needs to be
made. Mr. Moustakis has found that
assigning each technician to a specific van is
the best way to ensure that the vans are
treated with respect by the technicians. The
vans do not all operate at the same time
because the company has the technicians
split between day, night, and weekend shifts.
The shop manager, Igor, suggested
replacing the vans every four years as
opposed to every seven years. However, the
book keeper, Vincent, suggested that the
owner continue to replace the vans every
seven years.
In this report, all of the calculations,
tables, and graphs were done using Google
Sheets. All equations were taken from
Engineering Economic Analysis (Newman et
al. 2020).
Content
The vans that Mr. Speedy has in its fleet
have maintenance and operating costs that
increase as the van ages. The operating costs
start at $250 in the first year and increase by
$750 in each subsequent year. The
maintenance cost begins at $500 and
increases by $200 every year after. A new
van costs $14,000 and must be fitted with a
special liner that costs an additional $4,000.
Each van also contains a tool inventory
worth $5,000. The tool inventory can be
transferred from a retired van to a new van,
but the liner cannot be. This puts the
replacement cost at $18,000. All initial
analysis uses a 10% interest rate for the
Time Value of Money (TVM).
Using Equation (1), we can calculate the
EUAC of each van.
𝐴 = 750 + 950(𝐴/𝐺, 𝑖, 𝑛) + 18000(𝐴/𝐹, 𝑖, 𝑛)
(1)
Where A is the EUAC, (A/G,i,n) is the
gradient uniform series for interes i and
number of years n, and (A/F,i,n) is the
sinking fund factor for the same variables.
The EUAC of each van over a period of ten
years is shown in Exhibit 1.
1
Exhibit 1. EUAC of each van at 10%
interest
recovery factor was applied to the sum of
the tax savings up until that year to yield the
EUAB.
Using the results from the process above and
the same EUAC process from Equation 1,
the Equivalent Uniform Annual Worth
(EUAW) of the van can be calculated using
Equation 2.
𝐸𝑈𝐴𝑊 = 𝐸𝑈𝐴𝐵 − 𝐸𝑈𝐴𝐶
This analysis suggests that the ideal year
for replacement is year seven, because that
is the year with the lowest EUAC. However,
the EUAC for years six, seven, and eight are
very close and differ by less than $100
annually. This means that the business
owner will not be majorly impacted by
needing to replace the van one year sooner
or one year later should some situation
necessitating such deviation occur, such as a
large increase in the cost of vehicles or a
breakdown.
Option 1. The first portion of this case study
was to determine the difference between an
analysis using 10% interest and an analysis
using 6% interest 40% marginal tax rate. For
the purposes of this analysis it is assumed
that taxes on deductions are money not spent
and therefore a benefit. The MACRS
depreciation rate is shown in Exhibit 2.
Exhibit 2. MACRS five year depreciation
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
20%
32%
19.2%
11.52%
11.52%
5.76%
This benefit was calculated through the
following method: first, the depreciation
schedule for the vans was calculated using
the corresponding MACRS schedule. Then,
the marginal tax rate of 40% was applied to
this depreciation schedule, and the present
value of each of these tax savings was
calculated. Finally, for each year the capital
(2)
Exhibit 3 shows the EUAW of each van
over a period of ten years, contrasted with
the EUAC as previously calculated but using
the new TVM interest rate.
Exhibit 3. EUAW of each van at 6% interest
and 40% marginal tax rate
The results of this analysis recommend
replacement of each van when it reaches six
years of age. Years five and seven are of
very similar EUAW to year six, again
allowing for early or late replacement if
necessitated by external circumstances with
little overall impact on the annual upkeep.
Option 2. The second portion of this case
study was to determine what factors are the
most important in deciding the van
replacement schedule. In addition, this
portion contains two possible solutions to
the problem of not having enough backup
vans.
As can be seen in Exhibit 4, the
maintenance and operating costs increase
dramatically over time.
2
Exhibit 4. Projected maintenance and
operating costs for each van
This dramatic increase over time makes
the operating and maintenance costs
incredibly important to the EUAW analysis.
It was found that the difference between
replacement years six, seven, and eight for
the analysis using 10% interest was very
negligible. It was similarly found that the
difference between replacement years five,
six, and seven for the analysis using 6%
interest was very negligible. These years
were very similar and only differed by
approximately one hundred dollars each.
This means that while the recommended
replacement years are year seven and year
six respectively, it does not impact the
business owner very much if it is more
convenient to replace a year sooner or later.
This case study recommends two
possible ways to increase the amount of
available working vans. A possible solution
may lie in assigning the working vans as
“backup-backup” vans. By having a
technician borrow a van from a specific
other technician, it creates a sense of
accountability with stocking and taking care
of the van. This is similar to what the
business owner tried before, except the hope
is that there will not be any communication
breakdown between technicians and
mechanics. This method also makes it easier
to track who is using which van.
The second solution is to recommend
adding a fifth backup van to the fleet. The
proposal is that the business owner
transitions one of the older vans that has
already depreciated, but is still in decent
working condition, to be a backup van. This
van would have been retired in a few years
and a new van would need to be bought. By
buying the new van a few years early, this
minimizes the cost of adding a fifth backup
van to the fleet to just the cost of a new tool
inventory. The increase in van availability
will soon far outweigh the cost of a tool
inventory, because the company will not be
forced to decline repair jobs. In addition,
this will also increase employee happiness
because the technicians will not be
prevented from going on jobs and missing
out on their completion bonus.
Conclusion and Recommendation
After all of the preceding analysis, the
results indicate that the ideal time for
replacement would be after 6 years of use.
Without taking tax benefits into account, this
time is only marginally more expensive than
replacement after 7 years, and should save
many a headache over maintenance and
breakdowns. Taking tax benefits into
account, this option becomes the cheapest to
maintain annually in addition to the other
stated benefits.
Appendices
Appendix A: EUAC for 10% TVM
Year of
Replacem
ent
A
Maintenan
ce
A
Operating
A
Replacem
ent-Salvag
e
Total
1
500
250
18000
18750
2
595.2
607
8571.6
9773.8
3
694.6
979.75
5437.8
7112.15
4
776.2
1285.75
3879
5940.95
5
862
1607.5
2948.4
5417.9
6
944.8
1918
2332.8
5195.6
7
1024.4
2216.5
1897.2
5138.1
8
1100.8
2503
1573.2
5177
9
1174.4
2779
1324.8
5278.2
10
1245
3043.75
1128.6
5417.35
3
Appendix B: EUAW for 6% TVM, 40%
MTR
Year of A
Replac Mainte
ement nance
A
Replac
A
ementOperati Salvag
ng
e
A
Saving
s
Sched
ule
Total
Total-S
avings
1
500
250
18000
18750
1440.0
17309.
2
597
613.75
8737.2
9947.9
1859.2
8088.6
3
692.2
970.75
5653.8
7316.7
1709.5
5607.2
4
785.4
1320.2
5
4114.8
6220.4
5
1508.4
30949
4712.0
19051
5
876.8
1663
3193.2
5733
1387.9
4345.0
6
966
1997.5
2581.2
5544.7
1248.6
4296.0
7
1053.6
2326
2143.8
5523.4
1099.4
4423.9
8
1139
2646.2
1818
5603.2
988.36
4614.8
9
1222.6
2959.7
1566
5748.3
902.42
4845.9
10
1304.4
3266.5
1366.2
5937.1
834.28
5102.8
Deprec Market
iation
Value
Year
Deprec
iation
Tax
Saving
s
P
Deprec
iation
1
3600
14400
1440
1358.4
2
5760
8640
2304
2050.5
3
3456
5184
1382.4
1160.6
4
2073.6
3110.4
829.44
656.99
5
2073.6
1036.8
829.44
619.84
6
1036.8
0
414.72
292.37
7
0
0
0
0
8
0
0
0
0
9
0
0
0
0
10
0
0
0
0
Reference
1. Newnan, Donald G., Eschenbach,
Ted G., and Lavelle, Jerome P.,
Engineering Economic Analysis,
fourteenth edition Oxford
University Press (2020).
4