The document discusses models for determining the optimal replacement time for construction equipment based on minimizing total cost. It presents an infinite horizon model that estimates total costs on a present value basis for an existing piece of equipment and its future replacements. The model considers costs like initial investment, operation & maintenance, resale value, repairs, and downtime. A case study applies the model to optimization of replacement for a Poclain excavator. Input data on costs over the excavator's life are analyzed. The model is used to determine the replacement age and new equipment life that minimize total present costs.

1. ““Construction Equipment ReplacementConstruction Equipment Replacement
Model”Model”
ByBy
Anil H. KulkarniAnil H. Kulkarni
Under the guidance ofUnder the guidance of
Prof. Dr. S. R. SatheProf. Dr. S. R. Sathe
SeminarSeminar
OnOn
Pune Institute of Engineering and Technology PunePune Institute of Engineering and Technology Pune
(Formerly Govt. College of Engineering Pune – 5)(Formerly Govt. College of Engineering Pune – 5)

2. Contents
• Economic Life ProblemEconomic Life Problem
• Replacement ModelReplacement Model
• Consequential Cost EquationsConsequential Cost Equations
• Case studyCase study
• ConclusionConclusion
• ReferencesReferences

3. Solution for Economic Life
Problem
Minimizing costs
– Comparison of alternatives with equal income
Profit

4. Maximum Profit Life
Economic Life = Maximum profit life

5. Infinite Horizon Model
• Model aims at estimating total cost for existing
equipment and replacement on current rupees basis
TC(N1, N2, N3,…… Nk) = I0 + Σ [ ] –
+ + Σ [ ] –
+ + Σ [ ] –
TC= Total cost of series of machines at N*, It= Initial investment at ‘t’
th
N1
j = 1
O0j
(1+i)j
S0N1
(1+i)N1
N2
j = 1
ON1j
(1+i)N1+j
SN1N2
(1+i)N1+N2
N3
j = 2
ON2j
SN2N3
(1+i)N1+N2+j
(1+i)N1+N2+N3
IN1
(1+i)N1
IN1+N2
(1+i)N1+N2

6. Economic Life of Equipment
-40.00
-30.00
-20.00
-10.00
0.00
10.00
20.00
30.00
40.00
50.00
0 5 10 15 20 25
Millions
Replacewment Age in Years
CostinRs.
Total Cost Curve
O & M cost
Investment Cost
Resale Value
Minimum Total
Cost

7. Realistic Model for Equipment
Replacement
• Minimum cost equipment replacement model
• Based on present worth of discounted cash flow
• Model projects expected future life cycle cost for
existing machine plus future replacement to
infinite horizon and then discounts them back to
present value
• The model considers all significant cost categories
of present machine plus all of its future
replacements to an infinite horizon
• Arithmetic and geometric gradients are used in
order to forecast costs

8. Optimization function
Planning
Horizon
N L L L L
TPC(N,L)
0
O & M
O & M
I(N+L) – S(N+L)
I(N+2L) – S(N+2L)
I(N+3L) – S(N+3L)
I(N) – S(N)
I(N+4L) – S(N+4L)

9. Planning
Horizon
Alternative 1 Alternative 2 Alternative 3 Alternative 4
N = 1 N = 2N =2N = 4
L = 5
L = 3
L = 5
L = 5L = 3 L = 6
L = 3
L = 3
L = 3
L = 3
L = 3
L = 6
L = 6
TPC(1,3) TPC(4,3) TPC(2,5) TPC(2,6)
E
R1
R2
R3
R4
• Capitalized comparison of alternatives

10. Consequential Costs and Equations
PVE1(N) = EMV – [EMV – BE(EA)] * TX
1. Investment Cost
2. Depreciation
3. Resale value
PVR1(L) = RCN(1+ i)^L *(rf)
PVE2(N) = - ∑ [ BVE(j) – BVE(j+1)* TX / (1+i)^j.
PVR2(L) = - ∑ [ BVR(j -1) – BVR(j)] * TX / (1+ i)^j* (1+ i)^L * (rf).
PVE3(N) - { RVE(N + EA) – [RVE(N + EA) – BE(N + EA)* TX }/{1+ i}N
PVR3(L) = - {RVR(L) – [ RVR(L) – BVR(L)] *TX }* TX;

11. Consequential Costs and Equations
4. Repair cost
5. Maintenance cost
6. Consumables cost
7. Downtime cost
8. Accessory and miscellaneous cost
9. Insurance cost
PVEk(N) = A . (gf) .(1 – TX)
PVRk(L) = A . (gf) (1 – TX) . (1+ i)L . (rf)
N or L
A
A + G
A + 2G
A + 3G
PVEk(N)

12. Consequential Costs and Equations
• Obsolescence Cost
• Overhaul cost
PVE9(N) = EOA . (gf)
PVR9(L) = ROA / (1 + i) . (gf).(1 + i)L
. (rf)
PVR12(L) = PVR12. (1 + i)L
. (rf)
PVE12(L) = PVE12. (1 + i)L
.
• Derivation of total present cost
TPC(N, L) = PCE(N) + PCR(L) / (1+ i)^N;
Where
PCE(N) = ∑ PVEk(N) PCR(L) = ∑ PVRk(L)&

13. Optimization Strategy
• Optimize total cost function TPC(N,L)
• Range values for N and L
• Find the optimum value for TPC
• Corresponding N = Optimum replacement
future life of the existing Equipment.
• Corresponding L = Optimum life cycle of
the replacement equipment

14. Case Study
Equipment Performance Data
Name: Poclain (CK 90) D Equipment Code: 161 D 05
Date of Perchace: DD/MM/1999
1 2 3 4 5 6 7
1 Actual Working Hrs 800 2535 2783 2166 1853 2406 330
2 All up acquisition cost Rs 4020974#
3 Depriciation @(11.6%) 408575 817150 1225726 1634301 2042876 2451451 2860026 3268602
4 Depricated Value 3113625 2705050 2296474 1887899 1479324 1070749 662174 253598 11.60%
5 Resale Value
6 Repair Cost (Actual) -- -- -- -- -- -- --
Repair Cost (For 1500Hrs) -- -- -- -- -- -- --
7 Maintenance Cost (Actual) 18549.00 175385.00 439107.00 155838.00 136714.00 159193.00 39085.00
Maintenance Cost (For 1500Hrs) 34779.38 103778.11 236672.84 107921.05 110669.72 99247.51 177659.09 193768.00 15.53%
8 Consumables Cost(Actual) 152941 610556 617132 681607 728725 1084542 183106
Consumables Cost(For 1500 Hrs) 286764.38 361275.74 332625.94 472027.01 589901.51 676148.38 832300.00 777684.00 56644.00
9 Workshop Exp + Stores (Actual) 375 973 5480 54437 18091 36844 9581
Workshop Exp + Stores (For 1500 Hrs) 703.13 575.74 2953.65 37698.75 14644.63 22970.07 43550.00
10 Down Time (in Hrs) 145 809 105
Downtime % (For 1500 Hrs)
Downtime Cost
11 Insurance
Insurance Cost 24655.4 24655.4 24655.4 24655.4 24655.4 24655.4 0
Sr.
No. Title
At The End of Year Coming
Year Cost
Cost
Gradient
Rs 3522200/-
Sunk Cost
Sunk Cost
Insurance Cost At 0.7 % per year

15. Forecasting CostsForecsting Costs:
1) Consumable Costs
The graph shown is graph of Age of
equipment Vs.respective consumable cost
The linear trendline is drawn in order to
forecst the costs and are as below….
i) First year consumables cost = Rs.236904/-
ii)Coming Year Cost = Rs. 777684/-
iii) Cost gradient (Linear) is Rs. 63091/ Year
2) Maintenance Cost
I) The graph shows the trend of increase of maintenance
cost with age of equipment.
ii) The following table shows the details:
From Eqn Rise/ Yr. % Rise/Yr. Costs At
1 18549.0 70517.71 1st Year
2 175385.0 81472.36 0.1553462
3 439107.0 94128.78 0.1553462
4 155838.0 108751.33 0.1553462
5 136714.0 125645.43 0.1553462
6 159193.0 145163.96 0.1553462
7 39085.0 167714.62 0.1553462
8 193768.44 0.1553462
9 223869.63 0.1553462
10 258646.91 0.1553462
Age of
Eqpt. In Cost at Age
Trendline Equation Y=61036*e^0.1444X
15.53%
Coming
Yr.
Consumables Cost
y = 90130x + 146774
R
2
= 0.9373
0.00
200000.00
400000.00
600000.00
800000.00
1000000.00
0 1 2 3 4 5 6 7 8
147H5
Linear (147H5)
Maintenance Cost
y = 61036e
0.1444x
R
2
= 0.2708
1000.00
10000.00
100000.00
1000000.00
0 1 2 3 4 5 6 7 8
Age In Years
CostinRs.
Maintenance Cost
Expon. (Maintenance
Cost)

16. I) The graph shows the trend of increase of repair and misc.
cost with age of equipment.
ii) The following table shows the details:
From Eqn Rise/ Yr. % Rise/Yr. Costs At
1 375.0 76721.99 1st Year
2 973.0 91843.71 0.1970976
3 5480.0 109945.89 0.1970976
4 54437.0 131615.97 0.1970976
5 18091.0 157557.17 0.1970976
6 36844.0 188611.31 0.1970976
7 9581.0 225786.16 0.1970976
8 270288.08 0.1970976
9 323561.22 0.1970976
10 326050.66 0.0076939
Obsolescence Cost Calculation
Sr. no.
Age In
years
Equipment
New Cost
Resale
Value
Existing
Equipment
Replacemen
t Cost
Obsolesc
ence %*
Usage In
Hrs
Hourly
Replaceme
nt Cost
Obsolescen
ec Cost
1 0 3522200.0 3522200.00 0.00 10 0 0 0
2 1 3803976.0 528330.00 3275646.00 10 1500 2183.76 21837.64
3 2 4108294.1 158499.00 3949795.08 10 3000 2633.20 26331.97
4 3 4436957.6 71324.55 4365633.06 10 4500 2910.42 29104.22
5 4 4791914.2 42794.73 4749119.48 10 6000 3166.08 31660.80
6 5 5175267.4 32096.05 5143171.30 10 7500 3428.78 34287.81
7 6 5589288.7 28886.44 5560402.30 10 9000 3706.93 37069.35
8 7 6036431.8 30330.76 6006101.07 10 10500 4004.07 40040.67
From Chart: 1) First Year Obsolescenec Cost = Rs.21837.64 2) Cost Gradient = Rs. 31617.00
* Obsolescenece % is taken as per companies requirment.
19.71%
Coming
Yr.
3) Repair And Miscillanious Costs
Age of
Eqpt. In Cost at Age
Trendline Equation y =321.12* e^0.7626x
Repair And Misc. Costs
y = 321.12e0.7626x
R2
= 0.7985
10.00
100.00
1000.00
10000.00
100000.00
1000000.00
0 1 2 3 4 5 6 7 8Age In Years
CostInRs.
Repair And Misc. Cost
Expon. (Repair And Misc. Cost)
Obsolescence Cost Vs. Age
y = 1548.9x + 10602
R
2
= 0.9929
0
5
10
15
20
25
0 2 4 6 8
Thousands
Age In years
CostInRs.
Obsolescence Cost
Linear (Obsolescence Cost)

17. Input Sheet
Poclain CK 90
General Data
1 19.00 %
2 Inflation Rate = 8.00 %
3 35.00 %
4 Method of Depreciation = Prime Cost
5 Existing Asset Depriciation Rate = 11.60 %
6 Replacement Asset Depriciation Rate = 11.60 %
7 Assumed Useful Service Life of Asset = 20 Yrs.
8 = 9.00 %
9 Praportion of Borrowed Capital = 50.00 %
Existing Asset
1 Investment Cost for Asset = Rs. 3522200.00
2 Present Age of Asset = Years 7
3 Current Resale Value = Rs. 1761100.00
Cost Coiming Year(Rs.) Cost Gradient / Growth Rate(%)
4 Accessory Cost Rs 0.00 Rs / Yr 0.00
5 Consumables Cost Rs 777684.0 Rs / Yr 63091.0
6 Downtime Cost Rs 0.00 Rs / Yr 0.00
7 Obsolascenece Cost Rs 205089.00 Rs / Yr 31617.00
8 Maitainance Cost Rs 167714.6216 % / Yr 15.50
10 Repar & Stores Cost Rs 270288.00 % / Yr. 20.00
11 Insurance cost Rs 24655.40 % / Yr. Decay 0.00
12 Overhaul Cost = Rs 187965.00
13 Number of Years = Years 3
Between Overhauls
14 Minimum Expected = Rs 187965.00
Salvage Value
Cost of Capital Rate =
IncomeTax Rate =
Interest Cost Rate

18. Result TPC(N, L)
Replacement Asset
1 5589288.74
2 Estimated Rate of Decline of = % / Yr. 20.00
Resale Value of Each Repalcement
Cost Coiming Year(Rs.) Cost Gradient / Growth Rate(%)
2 Accessory Cost Rs 0.00 Rs / Yr 0.00
3 Consumables Cost Rs 236904.0 Rs / Yr 63091.00
4 Downtime Cost Rs 0.00 Rs / Yr 0.00
5 Obsolascenece Cost Rs 41145.47 Rs / Yr 31617.00
6 Maitainance Cost Rs 70517.7 % / Yr 15.50
7 Repair & Stores Cost Rs 76722.00 % / Yr. 20.00
8 Insurance cost Rs 28146.9 % / Yr. Decay 0.00
9 Overhaul Cost = Rs. 558928.87
10 Number of Years = Years 3
Between Overhauls
11 Minimum Expected = Rs. 558928.87
Salvage Value
Current Investment Cost for Asset = Rs
n L 1 2 3 4 5 6 7 8 9 10
1 20980829.0 19032623.6 18561182.8 17837682.7 17386715.5 17448547.1 17214134.2 17201274.2 17497204.3 17654367.9
2 20099294.1 18462146.7 18065977.9 17457994.7 17079030.7 17130989.9 16934004.3 16923197.7 17171878.4 17303948.6
3 19598964.3 18223210.1 17890295.2 17379384.9 17060927.8 17104591.0 16939056.9 16929975.7 17138951.0 17249934.5
4 19512966.9 18356871.0 18077110.6 17647774.2 17380163.2 17416855.0 17277750.7 17270119.4 17445728.9 17538992.3
5 19432050.8 18460541.6 18225448.8 17864661.9 17639778.7 17670612.1 17553717.8 17547304.9 17694876.0 17773248.6
6 19557057.9 18740663.6 18543106.6 18239924.4 18050946.9 18076857.3 17978626.8 17973237.8 18097247.1 18163106.4
7 19904792.6 19218747.0 19052732.7 18797957.7 18639153.1 18660926.6 18578379.9 18573851.4 18678060.9 18733404.8
8 20337283.3 19760774.4 19621266.6 19407170.0 19273720.7 19292017.8 19222650.8 19218845.3 19306416.3 19352923.8
9 20849315.6 20364854.4 20247620.9 20067707.8 19955565.5 19970941.2 19912649.6 19909451.8 19983040.8 20022122.8
10 21492401.0 21085290.7 20986775.2 20835587.7 20741350.5 20754271.2 20705286.7 20702599.4 20764439.0 20797281.0
Grand Total TPC(N, L)

19. Results Sheet
Results
Optium Total Presnt Cost = 16923197.66 Rs.
Existing Equipments Optimum Future Age = 2 Years
Replacement Equipment Life Cycle = 8 Years
Following Chart of the cost components shows the replacement decision is clearly obtained:
Chart: Showing Clear Behaviour of total present cost suggesting replacement at N =2 Years
The ERA Model analysis shows that the Future life of existing equipment will be 2 year and the Replacement life cycle of the future
replacement equipments will be 8 years. The results are tabulated as below.
1
3
5
7
9
S1
S4
S7
S10
15000000.0
16000000.0
17000000.0
18000000.0
19000000.0
20000000.0
21000000.0
22000000.0
Cost in Rs.
L in Years
N in Years
Total Present Cost Vs Age
Optimum Total Present Cost is
Seen At N = 2 and L = 8 Years

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