equipment replacement model1 modi

““Construction Equipment Replacement Construction Equipment Replacement Model”Model”

ByBy

Anil H. KulkarniAnil H. Kulkarni

Under the guidance of Under the guidance of

Prof. Dr. S. R. SatheProf. Dr. S. R. Sathe

Seminar Seminar

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)

Contents

• Economic Life ProblemEconomic Life Problem• Replacement ModelReplacement Model• Consequential Cost EquationsConsequential Cost Equations• Case studyCase study• ConclusionConclusion• References References

Solution for Economic Life Problem

Minimizing costs– Comparison of alternatives with equal income

Prof

it

Maximum Profit Life

Economic Life = Maximum profit life

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’

And Otj = Operating and maintenance cost for the jth year (t = Purchase)

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

ON2jSN2N3

(1+i)N1+N2+j (1+i)N1+N2+N3

IN1

(1+i)N1

IN1+N2

(1+i)N1+N2

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

Mill

ions

Replacewment Age in Years

Cos

t in

Rs.

Total Cost CurveO & M costInvestment CostResale Value

Minimum Total Cost

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

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)

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

Consequential Costs and Equations

PVE1(N) = EMV – [EMV – BE(EA)] * TX1. 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;


4. Repair cost5. Maintenance cost6. Consumables cost7. Downtime cost8. Accessory and miscellaneous cost9. Insurance cost

PVEk(N) = A . (gf) .(1 – TX)

PVRk(L) = A . (gf) (1 – TX) . (1+ i)L . (rf)

N or L

A A + GA + 2G

A + 3G

PVEk(N)


• 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 costTPC(N, L) = PCE(N) + PCR(L) / (1+ i)^N;

WherePCE(N) = ∑ PVEk(N) PCR(L) = ∑ PVRk(L) &

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

Case Study

Equipment Performance DataName: Poclain (CK 90) D Equipment Code: 161 D 05

Date of Perchace: DD/MM/1999

1 2 3 4 5 6 71 Actual Working Hrs 800 2535 2783 2166 1853 2406 3302 All up acquisition cost Rs 4020974#

3 Depriciation @(11.6%) 408575 817150 1225726 1634301 2042876 2451451 2860026 32686024 Depricated Value 3113625 2705050 2296474 1887899 1479324 1070749 662174 253598 11.60%5 Resale Value6 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 56644.009 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 43550.0010 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

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 At1 18549.0 70517.71 1st Year2 175385.0 81472.36 0.15534623 439107.0 94128.78 0.15534624 155838.0 108751.33 0.15534625 136714.0 125645.43 0.15534626 159193.0 145163.96 0.15534627 39085.0 167714.62 0.15534628 193768.44 0.15534629 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 + 146774R2 = 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 = 61036e0.1444x

R2 = 0.2708

1000.00

10000.00

100000.00

1000000.00

0 1 2 3 4 5 6 7 8Age In Years

Cos

t in

Rs.

Maintenance Cost

Expon. (MaintenanceCost)

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 At1 375.0 76721.99 1st Year2 973.0 91843.71 0.19709763 5480.0 109945.89 0.19709764 54437.0 131615.97 0.19709765 18091.0 157557.17 0.19709766 36844.0 188611.31 0.19709767 9581.0 225786.16 0.19709768 270288.08 0.19709769 323561.22 0.1970976

10 326050.66 0.0076939

Obsolescence Cost Calculation

Sr. no. Age In years

Equipment New Cost

Resale Value Existing Equipment

Replacement Cost

Obsolescence %*

Usage In Hrs

Hourly Replacement Cost

Obsolescenec Cost

1 0 3522200.0 3522200.00 0.00 10 0 0 02 1 3803976.0 528330.00 3275646.00 10 1500 2183.76 21837.643 2 4108294.1 158499.00 3949795.08 10 3000 2633.20 26331.974 3 4436957.6 71324.55 4365633.06 10 4500 2910.42 29104.225 4 4791914.2 42794.73 4749119.48 10 6000 3166.08 31660.806 5 5175267.4 32096.05 5143171.30 10 7500 3428.78 34287.817 6 5589288.7 28886.44 5560402.30 10 9000 3706.93 37069.358 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

Cos

t In

Rs.

Repair And Misc. Cost

Expon. (Repair And Misc. Cost)

Obsolescence Cost Vs. Age

y = 1548.9x + 10602R2 = 0.9929

0

5

10

15

20

25

0 2 4 6 8

Thou

sand

s

Age In years

Cos

t In

Rs. Obsolescence Cost

Linear (Obsolescence Cost)

Input SheetPoclain CK 90

General Data1 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 Asset1 Investment Cost for Asset = Rs. 3522200.002 Present Age of Asset = Years 73 Current Resale Value = Rs. 1761100.00

Cost Coiming Year(Rs.) Cost Gradient / Growth Rate(%)4 Accessory Cost Rs 0.00 Rs / Yr 0.005 Consumables Cost Rs 777684.0 Rs / Yr 63091.06 Downtime Cost Rs 0.00 Rs / Yr 0.007 Obsolascenece Cost Rs 205089.00 Rs / Yr 31617.008 Maitainance Cost Rs 167714.6216 % / Yr 15.50

10 Repar & Stores Cost Rs 270288.00 % / Yr. 20.0011 Insurance cost Rs 24655.40 % / Yr. Decay 0.0012 Overhaul Cost = Rs 187965.0013 Number of Years = Years 3

Between Overhauls 14 Minimum Expected = Rs 187965.00

Salvage Value

Cost of Capital Rate =

IncomeTax Rate =

Interest Cost Rate

Result TPC(N, L)

Replacement Asset1 5589288.742 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 0.003 Consumables Cost Rs 236904.0 Rs / Yr 63091.004 Downtime Cost Rs 0.00 Rs / Yr 0.005 Obsolascenece Cost Rs 41145.47 Rs / Yr 31617.006 Maitainance Cost Rs 70517.7 % / Yr 15.507 Repair & Stores Cost Rs 76722.00 % / Yr. 20.008 Insurance cost Rs 28146.9 % / Yr. Decay 0.009 Overhaul Cost = Rs. 558928.87

10 Number of Years = Years 3Between Overhauls

11 Minimum Expected = Rs. 558928.87Salvage Value

Current Investment Cost for Asset = Rs

n L 1 2 3 4 5 6 7 8 9 101 20980829.0 19032623.6 18561182.8 17837682.7 17386715.5 17448547.1 17214134.2 17201274.2 17497204.3 17654367.92 20099294.1 18462146.7 18065977.9 17457994.7 17079030.7 17130989.9 16934004.3 16923197.7 17171878.4 17303948.63 19598964.3 18223210.1 17890295.2 17379384.9 17060927.8 17104591.0 16939056.9 16929975.7 17138951.0 17249934.54 19512966.9 18356871.0 18077110.6 17647774.2 17380163.2 17416855.0 17277750.7 17270119.4 17445728.9 17538992.35 19432050.8 18460541.6 18225448.8 17864661.9 17639778.7 17670612.1 17553717.8 17547304.9 17694876.0 17773248.66 19557057.9 18740663.6 18543106.6 18239924.4 18050946.9 18076857.3 17978626.8 17973237.8 18097247.1 18163106.47 19904792.6 19218747.0 19052732.7 18797957.7 18639153.1 18660926.6 18578379.9 18573851.4 18678060.9 18733404.88 20337283.3 19760774.4 19621266.6 19407170.0 19273720.7 19292017.8 19222650.8 19218845.3 19306416.3 19352923.89 20849315.6 20364854.4 20247620.9 20067707.8 19955565.5 19970941.2 19912649.6 19909451.8 19983040.8 20022122.810 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)

Results SheetResults

Optium Total Presnt Cost = 16923197.66 Rs.Existing Equipments Optimum Future Age = 2 YearsReplacement 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

1) Collier C. A. And Jacques D. E. “Optimum Equipment Life By Minimum Life Cycle Costs”, Journal Of Construction Engineering And Management, ASCE, Vol. 110, No.2, June, 1984.2) Vorster M. C. And Sears G. A., “Model For Retiring , Replacing , Reassigning Construction Equipment.”, Journal Of Construction Engineering And Management, ASCE, Vol. 113, No.1, March 1987. 3) Jaafari A., And Mateffy V. K., “Realistic Model Foe Equipment Replacement”, Journal Of Construction Engineering And Management, ASCE, Vol. 116, No. 3, Sept, 1990. 4 Tsimberdonis a. i., and murphree e. l., “equipment management through operational failure costs”, Journal Of Construction Engineering And Management, ASCE, Vol. 120, No. 3, Sept 1994.5) Whittakar John., “Equipment Rates From Revenue Requirements”, Journal Of Construction Engineering And Management, ASCE, Vol.113, No. 2, June 1987.

6) Ittiphol B., And Touran Ali, “Case Study Of Obsolescence And Equipment Productivity”, Journal Of Construction Engineering And Management, ASCE, Vol.128, No 4, Aug. 2002.

7) Pmplikar S. S., “Anglicizing Downtime Costs Associated With Earthmoving Machinery”, Construction Engineering And Construction Reviw, July 2002.

8) Prabhu kumar t. k., “equipment planning and management for construction contracting”, JCM NICMAR.

9) R. Shukla, N. Satyamurthy, “Procurement Policy For Construction Equipment “, Jcm Nicmar.

10) Sharma S. C. And Arora N.D., “Equipment Management In Construction Projects”, NBM And CW, July 2004.

11) Vorster Mike., “Four Keys To Control Owning And Operating Costs”, Journal Of Construction Equipment, Oct, 2003.

12) Vorster Mike., “How To Estimate Market Value”, Journal Of Construction Equipment, June, 2004.

13) Panes V., Patavardhan N., And Phadake V. R., “Economics Of Owning And Operating Hydraulic Excavators”, CE & CR July 2004.

14) Bhujanga Rao V.V., “Construction Equipment Policy”, JCM NICMAR.

15) Vorster Mike., “six steps to demystify depreciation”, journal of construction equipment, December 2003.

16) Income Tax Rules 1962, Appendix I., Effective From The Assessment Year 2003.2004.17) Engineering Economics, By Blank.18) Purifoy.P.E., “Construction Planning And Methods”, Fifth Edition.

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