Download - Se 307-Chapter 11 Replacement Analysis
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Chapter 11Replacement Decisions
Replacement Analysis Fundamentals
Economic Service Life
Replacement Analysis When a Required Service is Long
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Replacement Terminology
Sunk cost: any past cost unaffected by any future decisions
Trade-in allowance: value offered by the vendor to reduce the price of a new equipment
Defender: an old machine
Challenger: a new machine
Current market value: selling price of the defender in the market place
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Sunk Cost associated with an
Asset’s Disposal (Example 11.1
Macintosh Printing Inc.)
$0 $5000 $10,000 $15,000 $20,000 $25,000 $30,000
Original investment (printing machine)
$10,000 $5000
Market value
$10,000
Lost investment(economic depreciation) Repair cost
$20,000
Sunk costs = $15,000
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Replacement Analysis Fundamentals
Replacement projects are decision problems involve the replacement of existing obsolete or worn-out assets.
When existing equipment should be replaced with more efficient equipment.
Examine replacement analysis fundamentals1) Approaches for comparing defender and challenger
2) Determination of economic service life
3) Replacement analysis when the required service period is long
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Replacement Decisions
Cash Flow Approach
Treat the proceeds from sale of the old machine as down payment toward purchasing the new machine.
This approach is meaningful when both the defender and challenger have the same service life.
Opportunity Cost Approach Treat the proceeds from
sale of the old machine as the investment required to keep the old machine.
This approach is more commonly practiced in replacement analysis.
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Example 11.2
Defender Market price:
$10,000 Remaining useful
life: 3 years Salvage value:
$2,500 O&M cost: $8,000
Challenger Cost: $15,000 Useful life: 3 years Salvage value:
$5,500 O&M cost: $6,000
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0 1 2 3 0 1 2 3
$8000
$2500
$15,000
$6000
$5500
(a) Defender (b) Challenger
$10,000
Sales proceeds from defender
Replacement Analysis – Cash Flow Approach
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Defender: PW(12%)D = $8,000 (P/A, 12%, 3) -$2,500 (P/F, 12%, 3)
= $17,434.90
AEC(12%)D = PW(12%)D(A/P, 12%, 3) = $7,259.10
Challenger: PW(12%)C = $5,000 + $6,000 (P/A, 12%, 3)
- $5,500 (P/F, 12%, 3) = $15,495.90
AEC(12%)C = PW(12%)C(A/P, 12%, 3) = $6,451.79
Replace the
defender now!
Annual Equivalent Cost - Cash Flow Approach
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Example 11.3 Comparison of Defender and Challenger
Based on Opportunity Cost Approach
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Defender:
PW(12%)D = -$10,000 - $8,000(P/A, 12%, 3) + $2,500(P/F, 12%, 3)
= -$27,434.90
AEC(12%)D = -PW(12%)D(A/P, 12%, 3)
= $11,422.64
Challenger:
PW(12%)C = -$15,000 - $6,000(P/A, 12%, 3) + $5,500(P/F, 12%, 3)
= -$25,495.90
AEC(12%)C = -PW(12%)C(A/P, 12%, 3)
= $10,615.33
Replace the defender now!
Annual Equivalent Cost - Opportunity Cost Approach
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Economic Service Life
Definition: Economic service life is the remaining useful life of an asset that results in the minimum annual equivalent cost.
Why do we need it?: We should use the respective economic service lives of the defender and the challenger when conducting a replacement analysis.
Ownership (Capital)cost
Operating cost
+
Minimize
An
nu
al E
qu
ival
ent
Co
st
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Economic Service Life Continue….
Capital cost have two components: Initial investment (I) and the salvage value (S) at the time of disposal.
The initial investment for the challenger is its purchase price. For the defender, we should treat the opportunity cost as its initial investment.
Use N to represent the length of time in years the asset will be kept; I is the initial investment, and SN is the salvage value at the end of the ownership period of N years.
The operating costs of an asset include operating and maintenance (O&M) costs, labor costs, material costs and energy consumption costs.
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Mathematical Relationship
Objective: Find n* that minimizes total AEC
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CR i I A P i N S A F i NN( ) ( / , , ) ( / , , )
OC i OC P F i n A P i Nnn
N
( ) ( / , , ) ( / , , )
1
AEC CR i OC i ( ) ( )
AE of Capital Cost:
AE of Operating Cost:
Total AE Cost:
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n*
AEC
OC (i)
CR(i)
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Example 11.4 Economic Service Life for a Lift Truck
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Steps to Determine an Economic Service Life
N = 1 (if you replace the asset every year) AEC1 = $18,000(A/P, 15%, 1) + $1,000 - $10,000
= $11,700
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N = 2 (if you replace the asset every other year)
AEC2 = [$18,000 + $1,000(P/A, 15%, 15%, 2)](A/P, 15%, 2)
- $7,500 (A/F, 15%, 2)
= $8,653
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N = 3, AEC3 = $7,406
N = 4, AEC4 = $6,678
N = 5, AEC5 = $6,642
N = 6, AEC6 = $6,258
N = 7, AEC7 = $6,394
Minimum cost
Economic Service Life
AEC if the Asset were Kept N Years
If you purchase the asset,it is most economical to replacethe asset for every 6 years
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Required Assumptions and Decision Frameworks
Now we understand how the economic service life of an asset is determined.
The next question is to decide whether now is the time to replace the defender.
Consider the following factors:
Planning horizon (study period) By planning horizon, it is mean that the service period required by the
defender and a sequence of future challengers. The infinite planning horizon is used when we are unable to predict when the activity under consideration will be terminated. In other situation, the project will have a definite and predictable duration. In these cases, replacement policy should be formulated based on a finite planning horizon.
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Decision Frameworks continue…….
Technology Predictions of technological patterns over the planning horizon refer to the
development of types of challengers that may replace those under study. A number of possibilities exist in predicting purchase cost, salvage value, and
operating cost as dictated by the efficiency of the machine over the life of an asset.
If we assume that all future machines will be same as those now in service, there is no technological progress in the area will occur.
In other cases, we may explicitly recognize the possibility of future machines that will be significantly more efficient, reliable, or productive than those currently on the market. (such as personal computers)
Relevant cash flow information Many varieties of predictions can be used to estimate the pattern of
revenue, cost and salvage value over the life of an asset.
Decision Criterion The AE method provides a more direct solution when the planning horizon
is infinite (endless). When the planning horizon is finite (fixed), the PW method is convenient to be used.
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Replacement Strategies under the Infinite Planning Horizon
Compute the economic lives of both defender and challenger. Let’s use ND* and NC* to indicate the economic lives of the defender and the challenger, respectively. The annual equivalent cost for the defender and the challenger at their respective economic lives are indicated by AED* and AEC* .
Compare AED* and AEC*. If AED* is bigger than AEC*, we know that it is more costly to keep the defender than to replace it with the challenger. Thus, the challenger should replace the defender now.
If the defender should not be replaced now, when should it be replaced? First, we need to continue to use until its economic life is over. Then, we should calculate the cost of running the defender for one more year after its economic life. If this cost is greater than AEC* the defender should be replaced at the end of is economic life. This process should be continued until you find the optimal replacement time. This approach is called marginal analysis, that is, to calculate the incremental cost of operating the defender for just one more year.
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Example 11.5 Relevant Cash Flow Information (Defender)
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ECONOMIC SERVICE LIFE OF DEFENDERGeneral equation for AE calculation for the defender is as follows:
AE (15%) = $6,200(A/P, 15%, N) + 2000 + $1,500 (A/G, 15%, N) – 1,000 (5 – N) (A/F, 15%, N) for N = 1,2,3,4, and 5
Cash flow diagram for defender When N = 4 years
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ECONOMIC SERVICE LIFE OF DEFENDER
N = 1
AE (15%)1 = $6,200 (A/P, 15%, 1) + 2000 + $1,500 (A/G, 15%, 1)
– 1,000 (5 – 1) (A/F, 15%, 1) AE (15%)1 = 7,130 + 2,000 + 0 – 4,000 = $5,130
OR
CR (15%)N = I (A/P, 15%, N) – SN (A/F, 15%, N)
AEOC =Σ [OCn (P/F, 15%, N)] (A/P, 15%, N)
CR (15%)1 = 6,200 (1.15) – 4,000 (1.0) = 7,130 – 4,000 = $3,130
AEOC1 = 2,000 (0.8696) (1.15) = 1739.2 x (1.15) = $2,000
Σ AE1 = CR (15%)1 + AEOC1 = 3,1,30 + 2,000 = $5,130
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Objective is : Find n* that minimizes total AEC
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CR i I A P i N S A F i NN( ) ( / , , ) ( / , , )
OC i OC P F i n A P i Nnn
N
( ) ( / , , ) ( / , , )
1
AEC CR i OC i ( ) ( )
AE of Capital Cost:
AE of Operating Cost:
Total AE Cost:
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N = 2
AE (15%)2 = $6,200 (A/P, 15%, 2) + 2000 + $1,500 (A/G, 15%, 2)
– 1,000 (5 – 2) (A/F, 15%, 2) AE (15%)2 = 3,813.62 + 2,000 + 697.65 – 1,395.3 = $5,116
OR
CR (15%)2 = I (A/P, 15%, 2) – S2 (A/F, 15%, 2)
CR (15%)2 = 6,200 (0.6151) – 3,000 (0.4651) = $2,418.32
AEOC2 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) ] (A/P, 15%, 2)
AEOC2 = [2,000 (0.8696) + 3,500 (0.7561)] (0.6151) = $2,697.55
Σ AE2 = CR (15%)2 + AEOC2 = 2,418.32 + 2,697.55 = $5,116
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N = 3
AE (15%)3 = $6,200 (A/P, 15%, 3) + 2000 + $1,500 (A/G, 15%, 3)
– 1,000 (5 – 3) (A/F, 15%, 3) AE (15%)3 = 2,715.6 + 2,000 + 1,360.65 – 576 = $5,500
OR
CR (15%)3 = I (A/P, 15%, 3) – S3 (A/F, 15%, 3)
CR (15%)3 = 6,200 (0.4380) – 2,000 (0.2880) = $2,139.6
AEOC3 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) ] x (A/P, 15%, 3)
AEOC3 = [2,000 (0.8696) + 3,500 (0.7561) + 5,000 (0.6575)] (0.6151)
AEOC3 = $3,360.7
Σ AE3 = CR (15%)3 + AEOC3 = 2,139.6 + 3,360.7 = $5,500
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N = 4
AE (15%)4 = $6,200 (A/P, 15%, 4) + 2000 + $1,500 (A/G, 15%, 4)
– 1,000 (5 – 4) (A/F, 15%, 4) AE (15%)4 = 3,813.62 + 2,000 + 697.65 – 1,395.3 = $5,961
ORCR (15%)4 = I (A/P, 15%, 4) – S4 (A/F, 15%, 4)
CR (15%)4 = 6,200 (0.3503) – 1,000 (0.2003) = $1,971.56
AEOC4 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) + OC4 (P/F, 15%, 4)] x (A/P, 15%, 4)
AEOC4 = [2,000 (0.8696) + 3,500 (0.7561) + 5,000 (0.6575) + 6,500 (0.5718) ] x (0.6151)
AEOC4 = $3,989.75
Σ AE4 = CR (15%)4 + AEOC4 = 1,971.56 + 3,989.75 = $5,961
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ECONOMIC SERVICE LIFE OF DEFENDERN = 5
AE (15%) 5 = $6,200 (A/P, 15%, 5) + 2000 + $1,500 (A/G, 15%, 5) – 1,000(5 – 5) (A/F, 15%, 3)
AE (15%)5 = 1,849.46 + 2,000 + 2,584.2 + 0 = $6,434
ORCR (15%)5 = I (A/P, 15%, 5) – S5 (A/F, 15%, 5)
CR (15%)5 = 6,200 (0. 2983) – 0 (0.1483) = $1,850
AEOC5 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) + OC4 (P/F, 15%, 4) + OC5 (P/F, 15%, 5)] x (A/P, 15%, 5)
AEOC5 = [2,000 (0.8696) + 3,500 (0.7561) + 5,000 (0.6575) + 6,500 (0.5718) + + 8,000 (0.4972)] x (0.2983)
AEOC5 = $4,584
Σ AE5 = CR (15%)5 + AEOC 5 = 1,850 + 4,584 = $6,434
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For N = 1 to 5, the results are as follows:
N = 1: AE (15%) = $5,130N = 2: AE (15%) = $5,116N = 3: AE (15%) = $5,500N = 4: AE (15%) = $5,961 N = 5: AE (15%) = $6,434
When N = 2 years, we get the lowest AE value. Thus the defender’s economic life is two years.
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AEC as a Function of the Life of the Defender (Example 11.5)
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ECONOMIC SERVICE LIFE OF CHALLENGER (Example 11.5)
Investment cost = $10,000 Salvage value
N = 1: $6,000 N > 1: decreases at a 15% over previous year
Operating cost N = 1: $2,000 N > 1: increases by $800 per year (G = $800) Rate of return 15%
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ECONOMIC SERVICE LIFE OF CHALLENGERGeneral equation for AE calculation for the challenger is as
follows:
AE (15%)N = $10,000(A/P, 15%, N) + 2000 + $800 (A/G, 15%, N)
– $6,000(1 – 15%)N-1 (A/F, 15%, N) for N = 1,2,3,4, and 5
N =1AE (15%)1 = $10,000(A/P, 15%, 1) + 2000 + $800 (A/G, 15%, 1)
– $6,000(0.85)1-1 (A/F, 15%, 1)AE (15%)1 = 11500 + 2,000 + 0 – 6,000 = $7,500
ORCR (15%)N = I (A/P, 15%, N) – SN (A/F, 15%, N)
AEOC =Σ [OCn (P/F, 15%, N)] (A/P, 15%, N)
CR (15%)1 = 10,000 (1.15) – 6,000 (1.0) = 11,500 – 6,000 = $5,500
AEOC1 = 2,000 (0.8696) (1.15) = 1739.2 x (1.15) = $2,000
Σ AE1 = CR (15%)1 + AEOC1 = 3,130 + 2,000 = $7,500
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N =2AE (15%)2 = $10,000(A/P, 15%, 2) + 2000 + $800 (A/G, 15%,
2) – $6,000(0.85)2-1 (A/F, 15%, 2)AE (15%)1 = 6151 + 2,000 + 372.08 – 2,372 = $6,151
OR
CR (15%)2 = I (A/P, 15%, 2) – S2 (A/F, 15%, 2)
CR (15%)2 = 10,000 (0.6151) – 5,100 (0.4651) = $3,779
AEOC2 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) ] (A/P, 15%, 2)
AEOC2 = [2,000 (0.8696) + 2,800 (0.7561)] (0.6151) = $2,372
Σ AE2 = CR (15%)2 + AEOC2 = 2,418.32 + 2,697.55 = $6,151
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N =3AE (15%)3 = $10,000(A/P, 15%, 3) + 2000 + $800 (A/G, 15%, 3)
– $6,000(0.85)3-1 (A/F, 15%, 3)AE (15%)3 = 4380 + 2,000 + 625.68 – 1,248.48 = $5,857
OR
CR (15%)3 = I (A/P, 15%, 3) – S3 (A/F, 15%, 3)
CR (15%)3 = 10,000 (0.4380) – 4335 (0.2880) = $3,132
AEOC3 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) ] x (A/P, 15%, 3)
AEOC3 = [2,000 (0.8696) + 2,800 (0.7561) + 3,600 (0.6575)] (0.4380)
AEOC3 = $2,725
Σ AE3 = CR (15%)3 + AEOC3 = 2,139.6 + 3,360.7 = $5,857
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N =4AE (15%)4 = $10,000(A/P, 15%, 4) + 2000 + $800 (A/G, 15%, 4)
– $6,000(0.85)4-1 (A/F, 15%, 4)AE (15%)4 = 3,503 + 2,000 + 1,061.04 – 738 = $5,826
OR
CR (15%)4 = I (A/P, 15%, 4) – S4 (A/F, 15%, 4)
CR (15%)4 = 10,000 (0.3503) – 3,685 (0.2003) = $2,765
AEOC4 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) + OC4 (P/F, 15%, 4)] x (A/P, 15%, 4)
AEOC4 = [2,000 (0.8696) + 2,800 (0.7561) + 3,600 (0.6575) + 4,400 (0.5718) ] x (0.3503)
AEOC4 = $3,061
Σ AE4 = CR (15%)4 + AEOC4 = 2,765 + 3,061 = $5,826
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N =5AE (15%)5 = $10,000(A/P, 15%, 5) + 2000 + $800 (A/G, 15%, 5)
– $6,000(0.85)5-1 (A/F, 15%, 5)AE (15%)5 = 2,983 + 2,000 + 1378.24 – 464.48 = $5,897
ORCR (15%)5 = I (A/P, 15%, 5) – S5 (A/F, 15%, 5)
CR (15%)5 = 10,000 (0. 2983) – 3,132 (0.1483) = $2,519
AEOC5 =Σ [ OC1 (P/F, 15%, 1) + OC2 (P/F, 15%, 2) + OC3 (P/F, 15%, 3) + OC4 (P/F, 15%, 4) + OC5 (P/F, 15%, 5)] x (A/P, 15%, 5)
AEOC5 = [2,000 (0.8696) + 2,800 (0.7561) + 3,600 (0.6575) + 4,400 (0.5718) + 5,200 (0.4972)] x (0.2983)
AEOC5 = $3,378
Σ AE5 = CR (15%)5 + AEOC 5 = 2,519 + 3,378 = $5,897
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The economic service life of the challenger is four years.
N = 1 year: AE(15%) = $7,500
N = 2 years: AE(15%) = $6,151
N = 3 years: AE(15%) = $5,857
N = 4 years: AE(15%) = $5,826
N = 5 years: AE(15%) = $5,897NC*=4 years
AEC*=$5,826
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Replacement Decisions
Should replace the defender now? No, because AECD < AECC
If not, when is the best time to replace the defender? Need to conduct the marginal analysis.
NC*= 4 years
AEC*=$5,826
*
*
2 years
$5,116D
D
N
AEC
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Marginal Analysis – When to Replace the Defender
Question: What is the additional (incremental) cost for keeping the defender one more year from the end of its economic service life, from Year 2 to Year 3?
Financial Data:
• Opportunity cost at the end of year 2: $3,000 (market value of the defender at the end year 2) • Operating cost for the 3rd year: $5,000
• Salvage value of the defender at the end of year 3: $2,000
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$3000
$2000
$5000
Step 1: Calculate the equivalent cost of retaining the defender one more from the end of its economic service life, say 2 to 3.
$3,000 (F/P,15%,1) + $5,000
- $2,000 = $6,450
Step 2: Compare this cost with AEC = $5,826 of the challenger.
Conclusion: Since keeping the defender for the 3rd year is more expensive than replacing it with the challenger, DO NOT keep the defender beyond its economic service life.
$6,450
2 3