INDR 202 - Chapter 12

INDR  202

ENGINEERING  ECONOMICS

CHAPTER  12

REPLACEMENT  DECISIONS

SPRING  2015

REPLACEMENT  DECISIONS

REPLACEMENT  ANALYSIS

REPLACEMENT  DECISION

replacement  of  existing  obsolete/worn-­out  assets

DEFENDER

existing  equipment

CHALLENGER

best  available  replacement  equipment

CURRENT MARKET VALUE of defender

TRADE-­IN ALLOWANCE offered by vendor to reduce the price of new equipment

EXAMPLE  1:  SUNK  COSTS

$0       $10,000   $20,000        $25,000 SUNK  COSTS  $15,000

ORIGINAL  INVESTMENT $20,000

MARKET  VALUE

$10,000

LOST  INVESTMENT

$10,000

REPAIR COST

REPLACEMENT  ANALYSIS

CASH-­FLOW  APPROACH

proceeds  from  sale  of  the  defender as  down  payment toward  purchasing  the  challenger

(equal analysis period for all alternatives)

OPPORTUNITY-­COST  APPROACH

proceeds  from  sale  of  the  defender as  investment required  to  keep  the defender

EXAMPLE  1:  CASH-­FLOW  APPROACH

0 1 2 3

$8,000

$2,500

DEFENDER

0 1 2 3

$6,000

$5,500

CHALLENGER

$15,000

$10,000 sales proceeds  

EXAMPLE  1:  CASH-­FLOW  APPROACH

DEFENDER

𝐴𝐸_# 12% = $2,500 𝐴|𝐹, 12%, 3 − $8,000 = −$7,259.10

CHALLENGER

𝐴𝐸₄ 12% = $5,500 𝐴|𝐹, 12%, 3 − $6,000 − $5,000 𝐴|𝑃, 12%, 3    

= −$6,451.79

EXAMPLE  1:  OPPORTUNITY-­COST  APPROACH

0 1 2 3

$8,000

$2,500

DEFENDER

0 1 2 3

$6,000

$5,500

CHALLENGER

$15,000

$10,000

EXAMPLE  1:  OPPORTUNITY-­COST  APPROACH

DEFENDER

𝐴𝐸_# 12% = $2,500 𝐴|𝐹, 12%, 3 − $8,000 − $10,000 𝐴|𝑃, 12%, 3

= −$11,422.64

CHALLENGER

𝐴𝐸₄ 12% = $5,500 𝐴|𝐹, 12%, 3 − $6,000 − $15,000 𝐴|𝑃, 12%, 3  

= −$10,615.33

ECONOMIC  SERVICE  LIFE

ECONOMIC  SERVICE  LIFE

useful  life  of  a  defender  (or  a  challenger)  that  results  in  the   minimum  annual  equivalent  cost  (ownership  &  operating)

ECONOMIC  SERVICE  LIFE

CAPITAL  COST

𝐶𝑅 𝑖 = 𝐼 𝐴|𝑃, 𝑖, 𝑁 − 𝑆

𝐴|𝐹, 𝑖, 𝑁

= 𝐼 − 𝑆

𝐴|𝑃, 𝑖, 𝑁 + 𝑖𝑆

OPERATING  COSTS

𝑂𝐶 𝑖 = B 𝑂𝐶

𝑃|𝐹, 𝑖, 𝑛

?

CEF

𝐴|𝑃, 𝑖, 𝑁

TOTAL  COST

ECONOMIC  SERVICE  LIFE

Useful  Life

EXAMPLE  2:  ECONOMIC  SERVICE  LIFE

Initial cost: $18,000

Operating costs: $1,000 in year 1 & 15% annual increase

Salvage value: $10,000 in year 1 & 25% annual decrease

Maximum life: 7 years

EXAMPLE  2:  ECONOMIC  SERVICE  LIFE

𝑁 = 1

EXAMPLE  2:  ECONOMIC  SERVICE  LIFE

𝑁 = 2

𝐴𝐸𝐶_H 15% = $18,000 + $1,000 𝑃|𝐴_F, 15%, 15%, 2 𝐴|𝑃, 15%, 2

EXAMPLE  2:  ECONOMIC  SERVICE  LIFE

Minimum  Cost

Economic  Service  Life

𝑁 = 6

𝑁 𝐴𝐸𝐶_? 15%

INDEFINITE  SERVICE  PERIOD

REPLACE  DEFENDER  NOW

Challenger cash flows occur for an infinite number of years starting now.

Challenger is replaced by an identical one if necessary.

REPLACE  DEFENDER  

𝒙

YEARS  LATER

Defender cash flows occur in the first 𝑥 years.

EXAMPLE  3:  INDEFINITE  SERVICE  PERIOD

REPLACE  DEFENDER  NOW

New machine cost: $10,000.

Operating cost: $2,200 in year 1 with 20% annual increase Salvage value: $6,000 in year 1 with 15% annual decrease

REPLACE  DEFENDER  

𝒙

YEARS  LATER

Repair cost to use broken machine for 5 years: $1,200.

Operating cost: $2,000 in year 1 with $1,500 annual increase Salvage value: $5,000 now with 25% annual decrease

EXAMPLE  3:  INDEFINITE  SERVICE  PERIOD

𝑁 = 1

:

𝐴𝐸𝐶

15% = $5,380

𝑁 = 2

:  

𝐴𝐸𝐶

15% = $5,203

𝑁 = 3

:  

𝐴𝐸𝐶

15% = $5,469

𝑁 = 4

:  

𝐴𝐸𝐶

15% = $5,844

𝑁 = 5

:  

𝐴𝐸𝐶

15% = $6,258

Remaining  Useful  (Economic)  Service  Life  of  Defender  

Minimum  Cost

EXAMPLE  3:  INDEFINITE  SERVICE  PERIOD

𝑁 = 1

:

𝐴𝐸𝐶

15% = $7,700

𝑁 = 2

:  

𝐴𝐸𝐶

15% = $6,184

𝑁 = 3

:  

𝐴𝐸𝐶

15% = $5,756

𝑁 = 4

:  

𝐴𝐸𝐶

15% = $5,625

𝑁 = 5

:  

𝐴𝐸𝐶

15% = $5,631

Economic  Service  Life  of  Challenger

Minimum  Cost

EXAMPLE  3:  INDEFINITE  SERVICE  PERIOD

CHALLENGER

𝑁

= 4

𝐴𝐸𝐶

15% = $5,625

DEFENDER

𝑁

= 2

𝐴𝐸𝐶

15% = $5,203

To replace  the  defender  now?

NO:  𝐴𝐸𝐶_# 15% < 𝐴𝐸𝐶₄ 15% ,  keep  it  by  

EXAMPLE  3:  MARGINAL  ANALYSIS

Incremental cost of keeping defender one more year from the end of its economic service life:

Opportunity cost at the end of year 2: $2,813 Operating cost in year 3: $5,000

Salvage value at the end of year 3: $2,109

STEP 1. Equivalent cost of keeping the defender in year 3

$2,813 𝐹|𝑃, 15%, 1 + $5,000 − $2,109 = $6,126

STEP 2. 𝐴𝐸𝐶₄ 15% = $5,625 < $6,126

TAX  CONSIDERATIONS

Whenever possible, after-­tax cash flows should be used

in replacement analysis.

EXAMPLE  1:  TAX  CONSIDERATIONS

MARKET  VALUE  $10,000

TAX  CREDIT

$4,693 40% = $1,877

NET  PROCEEDS  FROM  DISPOSAL  $11,877

$0 $10,000       $14,693 $20,000 DEPRECIATION

$5,307

$4,693 BOOK  LOSS

MARKET  VALUE  $10,000

DEPRECIATION  COST  BASIS  $20,000

EXAMPLE  3:  TAX  CONSIDERATIONS

REPLACE  DEFENDER  NOW

New machine cost: $10,000.

Operating cost: $2,000 in year 1 with $1,000 annual increase Salvage value: $6,000 in year 1 with 15% annual decrease

REPLACE  DEFENDER  

𝒙

YEARS  LATER

Repair cost to use broken machine for 5 years: $1,200.

Operating cost: $2,000 in year 1 with $1,500 annual increase Salvage value: $5,000 now with $1,000 annual decrease

EXAMPLE  3:  TAX  CONSIDERATIONS

Year Current Market  Value After-­Tax  Salvage Value

0 $5,000 $5,000(60%)  =  $3,000 1 $4,000 $4,000(60%)  =  $2,400 2 $3,000 $3,000(60%)  =  $1,800

3 $2,000 $2,000(60%)  =  $1,200

4 $1,000 $1,000(60%)  = $600

5 $0 $0

6 $0 $0

EXAMPLE  3:  TAX  CONSIDERATIONS

DEFENDER

Year Overhaul Operating  Cost After-­Tax  Operating  Cost

0 $1,200 $1,200(60%) =  $720

DEFENDER

𝑁 = 1

𝑁 = 2

𝑁 = 3

𝑁 = 4

EXAMPLE  3:  TAX  CONSIDERATIONS

EXAMPLE  3:  TAX  CONSIDERATIONS

Annual  Equivalent  Cost

SUMMARY

In replacement analysis,

defender

is an existing asset &

challenger

is the best available replacement candidate.

Current market value

is the value to be used in economic

analysis of a defender.

Sunk costs

cannot be changed by future decisions, so are

not considered in replacement analysis.

Two basic approaches to replacement problems are:

§ cash-­flow approach, explicitly considering actual cash flow

consequences for replacement alternatives as they occur,

§ opportunity-­cost approach, viewing proceeds from the sale

SUMMARY

Economic service life

is the remaining useful life of a

defender or a challenger, that results in minimum annual

equivalent cost. Replacement analysis uses economic

service lives of defender & challenger.

The ultimate question in replacement analysis is NOT

whether

to replace the defender, but

when

to do so.

Whenever  possible,  all  replacement  decisions  should  be