After-Tax Opportunity Cost of Keeping the Defender now:
Note that the cost of retaining the defender on after-tax basis is $8,285, instead of
$7,700. The scheduled depreciation amount during the fourth year of ownership
with a 7–year MACRS property is $3,122.
Period (n)
Depreciation
Book Value
1
$3,573
$21,427
Since the asset will be disposed of during the recovery period, the allowed
depreciation amount will be (0.5) ($3,122) = $1,561. Then, the book value becomes
2
$6,122
$15,305
3
$4,373
$10,932
4
$3,122
5
$2,232
6
$2,231
7
$2,231
8
$1,116
(b) ,
10 years
C
N=
AEC
C
=$4319.2
(c) Marginal analysis:
• From n = 1 to n = 2:
14.32
(a) Economic service life = 6 years with MARR of 15%
Tax Rat e 40%
I nvest men
$10, 000
MA RR 15%
Book val u
$10, 000
Per mi t t ed Annual Depr eci at i on Amount s over t he
Hol di ng
Hol di ng Per i od Tot al Book
Per i od 1 2 3 4 5 6 7 8
Depr eci at i o
Val ue
0$10, 000
1$2, 000 $2, 000 $8, 000
Tax Shi el d
Per i od 1 2 3 4 5 6 7 8 O& M Co s t s O& M Co s t s
0 `
1$1, 500 $1, 304 $783
2$1, 500 $2, 100 $2, 892 $1, 735
0
1$5, 300 ( $2, 700) ( $1, 080) $6, 380 $783 $696 $87 $100 $5, 120 $5, 220
(b) Economic service life = 5 years with MARR of 10%
14.33
Tax Rate 40% Investment $10,000
MARR 10% Book value $10,000
Permitted Annual Depreciation Amounts over the
Holding Holding Period Total Book
Period 12345678Depreciation Value
0$10,000
1$2,000 $2,000 $8,000
Annual O&M Costs over the Holding Period Total PW
Holding Total PW of of A/T
Period 1 2 3 4 5 6 7 8 O&M Costs O&M Costs
0`
1$1,500 $1,364 $818
Expected Net A/T A/T Operating Costs (in PW) Total
Holding Market Taxable Gains Market over the Holding Period OC(10%) CR(10%) AEC(10%)
Period Value Gains Tax Value O&M Costs Tax Shield Total OC
0
1$5,300 ($2,700) ($1,080) $6,380 $818 $727 $91 $100 $4,620 $4,720
2$3,900 ($2,500) ($1,000) $4,900 $1,860 $1,256 $603 $348 $3,429 $3,776
(a) At i = 12%, the economic service life = 8 years:
(b) At i = 20%, the economic service life = 10 years
Tax Rate 40% Investment $30,000
MARR 12% Book value $30,000
Permitted Annual Depreciation Amounts over the
Holding Holding Period Total Book
Period 1 2 3 4 5 6 7 8 9 10 Depreciation Value
0
1
$3,000
$3,000 $27,000
2
$3,000 $3,000
$6,000 $24,000
3
$9,000 $21,000
4
$3,000 $3,000 $3,000 $3,000
5
$3,000 $3,000 $3,000 $3,000 $3,000
6
$3,000 $3,000 $3,000 $3,000 $3,000 $3,000
7
$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000
8
$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000
9
$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000
$3,000 $3,000 $3,000
10
$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000
$30,000 $0
Annual O&M Costs over the Holding Period Total PW
Holding Total PW of of A/T
Period 1 2 3 4 5 6 7 8 O&M Costs O&M Costs
0`
1$3,000 $2,679 $1,607
2$3,000 $3,450 $5,429 $3,257
3$3,000 $3,450 $3,968 $8,253 $4,952
4$3,000 $3,450 $3,968 $4,563 $11,153 $6,692
5$3,000 $3,450 $3,968 $4,563 $5,247 $14,130 $8,478
6$3,000 $3,450 $3,968 $4,563 $5,247 $6,034 $17,187 $10,312
7$3,000 $3,450 $3,968 $4,563 $5,247 $6,034 $6,939 $20,326 $12,196
8$3,000 $3,450 $3,968 $4,563 $5,247 $6,034 $6,939 $7,980 $23,549 $14,130
9$3,000 $3,450 $3,968 $4,563 $5,247 $6,034 $6,939 $7,980 $9,177 $26,859 $16,115
Expected Net A/T A/T Operating Costs (in PW) Total
Holding Market Taxable Gains Market over the Holding Period OC(12%) CR(12%) AEC(12%)
Period Value Gains Tax Value O&M Costs Tax Shield Total OC
0
1
$20,000
($7,000) ($2,800) $22,800 $1,607 $1,071 $536 $600 $10,800 $11,400
2
$18,000
($6,000) ($2,400) $20,400 $3,257 $2,028 $1,229 $727 $8,128 $8,856
3
$16,000
($5,000) ($2,000) $18,000 $4,952 $2,882 $2,070 $862 $7,156 $8,018
4
5
$12,000
($3,000) ($1,200) $13,200 $8,478 $4,326 $4,153 $1,152 $6,244 $7,396
6
$10,000
9
Tax Rat e 40% I nvest ment $30, 000
MA RR 20% Book val ue $30, 000
Per mi t t ed Annual Depr eci at i on Amount s over t he
Hol di ng Hol di ng Per i od Tot al Book
Per i od 1 2 3 4 5 6 7 8 9 10
Depr eci at i on
Val ue
0
1$3,000 $3, 000 $27, 000
2$3,000 $3,000 $6, 000 $24, 000
10 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $30, 000 $0
Annual O&M Cost s over t he Hol di ng Per i od Tot al PW
Hol di ng
Tot al PW of
of A/T
Per i od 1 2 3 4 5 6 7 8 O& M Co s t s O& M Co s t s
0`
1$3, 000 $2, 500 $1, 500
2$3, 000 $3, 450 $4, 896 $2, 938
10 $3, 000 $3, 450 $3, 968 $4, 563 $5, 247 $6, 034 $6, 939 $7, 980 $9, 177 $10, 554 $20, 798 $12, 479
Expect ed Net A/T A/ T Oper at i ng Cost s ( i n PW) Tot al
Hol di ng Mar ket Taxabl e Gai ns Mar ket over t he Hol di ng Per i od OC( 20%) CR( 2 0 %) AEC( 20 %)
Per i od Val ue Gai ns Tax Val ue O& M Co s t s
Tax Shi el d
Tot al OC
0
1$20, 000 ( $7, 000) ( $2, 800) $22, 800 $1, 500 $1, 000 $500 $600 $13, 200 $13, 800
2$18, 000 ( $6, 000) ( $2, 400) $20, 400 $2, 938 $1, 833 $1, 104 $723 $10, 364 $11, 086
(c) At i = 0%, the economic service life = 5 years:
• Capital recovery cost:
gain
= −
nn
SB
n
• Equivalent annual O&M cost:
• Depreciation tax credit:
• Minimum total annual equivalent cost:
Using Excel with trial and error method, we can get the years.
5n=
nAEC(0%)
17,800.00$
25,535.00$
34,883.50$
7000
8000
9000
Economic Service Life
14.34 Economic service life
With i = 12% and tax rate = 40%: Economic service life = 1 year
Tax Rat e 40% I nvest ment $15, 000
MA R R 12% Book val ue $15, 000
Per mi t t ed Annual Depr eci at i on Amount s ov er t he
Hol di ng Hol di ng Per i od Tot al Book
Per i od 1 2 3 4 5 6 7 8 Depr eci at i on Val ue
0
5$3,000 $4,800 $2,880 $1,728 $864 $13, 272 $1, 728
0. 2 0. 32 0. 192 0. 1152 0. 1152
Annual O&M Cost s over t he Hol di ng Per i od Tot al PW
Hol di ng Tot al PW of of A/ T
Per i od 1 2 3 4 5 6 7 8 O& M Co s t s O& M Co s t s
0`
Expect ed Ne t A/ T A/ T Oper at i ng Cost s ( i n PW) Tot al
Hol di ng Ma r k e t Taxabl e Ga i n s Ma r k e t over t he Hol di ng Per i od OC( 12%) CR( 12%) AEC( 12%)
Per i od Val ue Ga i n s Tax Val ue O&M Co s t s Tax Shi el d T o t a l OC
0
1$12, 800 $800 $320 $12, 480 $1, 339 $1, 071 $268 $300 $4, 320 $4, 620
14.35
(a) Challenger
Financial Data n0123456789-10
Depreciation $21,435 $36,735 $26,235 $18,735 $13,395 $13,380 $13,395 $6,690 $0
Cas h Flow S tatement
+(1-0.40)*(Savings) 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000 18,000
+(.4)*(Depreciation) 8,574 14,694 10,494 7,494 5,358 5,352 5,358 2,676 0
Financial Data n0123456789-10.
Depreciation $12,000 $12,000 $12,000 $12,000 $12,000 $12,000
Book value $72,000 $60,000 $48,000 $36,000 $24,000 $12,000 $0
Current market value
(c) Defender with a current market value of $ 45,000
Financial Data n0 1 2 3 4 5 6 7 8 9-10.
Cas h Flow Statement
(d) Challenger with an extended service life of 12 years
Financial Data n0 1 2 3 4 5 6 7 8 9-12
Depreciation $21,435 $36,735 $26,235 $18,735 $13,395 $13,380 $13,395 $6,690
Book value $150,000 $128,565 $91,830 $65,595 $46,860 $33,465 $20,085 $6,690 $0
14.36 (a) and (b):
(a) Defender (Model A) Decision: Replace Model A with
Original Investment = $150,000 Model B
n0 123456(b) It is rather difficult to predict
Depreciation $26,235 $18,735 $13,395 $13,380 $13,395 $6,690 what technological advances would
Book value $91,836 $65,601 $46,866 $33,471 $20,091 $6,696 $6 be made on typical equipment in the
Current market value $0 future.If the industrial engineer had
expected a more efficient lathe to be
Cash Flow Statement available in one or two years, he
n0 12345678910
Depreciation $42,870 $73,470 $52,470 $37,470 $26,790 $26,760 $26,790 $13,380
Book value $300,000 ####### ####### ####### $93,720 $66,930 $40,170 $13,380 $0
Savings $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000 $75,000
Cash Flow Statement
14.37 Replacement Analysis
(a) Keep the defender
Financial Data n-4 -3 -2 -1 0123456
Depreciation $2,858 $4,898 $3,498 $2,498 $1,786 $1,784 $1,786 $892
Cas h Flow Statement
(b) Replace the defender
Financial Data n12345678910-11 12
Depreciation $3,001 $5,143 $3,673 $2,623 $1,875 $1,873 $1,875 $937 $0 $0 $0
Book value $21,000 $17,999 $12,856 $9,183 $6,560 $4,685 $2,812 $937 ($0) ($0) ($0) ($0)
O&M cost $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 $1,000 1000
Cas h Flow Statement
14.38 (a) and (b): Replace defender now
Option 1 : Keep the defender
n0123
O&M cost $3,000 $4,500 $6,000
Cash Flow Statement
Option 2 : Replace the defender
n0123
Depreciation $2,000 $2,667 $444
Book value $6,000 $4,000 $1,333 $889
O&M cost $2,000 $3,000 $4,000
14.39 (a), (b), and (c):
Option 1 : Keep the defender
Financial Data n0 1 2 3 4 5
Depreciation $800 $800 $800 $800 $800
Book value $4,000 $3,200 $2,400 $1,600 $800 $0
PW (10%) = ($387) AEC(10%) = $102
Option 2 : Replace the defender
Financial Data n0 1 2 3 4 5
Depreciation $1,429 $2,449 $1,749 $1,249 $446
Book value $10,000 $8,571 $6,122 $4,373 $3,124 $2,678
14.40
(a) Replacement analysis
(b) Break–even market value: Let X denote the current market value of the old
machine. Then, the opportunity cost for not replacing the old machine now is
given by
Option 1 : Keep the defender
Financial Data n0 1 2 3 4 5
Cas h Flow S tatement
(-0.6)*(O&M cost) ($4,200) ($4,200) ($4,200) ($4,200) ($4,200)
+(.4)*(Depreciation) $0 $0 $0 $0 $0
Financial Data n0 1 2 3 4 5
Depreciation $1,715 $2,939 $2,099 $1,499 $535
Book value $12,000 $10,285 $7,346 $5,248 $3,749 $3,214
O&M cos t $5,000 $5,000 $5,000 $5,000 $5,000
Increased Revenue $1,500 $1,500 $1,500 $1,500 $1,500
Cas h Flow S tatement
14.41 Replacement analysis: Let X denote the current market value of the old call–
switching system:
To justify the new call-switching system now, we must have
• Challenger:
Financial Data n0 1 2 3 4 5
Depreciation $40,000 $64,000 $38,400 $23,040 $23,040
Book value $200,000 $160,000 $96,000 $57,600 $34,560 $11,520
Financial Data n6 7 8 9 10
Depreciation $11,520 $0 $0 $0 $0
Book value $0 $0 $0 $0 $0
Salvage value
O&M cost $5,000 $5,000 $5,000 $5,000 $5,000