PROBLEM 5.10
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
10.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$1,000.00 –$1,000.00 1.00000 -$1,000.00
1 $600.00 -$300.00 $300.00 0.90909 $272.73
2 $600.00 -$300.00 $300.00 0.82645 $247.93
3 $700.00 -$300.00 $400.00 0.75131 $300.53
4 $700.00 -$300.00 $400.00 0.68301 $273.21
5 $700.00 -$300.00 $400.00 0.62092 $248.37
$342.76 <- PW
0.26380 <- (A|P i%,n)
$90.42 <- AW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S PMT FUNCTION
IS NOT USED TO COMPUTE AW DIRECTLY.
SOLUTION USING EXCEL’S NPV AND PMT FUNCTIONS
AW = $90.42 =-PMT(10%,5,NPV(10%,E7:E11)+E6)
ALTERNATIVELY,
AW = -$1,000(A|P 10%,5) + $300 + $100(F|A 10%,3)(A|F 10%,5)
AW = -$1,000(0.26380) + $300 + $100(3.31000)(0.16380)
AW = $90.42
b DECISION RULE
IF AW >= 0, ACCEPT; OTHERWISE, REJECT
c HOME INNOVATION SHOULD PURSUE THE NEW PRODUCT
PROBLEM 5.11
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
8.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$6,000.00 –$6,000.00 1.00000 -$6,000.00
1 $1,000.00 $1,000.00 0.92593 $925.93
2 $1,000.00 $1,000.00 0.85734 $857.34
3 $1,000.00 $1,000.00 0.79383 $793.83
4 $1,000.00 $1,000.00 0.73503 $735.03
5 $1,000.00 $1,000.00 0.68058 $680.58
6 $3,000.00 $3,000.00 0.63017 $1,890.51
-$116.78 <- PW
0.21632 <- (A|P i%,n)
-$25.26 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$25.26 =1000+PMT(8%,6,6000,-2000)
SOLUTION USING FACTOR TABLES
AW = $1,000 – $6,000(A|P 8%,6) + $2,000(A|F 8%,6)
AW = $1,000 – $6,000(0.21632) + $2,000(0.13632)
AW = -$25.28
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c MAYBERRY SHOULD NOT IMPLEMENT THE DESIGN CHANGE
PROBLEM 5.12
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
24.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$10,000.00 –$10,000.00 1.00000 -$10,000.00
1 $30,000.00 -$25,000.00 $5,000.00 0.80645 $4,032.26
2 $30,000.00 -$25,000.00 $5,000.00 0.65036 $3,251.82
3 $33,000.00 -$25,000.00 $8,000.00 0.52449 $4,195.90
$1,479.98 <- PW
0.50472 <- (A|P i%,n)
$746.97 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $746.97 =5000+PMT(24%,3,10000,-3000)
SOLUTION USING FACTOR TABLES
AW = $5,000 – $10,000(A|P 24%,3) + $3,000(A|F 24%,3)
AW = $5,000 – $10,000(0.50472) + $3,000(0.26472)
AW = $746.96
b DECISION RULE
IF AW >= 0, ACCEPT; OTHERWISE, REJECT
c NANCY SHOULD BUY THE TRUCK
PROBLEM 5.13
a
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
VENDOR A SOFTWARE
10.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$380,000.00 -$380,000.00 1.00000 -$380,000.00
1 $125,000.00 $125,000.00 0.90909 $113,636.36
2 $125,000.00 $125,000.00 0.82645 $103,305.79
3 $125,000.00 $125,000.00 0.75131 $93,914.35
4 $125,000.00 $125,000.00 0.68301 $85,376.68
$16,233.18 <- PW
0.31547 <- (A|P i%,n)
$5,121.09 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $5,121.09 =125000+PMT(10%,4,380000)
SOLUTION USING FACTOR TABLES
AW = $125,000 – $380,000(A|P 10%,4)
AW = $125,000 – $380,000(0.31547)
AW = $5,121.40
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
VENDOR B SOFTWARE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$280,000.00 -$280,000.00 1.00000 -$280,000.00
1 $95,000.00 $95,000.00 0.90909 $86,363.64
2 $95,000.00 $95,000.00 0.82645 $78,512.40
3 $95,000.00 $95,000.00 0.75131 $71,374.91
4 $95,000.00 $95,000.00 0.68301 $64,886.28
$21,137.22 <- PW
0.31547 <- (A|P i%,n)
$6,668.17 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $6,668.17 =95000+PMT(10%,4,280000)
SOLUTION USING FACTOR TABLES
AW = $95,000 – $280,000(A|P 10%,4)
AW = $95,000 – $280,000(0.31547)
AW = $6,668.40
b DECISION RULE
SELECT THE PROJECT WITH THE HIGHEST AW
c MANUEL’S MANUFACTURING SHOULD BUY FROM VENDOR B
PROBLEM 5.14
HEAT LOSS WITH NO INSULATION = $1.50/YR/FT
HEAT LOSS WITH 1 INCH INSULATION IS (1.50)(1 – 0.89) = $0.165/YR/FT
HEAT LOSS WITH 2 INCH INSULATION IS (1.50)(1 – 0.92) = $0.12/YR/FT
NO INSULATION
ANNUAL HEAT LOSS = (1.50)(250,000) = $375,000
SINCE THERE IS NO INVESTMENT, THE AW = -$375,000
1 INCH INSULATION
ANNUAL HEAT LOSS =( 0.165)(250,000) = $41,250
INSULATION COST = (0.40)(250,000) = $100,000
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
10.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$100,000.00 -$100,000.00 1.00000 –$100,000.00
1 $0.00 -$41,250.00 -$41,250.00 0.90909 -$37,500.00
2 $0.00 -$41,250.00 -$41,250.00 0.82645 -$34,090.91
3 $0.00 -$41,250.00 -$41,250.00 0.75131 -$30,991.74
4 $0.00 -$41,250.00 -$41,250.00 0.68301 -$28,174.31
5 $0.00 -$41,250.00 -$41,250.00 0.62092 -$25,613.00
6 $0.00 -$41,250.00 -$41,250.00 0.56447 -$23,284.55
7 $0.00 -$41,250.00 -$41,250.00 0.51316 -$21,167.77
8 $0.00 -$41,250.00 -$41,250.00 0.46651 -$19,243.43
9 $0.00 -$41,250.00 -$41,250.00 0.42410 -$17,494.03
10 $0.00 -$41,250.00 -$41,250.00 0.38554 -$15,903.66
-$353,463.39 <- PW
0.16275 <- (A|P i%,n)
-$57,524.54 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$57,524.54 =-41250+PMT(10%,10,100000)
SOLUTION USING FACTOR TABLES
AW = -$41,250 – $100,000(A|P 10%,10)
AW = -$41,250 – $100,000(0.16275) = -$57,525
AW = -$57,525.00
2 INCH INSULATION
ANNUAL HEAT LOSS = (0.12)(250,000) = $30,000
INSULATION COST = (0.85)(250,000) = $212,500
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$212,500.00 -$212,500.00 1.00000 –$212,500.00
1 $0.00 -$30,000.00 -$30,000.00 0.90909 -$27,272.73
2 $0.00 -$30,000.00 -$30,000.00 0.82645 -$24,793.39
3 $0.00 -$30,000.00 -$30,000.00 0.75131 -$22,539.44
4 $0.00 -$30,000.00 -$30,000.00 0.68301 -$20,490.40
5 $0.00 -$30,000.00 -$30,000.00 0.62092 -$18,627.64
6 $0.00 -$30,000.00 -$30,000.00 0.56447 -$16,934.22
7 $0.00 -$30,000.00 -$30,000.00 0.51316 -$15,394.74
8 $0.00 -$30,000.00 -$30,000.00 0.46651 -$13,995.22
9 $0.00 -$30,000.00 -$30,000.00 0.42410 -$12,722.93
10 $0.00 -$30,000.00 -$30,000.00 0.38554 -$11,566.30
-$396,837.01 <- PW
0.16275 <- (A|P i%,n)
-$64,583.40 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$64,583.40 =-30000+PMT(10%,10,212500)
SOLUTION USING FACTOR TABLES
AW = -$30,000 – $212,500(A|P 10%,10)
AW = -$30,000 – $212,500(0.16275) = -$64,584.38
AW = -$64,584.38
THE HIGHEST ANNUAL WORTH IS THE 1 INCH INSULATION, THEREFORE, IT IS RECOMMENDED.
PROBLEM 5.15
POLISHER 1
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
15.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$20,000.00 –$20,000.00 1.00000 -$20,000.00
1 $4,465.00 $4,465.00 0.86957 $3,882.61
2 $4,465.00 $4,465.00 0.75614 $3,376.18
3 $4,465.00 $4,465.00 0.65752 $2,935.81
4 $4,465.00 $4,465.00 0.57175 $2,552.88
5 $4,465.00 $4,465.00 0.49718 $2,219.89
6 $4,465.00 $4,465.00 0.43233 $1,930.34
7 $4,465.00 $4,465.00 0.37594 $1,678.56
8 $4,465.00 $4,465.00 0.32690 $1,459.62
9 $4,465.00 $4,465.00 0.28426 $1,269.23
10 $4,465.00 $4,465.00 0.24718 $1,103.68
$2,408.80 <- PW
0.19925 <- (A|P i%,n)
$479.96 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $479.96 =4465+PMT(15%,10,20000)
SOLUTION USING FACTOR TABLES
AW = $4,465.00 – $20,000(A|P 15%,10)
AW = $4,465.00 – $20,000(0.19925)
AW = $480.00
POLISHER 2
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$10,000.00 –$10,000.00 1.00000 -$10,000.00
1 $1,770.00 $1,770.00 0.86957 $1,539.13
2 $1,770.00 $1,770.00 0.75614 $1,338.37
3 $1,770.00 $1,770.00 0.65752 $1,163.80
4 $1,770.00 $1,770.00 0.57175 $1,012.00
5 $1,770.00 $1,770.00 0.49718 $880.00
6 $1,770.00 $1,770.00 0.43233 $765.22
7 $1,770.00 $1,770.00 0.37594 $665.41
8 $1,770.00 $1,770.00 0.32690 $578.62
9 $1,770.00 $1,770.00 0.28426 $503.14
10 $1,770.00 $1,770.00 0.24718 $437.52
-$1,116.78 <- PW
0.19925 <- (A|P i%,n)
-$222.52 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$222.52 =1770+PMT(15%,10,10000)
SOLUTION USING FACTOR TABLES
AW = $1,770.00 – $10,000(A|P 15%,10)
AW = $1,770.00 – $10,000(0.19925)
AW = -$222.50
POLISHER 3
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$15,000.00 –$15,000.00 1.00000 -$15,000.00
1 $3,580.00 $3,580.00 0.86957 $3,113.04
2 $3,580.00 $3,580.00 0.75614 $2,706.99
3 $3,580.00 $3,580.00 0.65752 $2,353.91
4 $3,580.00 $3,580.00 0.57175 $2,046.88
5 $3,580.00 $3,580.00 0.49718 $1,779.89
6 $3,580.00 $3,580.00 0.43233 $1,547.73
7 $3,580.00 $3,580.00 0.37594 $1,345.85
8 $3,580.00 $3,580.00 0.32690 $1,170.31
9 $3,580.00 $3,580.00 0.28426 $1,017.66
10 $3,580.00 $3,580.00 0.24718 $884.92
$2,967.19 <- PW
0.19925 <- (A|P i%,n)
$591.22 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $591.22 =3580+PMT(15%,10,15000)
SOLUTION USING FACTOR TABLES
AW = $3,580.00 – $15,000(A|P 15%,10)
AW = $3,580.00 – $15,000(0.19925)
AW = $591.25
b FINAL FINISHING SHOULD PURCHASE POLISHER 3 SINCE IT HAS THE HIGHEST AW
PROBLEM 5.16
a SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
LAGRANGE
15.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$1,260,000.00 -$1,260,000.00 1.00000 -$1,260,000.00
1 $480,000.00 $480,000.00 0.86957 $417,391.30
2 $480,000.00 $480,000.00 0.75614 $362,948.96
3 $480,000.00 $480,000.00 0.65752 $315,607.79
4 $480,000.00 $480,000.00 0.57175 $274,441.56
5 $480,000.00 $480,000.00 0.49718 $238,644.83
6 $480,000.00 $480,000.00 0.43233 $207,517.25
7 $480,000.00 $480,000.00 0.37594 $180,449.78
8 $480,000.00 $480,000.00 0.32690 $156,912.85
9 $480,000.00 $480,000.00 0.28426 $136,445.96
10 $480,000.00 $480,000.00 0.24718 $118,648.66
11 $480,000.00 $480,000.00 0.21494 $103,172.75
12 $480,000.00 $480,000.00 0.18691 $89,715.43
$1,341,897.12 <- PW
0.18448 <- (A|P i%,n)
$247,554.22 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $247,554.22 =480000+PMT(15%,12,1260000)
SOLUTION USING FACTOR TABLES
AW = $480,000.00 – $1,260,000(A|P 15%,12)
AW = $480,000.00 – $1,260,000(0.18448)
AW = $247,555.20
AUBURN
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$1,000,000.00 -$1,000,000.00 1.00000 -$1,000,000.00
1 $410,000.00 $410,000.00 0.86957 $356,521.74
2 $410,000.00 $410,000.00 0.75614 $310,018.90
3 $410,000.00 $410,000.00 0.65752 $269,581.66
4 $410,000.00 $410,000.00 0.57175 $234,418.83
5 $410,000.00 $410,000.00 0.49718 $203,842.46
6 $410,000.00 $410,000.00 0.43233 $177,254.31
7 $410,000.00 $410,000.00 0.37594 $154,134.19
8 $410,000.00 $410,000.00 0.32690 $134,029.73
9 $410,000.00 $410,000.00 0.28426 $116,547.59
10 $410,000.00 $410,000.00 0.24718 $101,345.73
11 $410,000.00 $410,000.00 0.21494 $88,126.72
12 $410,000.00 $410,000.00 0.18691 $76,631.93
$1,222,453.79 <- PW
0.18448 <- (A|P i%,n)
$225,519.22 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $225,519.22 =410000+PMT(15%,12,1000000)
SOLUTION USING FACTOR TABLES
AW = $410,000.00 – $1,000,000(A|P 15%,12)
AW = $410,000.00 – $1,000,000(0.18448) = $225,520.00
AW = $225,520.00
ANNISTON
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$1,620,000.00 -$1,620,000.00 1.00000 -$1,620,000.00
1 $520,000.00 $520,000.00 0.86957 $452,173.91
2 $520,000.00 $520,000.00 0.75614 $393,194.71
3 $520,000.00 $520,000.00 0.65752 $341,908.44
4 $520,000.00 $520,000.00 0.57175 $297,311.69
5 $520,000.00 $520,000.00 0.49718 $258,531.90
6 $520,000.00 $520,000.00 0.43233 $224,810.35
7 $520,000.00 $520,000.00 0.37594 $195,487.26
8 $520,000.00 $520,000.00 0.32690 $169,988.92
9 $520,000.00 $520,000.00 0.28426 $147,816.45
10 $520,000.00 $520,000.00 0.24718 $128,536.05
11 $520,000.00 $520,000.00 0.21494 $111,770.48
12 $520,000.00 $520,000.00 0.18691 $97,191.72
$1,198,721.88 <- PW
0.18448 <- (A|P i%,n)
$221,141.14 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $221,141.14 =520000+PMT(15%,12,1620000)
SOLUTION USING FACTOR TABLES
AW = $520,000.00 – $1,620,000(A|P 15%,12)
AW = $520,000.00 – $1,620,000(0.18448) = $221,142.40
AW = $221,142.40
b DECISION RULE
SELECT THE PROJECT WITH THE HIGHEST AW
c QUANTUM LOGISTICS SHOULD BUILD IN LAGRANGE
PROBLEM 5.17
LET X BE THE NUMBER OF UNITS SOLD ANNUALLY
AW(B) = $1,000 + 0.5X
NEXT, SOLVE FOR AW(A)
USING EXCEL’S PMT FUNCTION
AW = 4882.36185 =-PMT(10%,10,30000)
USING FACTOR TABLES
AW = $30,000(A|P 10%,10) = $30,000(0.16275) = $4,882.50
FOR NADINE TO BE INDIFFERENT, AW(A) AND AW(B) MUST BE EQUAL, THEREFORE,
$4,882.50 = $1,000 + $0.50(X)
0.5X = 3,882.51
X = 7,765.02 OR APPROXIMATELY 7,765 UNITS
PROBLEM 5.18
a MACHINE 7745
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
6.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$10,000.00 –$10,000.00 1.00000 -$10,000.00
1 -$300.00 -$300.00 0.94340 -$283.02
2 -$300.00 -$300.00 0.89000 -$267.00
3 -$300.00 -$300.00 0.83962 -$251.89
4 -$300.00 -$300.00 0.79209 -$237.63
5 -$300.00 -$300.00 0.74726 -$224.18
6 -$300.00 -$300.00 0.70496 -$211.49
7 -$300.00 -$300.00 0.66506 -$199.52
8 -$300.00 -$300.00 0.62741 -$188.22
9 -$300.00 -$300.00 0.59190 -$177.57
10 $1,000.00 -$300.00 $700.00 0.55839 $390.88
-$11,649.63 <- PW
0.13587 <- (A|P i%,n)
-$1,582.81 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$1,582.81 =-300+PMT(6%,10,10000,-1000)
SOLUTION USING FACTOR TABLES
AW = -$300.00 –$10,000.00(A|P 6%,10) + $400.00(A|F 6%,10)
AW = -$300.00 –$10,000.00(0.13587) + $1,000.00(0.07587)
AW = -$1,582.83
MACHINE A37Y
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$8,000.00 –$8,000.00 1.00000 -$8,000.00
1 -$300.00 -$300.00 0.94340 -$283.02
2 -$300.00 -$300.00 0.89000 -$267.00
3 -$300.00 -$300.00 0.83962 -$251.89
4 -$300.00 -$300.00 0.79209 -$237.63
5 -$300.00 -$300.00 0.74726 -$224.18
6 -$300.00 -$300.00 0.70496 -$211.49
7 -$300.00 -$300.00 0.66506 -$199.52
8 -$300.00 -$300.00 0.62741 -$188.22
9 -$300.00 -$300.00 0.59190 -$177.57
10 -$300.00 -$300.00 0.55839 -$167.52
-$10,208.03 <- PW
0.13587 <- (A|P i%,n)
-$1,386.94 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$1,386.94 =-300+PMT(6%,10,8000)
SOLUTION USING FACTOR TABLES
AW = -$300.00 –$8,000.00(A|P 6%,10)
AW = -$300.00 –$8,000.00(0.13587)
AW = -$1,386.96
b DECISION RULE
SELECT THE PROJECT WITH THE HIGHEST AW
c MACHINE A37Y SHOULD BE PURCHASED
PROBLEM 5.19
POLISHER 1
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
15.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$20,000.00 –$20,000.00 1.00000 -$20,000.00
1 $4,465.00 $4,465.00 0.86957 $3,882.61
2 $4,465.00 $4,465.00 0.75614 $3,376.18
3 $4,465.00 $4,465.00 0.65752 $2,935.81
4 $4,465.00 $4,465.00 0.57175 $2,552.88
5 $4,465.00 $4,465.00 0.49718 $2,219.89
6 $4,465.00 $4,465.00 0.43233 $1,930.34
7 $4,465.00 $4,465.00 0.37594 $1,678.56
8 $4,465.00 $4,465.00 0.32690 $1,459.62
9 $4,465.00 $4,465.00 0.28426 $1,269.23
10 $4,465.00 $4,465.00 0.24718 $1,103.68
$2,408.80 <- PW
0.19925 <- (A|P i%,n)
$479.96 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $479.96 =4465+PMT(15%,10,20000)
SOLUTION USING FACTOR TABLES
AW = $4,465.00 – $20,000(A|P 15%,10)
AW = $4,465.00 – $20,000(0.19925)
AW = $480.00
POLISHER 2
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$10,000.00 –$10,000.00 1.00000 -$10,000.00
1 $1,770.00 $1,770.00 0.86957 $1,539.13
2 $1,770.00 $1,770.00 0.75614 $1,338.37
3 $1,770.00 $1,770.00 0.65752 $1,163.80
4 $1,770.00 $1,770.00 0.57175 $1,012.00
5 $1,770.00 $1,770.00 0.49718 $880.00
6 $1,770.00 $1,770.00 0.43233 $765.22
7 $1,770.00 $1,770.00 0.37594 $665.41
8 $1,770.00 $1,770.00 0.32690 $578.62
9 $1,770.00 $1,770.00 0.28426 $503.14
10 $1,770.00 $1,770.00 0.24718 $437.52
-$1,116.78 <- PW
0.19925 <- (A|P i%,n)
-$222.52 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$222.52 =1770+PMT(15%,10,10000)
SOLUTION USING FACTOR TABLES
AW = $1,770.00 – $10,000(A|P 15%,10)
AW = $1,770.00 – $10,000(0.19925)
AW = -$222.50
POLISHER 3
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$15,000.00 –$15,000.00 1.00000 -$15,000.00
1 $3,580.00 $3,580.00 0.86957 $3,113.04
2 $3,580.00 $3,580.00 0.75614 $2,706.99
3 $3,580.00 $3,580.00 0.65752 $2,353.91
4 $3,580.00 $3,580.00 0.57175 $2,046.88
5 $3,580.00 $3,580.00 0.49718 $1,779.89
6 $3,580.00 $3,580.00 0.43233 $1,547.73
7 $3,580.00 $3,580.00 0.37594 $1,345.85
8 $3,580.00 $3,580.00 0.32690 $1,170.31
9 $3,580.00 $3,580.00 0.28426 $1,017.66
10 $3,580.00 $3,580.00 0.24718 $884.92
$2,967.19 <- PW
0.19925 <- (A|P i%,n)
$591.22 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $591.22 =3580+PMT(15%,10,15000)
SOLUTION USING FACTOR TABLES
AW = $3,580.00 – $15,000(A|P 15%,10)
AW = $3,580.00 – $15,000(0.19925)
AW = $591.25
b FINAL FINISHING SHOULD PURCHASE POLISHER 3 SINCE IT HAS THE HIGHEST AW
PROBLEM 5.20
a SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
PROJECT A
12.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$50,000.00 –$50,000.00 1.00000 -$50,000.00
1 $20,000.00 -$12,500.00 $7,500.00 0.89286 $6,696.43
2 $20,000.00 -$12,500.00 $7,500.00 0.79719 $5,978.95
3 $20,000.00 -$12,500.00 $7,500.00 0.71178 $5,338.35
4 $20,000.00 -$12,500.00 $7,500.00 0.63552 $4,766.39
5 $20,000.00 -$12,500.00 $7,500.00 0.56743 $4,255.70
6 $20,000.00 -$12,500.00 $7,500.00 0.50663 $3,799.73
7 $20,000.00 -$12,500.00 $7,500.00 0.45235 $3,392.62
8 $20,000.00 -$12,500.00 $7,500.00 0.40388 $3,029.12
9 $20,000.00 -$12,500.00 $7,500.00 0.36061 $2,704.58
10 $20,000.00 -$12,500.00 $7,500.00 0.32197 $2,414.80
11 $20,000.00 -$12,500.00 $7,500.00 0.28748 $2,156.07
12 $20,000.00 -$12,500.00 $7,500.00 0.25668 $1,925.06
13 $20,000.00 -$12,500.00 $7,500.00 0.22917 $1,718.81
14 $20,000.00 -$12,500.00 $7,500.00 0.20462 $1,534.65
15 $20,000.00 -$12,500.00 $7,500.00 0.18270 $1,370.22
16 $20,000.00 -$12,500.00 $7,500.00 0.16312 $1,223.41
17 $20,000.00 -$12,500.00 $7,500.00 0.14564 $1,092.33
18 $20,000.00 -$12,500.00 $7,500.00 0.13004 $975.30
19 $20,000.00 -$12,500.00 $7,500.00 0.11611 $870.80
20 $20,000.00 -$12,500.00 $7,500.00 0.10367 $777.50
$6,020.83 <- PW
0.13388 <- (A|P i%,n)
$806.06 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $806.06 =7500+PMT(12%,20,50000)
SOLUTION USING FACTOR TABLES
AW = $7,500.00 – $50,000(A|P 12%,20)
AW = $7,500.00 – $50,000(0.13388)
AW = $806.00
PROJECT B
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$75,000.00 –$75,000.00 1.00000 -$75,000.00
1 $28,000.00 -$18,000.00 $10,000.00 0.89286 $8,928.57
2 $28,000.00 -$18,000.00 $10,000.00 0.79719 $7,971.94
3 $28,000.00 -$18,000.00 $10,000.00 0.71178 $7,117.80
4 $28,000.00 -$18,000.00 $10,000.00 0.63552 $6,355.18
5 $28,000.00 -$18,000.00 $10,000.00 0.56743 $5,674.27
6 $28,000.00 -$18,000.00 $10,000.00 0.50663 $5,066.31
7 $28,000.00 -$18,000.00 $10,000.00 0.45235 $4,523.49
8 $28,000.00 -$18,000.00 $10,000.00 0.40388 $4,038.83
9 $28,000.00 -$18,000.00 $10,000.00 0.36061 $3,606.10
10 $28,000.00 -$18,000.00 $10,000.00 0.32197 $3,219.73
11 $28,000.00 -$18,000.00 $10,000.00 0.28748 $2,874.76
12 $28,000.00 -$18,000.00 $10,000.00 0.25668 $2,566.75
13 $28,000.00 -$18,000.00 $10,000.00 0.22917 $2,291.74
14 $28,000.00 -$18,000.00 $10,000.00 0.20462 $2,046.20
15 $28,000.00 -$18,000.00 $10,000.00 0.18270 $1,826.96
16 $28,000.00 -$18,000.00 $10,000.00 0.16312 $1,631.22
17 $28,000.00 -$18,000.00 $10,000.00 0.14564 $1,456.44
18 $28,000.00 -$18,000.00 $10,000.00 0.13004 $1,300.40
19 $28,000.00 -$18,000.00 $10,000.00 0.11611 $1,161.07
20 $28,000.00 -$18,000.00 $10,000.00 0.10367 $1,036.67
-$305.56 <- PW
0.13388 <- (A|P i%,n)
-$40.91 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$40.91 =10000+PMT(12%,20,75000)
ALTERNATIVELY,
AW = $10,000.00 – $75,000(A|P 12%,20)
AW = $10,000.00 – $75,000(0.13388)
AW = -$41.00
b TEMPURA SHOULD PURSUE PROJECT A SINCE IT HAS THE HIGHEST AW
PROBLEM 5.21
a AT A PRODUCTION RATE OF 200 UNITS/YEAR THE SERVICE WOULD COST $18,000/YR.
IF THE EQUIPMENT IS PURCHASED THE SAVED SERVICE COST LOOKS LIKE A REVENUE.
AT A PRODUCTION RATE OF 200 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $5,000/YR
AT 200 UNITS/YEAR
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
12.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$100,000.00 -$100,000.00 1.00000 -$100,000.00
1 $18,000.00 -$12,000.00 $6,000.00 0.89286 $5,357.14
2 $18,000.00 -$12,000.00 $6,000.00 0.79719 $4,783.16
3 $18,000.00 -$12,000.00 $6,000.00 0.71178 $4,270.68
4 $18,000.00 -$12,000.00 $6,000.00 0.63552 $3,813.11
5 $18,000.00 -$12,000.00 $6,000.00 0.56743 $3,404.56
6 $18,000.00 -$12,000.00 $6,000.00 0.50663 $3,039.79
7 $18,000.00 -$12,000.00 $6,000.00 0.45235 $2,714.10
8 $18,000.00 -$12,000.00 $6,000.00 0.40388 $2,423.30
9 $18,000.00 -$12,000.00 $6,000.00 0.36061 $2,163.66
10 $18,000.00 -$12,000.00 $6,000.00 0.32197 $1,931.84
-$66,098.66 <- PW
0.17698 <- (A|P i%,n)
-$11,698.42 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$11,698.42 =6000+PMT(12%,10,100000)
SOLUTION USING FACTOR TABLES
AW = $6,000.00 -$100,000(A|P 12%,10)
AW = $6,000.00 -$100,000(0.17698) = -$11,698.00
AW = -$11,698.00
SINCE THE AW IS NEGATIVE, THE SERVICE CONTRACT IS PREFERRED OVER THE EQUIPMENT
b AT A PRODUCTION RATE OF 500 UNITS/YEAR THE SERVICE WOULD COST $45,000/YR
AT A PRODUCTION RATE OF 500 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $12,500/YR
AT 500 UNITS/YEAR
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$100,000.00 -$100,000.00 1.00000 -$100,000.00
1 $45,000.00 -$19,500.00 $25,500.00 0.89286 $22,767.86
2 $45,000.00 -$19,500.00 $25,500.00 0.79719 $20,328.44
3 $45,000.00 -$19,500.00 $25,500.00 0.71178 $18,150.40
4 $45,000.00 -$19,500.00 $25,500.00 0.63552 $16,205.71
5 $45,000.00 -$19,500.00 $25,500.00 0.56743 $14,469.38
6 $45,000.00 -$19,500.00 $25,500.00 0.50663 $12,919.09
7 $45,000.00 -$19,500.00 $25,500.00 0.45235 $11,534.90
8 $45,000.00 -$19,500.00 $25,500.00 0.40388 $10,299.02
9 $45,000.00 -$19,500.00 $25,500.00 0.36061 $9,195.56
10 $45,000.00 -$19,500.00 $25,500.00 0.32197 $8,210.32
$44,080.69 <- PW
0.17698 <- (A|P i%,n)
$7,801.58 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $7,801.58 =25500+PMT(12%,10,100000)
SOLUTION USING FACTOR TABLES
AW = $25,500.00 – $100,000(A|P 12%,10)
AW = $25,500.00 – $100,000(0.17698)
AW = $7,802.00
SINCE THE AW IS POSITIVE, THE EQUIPMENT IS PREFERRED OVER THE SERVICE CONTRACT
c FOR BREAKEVEN THE ANNUAL WORTH OF BENEFITS MUST EQUAL THE ANNUAL WORTH OF COSTS
90(X) = 100,000(A|P 12%,10) + (7,000+25(X))
90(X) = 100,000(0.17698) + (7,000+25(X))
90X = 17,698 + 7,000 + 25X
65X = 24,698
X = 379.97 OR APPROXIMATELY 380 UNITS/YR
PROBLEM 5.22
PURCHASE
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
10.00%
EOY PURCHASE SAVINGS NET CF (P|F i%,n) PW OF CF
0 -$60,000.00 -$60,000.00 1.00000 -$60,000.00
1 $23,000.00 $23,000.00 0.90909 $20,909.09
2 $23,000.00 $23,000.00 0.82645 $19,008.26
3 $10,000.00 $23,000.00 $33,000.00 0.75131 $24,793.39
$4,710.74 <- PW
0.40211 <- (A|P i%,n)
$1,894.26 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $1,894.26 =23000+PMT(10%,3,60000,-10000)
SOLUTION USING FACTOR TABLES
AW = $23,000 – $60,000(A|P 10%,3) + $10,000(A|F 10%,3)
AW = $23,000 – $60,000(0.40211) + $10,000(0.30211)
AW = $1,894.50
LEASE
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
EOY LEASE SAVINGS NET CF (P|F i%,n) PW OF CF
0 -$21,000.00 -$21,000.00 1.00000 -$21,000.00
1 -$21,000.00 $23,000.00 $2,000.00 0.90909 $1,818.18
2 -$21,000.00 $23,000.00 $2,000.00 0.82645 $1,652.89
3 $23,000.00 $23,000.00 0.75131 $17,280.24
-$248.69 <- PW
0.40211 <- (A|P i%,n)
-$100.00 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$100.00 =2000+PMT(10%,3,21000,-21000)
SOLUTION USING FACTOR TABLES
AW = $2,000 – $21,000(A|P 10%,3) + $21,000(A|F 10%,3)
AW = $2,000 – $21,000(0.40211) + $21,000(0.30211) = -$100.00
AW = -$100.00