FE PROBLEM 5.1
b. $31,050
rationale: $150,000(A|P 8%,30) – $25,000(A|F 8%,30) + $17,500 = $30,599.32
FE PROBLEM 5.2
c. 0.0
FE PROBLEM 5.3
c. BOTH I AND II
rationale: SINCE PW=AW(P|A i%,n) AND FW=AW(F|A i%,n) AND AW=0 THEN
PW=0 AND FW=0
FE PROBLEM 5.4
a. $263,250
rationale: AW = $200,000(P|A1 8%,10%,7)(A|P 8%,7) = $263,288
FE PROBLEM 5.5
d. $15,223
rationale: AW = $11,000 + $800(A|G 10%,15) = $15,223.12
FE PROBLEM 5.6
c. $280
rationale: $2,500(A|F 8%,7) = $280.25
FE PROBLEM 5.7
c. $41,450
rationale: $1,000(F|A 8%,19) = $41,446.30
FE PROBLEM 5.8
d. $53,597
rationale: $800(F|A 8%,25)-$800(F|A 8%,2)(F|P 8%,14) = $53,597.22
FE PROBLEM 5.9
b. $7,555
rationale: $3,000(F|P 8%,12) = $7,554.60
FE PROBLEM 5.10
b. $3,467,000
rationale: FW = $150,000(F|P 8%,30)+$17,500(F|A 8%,30)-$25,000 = $3,466,861
PROBLEM 5.1
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 -$75,000.00 -$75,000.00 1.00000 -$75,000.00
1 $18,500.00 $18,500.00 0.90909 $16,818.18
2 $18,500.00 $18,500.00 0.82645 $15,289.26
3 $18,500.00 $18,500.00 0.75131 $13,899.32
4 $18,500.00 $18,500.00 0.68301 $12,635.75
5 $18,500.00 $18,500.00 0.62092 $11,487.04
-$4,870.44 <- PW
0.26380 <- (A|P i%,n)
-$1,284.81 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = -$1,284.81 =18500+PMT(10%,5,75000)
SOLUTION USING FACTOR TABLES
AW = $18,500 – $75,000(A|P 10%,5)
AW = $18,500 – $75,000(0.26380)
AW = -$1,285.00
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c CARLISLE SHOULD REJECT THE FILTER BASED ON ITS ECONOMIC MERITS
PROBLEM 5.2
a
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 -$5,000.00 -$5,000.00 1.00000 -$5,000.00
1 -$200.00 -$200.00 0.94340 -$188.68
2 $2,000.00 -$300.00 $1,700.00 0.89000 $1,512.99
3 $4,000.00 -$600.00 $3,400.00 0.83962 $2,854.71
4 $3,000.00 -$1,000.00 $2,000.00 0.79209 $1,584.19
5 $1,600.00 -$1,500.00 $100.00 0.74726 $74.73
$837.93 <- PW
0.23740 <- (A|P i%,n)
$198.92 <- 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 = $198.92 =-PMT(6%,5,NPV(6%,E7:E11)+E6)
SOLUTION USING FACTOR TABLES
AW = (-$5,000-$200(P|F 6%,1)+$1,700(P|F 6%,2)+$3,400(P|F 6%,3)+$2,000(P|F 6%,4)+$100(P|F 6%,5))(A|P 6%,5)
AW = (-$5,000-$200(0.94340)+$1,700(0.89000)+$3,400(0.83962)+$2,000(0.79209)+$100(0.74726))(0.23740)
AW = $198.93
b DECISION RULE
IF AW >= 0, ACCEPT; OTHERWISE, REJECT
c DURATECH SHOULD IMPLEMENT THE PROCESS IMPROVEMENT
PROBLEM 5.3
NEW ANNUAL INSURANCE PREMIUM = ($720,000/$100)($0.40) = $2,880
a 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 $4,120.00 -$400.00 $3,720.00 0.86957 $3,234.78
2 $4,120.00 -$400.00 $3,720.00 0.75614 $2,812.85
3 $4,120.00 -$400.00 $3,720.00 0.65752 $2,445.96
4 $4,120.00 -$400.00 $3,720.00 0.57175 $2,126.92
5 $4,120.00 -$400.00 $3,720.00 0.49718 $1,849.50
6 $4,120.00 -$400.00 $3,720.00 0.43233 $1,608.26
7 $4,120.00 -$400.00 $3,720.00 0.37594 $1,398.49
8 $4,120.00 -$400.00 $3,720.00 0.32690 $1,216.07
9 $4,120.00 -$400.00 $3,720.00 0.28426 $1,057.46
10 $4,120.00 -$400.00 $3,720.00 0.24718 $919.53
11 $4,120.00 -$400.00 $3,720.00 0.21494 $799.59
12 $4,120.00 -$400.00 $3,720.00 0.18691 $695.29
13 $4,120.00 -$400.00 $3,720.00 0.16253 $604.60
14 $4,120.00 -$400.00 $3,720.00 0.14133 $525.74
15 $4,120.00 -$400.00 $3,720.00 0.12289 $457.17
16 $4,120.00 -$400.00 $3,720.00 0.10686 $397.54
17 $4,120.00 -$400.00 $3,720.00 0.09293 $345.68
18 $4,120.00 -$400.00 $3,720.00 0.08081 $300.60
19 $4,120.00 -$400.00 $3,720.00 0.07027 $261.39
20 $4,120.00 -$400.00 $3,720.00 0.06110 $227.29
$3,284.71 <- PW
0.15976 <- (A|P i%,n)
$524.77 <- AW
SOLUTION USING EXCEL’S PMT FUNCTION DIRECTLY
AW = $524.77 =3720+PMT(15%,20,20000)
SOLUTION USING FACTOR TABLES
AW = $3,720 – $20,000(A|P 15%,20)
AW = $3,720 – $20,000(0.15976)
AW = $524.80
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c YES, ECONOMICALLY JUSTIFIED – EDDIE SHOULD BUY THE SPRINKLER SYSTEM
PROBLEM 5.4
THE MAXIMUM AMOUNT IS THE ONE THAT SETS THE AW OF THE PAYMENT EQUAL TO AW
OF THE BENEFITS.
LET X BE THE AMOUNT PAID
SOLUTION USING FACTOR TABLES
X(A|P 7%,12) = $10,000
X = $10,000 / (A|P 7%,12)
X = $10,000 / (0.12590)
X = $79,428.12
SOLUTION USING EXCEL’S PMT FUNCTION
X = $79,426.86 =-10000/PMT(7%,12,1)
SOLUTION USING EXCEL’S SOLVER
0.07
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$79,426.86 -$79,426.86 1.00000 -$79,426.86
1 $10,000.00 $10,000.00 0.93458 $9,345.79
2 $10,000.00 $10,000.00 0.87344 $8,734.39
3 $10,000.00 $10,000.00 0.81630 $8,162.98
4 $10,000.00 $10,000.00 0.76290 $7,628.95
5 $10,000.00 $10,000.00 0.71299 $7,129.86
6 $10,000.00 $10,000.00 0.66634 $6,663.42
7 $10,000.00 $10,000.00 0.62275 $6,227.50
8 $10,000.00 $10,000.00 0.58201 $5,820.09
9 $10,000.00 $10,000.00 0.54393 $5,439.34
10 $10,000.00 $10,000.00 0.50835 $5,083.49
11 $10,000.00 $10,000.00 0.47509 $4,750.93
12 $10,000.00 $10,000.00 0.44401 $4,440.12
$0.00 <- PW
$0.00 <- AW =-PMT(7%,12,G34)
TO IMPLEMENT SOLVER:
(1) SET TARGET CELL: G30 THE AW
(2) EQUAL TO: VALUE OF: ZERO THE TARGET AW VALUE
(3) BY CHANGING CELLS: D15 THE PURCHASE PRICE TO BE DETERMINED
MAXIMUM PURCHASE PRICE IS $79,426.86
PROBLEM 5.5
LOAN PAYMENTS = $25,000*(A|P 15%,3) = 25000*(0.43798) = $10,949.50
USING EXCEL’S PMT FUNCTION
PMT = $10,949.42 =-PMT(15%,3,25000)
a SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
0.18
EOY + INV CF – INV CF + LOAN CF – LOAN CF NET CF (P|F i%,n) PW OF CF
0########## $25,000.00 -$75,000.00 1.00000 -$75,000.00
1 $55,000.00 -$25,000.00 -$10,949.50 $19,050.50 0.84746 $16,144.49
2 $55,000.00 -$25,000.00 -$10,949.50 $19,050.50 0.71818 $13,681.77
3 $55,000.00 -$25,000.00 -$10,949.50 $19,050.50 0.60863 $11,594.72
4 $55,000.00 -$25,000.00 $30,000.00 0.51579 $15,473.67
5 $60,000.00 -$25,000.00 $35,000.00 0.43711 $15,298.82
-$2,806.52 <- PW
0.31978 <- (A|P i%,n)
-$897.46 <- 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 = -$897.46 =-PMT(18%,5,NPV(18%,G12:G16)+G11)
SOLUTION USING FACTOR TABLES
AW = (-$75,000+$19,050.50(P|A 18%,3)+$30,000(P|F 18%,4)+$35,000(P|F 18%,5))(A|P 18%,5)
AW = (-$75,000+$19,050.50(2.17427)+$30,000(0.51579)+$35,000(0.43711))(0.31978)
AW = -$897.47
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c GALVANIZED PRODUCTS SHOULD NOT PURCHASE THE NEW COMPUTER SYSTEM
PROBLEM 5.6
a
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
13.50%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$1,400.00 -$1,400.00 1.00000 -$1,400.00
1 $0.00 $0.00 0.88106 $0.00
2 $500.00 $500.00 0.77626 $388.13
3 $500.00 $500.00 0.68393 $341.97
4 $500.00 $500.00 0.60258 $301.29
5 $500.00 $500.00 0.53091 $265.45
6 $0.00 $0.00 0.46776 $0.00
7 $500.00 $500.00 0.41213 $206.06
8 $600.00 $600.00 0.36311 $217.86
9 $700.00 $700.00 0.31992 $223.94
10 $800.00 $800.00 0.28187 $225.49
11 $900.00 $900.00 0.24834 $223.51
12 -$1,000.00 -$1,000.00 0.21880 -$218.80
13 -$2,000.00 -$2,000.00 0.19278 -$385.55
14 -$3,000.00 -$3,000.00 0.16985 -$509.54
15 $1,400.00 $1,400.00 0.14964 $209.50
$89.32 <- PW
0.15876 <- (A|P i%,n)
$14.18 <- 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 = $14.18 =-PMT(13.5%,15,NPV(13.5%,E7:E21)+E6)
SOLUTION USING FACTOR TABLES
AW = (-$1,400+$500(P|A 13.5%,4)(P|F 13.5%,1)+($500(P|A 13.5%,5)+$100(P|G 13.5%,5))(P|F 13.5%,6)+
(-$1,000(P|A 13.5%,3)-$1,000(P|G 13.5%,3))(P|F 13.5%,11)+$1,400(P|F 13.5%,15))(A|P 13.5%,15)
AW = (-$1,400+$500(2.94383)(0.88106)+{$500(3.47474)+$100(6.07551))(0.46776)+
(-$1,000(2.34125)-$1,000(2.14412))(0.24834)+$1,400(0.14964)0(0.15876)
AW = $14.18
b DECISION RULE
IF AW >= 0, ACCEPT; OTHERWISE, REJECT
c QRU SHOULD INVEST
PROBLEM 5.7
SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
18.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$12.00 -$12.00 1.00000 -$12.00
1 -$1.00 -$1.00 0.84746 -$0.85
2 $5.00 $5.00 0.71818 $3.59
3 $2.00 $2.00 0.60863 $1.22
4 $5.00 $5.00 0.51579 $2.58
5 $5.00 $5.00 0.43711 $2.19
6 $2.00 $2.00 0.37043 $0.74
7 $5.00 $5.00 0.31393 $1.57
-$0.96 <- PW
0.26236 <- (A|P i%,n)
-$0.25 <- 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 = -$0.25 =-PMT(18%,7,NPV(18%,E8:E14)+E7)
SOLUTION USING FACTOR TABLES
AW = (-$12-$1(P|F 18%,1)+$5(P|F 18%,2)+$2(P|F 18%,3)+$5(P|F 18%,4)+$5(P|F 18%,5)+$2(P|F 18%,6)+$5(P|F 18%,7))(A|P 18%,7)
AW = (-$12-$1(0.84746)+$5(0.71818)+$2(0.60863)+$5(0.51579)+$5(0.43711)+$2(0.3704)+$5(0.31393))(0.26236)
AW = -$0.25
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c IMAGINEERING SHOULD NOT INVEST
PROBLEM 5.8
aSOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
12.00%
EOY + CF – CF NET CF (P|F i%,n) PW OF CF
0 -$2.00 -$2.00 1.00000 -$2.00
1 -$10.00 -$10.00 0.89286 -$8.93
2 -$12.00 -$12.00 0.79719 -$9.57
3 -$14.00 -$14.00 0.71178 -$9.96
4 -$16.00 -$16.00 0.63552 -$10.17
5 -$18.00 -$18.00 0.56743 -$10.21
6 $200.00 $200.00 0.50663 $101.33
7 -$10.00 -$10.00 0.45235 -$4.52
8 -$12.00 -$12.00 0.40388 -$4.85
9 -$14.00 -$14.00 0.36061 -$5.05
10 -$100.00 -$100.00 0.32197 -$32.20
$3.87 <- PW
0.17698 <- (A|P i%,n)
$0.68 <- 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 = $0.68 =-PMT(12%,10,NPV(12%,E7:E16)+E6)
SOLUTION USING FACTOR TABLES
AW = (-$2-$10(P|A 12%,5)-$2(P|G 12%,5)+$200(P|F 12%,6)+(-$10(P|A 12%,3)-$2(P|G 12%,3))(P|F 12%,6)-$100(P|F 12%,10)0(A|P 12%,10)
AW = (-$2-$10(3.60478)-$2(6.39702)+$200(0.50663)+(-$10(2.40183)-$2(2.22075))(0.50663)-$100(0.32197))(0.17698)
AW = $0.68
b DECISION RULE
IF AW >= 0, ACCEPT; OTHERWISE, REJECT
c JUPITER SHOULD INVEST
PROBLEM 5.9
LOAN PAYMENTS = $20,000(F|P 8%,1)(A|P 8%,3) = $20,000(1.08000)(0.38803) = $8,381.45
USING EXCEL’S PMT FUNCTION
PMT = $8,381.52
a SOLUTION BASED ON INDIVIDUAL CASH FLOWS AND P|F FACTORS THEN A|P FACTOR
10.00%
EOY + INV CF – INV CF + LOAN CF – LOAN CF NET CF (P|F i%,n) PW OF CF
0 -$40,000.00 $20,000.00 -$20,000.00 1.00000 -$20,000.00
1 $12,000.00 -$2,000.00 $10,000.00 0.90909 $9,090.91
2 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.82645 $1,337.64
3 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.75131 $1,216.04
4 $12,000.00 -$2,000.00 -$8,381.45 $1,618.55 0.68301 $1,105.49
5 $12,000.00 -$2,000.00 $10,000.00 0.62092 $6,209.21
6 $12,000.00 -$2,000.00 $10,000.00 0.56447 $5,644.74
7 $19,500.00 -$2,000.00 $17,500.00 0.51316 $8,980.27
$13,584.31 <- PW
0.20541 <- (A|P i%,n)
$2,790.29 <- 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 = $2,790.29 =-PMT(10%,7,NPV(10%,G11:G17)+G10)
SOLUTION USING FACTOR TABLES
AW = $10,000-$20,0000(A|P 10%,7)-($10,000-$1,618.55)(P|A 10%,3)(P|F 10%,1))(A|P 10%,7)+$7,500(A|F 10%,7)
AW = $10,000-$20,0000(0.20541)-($10,000-$1,618.55)(2.48685)(0.90909))(0.20541)+$7,500(0.10541)
AW = $2,790.16
b DECISION RULE
IF AW > 0, ACCEPT; OTHERWISE, REJECT
c AEROTRON ELECTRONICS SHOULD PURCHASE THE WATER FILTRATION SYSTEM