PROBLEM 5.46
a SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
POLISHER 1
15.00%
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$20,000.00 -$20,000.00 4.04556 -$80,911.15
1 $4,465.00 $4,465.00 3.51788 $15,707.32
2 $4,465.00 $4,465.00 3.05902 $13,658.54
3 $4,465.00 $4,465.00 2.66002 $11,876.99
4 $4,465.00 $4,465.00 2.31306 $10,327.82
5 $4,465.00 $4,465.00 2.01136 $8,980.71
6 $4,465.00 $4,465.00 1.74901 $7,809.31
7 $4,465.00 $4,465.00 1.52088 $6,790.71
10 $4,465.00 $4,465.00 1.00000 $4,465.00
$9,744.95 <- FW
FW = -$20,000(F|P 15%,10) + $4,465(F|A 15%,10)
FW = -$20,000(4.04556) + $4,465(20.30372)
FW = $9,744.91
POLISHER 2
0 -$10,000.00 -$10,000.00 4.04556 -$40,455.58
1 $1,770.00 $1,770.00 3.51788 $6,226.64
2 $1,770.00 $1,770.00 3.05902 $5,414.47
3 $1,770.00 $1,770.00 2.66002 $4,708.24
4 $1,770.00 $1,770.00 2.31306 $4,094.12
5 $1,770.00 $1,770.00 2.01136 $3,560.10
6 $1,770.00 $1,770.00 1.74901 $3,095.74
8 $1,770.00 $1,770.00 1.32250 $2,340.83
9 $1,770.00 $1,770.00 1.15000 $2,035.50
-$4,518.00 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$4,518.00 =FV(15%,10,-1770,10000)
SOLUTION USING FACTOR TABLES
FW = -$10,000(F|P 15%,10) + $1,770(F|A 15%,10)
FW = -$10,000(4.04556) + $1,770(20.30372)
FW = -$4,518.02
POLISHER 3
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$15,000.00 -$15,000.00 4.04556 -$60,683.37
1 $3,580.00 $3,580.00 3.51788 $12,594.00
2 $3,580.00 $3,580.00 3.05902 $10,951.30
5 $3,580.00 $3,580.00 2.01136 $7,200.66
6 $3,580.00 $3,580.00 1.74901 $6,261.44
7 $3,580.00 $3,580.00 1.52088 $5,444.73
8 $3,580.00 $3,580.00 1.32250 $4,734.55
9 $3,580.00 $3,580.00 1.15000 $4,117.00
10 $3,580.00 $3,580.00 1.00000 $3,580.00
SOLUTION USING EXCEL’S FV FUNCTION
FW = $12,003.95 =FV(15%,10,-3580,15000)
SOLUTION USING FACTOR TABLES
FW = -$15,000(F|P 15%,10) + $3,580(F|A 15%,10)
FW = -$15,000(4.04556) + $3,580(20.30372)
b FINAL FINISHING SHOULD PURCHASE POLISHER 3
PROBLEM 5.47
a SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
A001
10.00%
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$210.00 -$210.00 1.46410 -$307.46
1 $80.00 $80.00 1.33100 $106.48
2 $90.00 $90.00 1.21000 $108.90
3 $100.00 $100.00 1.10000 $110.00
4 $110.00 $110.00 1.00000 $110.00
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S FV FUNCTION
SOLUTION USING FACTOR TABLES
FW = -$210(F|P 10%,4) + $80(F|A 10%,4) + $10(A|G 10%,4)(F|A 10%,4)
FW = -$210(1.46410) + $80(4.64100) + $10(1.3817)(4.64100)
FW = $127.94
B002
0 -$110.00 -$110.00 1.46410 -$161.05
1 $60.00 $60.00 1.33100 $79.86
2 $60.00 $60.00 1.21000 $72.60
3 $60.00 $60.00 1.10000 $66.00
4 $70.00 $70.00 1.00000 $70.00
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$110(F|P 10%,4) + $60(F|A 10%,4) + $10
FW = -$110(1.46410) + $60(4.64100) + $10
FW = $127.41
C003
10.00%
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$160.00 -$160.00 1.46410 -$234.26
1 $80.00 $80.00 1.33100 $106.48
2 $80.00 $80.00 1.21000 $96.80
3 $80.00 $80.00 1.10000 $88.00
4 $80.00 $80.00 1.00000 $80.00
$137.02 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = $137.02 =FV(10%,4,-80,160)
SOLUTION USING FACTOR TABLES
FW = -$160(F|P 10%,4) + $80(F|A 10%,4)
FW = -$160(1.46410) + $80(4.64100)
FW = $137.02
b XANADU SHOULD ACCEPT ALTERNATIVE C003
PROBLEM 5.48
THE STUDENT IS EXPECTED TO DEDUCE THAT THE SAVINGS ACCOUNT INTEREST RATE,
12%/YR COMPOUNDED MONTHLY, SHOULD BE USED FOR MARR.
THIS LEADS TO A PERIOD INTEREST RATE OF 1% PER MONTH.
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
SAVINGS CERTIFICATE
1.00%
EOM + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$12,000.00 -$12,000.00 1.81670 -$21,800.36
1 $100.00 $100.00 1.79871 $179.87
2 $100.00 $100.00 1.78090 $178.09
3 $100.00 $100.00 1.76327 $176.33
4 $100.00 $100.00 1.74581 $174.58
5 $100.00 $100.00 1.72852 $172.85
6 $100.00 $100.00 1.71141 $171.14
7 $100.00 $100.00 1.69447 $169.45
10 $100.00 $100.00 1.64463 $164.46
11 $100.00 $100.00 1.62835 $162.83
12 $100.00 $100.00 1.61223 $161.22
13 $100.00 $100.00 1.59626 $159.63
14 $100.00 $100.00 1.58046 $158.05
15 $100.00 $100.00 1.56481 $156.48
16 $100.00 $100.00 1.54932 $154.93
19 $100.00 $100.00 1.50375 $150.38
20 $100.00 $100.00 1.48886 $148.89
21 $100.00 $100.00 1.47412 $147.41
22 $100.00 $100.00 1.45953 $145.95
23 $100.00 $100.00 1.44508 $144.51
24 $100.00 $100.00 1.43077 $143.08
28 $100.00 $100.00 1.37494 $137.49
29 $100.00 $100.00 1.36133 $136.13
30 $100.00 $100.00 1.34785 $134.78
31 $100.00 $100.00 1.33450 $133.45
32 $100.00 $100.00 1.32129 $132.13
33 $100.00 $100.00 1.30821 $130.82
34 $100.00 $100.00 1.29526 $129.53
35 $100.00 $100.00 1.28243 $128.24
36 $100.00 $100.00 1.26973 $126.97
37 $100.00 $100.00 1.25716 $125.72
38 $100.00 $100.00 1.24472 $124.47
39 $100.00 $100.00 1.23239 $123.24
43 $100.00 $100.00 1.18430 $118.43
44 $100.00 $100.00 1.17258 $117.26
45 $100.00 $100.00 1.16097 $116.10
46 $100.00 $100.00 1.14947 $114.95
49 $100.00 $100.00 1.11567 $111.57
50 $100.00 $100.00 1.10462 $110.46
51 $100.00 $100.00 1.09369 $109.37
52 $100.00 $100.00 1.08286 $108.29
53 $100.00 $100.00 1.07214 $107.21
56 $100.00 $100.00 1.04060 $104.06
57 $100.00 $100.00 1.03030 $103.03
58 $100.00 $100.00 1.02010 $102.01
59 $100.00 $100.00 1.01000 $101.00
60 $13,100.00 $13,100.00 1.00000 $13,100.00
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$633.39 =FV(1%,60,-100,12000)+13000
SOLUTION USING FACTOR TABLES
FW = -$12,000(F|P 1%,60) + $100(F|A 1%,60) + $13,000
FW = -$12,000(1.81670) + $100(81.66967) + $13,000
FW = -$633.43
RACE HORSE
0 -$12,000.00 -$12,000.00 1.81670 -$21,800.36
1 $0.00 $0.00 1.79871 $0.00
2 $0.00 $0.00 1.78090 $0.00
3 $0.00 $0.00 1.76327 $0.00
4 $0.00 $0.00 1.74581 $0.00
5 $0.00 $0.00 1.72852 $0.00
6 $0.00 $0.00 1.71141 $0.00
7 $0.00 $0.00 1.69447 $0.00
8 $0.00 $0.00 1.67769 $0.00
18 $0.00 $0.00 1.51879 $0.00
19 $0.00 $0.00 1.50375 $0.00
20 $0.00 $0.00 1.48886 $0.00
21 $0.00 $0.00 1.47412 $0.00
22 $0.00 $0.00 1.45953 $0.00
23 $0.00 $0.00 1.44508 $0.00
33 $0.00 $0.00 1.30821 $0.00
34 $0.00 $0.00 1.29526 $0.00
35 $0.00 $0.00 1.28243 $0.00
36 $0.00 $0.00 1.26973 $0.00
37 $0.00 $0.00 1.25716 $0.00
38 $0.00 $0.00 1.24472 $0.00
45 $0.00 $0.00 1.16097 $0.00
46 $0.00 $0.00 1.14947 $0.00
47 $0.00 $0.00 1.13809 $0.00
48 $0.00 $0.00 1.12683 $0.00
49 $0.00 $0.00 1.11567 $0.00
50 $0.00 $0.00 1.10462 $0.00
51 $0.00 $0.00 1.09369 $0.00
52 $0.00 $0.00 1.08286 $0.00
53 $0.00 $0.00 1.07214 $0.00
54 $0.00 $0.00 1.06152 $0.00
55 $0.00 $0.00 1.05101 $0.00
56 $0.00 $0.00 1.04060 $0.00
57 $0.00 $0.00 1.03030 $0.00
58 $0.00 $0.00 1.02010 $0.00
59 $0.00 $0.00 1.01000 $0.00
60 $20,000.00 $20,000.00 1.00000 $20,000.00
-$1,800.36 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
THE FUTURE WORTH OF THE SAVINGS ACCOUNT IS ZERO SINCE IT EARNS EXACTLY MARR
PROBLEM 5.49
a SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
DRILL PRESS T
10.00%
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$20,000.00 -$20,000.00 2.59374 -$51,874.85
1 -$14,000.00 -$14,000.00 2.35795 -$33,011.27
2 -$14,000.00 -$14,000.00 2.14359 -$30,010.24
3 -$14,000.00 -$14,000.00 1.94872 -$27,282.04
4 -$14,000.00 -$14,000.00 1.77156 -$24,801.85
5 -$14,000.00 -$14,000.00 1.61051 -$22,547.14
6 -$14,000.00 -$14,000.00 1.46410 -$20,497.40
8 -$14,000.00 -$14,000.00 1.21000 -$16,940.00
9 -$14,000.00 -$14,000.00 1.10000 -$15,400.00
10 -$9,000.00 -$9,000.00 1.00000 -$9,000.00
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$269,998.79 =FV(10%,10,14000,20000)+5000
DRILL PRESS M
0 -$30,000.00 -$30,000.00 2.59374 -$77,812.27
1 -$10,000.00 -$10,000.00 2.35795 -$23,579.48
2 -$10,000.00 -$10,000.00 2.14359 -$21,435.89
3 -$10,000.00 -$10,000.00 1.94872 -$19,487.17
4 -$10,000.00 -$10,000.00 1.77156 -$17,715.61
5 -$10,000.00 -$10,000.00 1.61051 -$16,105.10
7 -$10,000.00 -$10,000.00 1.33100 -$13,310.00
8 -$10,000.00 -$10,000.00 1.21000 -$12,100.00
9 -$10,000.00 -$10,000.00 1.10000 -$11,000.00
10 -$3,000.00 -$3,000.00 1.00000 -$3,000.00
-$230,186.52 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$230,186.52 =FV(10%,10,10000,30000)+7000
SOLUTION USING FACTOR TABLES
FW = -$30,000(F|P 10%,10) – $10,000(F|A 10%,10) + $7,000
FW = -$30,000(2.59374) – $10,000(15.93742) + $7,000
FW = -$230,186.40
b ZUNNI’S MANUFACTURING SHOULD PURCHASE DRILL M
PROBLEM 5.50
IF THE EQUIPMENT IS PURCHASED, THE SERVICE COST IS SAVED AND THUS LOOKS LIKE
A REVENUE TO THE PROJECT.
a AT A PRODUCTION RATE OF 200 UNITS/YEAR THE SERVICE WOULD COST $18,000/YR
AT A PRODUCTION RATE OF 200 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $5,000/YR
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
AT 200 UNITS/YEAR
12.00%
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$100,000.00 -$100,000.00 3.10585 -$310,584.82
1 $18,000.00 -$12,000.00 $6,000.00 2.77308 $16,638.47
2 $18,000.00 -$12,000.00 $6,000.00 2.47596 $14,855.78
3 $18,000.00 -$12,000.00 $6,000.00 2.21068 $13,264.09
4 $18,000.00 -$12,000.00 $6,000.00 1.97382 $11,842.94
5 $18,000.00 -$12,000.00 $6,000.00 1.76234 $10,574.05
6 $18,000.00 -$12,000.00 $6,000.00 1.57352 $9,441.12
9 $18,000.00 -$12,000.00 $6,000.00 1.12000 $6,720.00
10 $18,000.00 -$12,000.00 $6,000.00 1.00000 $6,000.00
-$205,292.41 <- FW
FW = -$205,292.41 =FV(12%,10,-6000,100000)
SOLUTION USING FACTOR TABLES
FW = -$100,000(F|P 12%,10) + 6,000(F|A 12%,10)
FW = -$100,000(3.10585) + 6,000(17.54874)
FW = -$205,292.56
THEREFORE, THE SERVICE CONTRACT IS PREFERRED OVER THE EQUIPMENT
AT A PRODUCTION RATE OF 500 UNITS/YEAR THE VARIABLE OPERATING COSTS ARE $12,500/YR
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
AT 500 UNITS/YEAR
EOY + CF – CF NET CF (F|P i%,n-t) FW OF CF
0 -$100,000.00 -$100,000.00 3.10585 -$310,584.82
1 $45,000.00 -$19,500.00 $25,500.00 2.77308 $70,713.51
2 $45,000.00 -$19,500.00 $25,500.00 2.47596 $63,137.06
3 $45,000.00 -$19,500.00 $25,500.00 2.21068 $56,372.38
4 $45,000.00 -$19,500.00 $25,500.00 1.97382 $50,332.48
5 $45,000.00 -$19,500.00 $25,500.00 1.76234 $44,939.71
6 $45,000.00 -$19,500.00 $25,500.00 1.57352 $40,124.74
7 $45,000.00 -$19,500.00 $25,500.00 1.40493 $35,825.66
8 $45,000.00 -$19,500.00 $25,500.00 1.25440 $31,987.20
9 $45,000.00 -$19,500.00 $25,500.00 1.12000 $28,560.00
10 $45,000.00 -$19,500.00 $25,500.00 1.00000 $25,500.00
$136,907.92 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = $136,907.92
=FV(12%,10,-25500,100000)
SOLUTION USING FACTOR TABLES
FW = -$100,000(F|P 12%,10) + 25,500(F|A 12%,10)
FW = -$100,000(3.10585) + 25,500(17.54874)
c FOR BREAKEVEN THE FUTURE WORTH OF BENEFITS MUST EQUAL THE FUTURE WORTH OF COSTS
PROBLEM 5.51
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
GATE 1
20.00%
EOY GATE O&M NET CF (F|P i%,n-t) FW OF CF
0 -$15,000.00 -$15,000.00 2.48832 -$37,324.80
1 -$6,500.00 -$6,500.00 2.07360 -$13,478.40
2 -$6,500.00 -$6,500.00 1.72800 -$11,232.00
3 -$6,500.00 -$6,500.00 1.44000 -$9,360.00
4 -$6,500.00 -$6,500.00 1.20000 -$7,800.00
5 $0.00 -$6,500.00 -$6,500.00 1.00000 -$6,500.00
-$85,695.20 <– FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$15,000(F|P 20%,5) – $6,500(F|A 20%,5)
FW = -$15,000(2.48832) – $6,500(7.44160)
FW = -$85,695.20
GATE 2
0 -$19,000.00 -$19,000.00 2.48832 -$47,278.08
1 -$5,600.00 -$5,600.00 2.07360 -$11,612.16
2 -$5,600.00 -$5,600.00 1.72800 -$9,676.80
3 -$5,600.00 -$5,600.00 1.44000 -$8,064.00
4 -$5,600.00 -$5,600.00 1.20000 -$6,720.00
5 $2,000.00 -$5,600.00 -$3,600.00 1.00000 -$3,600.00
-$86,951.04 <– FW
FW = -$86,951.04 =FV(20%,5,5600,19000)+2000
SOLUTION USING FACTOR TABLES
FW = -$19,000(F|P 20%,5) – $5,600(F|A 20%,5) + $2,000
FW = -$19,000(2.48832) – $5,600(7.44160) + $2,000
FW = -$86,951.04
GATE 3
EOY GATE O&M NET CF (F|P i%,n-t) FW OF CF
0 -$24,000.00 -$24,000.00 2.48832 -$59,719.68
1 -$4,000.00 -$4,000.00 2.07360 -$8,294.40
2 -$4,000.00 -$4,000.00 1.72800 -$6,912.00
3 -$4,000.00 -$4,000.00 1.44000 -$5,760.00
4 -$4,000.00 -$4,000.00 1.20000 -$4,800.00
5 $5,000.00 -$4,000.00 $1,000.00 1.00000 $1,000.00
-$84,486.08 <– FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$84,486.08 =FV(20%,5,4000,24000)+5000
SOLUTION USING FACTOR TABLES
FW = -$24,000(F|P 20%,5) – $4,000(F|A 20%,5) + $5,000
FW = -$24,000(2.48832) – $4,000(7.44160) + $5,000
FW = -$84,486.08
DECISION: PREFER GATE 3, IT HAS THE HIGHEST (LEAST NEGATIVE) FW.
PROBLEM 5.52
LOAN PAYMENT = $30,000(A|P 12%,4) = $30,000(0.32923) = $9876.90
OR
USING EXCEL‘S PMT FUNCTION
PMT = $9,877.03 =PMT(12%,4,-30000)
SPRINKLER SYSTEM
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
15.00%
EOY SPRINKLERS LOAN O&M SAVINGS NET CF (F|P i%,n-t) FW OF CF
0 -$30,000.00 $30,000.00 $0.00 3.51788 $0.00
1 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 3.05902 -$11,859.93
2 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 2.66002 -$10,312.99
3 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 2.31306 -$8,967.81
4 -$9,877.03 -$9,000.00 $15,000.00 -$3,877.03 2.01136 -$7,798.10
5 -$9,000.00 $15,000.00 $6,000.00 1.74901 $10,494.04
6 -$9,000.00 $15,000.00 $6,000.00 1.52088 $9,125.25
7 -$9,000.00 $15,000.00 $6,000.00 1.32250 $7,935.00
8 -$9,000.00 $15,000.00 $6,000.00 1.15000 $6,900.00
9 $2,000.00 -$9,000.00 $15,000.00 $8,000.00 1.00000 $8,000.00
$3,515.46 <- FW
SOLUTION USING EXCEL’S FUNCTIONS
FW = $3,515.46 =FV(15%,5,-6000)+FV(15%,5,,FV(15%,4,PMT(12%,4,30000)+6000))+2000
SOLUTION USING FACTOR TABLES
FW = -$3,877.03(F|A 15%,4)(F|P 15%,5) + $6,000(F|A 15%,5) + $2,000
FW = -$3,877.03(4.99338)(2.01136) + $6,000(6.74238) + $2,000
FW = $3,515.39
DECISION: SINCE THE FW IS POSITIVE, THE SPRINKLER SYSTEM IS ECONOMICALLY ATTRACTIVE
PROBLEM 5.53
LIGHT BAR
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
10.00%
EOY BAR REVENUE NET CF (F|P i%,n-t) FW OF CF
0 -$6,000.00 -$6,000.00 1.77156 -$10,629.37
1 $2,000.00 $2,000.00 1.61051 $3,221.02
2 $2,000.00 $2,000.00 1.46410 $2,928.20
3 $2,000.00 $2,000.00 1.33100 $2,662.00
4 $2,000.00 $2,000.00 1.21000 $2,420.00
5 $2,000.00 $2,000.00 1.10000 $2,200.00
$4,801.85 <- FW
SOLUTION USING EXCEL’S FV FUNCTION
FW = -$6,000(F|P 10%,6) + $2,000(F|A 10%,6)
FW = -$6,000(1.77156) + $2,000(7.71561)
FW = $4,801.86
SLIDING SPOTS
0 -$14,000.00 -$14,000.00 1.77156 -$24,801.85
1 $3,500.00 $3,500.00 1.61051 $5,636.79
2 $3,500.00 $3,500.00 1.46410 $5,124.35
3 $3,500.00 $3,500.00 1.33100 $4,658.50
4 $3,500.00 $3,500.00 1.21000 $4,235.00
5 $3,500.00 $3,500.00 1.10000 $3,850.00
$2,202.78 <- FW
FW = $2,202.78 =FV(10%,6,-3500,14000)
SOLUTION USING FACTOR TABLES
FW = -$14,000(F|P 10%,6) + $3,500(F|A 10%,6)
FW = -$14,000(1.77156) + $3,500(7.71561)
FW = $2,202.80
REFLECTED BEAM
EOY BEAM REVENUE NET CF (F|P i%,n-t) FW OF CF
0 -$20,000.00 -$20,000.00 1.77156 -$35,431.22
1 $0.00 $0.00 1.61051 $0.00
2 $2,300.00 $2,300.00 1.46410 $3,367.43
3 $4,600.00 $4,600.00 1.33100 $6,122.60
4 $6,900.00 $6,900.00 1.21000 $8,349.00
5 $9,200.00 $9,200.00 1.10000 $10,120.00
6 $11,500.00 $11,500.00 1.00000 $11,500.00
$4,027.81 <- FW
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S FV FUNCTION
IS NOT USED TO COMPUTE FW DIRECTLY.
SOLUTION USING EXCEL’S NPV AND FV FUNCTIONS
FW = $4,027.81 =FV(10%,6,,-NPV(10%,E52:E57)-E51)
SOLUTION USING FACTOR TABLES
FW = -$20,000(F|P 10%,6) + $2,300(A|G 10%,6)(F|A 10%,6)
FW = -$20,000(1.77156) + $2,300(2.22356)(7.71561)
FW = $4,027.88
DECISION: LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST FW.
PROBLEM 5.54
DESIGN 1 (IN M$)
SOLUTION USING INDIVIDUAL CASH FLOWS AND F|P FACTORS
10.00%
EOY NET CF (F|P i%,n-t) FW OF CF
0 -$15.00 1.33100 -$19.97
1 -$2.50 1.21000 -$3.03
2 -$2.50 1.10000 -$2.75
3 -$2.50 1.00000 -$2.50
FW = -$15.00(F|P 10%,3) – $2.50(F|A 10%,3)
FW = -$15.00(1.33100) – $2.50(3.31000)
0 -$20.00 1.33100 -$26.62
1 -$1.50 1.21000 -$1.82
2 -$1.50 1.10000 -$1.65
3 -$1.50 1.00000 -$1.50
FW = -$20.00(F|P 10%,3) – $1.50(F|A 10%,3)
FW = -$20.00(1.33100) – $1.50(3.31000)
DECISION: PREFER DESIGN 1, IT HAS THE HIGHEST (LEAST NEGATIVE) FW
PROBLEM 5.55
OPTION 1: $100,000 IN CD, $0 IN VENTURES, $0 IN BANK ACCOUNT
SOLUTION USING EXCEL’S FV FUNCTION
FW =
$146,410.00 =FV(10%,4,,-100000)
SOLUTION USING FACTOR TABLES
FW = $100,000(F|P 10%,4)
FW = $100,000(1.46410)
FW =
$146,410.00
$135,201.74 =50000+FV(7%,4,,-65000)
$135,202.00
$150,615.35 =FV(7%,4,-10000)+80000+FV(7%,4,,-20000)
$150,615.40
$138,227.84 =FV(7%,2,,-40000)+40000+FV(7%,4,,-40000)
$138,228.00
PROBLEM 5.56
a MONEY AVAILABLE FOR LIGHTING ENHANCEMENT IS $20,000 SINCE THIS IS THE
COST OF THE MOST EXPENSIVE ALTERNATIVE.
SOLUTION APPROACH IS TO SUM THE FW OF THE INVESTMENT RETURNS PLUS THE FW OF THE
RESIDUAL INVESTMENT TO DETERMINE TOTAL PORTFOLIO VALUE
OPTION 1: LIGHT BAR, CASH FLOWS = -$6,000; $2,000; $2,000; $2,000; $2,000; $2,000; $2,000, BANK ACCOUNT = $14,000
SOLUTION USING EXCEL’S FV FUNCTION
FW =
$40,233.07 =FV(10%,6,-2000) + FV(,10%,6,,-14000)
SOLUTION USING FACTOR TABLES
FW = $2,000(F|A 10%,6) + $14,000(F|P 10%,6)
FW = $2,000(7.71561) + $14,000(1.77156)
FW =
$40,233.06
OPTION 2: SLIDING SPOTS, CASH FLOWS = -$14,000; $3,500; $3,500; $3,500; $3,500; $3,500; $3,500, BANK ACCOUNT = $6,000
SOLUTION USING EXCEL’S FV FUNCTION
FW =
$37,634.00 =FV(10%,6,-2000) + FV(,10%,6,,-14000)
SOLUTION USING FACTOR TABLES
FW = $3,500(F|A 10%,6) + $6,000(F|P 10%,6)
FW = $3,500(7.71561) + $6,000(1.77156)
FW =
$37,634.00
OPTION 3: REFLECTED BEAM, CASH FLOWS = -$20,000; $0; $2,300; $4,600; $6,900; $9,200; $11,500, BANK ACCOUNT = $0
$39,459.08
DECISION: OPTION 1, THE LIGHT BAR IS PREFERRED SINCE IT HAS THE HIGHEST PORTFOLIO VALUE.