B-C -$17,520,000.00 ############ -$12,860,000.00
SB WINS
SB IS WINNER
PROBLEM 4.45
INCREMENTAL
EAST WEST WEST OVER EAST
FIRST COST $3,500,000.00 $5,000,000.00 $1,500,000.00
SALVAGE $0.00 $0.00 $0.00
MAINTENANCE
$120,000.00 $90,000.00 -$30,000.00
BENEFITS (RE
$0.00 $220,000.00 $220,000.00
SERVICE LIF
20
INTEREST RA
7.00%
EOY INCREMENT FOR
WEST-EAST BENEFIT
COSTS
0$1,500,000.00
1$220,000.00 -$30,000.00
2$220,000.00 -$30,000.00
3$220,000.00 -$30,000.00
4$220,000.00 -$30,000.00
5$220,000.00 -$30,000.00
6$220,000.00 -$30,000.00
7$220,000.00 -$30,000.00
8$220,000.00 -$30,000.00
9$220,000.00 -$30,000.00
10 $220,000.00 -$30,000.00
11 $220,000.00 -$30,000.00
12 $220,000.00 -$30,000.00
13 $220,000.00 -$30,000.00
14 $220,000.00 -$30,000.00
15 $220,000.00 -$30,000.00
16 $220,000.00 -$30,000.00
17 $220,000.00 -$30,000.00
18 $220,000.00 -$30,000.00
19 $220,000.00 -$30,000.00
20 $220,000.00 -$30,000.00
PW $2,330,683.13 $1,182,179.57
PROBLEM 4.46
VEHICLES AFFECTED PER DAY 12,000
PRIVATE VEHICLES PER DAY 9,000
COMMERCIAL VEHICLES PER DAY 3,000
DAYS PER YEAR 300
EXTRA START-STOPS PER VEHICLE PER DAY 3
COST OF START-STOP PER VEHICLE $0.03
EXTRA WAITING PER VEHICLE PER DAY 2 MINUTES
COST OF WAITING PER HOUR – PRIVATE $18.00
COST OF WAITING PER HOUR – COMMERCIAL $45.00
PERCENTAGE OF AFFECTED VEHICLES 10.00%
PERCENTAGE REDUCTION IN START-STOPS AND WAITING 90.00%
BENEFITS DUE TO START-STOP REDUCTION PER YEAR $29,160.00
BENEFITS DUE TO WAITING REDUCTION PER YEAR $267,300.00
TOTAL BENEFITS PER YEAR $296,460.00
INTEREST RATE 7.00%
PLANNING HORIZON 10
ALLOWABLE INITIAL COST OF PROJECT $2,082,210.98
PROBLEM 4.47
a
5.00% CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$100,000.00 -$100,000.00 1.00000 -$100,000.00 -$100,000.00
1 $12,000.00 -$2,000.00 $10,000.00 0.95238 $9,523.81 -$90,476.19
2 $12,000.00 -$2,000.00 $10,000.00 0.90703 $9,070.29 -$81,405.90
3 $12,000.00 -$2,000.00 $10,000.00 0.86384 $8,638.38 -$72,767.52
4 $12,000.00 -$2,000.00 $10,000.00 0.82270 $8,227.02 -$64,540.49
5 $12,000.00 -$2,000.00 $10,000.00 0.78353 $7,835.26 -$56,705.23
6 $12,000.00 -$2,000.00 $10,000.00 0.74622 $7,462.15 -$49,243.08
7 $12,000.00 -$2,000.00 $10,000.00 0.71068 $7,106.81 -$42,136.27
8 $12,000.00 -$2,000.00 $10,000.00 0.67684 $6,768.39 -$35,367.87
9 $12,000.00 -$2,000.00 $10,000.00 0.64461 $6,446.09 -$28,921.78
10 $12,000.00 -$2,000.00 $10,000.00 0.61391 $6,139.13 -$22,782.65
11 $12,000.00 -$2,000.00 $10,000.00 0.58468 $5,846.79 -$16,935.86
12 $12,000.00 -$2,000.00 $10,000.00 0.55684 $5,568.37 -$11,367.48
13 $12,000.00 -$2,000.00 $10,000.00 0.53032 $5,303.21 -$6,064.27
14 $12,000.00 -$2,000.00 $10,000.00 0.50507 $5,050.68 -$1,013.59
15 $12,000.00 -$2,000.00 $10,000.00 0.48102 $4,810.17 $3,796.58
LINEAR INTERPOLATION OF DPBP: 14.21 <- DPBP =(ABS(H20)/(H21-H20))+B20
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 14.21 =NPER(5%,10000,-100000)
b DECISION RULE
IF DPBP <= 3, ACCEPT; OTHERWISE, REJECT
c BAILEY SHOULD NOT BUY THE GANG PUNCH
PROBLEM 4.48
a
10.00% CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$1,000.00 -$1,000.00 1.00000 -$1,000.00 -$1,000.00
1 $600.00 -$300.00 $300.00 0.90909 $272.73 -$727.27
2 $600.00 -$300.00 $300.00 0.82645 $247.93 -$479.34
3 $700.00 -$300.00 $400.00 0.75131 $300.53 -$178.81
4 $700.00 -$300.00 $400.00 0.68301 $273.21 $94.39
5 $700.00 -$300.00 $400.00 0.62092 $248.37
LINEAR INTERPOLATION OF DPBP: 3.65 <- DPBP =(ABS(H10)/(H11-H10))+B10
DUE TO THE NON-UNIFORM NATURE OF THE NET CF SERIES, EXCEL’S NPER FUNCTION
IS NOT USED TO COMPUTE DPBP.
b DECISION RULE
IF DPBP <= 3, ACCEPT; OTHERWISE, REJECT
c HOME INNOVATIONS SHOULD NOT PURSUE THE NEW PRODUCT
SINCE THE NET CF SERIES IS NOT A UNIFORM SERIES, EXCEL’S NPER FUNCTION
CANNOT BE USED TO COMPUTE DPBP
PROBLEM 4.49
a VENDOR A SOFTWARE
10.00% CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$380,000.00 -$380,000.00 1.00000 -$380,000.00 -$380,000.00
1 $125,000.00 $125,000.00 0.90909 $113,636.36 -$266,363.64
2 $125,000.00 $125,000.00 0.82645 $103,305.79 -$163,057.85
3 $125,000.00 $125,000.00 0.75131 $93,914.35 -$69,143.50
4 $125,000.00 $125,000.00 0.68301 $85,376.68 $16,233.18
LINEAR INTERPOLATION OF DPBP: 3.81 <- DPBP =(ABS(H9)/(H10-H9))+B9
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 3.802 =NPER(10%,E7,E6)
VENDOR B SOFTWARE
CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$280,000.00 -$280,000.00 1.00000 -$280,000.00 -$280,000.00
1 $95,000.00 $95,000.00 0.90909 $86,363.64 -$193,636.36
2 $95,000.00 $95,000.00 0.82645 $78,512.40 -$115,123.97
3 $95,000.00 $95,000.00 0.75131 $71,374.91 -$43,749.06
4 $95,000.00 $95,000.00 0.68301 $64,886.28 $21,137.22
LINEAR INTERPOLATION OF DPBP: 3.67 <- DPBP =(ABS(H25)/(H26-H25))+B25
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 3.664 =NPER(10%,E23,E22)
b SHORTEST DPBP IS VENDOR B
c THIS DECISION AGREES WITH THE RECOMMENDATION FROM THE PW ANALYSIS
PROBLEM 4.50
a NOTE THAT THE ESTIMATED LIVES ARE DIFFERENT SO A COMMON PLANNING HORIZON MUST BE
ESTABLISHED. 10 YEARS IS SELECTED IN THE ANALYSIS BELOW.
MODEL 127B
8.00% CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$50,000.00 -$50,000.00 1.00000 -$50,000.00 -$50,000.00
1 $19,400.00 -$10,000.00 $9,400.00 0.92593 $8,703.70 -$41,296.30
2 $19,400.00 -$10,000.00 $9,400.00 0.85734 $8,058.98 -$33,237.31
3 $19,400.00 -$10,000.00 $9,400.00 0.79383 $7,462.02 -$25,775.29
4 $19,400.00 -$10,000.00 $9,400.00 0.73503 $6,909.28 -$18,866.01
5 $19,400.00 -$10,000.00 $9,400.00 0.68058 $6,397.48 -$12,468.53
6 $19,400.00 -$10,000.00 $9,400.00 0.63017 $5,923.59 -$6,544.93
7 $19,400.00 -$10,000.00 $9,400.00 0.58349 $5,484.81 -$1,060.12
8 $19,400.00 -$10,000.00 $9,400.00 0.54027 $5,078.53 $4,018.41
9 $19,400.00 -$10,000.00 $9,400.00 0.50025 $4,702.34 $8,720.75
10 $29,400.00 -$10,000.00 $19,400.00 0.46319 $8,985.95 $17,706.70
LINEAR INTERPOLATION OF DPBP: 7.21 <- DPBP =(ABS(H17)/(H18-H17))+B17
BY REVIEWING THE CUMULATIVE PW OF CF COLUMN, WE CAN SEE THAT THE DPBP OCCURS PRIOR TO
YEAR 10 WHERE THE NON-UNIFORM CASH FLOW OCCURS, SO WE CAN USE THE NPER FUNCTION TO DETERMINE
THE VALUE OF DPBP
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 7.202 =NPER(8%,E11,E10)
MODEL 334A
CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$80,000.00 -$80,000.00 1.00000 -$80,000.00 -$80,000.00
1 $26,000.00 -$6,000.00 $20,000.00 0.92593 $18,518.52 -$61,481.48
2 $26,000.00 -$6,000.00 $20,000.00 0.85734 $17,146.78 -$44,334.71
3 $26,000.00 -$6,000.00 $20,000.00 0.79383 $15,876.64 -$28,458.06
4 $26,000.00 -$6,000.00 $20,000.00 0.73503 $14,700.60 -$13,757.46
9 $26,000.00 -$6,000.00 $20,000.00 0.50025 $10,004.98 -$9,508.90
10 $26,000.00 -$6,000.00 $20,000.00 0.46319 $9,263.87 -$245.03
PROBLEM 4.51
a LAGRANGE
15.00% CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$1,260,000.00 -$1,260,000.00 1.00000 -$1,260,000.00 -$1,260,000.00
1 $480,000.00 $480,000.00 0.86957 $417,391.30 -$842,608.70
2 $480,000.00 $480,000.00 0.75614 $362,948.96 -$479,659.74
3 $480,000.00 $480,000.00 0.65752 $315,607.79 -$164,051.94
4 $480,000.00 $480,000.00 0.57175 $274,441.56 $110,389.61
5 $480,000.00 $480,000.00 0.49718 $238,644.83 $349,034.45
6 $480,000.00 $480,000.00 0.43233 $207,517.25 $556,551.69
7 $480,000.00 $480,000.00 0.37594 $180,449.78 $737,001.47
8 $480,000.00 $480,000.00 0.32690 $156,912.85 $893,914.32
9 $480,000.00 $480,000.00 0.28426 $136,445.96 $1,030,360.28
10 $480,000.00 $480,000.00 0.24718 $118,648.66 $1,149,008.94
11 $480,000.00 $480,000.00 0.21494 $103,172.75 $1,252,181.69
12 $480,000.00 $480,000.00 0.18691 $89,715.43 $1,341,897.12
LINEAR INTERPOLATION OF DPBP: 3.60 <- DPBP =(ABS(H10)/(H11-H10))+B10
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 3.581 =NPER(15%,E8,E7)
AUBURN
CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$1,000,000.00 -$1,000,000.00 1.00000 -$1,000,000.00 -$1,000,000.00
1 $410,000.00 $410,000.00 0.86957 $356,521.74 -$643,478.26
2 $410,000.00 $410,000.00 0.75614 $310,018.90 -$333,459.36
3 $410,000.00 $410,000.00 0.65752 $269,581.66 -$63,877.70
4 $410,000.00 $410,000.00 0.57175 $234,418.83 $170,541.13
5 $410,000.00 $410,000.00 0.49718 $203,842.46 $374,383.59
6 $410,000.00 $410,000.00 0.43233 $177,254.31 $551,637.90
7 $410,000.00 $410,000.00 0.37594 $154,134.19 $705,772.09
8 $410,000.00 $410,000.00 0.32690 $134,029.73 $839,801.82
9 $410,000.00 $410,000.00 0.28426 $116,547.59 $956,349.41
10 $410,000.00 $410,000.00 0.24718 $101,345.73 $1,057,695.14
11 $410,000.00 $410,000.00 0.21494 $88,126.72 $1,145,821.86
12 $410,000.00 $410,000.00 0.18691 $76,631.93 $1,222,453.79
LINEAR INTERPOLATION OF DPBP: 3.24 <- DPBP =(ABS(H32)/(H33-H32))+B32
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 3.259 =NPER(15%,E31,E30)
ANNISTON
CUMULATIVE
EOY + CF – CF NET CF (P|F i%,n) PW OF CF PW OF CF
0 -$1,620,000.00 -$1,620,000.00 1.00000 -$1,620,000.00 -$1,620,000.00
1 $520,000.00 $520,000.00 0.86957 $452,173.91 -$1,167,826.09
2 $520,000.00 $520,000.00 0.75614 $393,194.71 -$774,631.38
3 $520,000.00 $520,000.00 0.65752 $341,908.44 -$432,722.94
4 $520,000.00 $520,000.00 0.57175 $297,311.69 -$135,411.25
5 $520,000.00 $520,000.00 0.49718 $258,531.90 $123,120.65
6 $520,000.00 $520,000.00 0.43233 $224,810.35 $347,931.00
7 $520,000.00 $520,000.00 0.37594 $195,487.26 $543,418.26
8 $520,000.00 $520,000.00 0.32690 $169,988.92 $713,407.18
9 $520,000.00 $520,000.00 0.28426 $147,816.45 $861,223.64
10 $520,000.00 $520,000.00 0.24718 $128,536.05 $989,759.69
11 $520,000.00 $520,000.00 0.21494 $111,770.48 $1,101,530.16
12 $520,000.00 $520,000.00 0.18691 $97,191.72 $1,198,721.88
LINEAR INTERPOLATION OF DPBP: 4.52 <- DPBP =(ABS(H57)/(H58-H57))+B57
SOLUTION USING EXCEL’S NPER FUNCTION
DPBP = NPER(i,NET CF FOR t=1,INVESTMENT)
DPBP = 4.506 =NPER(15%,E54,E53)
b AUBURN IS PREFERRED
c THIS DECISION IS INCONSISTENT WITH PW ANALYSIS
PROBLEM 4.52
CC(CONSTRUCTION) = $10,000,000
CC(ANNUAL MAINTENANCE) = ($700,000+$75,000(A|G 4%,5))/0.04
USING EXCEL,
CC(ANNUAL MAINTENANCE) =1000*PMT(4%,5,-NPV(4%,700,775,850,925,1000))/0.04
CC(ANNUAL MAINTENANCE) = $21,103,020.28
CC(MAJOR REPAIRS) = ($2,000,000(A|F 4%,5))/0.04
CC(MAJOR REPAIRS) = ($2,000,000(0.18463))/0.04 = $9,231,500
USING EXCEL,
CC(MAJOR REPAIRS) =PMT(4%,5,,-2000000)/0.04
CC(MAJOR REPAIRS) = $9,231,355.67
TOTAL CC = $10,000,000 + $21,103,018 + $9,231,500 = $40,334,518.
USING EXCEL,
TOTAL CC = $10,000,000 + $21,103,020.28 + $9,231,355.67 = $40,334,375.95.
PROBLEM 4.53
DESIGN A
CC(INITIAL COST) = $2,500,000
CC(ANNUAL MAINTENANCE) = $800,000/0.05 = $16,000,000
CC(MAJOR REPAIRS) = ($1,250,000(A|F 5%,5))/0.05
CC(MAJOR REPAIRS) = ($1,250,000(0.18097))/0.05 = $4,524,250
USING EXCEL,
CC(MAJOR REPAIRS) =PMT(5%,5,,-1250000)/0.05
CC(MAJOR REPAIRS) = $4,524,369.95
TOTAL CC = $2,500,000 + $16,000,000 + $4,524,250 = $23,024,250
USING EXCEL,
TOTAL CC = $2,500,000 + $16,000,000 + $4,524,369.95 = $23,024,369.95
DESIGN B
CC(INITIAL COST) = $5,750,000
CC(ANNUAL MAINTENANCE) = $600,000/0.05 = $12,000,000
CC(MAJOR REPAIRS) = ($3,000,000(A|F 5%,10))/0.05
CC(MAJOR REPAIRS) = ($3,000,000(0.7950))/0.05 = $4,770,000
USING EXCEL,
CC(MAJOR REPAIRS) =PMT(5%,10,,-3000000)/0.05
CC(MAJOR REPAIRS) = $4,770,274.50
TOTAL CC = $5,750,000 + $12,000,000 + $4,770,274.50 = $22,520,274.50
PROBLEM 4.54
CC(CONSTRUCTION) = $2,000,000
CC(ANNUAL MAINTENANCE) = $50,000/0.10 = $500,000
CC(INSPECTION) = $250,000(A|F 10%,5)/0.10 = 250,000(0.16380)/0.10 = $409,500
USING EXCEL,
CC(INSPECTION) =PMT(10%,5,,-250000)/0.1
CC(INSPECTION) = $409,493.70
TOTAL CC = $2,000,000 + $500,000 + $409,500 = $2,909,500
USING EXCEL,
TOTAL CC = $2,000,000 + $500,000 + $409,493.70 = $2,909,493.70
PROBLEM 4.55
CC = ($1,000 + $1,000(A|G 0.5%,12))/0.005
CC = ($1,000 + $1,000(5.44057))/0.005
CC = 1,288,114
USING EXCEL,
CC =1000*PMT(0.005,12,-NPV(0.5%,1,2,3,4,5,6,7,8,9,10,11,12))/0.005
CC = $1,288,113.74
MINIMUM TICKET PRICE = 1,288,114 / 1,000,000 = $1.288114 OR APPROXIMATELY $1.29
PROBLEM 4.56
a A = $500,000(A|P 4%,20)
A = $500,000(0.07358)
A = $36,790
USING EXCEL,
A =PMT(4%,20,-500000)
A = $36,790.88
b A = $500,000(A|P 4%,30)
A = $500,000(0.05783)
A = $28,915
USING EXCEL,
A =PMT(4%,30,-500000)
A = $28,915.05
c A = $500,000(A|P 4%,50)
A = $500,000(0.04655)
A = $23,275
USING EXCEL,
A =PMT(4%,50,-500000)
A = $23,275.10
d A = P * I
A = $500,000 (0.04)
A = $20,000
PROBLEM 4.57
P = $500,000
i = 4.00%
YEARS (A|P 4%,n) SCHOLARSHIPS
1 1.04000 $520,000
2 0.53020 $265,098
3 0.36035 $180,174
4 0.27549 $137,745
5 0.22463 $112,314
6 0.19076 $95,381
7 0.16661 $83,305
8 0.14853 $74,264
9 0.13449 $67,246
10 0.12329 $61,645
11 0.11415 $57,075
12 0.10655 $53,276
13 0.10014 $50,072
14 0.09467 $47,334
15 0.08994 $44,971
16 0.08582 $42,910
17 0.08220 $41,099
18 0.07899 $39,497
19 0.07614 $38,069
20 0.07358 $36,791
21 0.07128 $35,640
22 0.06920 $34,599
23 0.06731 $33,655
24 0.06559 $32,793
25 0.06401 $32,006
26 0.06257 $31,284
27 0.06124 $30,619
28 0.06001 $30,006
29 0.05888 $29,440
30 0.05783 $28,915
31 0.05686 $28,428
32 0.05595 $27,974
33 0.05510 $27,552
34 0.05431 $27,157
35 0.05358 $26,789
36 0.05289 $26,443
37 0.05224 $26,120
38 0.05163 $25,816
39 0.05106 $25,530
40 0.05052 $25,262
41 0.05002 $25,009
42 0.04954 $24,770
43 0.04909 $24,545
44 0.04866 $24,332
45 0.04826 $24,131
46 0.04788 $23,941
47 0.04752 $23,761
48 0.04718 $23,590
49 0.04686 $23,429
50 0.04655 $23,275
51 0.04626 $23,129
52 0.04598 $22,991
53 0.04572 $22,860
54 0.04547 $22,735
55 0.04523 $22,616
56 0.04500 $22,502
57 0.04479 $22,395
58 0.04458 $22,292
59 0.04439 $22,194
60 0.04420 $22,101
61 0.04402 $22,012
62 0.04385 $21,927
63 0.04369 $21,846
64 0.04354 $21,769
65 0.04339 $21,695
66 0.04325 $21,625
67 0.04311 $21,557
68 0.04299 $21,493
69 0.04286 $21,431
70 0.04275 $21,373
71 0.04263 $21,316
$0
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
010 20 30 40 50 60 70 80 90 100
Dollars
Endowment Life (years)
Scholarship Dollars versus Endowment Life
for a $500,000 Endowment
72 0.04252 $21,262
73 0.04242 $21,211
74 0.04232 $21,162
75 0.04223 $21,115
76 0.04214 $21,069
77 0.04205 $21,026
78 0.04197 $20,985
79 0.04189 $20,945
80 0.04181 $20,907
81 0.04174 $20,871
82 0.04167 $20,836
83 0.04160 $20,802
84 0.04154 $20,770
85 0.04148 $20,740
86 0.04142 $20,710
87 0.04136 $20,682
88 0.04131 $20,655
89 0.04126 $20,629
90 0.04121 $20,604
91 0.04116 $20,580
92 0.04111 $20,557
93 0.04107 $20,535
94 0.04103 $20,514
95 0.04099 $20,494
96 0.04095 $20,474
97 0.04091 $20,456
98 0.04088 $20,438
99 0.04084 $20,420
100 0.04081 $20,404
PROBLEM 4.58
EOY + CF – CF NET CF
0$100.00 -$1,100.00 -$1,000.00
1$300.00 -$50.00 $250.00
2$500.00 -$250.00 $250.00
3$400.00 -$150.00 $250.00
4$350.00 -$100.00 $250.00
5$250.00 $0.00 $250.00
EQUIVALENT ANNUAL WORTH = -$1,000(A|P 6%,5) + $250
EQUIVALENT ANNUAL WORTH = -$1,000(0.23740) + $250
EQUIVALENT ANNUAL WORTH = $12.60
USING EXCEL,
AW =250+PMT(6%,5,1000)
AW = $12.60
CC = AW / i
CC = $12.60 / 0.06
CC = $210.00
PROBLEM 4.59
THERE WILL BE 40 DEPOSITS OF $4,000
THE AMOUNT IN THE ACCOUNT AT THE TIME OF THE LAST DEPOSIT IS:
F = $4,000(F|A 8%,40)
F = $4,000(259.05652)
F = $1,036,226.08
USING EXCEL,
F =FV(8%,40,-4000)
F = $1,036,226.07
THIS AMOUNT WILL DRAW INTEREST FOR 2 YEARS TO POSITION IT ONE PERIOD
BEFORE THE FIRST WITHDRAWAL
F = $1,036,226.08(F|P 8%,2)
F = $1,036,226.08(1.16640)
F = $1,208,654.10
USING EXCEL,
a WITHDRAWALS FOR 20 YEARS
A = $1,208,654.10(A|P 8%,20)
A = $123,101.42
USING EXCEL,
A =PMT(8%,20,-FV(8%,2,,FV(8%,40,4000)))
A = $123,104.09
A = $1,208,654.10(0.08883)
A = $107,364.74
USING EXCEL,
A =PMT(8%,30,-FV(8%,2,,FV(8%,40,4000)))
A = $107,361.64
A = $1,208,654.09*i
A = $1,208,654.09(0.08)
A = $96,692.33