PROBLEM 4.33
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
ALTERNATIVE W
11.00%
EOY CF (P|F i%,n) PW OF CF
0 -$100,000.00 1.00000 -$100,000.00
1 $20,000.00 0.90090 $18,018.02
2 $20,000.00 0.81162 $16,232.45
3 $50,000.00 0.73119 $36,559.57
4 $80,000.00 0.65873 $52,698.48
5 $110,000.00 0.59345 $65,279.65
$88,788.16 <- PW
SOLUTION USING EXCEL’S NPV FUNCTION
PW = INVESTMENT + NPV(i,NET CF FOR t=1,n)
SOLUTION USING FACTOR TABLES
PW = -$100,000 + $20,000(P|A 11%,5) + $30,000(P|G 11%,4)(P|F 11%,1)
PW = -$100,000 + $20,000(3.69590) + $30,000(4.25020)(0.90090)
ALTERNATIVE X
EOY CF (P|F i%,n) PW OF CF
0 -$150,000.00 1.00000 -$150,000.00
1 $40,000.00 0.90090 $36,036.04
4 $55,000.00 0.65873 $36,230.20
5 $60,000.00 0.59345 $35,607.08
6 $65,000.00 0.53464 $34,751.65
7 $70,000.00 0.48166 $33,716.09
$99,423.64 <- PW
PW = INVESTMENT + NPV(i,NET CF FOR t=1,n)
PW = $99,423.64 =C31+NPV(0.11,C32:C38)
SOLUTION USING FACTOR TABLES
PW = -$150,000 + $40,000(P|A 11%,7) + $5,000(P|G 11%,7)
PW = -$150,000 + $40,000(4.71220) + $5,000(12.18716)
ALTERNATIVE X IS PREFERRED
PROBLEM 4.34
SOLUTION USING INDIVIDUAL CASH FLOWS AND P|F FACTORS
OPTION 1
12.00%
EOY CF (P|F i%,n) PW OF CF
0 -$100,000.00 1.00000 -$100,000.00
1$16,500.00 0.89286 $14,732.14
2$16,500.00 0.79719 $13,153.70
3$16,500.00 0.71178 $11,744.37
4$16,500.00 0.63552 $10,486.05
5$16,500.00 0.56743 $9,362.54
6$16,500.00 0.50663 $8,359.41
12 $16,500.00 0.25668 $4,235.14
$2,207.17 <- PW
PW = INVESTMENT + PV(i,n,-NET CF FOR t=1)
PW = $2,207.17 =C7+PV(0.12,12,-C8)
PW = -$100,000 – $16,500(P|A 12%,12)
PW = -$100,000 + $16,500(6.19437)
OPTION 2
2$14,300.00 0.79719 $11,399.87
3$14,300.00 0.71178 $10,178.46
4$14,300.00 0.63552 $9,087.91
5$14,300.00 0.56743 $8,114.20
6$14,300.00 0.50663 $7,244.83
7$14,300.00 0.45235 $6,468.59
$1,193.97 <- PW
PW = INVESTMENT + NPV(i,NET CF FOR t=1,n)
PW = $1,193.97 =C39+NPV(0.12,C40:C48)
SOLUTION USING EXCEL’S PV FUNCTION
PW = INVESTMENT + PV(i,n,-NET CF FOR t=1)
PW = $1,193.97 =C39+PV(0.12,9,-C40)
SOLUTION USING FACTOR TABLES
PW = -$75,000 + $14,300(P|A 12%,9)
PW = -$75,000 + $14,300(5.32825)
PW = $1,193.97
OPTION 1 IS PREFERRED
PROBLEM 4.35
E SERIES
8.00%
EOY (P|F i%,n) CF PW OF CF
01.00000 -$40,000.00 -$40,000.00
10.92593 $9,400.00 $8,703.70
20.85734 $9,400.00 $8,058.98
30.79383 $9,400.00 $7,462.02
40.73503 $9,400.00 $6,909.28
50.68058 $9,400.00 $6,397.48
60.63017 $9,400.00 $5,923.59
70.58349 $19,400.00 $11,319.71
$14,774.78 <- PW
SOLUTION USING EXCEL’S NPV FUNCTION
PW = INVESTMENT + NPV(i,NET CF FOR t=1,n)
PW = $14,774.78 =D6+NPV(0.08,D7:D13)
SOLUTION USING EXCEL’S PV FUNCTION
PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n)
SOLUTION USING FACTOR TABLES
PW = -$40,000 + $9,400(P|A 8%,7) + $10,000(P|F 8%,7)
PW = $14,774.78
M SERIES
01.00000 -$60,000.00 -$60,000.00
10.92593 $20,000.00 $18,518.52
20.85734 $20,000.00 $17,146.78
30.79383 $20,000.00 $15,876.64
40.73503 $20,000.00 $14,700.60
50.68058 $20,000.00 $13,611.66
60.63017 $0.00 $0.00
70.58349 $0.00 $0.00
$19,854.20 <- PW
SOLUTION USING EXCEL’S PV FUNCTION
PW = INVESTMENT + PV(i,n,-NET CF FOR t=1,-SV FOR t=n)
SOLUTION USING FACTOR TABLES
PW = -$60,000 + $20,000(P|A 8%,5)
PW = $19,854.20
M SERIES IS PREFERRED
PROBLEM 4.36
INTEREST 7.00% FIRST COST $325,000.00
VISITORS 1S
100,000 ANN COST $80,000.00
INCR IN VISIT
30,000 SALVAGE $60,000.00
BENEFIT PER V
$0.80
EOY VISITORS BEN/VISIT BENEFIT COST
0$325,000.00
1100,000 $0.80 $80,000.00 $80,000.00
2130,000 $0.80 $104,000.00 $80,000.00
3160,000 $0.80 $128,000.00 $80,000.00
4190,000 $0.80 $152,000.00 $80,000.00
5220,000 $0.80 $176,000.00 $80,000.00
6250,000 $0.80 $200,000.00 $80,000.00
7280,000 $0.80 $224,000.00 $80,000.00
8310,000 $0.80 $248,000.00 $80,000.00
9340,000 $0.80 $272,000.00 $80,000.00
10 370,000 $0.80 $296,000.00 $20,000.00
PW $1,227,059.76 $856,385.57
B/C 1.432835645 YES, SUPPORT
B-C $370,674.20 YES, SUPPORT
PROBLEM 4.37
ANNUAL BENEFIT PER MAN= 6
COST TO REMOVE STONE= 1
NUMBER OF STONES= 100
NUMBER OF MEN= 10
LIFE SPAN= 10
INTEREST RATE= 2.00%
MANAGEMENT CHARGE PAID PER PERSON= $16.95 GOAL SEEK CHANGED CELL
a INDIVIDUAL ANALYSIS
WORKING ALONE
EOY BENEFIT COST
0 $100.00
1 $6.00 $0.00
2 $6.00 $0.00
3 $6.00 $0.00
4 $6.00 $0.00
5 $6.00 $0.00
6 $6.00 $0.00
7 $6.00 $0.00
8 $6.00 $0.00
9 $6.00 $0.00
10 $6.00 $0.00
PW $53.90 $100.00
B/C 0.54
b INDIVIDUAL ANALYSIS
WORKING COLLECTIVELY
EOY BENEFIT COST
0 $10.00
1 $6.00 $0.00
2 $6.00 $0.00
3 $6.00 $0.00
4 $6.00 $0.00
5 $6.00 $0.00
6 $6.00 $0.00
7 $6.00 $0.00
8 $6.00 $0.00
9 $6.00 $0.00
10 $6.00 $0.00
PW $53.90 $10.00
B/C 5.39
c INDIVIDUAL ANALYSIS
WORKING COLLECTIVELY
PLUS MANAGER
EOY BENEFIT COST
0 $26.95
1 $6.00 $0.00
2 $6.00 $0.00
3 $6.00 $0.00
4 $6.00 $0.00
5 $6.00 $0.00
6 $6.00 $0.00
7 $6.00 $0.00
8 $6.00 $0.00
9 $6.00 $0.00
10 $6.00 $0.00
PW $53.90 $26.95
B/C 2.00 GOAL SEEK SET CELL
USED GOAL SEEK TO SET B/C= 2.00
TOTAL MANAGEMENT CHARGE = 10*$16.95= $169.50
PROBLEM 4.38
a INTEREST 8.00%
PLANNING HORIZON 10
INITIAL RENOVATION COST $33,000.00
INITIAL NEW EQUIPMENT COST
$21,000.00
INITIAL E-ACCESS COST $17,500.00
SALVAGE % 30.00%
MAINTENANCE/YR $3,500.00
E-VOLUME RENEWAL/YR $4,000.00
INCR
33,500 $7,000.00 $7,500.00
44,000 $8,000.00 $7,500.00
54,500 $9,000.00 $7,500.00
65,000 $10,000.00 $7,500.00
10 7,000 $14,000.00 -$2,400.00
DO NOT APPROVE
INITIAL E-ACCESS COST $17,500.00
SALVAGE % 30.00%
MAINTENANCE/YR $3,500.00
E-VOLUME RENEWAL/YR $4,000.00
INCR
EOY INCR VISITS BENEFITS COSTS
33500 $13,786.63 $7,500.00
44000 $15,756.15 $7,500.00
54500 $17,725.67 $7,500.00
65000 $19,695.18 $7,500.00
75500 $21,664.70 $7,500.00
86000 $23,634.22 $7,500.00
96500 $25,603.74 $7,500.00
10 7000 $27,573.26 -$2,400.00
PW= $117,239.99 $117,239.99
B-C= $0.00
<–SOLVER TARGET CELL
MINIMUM BENEFIT/VISIT=
$3.94
PROBLEM 4.39
INITIAL COST PHYS FACIL $1,800,000.00
NEW SPECIES $310,000.00
FIRST YEAR ANNUAL COST $145,000.00
PERCENT INCREASE EACH YR 3.00%
SALVAGE % FACIL 40.00%
SALVAGE VALUE FACIL $720,000.00
INTEREST 7.00%
PLANNING HORIZON 20
EOY COST
0$2,110,000.00
1$145,000.00
2$149,350.00
3$153,830.50
4$158,445.42
5$163,198.78
6$168,094.74
7$173,137.58
8$178,331.71
9$183,681.66
12 $200,713.91
13 $206,735.33
17 $232,682.43
18 $239,662.91
19 $246,852.79
20 -$465,741.62
ATTENDEES/YR 1,500,000
NEEDED BENEFIT/ATTENDEE $0.2427
PROBLEM 4.40
OVERNIGHT BENEFITS PER FAMILY= $12.00
NUMBER OF NIGHTS PER FAMILY= 8
NUMBER OF FAMILIES PER SEASON= 250
BENEFITS PER DAY FOR DAY-USERS= $4.00
NUMBER OF DAY USERS PER SEASON=
2,200
TOTAL BENEFITS PER YEAR= $32,800.00
ANNUAL COST OF FACILITY= $30,000.00
a B/C= 1.09
b B-C= $2,800.00
PROBLEM 4.41
DN A B C
BENEFITS $0.00 $200,000.00 $300,000.00 $400,000.00
DISBENEFITS
$0.00 $37,000.00 $69,000.00 $102,000.00
NET BENEFITS
$0.00 $163,000.00 $231,000.00 $298,000.00
COSTS $0.00 $150,000.00 $234,000.00 $312,000.00
SAVINGS $0.00 $15,000.00 $31,000.00 $42,000.00
NET COSTS $0.00 $135,000.00 $203,000.00 $270,000.00
a B/C NA 1.21 1.14 1.10
b INCREMENT A-DN B-A C-B
ΔB/ΔC NA 1.21 1.00 1.00
A, B, AND C ARE EQUALLY DESIRABLE
c B-C $0.00 $28,000.00 $28,000.00 $28,000.00
A, B, AND C ARE EQUALLY DESIRABLE
PROBLEM 4.42
INTEREST RA
7.00%
PLAN HORIZON
15
SALVAGE % 50.00%
ROUTE A ROUTE B ROUTE C
FIRST COST $4,000,000.00 FIRST COST $6,000,000.00 FIRST COST $9,000,000.00
SALVAGE $2,000,000.00 SALVAGE $3,000,000.00 SALVAGE $4,500,000.00
ANNUAL COS
$210,000.00 ANNUAL COST $180,000.00 ANNUAL COST $260,000.00
BENEFITS $500,000.00 BENEFITS $850,000.00 BENEFITS $1,000,000.00
EOY NET BENEFITS NET COST EOY NET BENEFITS NET COST EOY NET BENEFITS NET COST
0 $4,000,000.00 0 $6,000,000.00 0 $9,000,000.00
1 $500,000.00 $210,000.00 1 $850,000.00 $180,000.00 1 $1,000,000.00 $260,000.00
2 $500,000.00 $210,000.00 2 $850,000.00 $180,000.00 2 $1,000,000.00 $260,000.00
3 $500,000.00 $210,000.00 3 $850,000.00 $180,000.00 3 $1,000,000.00 $260,000.00
4 $500,000.00 $210,000.00 4 $850,000.00 $180,000.00 4 $1,000,000.00 $260,000.00
5 $500,000.00 $210,000.00 5 $850,000.00 $180,000.00 5 $1,000,000.00 $260,000.00
6 $500,000.00 $210,000.00 6 $850,000.00 $180,000.00 6 $1,000,000.00 $260,000.00
7 $500,000.00 $210,000.00 7 $850,000.00 $180,000.00 7 $1,000,000.00 $260,000.00
8 $500,000.00 $210,000.00 8 $850,000.00 $180,000.00 8 $1,000,000.00 $260,000.00
9 $500,000.00 $210,000.00 9 $850,000.00 $180,000.00 9 $1,000,000.00 $260,000.00
10 $500,000.00 $210,000.00 10 $850,000.00 $180,000.00 10 $1,000,000.00 $260,000.00
11 $500,000.00 $210,000.00 11 $850,000.00 $180,000.00 11 $1,000,000.00 $260,000.00
12 $500,000.00 $210,000.00 12 $850,000.00 $180,000.00 12 $1,000,000.00 $260,000.00
13 $500,000.00 $210,000.00 13 $850,000.00 $180,000.00 13 $1,000,000.00 $260,000.00
14 $500,000.00 $210,000.00 14 $850,000.00 $180,000.00 14 $1,000,000.00 $260,000.00
15 $500,000.00 -$1,790,000.00 15 $850,000.00 -$2,820,000.00 15 $1,000,000.00 -$4,240,000.00
PW $4,553,957.00 $5,187,769.90 PW $7,741,726.90 $6,552,086.46 PW $9,107,914.01 $9,737,050.55
B-C -$633,812.90 B-C $1,189,640.44 CONSTRUCT B B-C -$629,136.55
PROBLEM 4.43
OPTION 1 OPTION 2 OPTION 3
BENEFITS $400,000 $550,000 $575,000
DISBENEFIT
S
$78,000 $125,000 $180,000
COSTS $235,000 $390,000 $480,000
SAVINGS $25,000 $65,000 $90,000
NET BENEFIT
$322,000 $425,000 $395,000
NET COSTS $210,000 $325,000 $390,000
a B/C 1.53 1.31 1.01
CANNOT TELL FROM B/C WHICH IS BEST
b INCREMENT
OPT 2-OPT 1
OPT 3-OPT 1
ΔB $103,000 $73,000
ΔC $115,000 $180,000
ΔB/ΔC 0.90 0.41
SELECT OPTION 1 SINCE ΔB/ΔC <1 FOR OPTIONS 2 AND 3
c B-C $112,000 $100,000 $5,000
dOPTION 1 OPTION 2
BENEFITS $400,000 $550,000
DISBENEFIT
S
$78,000 $125,000
COSTS $235,000 $378,000 <–SOLVER CHANGED CELL
SAVINGS $25,000 $65,000
NET BENEFIT
$322,000 $425,000
NET COSTS $210,000 $313,000
INCREMENT OPT 2-OPT 1
ΔB $103,000
ΔC $103,000
ΔB/ΔC 1.00
<–SOLVER TARGET CELL
B-C $112,000 $112,000
$378,000 COSTS OPTION 2
PROBLEM 4.44
MARR 7.00%
STUDY PERIO
20
NSA SB
INITIAL COST
$2,400,000.00 $4,200,000.00 $5,200,000.00
SALVAGE % 20.00% 20.00% 20.00%
ANNUAL COST
$155,000.00 $88,000.00 $125,000.00
USER COST $625,000.00 $410,000.00 $310,000.00
N (NORTH) SA (SOUTH A) SB (SOUTH B)
EOY COST USER COST EOY COST USER COST EOY COST USER COST
(DISBENEFIT) (DISBENEFIT) (DISBENEFIT)
0 $2,400,000.00 0 $4,200,000.00 0 $5,200,000.00
1 $155,000.00 $625,000.00 1 $88,000.00 $410,000.00 1 $125,000.00 $310,000.00
2 $155,000.00 $625,000.00 2 $88,000.00 $410,000.00 2 $125,000.00 $310,000.00
3 $155,000.00 $625,000.00 3 $88,000.00 $410,000.00 3 $125,000.00 $310,000.00
4 $155,000.00 $625,000.00 4 $88,000.00 $410,000.00 4 $125,000.00 $310,000.00
5 $155,000.00 $625,000.00 5 $88,000.00 $410,000.00 5 $125,000.00 $310,000.00
6 $155,000.00 $625,000.00 6 $88,000.00 $410,000.00 6 $125,000.00 $310,000.00
7 $155,000.00 $625,000.00 7 $88,000.00 $410,000.00 7 $125,000.00 $310,000.00
8 $155,000.00 $625,000.00 8 $88,000.00 $410,000.00 8 $125,000.00 $310,000.00
9 $155,000.00 $625,000.00 9 $88,000.00 $410,000.00 9 $125,000.00 $310,000.00
10 $155,000.00 $625,000.00 10 $88,000.00 $410,000.00 10 $125,000.00 $310,000.00
11 $155,000.00 $625,000.00 11 $88,000.00 $410,000.00 11 $125,000.00 $310,000.00
12 $155,000.00 $625,000.00 12 $88,000.00 $410,000.00 12 $125,000.00 $310,000.00
13 $155,000.00 $625,000.00 13 $88,000.00 $410,000.00 13 $125,000.00 $310,000.00
14 $155,000.00 $625,000.00 14 $88,000.00 $410,000.00 14 $125,000.00 $310,000.00
15 $155,000.00 $625,000.00 15 $88,000.00 $410,000.00 15 $125,000.00 $310,000.00
16 $155,000.00 $625,000.00 16 $88,000.00 $410,000.00 16 $125,000.00 $310,000.00
17 $155,000.00 $625,000.00 17 $88,000.00 $410,000.00 17 $125,000.00 $310,000.00
18 $155,000.00 $625,000.00 18 $88,000.00 $410,000.00 18 $125,000.00 $310,000.00
19 $155,000.00 $625,000.00 19 $88,000.00 $410,000.00 19 $125,000.00 $310,000.00
20 -$325,000.00 $625,000.00 20 -$752,000.00 $410,000.00 20 -$915,000.00 $310,000.00
PW $3,918,031.09 $6,621,258.90 $4,915,201.29 $4,343,545.84 $6,255,496.02 $3,284,144.42
a INCREMENT SA-N SB-SA
ΔBENEFIT PW $2,277,713.06 $1,059,401.42
ΔCOST PW $997,170.20 $1,340,294.73
ΔB/ΔC 2.28 0.79
SA WINS SA WINS
SA IS WINNER
bB-C -$10,539,289.99 -$9,258,747.13 -$9,539,640.43
SA WINS
SA IS WINNER
c MARR 0.00%
STUDY PERIO
20
NSA SB
INITIAL COST
$2,400,000.00 $4,200,000.00 $5,200,000.00
SALVAGE % 20.00% 20.00% 20.00%
ANNUAL COST
$155,000.00 $88,000.00 $125,000.00
USER COST $625,000.00 $410,000.00 $310,000.00
N (NORTH) SA (SOUTH A) SB (SOUTH B)
EOY COST USER COST EOY COST USER COST EOY COST USER COST
(DISBENEFIT) (DISBENEFIT) (DISBENEFIT)
0 $2,400,000.00 0 $4,200,000.00 0 $5,200,000.00
1 $155,000.00 $625,000.00 1 $88,000.00 $410,000.00 1 $125,000.00 $310,000.00
2 $155,000.00 $625,000.00 2 $88,000.00 $410,000.00 2 $125,000.00 $310,000.00
3 $155,000.00 $625,000.00 3 $88,000.00 $410,000.00 3 $125,000.00 $310,000.00
4 $155,000.00 $625,000.00 4 $88,000.00 $410,000.00 4 $125,000.00 $310,000.00
5 $155,000.00 $625,000.00 5 $88,000.00 $410,000.00 5 $125,000.00 $310,000.00
6 $155,000.00 $625,000.00 6 $88,000.00 $410,000.00 6 $125,000.00 $310,000.00
7 $155,000.00 $625,000.00 7 $88,000.00 $410,000.00 7 $125,000.00 $310,000.00
8 $155,000.00 $625,000.00 8 $88,000.00 $410,000.00 8 $125,000.00 $310,000.00
9 $155,000.00 $625,000.00 9 $88,000.00 $410,000.00 9 $125,000.00 $310,000.00
10 $155,000.00 $625,000.00 10 $88,000.00 $410,000.00 10 $125,000.00 $310,000.00
11 $155,000.00 $625,000.00 11 $88,000.00 $410,000.00 11 $125,000.00 $310,000.00
12 $155,000.00 $625,000.00 12 $88,000.00 $410,000.00 12 $125,000.00 $310,000.00
13 $155,000.00 $625,000.00 13 $88,000.00 $410,000.00 13 $125,000.00 $310,000.00
14 $155,000.00 $625,000.00 14 $88,000.00 $410,000.00 14 $125,000.00 $310,000.00
15 $155,000.00 $625,000.00 15 $88,000.00 $410,000.00 15 $125,000.00 $310,000.00
16 $155,000.00 $625,000.00 16 $88,000.00 $410,000.00 16 $125,000.00 $310,000.00
17 $155,000.00 $625,000.00 17 $88,000.00 $410,000.00 17 $125,000.00 $310,000.00
18 $155,000.00 $625,000.00 18 $88,000.00 $410,000.00 18 $125,000.00 $310,000.00
19 $155,000.00 $625,000.00 19 $88,000.00 $410,000.00 19 $125,000.00 $310,000.00
20 -$325,000.00 $625,000.00 20 -$752,000.00 $410,000.00 20 -$915,000.00 $310,000.00
$5,020,000.00 $12,500,000.00 $5,120,000.00 $8,200,000.00 $6,660,000.00 $6,200,000.00
INCREMENT SA-N SB-SA
ΔBENEFIT PW $4,300,000.00 $2,000,000.00
ΔCOST PW $100,000.00 $1,540,000.00
ΔB/ΔC 43.00 1.30
SA WINS SB WINS