PROBLEM 6.28
a ONE SIGN CHANGE, THEREFORE, ONE POSITIVE REAL ROOT
b EOY CF CUM CF
0 -$100.00 -$100.00
1$25.00 -$75.00
2$25.00 -$50.00
3$25.00 -$25.00
4$25.00 $0.00
5$25.00 $25.00
6$25.00 $50.00
ONE SIGN CHANGE, THEREFORE, UNIQUE POSITIVE REAL ROOT
c EOY CF
0 -$100.00
1$25.00
2$25.00
3$25.00
4$25.00
5$25.00
6$25.00
IRR = IRR(CF_COLUMN)
IRR = 12.98%
d IRR >= MARR; THEREFORE, ATTRACTIVE
PROBLEM 6.29
a ONE SIGN CHANGE, THEREFORE, ONE POSITIVE REAL ROOT
b EOY CF CUM CF
0 -$100.00 -$100.00
1$15.00 -$85.00
2$15.00 -$70.00
3$15.00 -$55.00
4$15.00 -$40.00
5$15.00 -$25.00
6$15.00 -$10.00
NO SIGN CHANGE, THEREFORE, NO CONCLUSION CAN BE DRAWN
c EOY CF
0 -$100.00
1$15.00
2$15.00
3$15.00
4$15.00
5$15.00
6$15.00
IRR = IRR(CF_COLUMN)
IRR = -2.93%
d IRR < MARR; THEREFORE, NOT ATTRACTIVE
PROBLEM 6.30
a FOUR SIGN CHANGES, THEREFORE, EITHER 4, 2, OR 0 POSITIVE REAL ROOTS GRAPHIC PRESENTATION OF PW VERSUS i
b EOY CF CUM CF i PW
0 -$100.00 -$100.00 0.00 -$25.00
1 $25.00 -$75.00 0.01 -$20.50
2 $200.00 $125.00 0.02 -$16.47
3 -$100.00 $25.00 0.03 -$12.87
4 $250.00 $275.00 0.04 -$9.67
5 -$200.00 $75.00 0.05 -$6.82
6 -$100.00 -$25.00 0.06 -$4.30
0.07 -$2.09
MULTIPLE SIGN CHANGES, THEREFORE, NO CONCLUSION 0.08 -$0.14
0.09 $1.55
c EOY CF 0.10 $3.01
0 -$100.00 0.11 $4.26
1 $25.00 0.12 $5.31
2 $200.00 0.13 $6.19
3 -$100.00 0.14 $6.91
4 $250.00 0.15 $7.49
5 -$200.00 0.16 $7.92
6 -$100.00 0.17 $8.24
0.18 $8.44
BY EXAMINING THE GRAPH OF PW VS i, TWO ROOTS ARE APPARENT 0.19 $8.54
BY USING THE [GUESS] OPTION OF EXCEL’S IRR FUNCTION, 0.20 $8.55
THESE TWO ROOTS CAN BE LOCATED 0.21 $8.47
0.22 $8.32
IRR = IRR(CF_COLUMN, GUESS) 0.23 $8.09
0.24 $7.80
IRR = IRR(CF_COLUMN,10%) 0.25 $7.45
IRR = 8.08% 0.26 $7.05
0.27 $6.60
IRR = IRR(CF_COLUMN,40%) 0.28 $6.11
IRR = 37.43% 0.29 $5.57
0.30 $5.01
d SINCE THE PW OF THE INVESTMENT AT MARR IS POSITIVE, 0.31 $4.41
THE INVESTMENT IS ATTRACTIVE 0.32 $3.78
0.33 $3.13
0.34 $2.45
0.35 $1.76
0.36 $1.05
0.37 $0.32
0.38 -$0.42
0.39 -$1.17
0.40 -$1.94
0.41 -$2.71
0.42 -$3.48
0.43 -$4.27
0.44 -$5.05
0.45 -$5.84
0.46 -$6.64
0.47 -$7.43
0.48 -$8.22
0.49 -$9.02
0.50 -$9.81
-30
-25
-20
-15
-10
-5
0
5
10
15
0% 10% 20% 30% 40% 50% 60%
VALUES OF PW
VALUES OF i
PW versus i
PROBLEM 6.31
a SIX SIGN CHANGES, THEREFORE, EITHER 6, 4, 2, OR 0 POSITIVE REAL ROOTS GRAPHIC PRESENTATION OF PW VERSUS i
b EOY CF CUM CF i PW
0 -$100.00 -$100.00 0.00 -$200.00
1 $800.00 $700.00 0.01 -$170.15
2 -$750.00 -$50.00 0.02 -$142.49
3 $900.00 $850.00 0.03 -$116.84
4 -$950.00 -$100.00 0.04 -$93.06
5 $700.00 $600.00 0.05 -$70.98
6 -$800.00 -$200.00 0.06 -$50.50
0.07 -$31.48
MULTIPLE SIGN CHANGES, THEREFORE, NO CONCLUSION 0.08 -$13.82
5 $700.00 0.16 $89.12
6 -$800.00 0.17 $98.25
0.18 $106.73
BY EXAMINING THE GRAPH OF PW VS i, TWO ROOTS ARE APPARENT 0.19 $114.60
d SINCE THE PW OF THE INVESTMENT AT MARR IS POSITIVE, 0.31 $174.56
0.35 $184.81
0.38 $190.43
0.39 $191.98
0.43 $196.77
0.45 $198.45
0.47 $199.72
0.49 $200.63
0.51 $201.22
0.53 $201.53
0.55 $201.60
0.57 $201.45
0.59 $201.11
0.61 $200.60
0.63 $199.93
0.65 $199.14
0.67 $198.23
0.69 $197.21
0.71 $196.11
0.73 $194.93
0.75 $193.68
0.77 $192.37
0.79 $191.01
0.81 $189.60
0.83 $188.16
0.85 $186.68
0.87 $185.18
0.89 $183.65
0.91 $182.10
0.93 $180.54
0.95 $178.97
0.97 $177.39
0.99 $175.80
1.01 $174.20
1.03 $172.61
-150
-100
-50
200
250
VALUES OF PW
PW versus i
1.04 $171.81
1.05 $171.01
1.06 $170.21
1.07 $169.42
1.08 $168.62
1.09 $167.82
1.10 $167.03
1.11 $166.24
1.12 $165.45
1.13 $164.65
1.15 $163.08
1.17 $161.51
1.19 $159.95
1.21 $158.40
1.23 $156.86
1.25 $155.33
1.27 $153.80
1.29 $152.29
1.31 $150.80
1.33 $149.31
1.35 $147.83
1.37 $146.37
1.39 $144.92
1.41 $143.48
1.43 $142.06
1.45 $140.65
1.47 $139.25
1.49 $137.86
1.51 $136.49
1.53 $135.13
1.55 $133.78
1.57 $132.44
1.59 $131.12
1.61 $129.81
1.63 $128.52
1.65 $127.23
1.67 $125.96
1.69 $124.70
1.71 $123.46
1.73 $122.22
1.75 $121.00
1.77 $119.79
1.79 $118.60
1.81 $117.41
1.83 $116.24
1.85 $115.07
1.87 $113.92
1.89 $112.79
1.91 $111.66
1.93 $110.54
1.95 $109.44
1.97 $108.34
1.99 $107.26
2.01 $106.19
2.03 $105.12
2.05 $104.07
2.07 $103.03
2.09 $102.00
2.11 $100.98
2.13 $99.97
2.14 $99.47
2.15 $98.97
2.16 $98.47
2.17 $97.97
2.18 $97.48
2.19 $96.99
2.20 $96.50
2.21 $96.02
2.23 $95.06
2.25 $94.10
2.27 $93.16
2.29 $92.22
2.31 $91.29
2.33 $90.38
2.35 $89.47
2.37 $88.56
2.39 $87.67
2.41 $86.79
2.43 $85.91
2.45 $85.04
2.47 $84.18
2.49 $83.33
2.51 $82.48
2.53 $81.65
2.55 $80.82
2.57 $80.00
2.59 $79.18
2.61 $78.37
2.63 $77.57
2.65 $76.78
2.67 $75.99
2.69 $75.22
2.71 $74.44
2.73 $73.68
2.75 $72.92
2.77 $72.17
2.79 $71.42
2.81 $70.68
2.83 $69.95
2.85 $69.22
2.87 $68.50
2.89 $67.79
2.91 $67.08
2.93 $66.38
2.95 $65.68
2.97 $64.99
2.99 $64.31
3.01 $63.63
3.03 $62.95
3.05 $62.28
3.07 $61.62
3.09 $60.96
3.11 $60.31
3.13 $59.67
3.15 $59.02
3.17 $58.39
3.19 $57.76
3.21 $57.13
3.22 $56.82
3.23 $56.51
3.24 $56.20
3.25 $55.89
3.26 $55.59
3.27 $55.28
3.28 $54.98
3.29 $54.68
3.30 $54.37
3.31 $54.07
3.33 $53.48
3.35 $52.88
3.37 $52.30
3.39 $51.71
3.41 $51.13
3.43 $50.56
3.45 $49.99
3.47 $49.42
3.49 $48.86
3.51 $48.31
3.53 $47.75
3.55 $47.20
3.57 $46.66
3.59 $46.12
3.61 $45.58
3.63 $45.05
3.65 $44.52
3.67 $43.99
3.69 $43.47
3.71 $42.96
3.73 $42.44
3.75 $41.93
3.77 $41.43
3.79 $40.92
3.81 $40.42
3.83 $39.93
3.85 $39.44
3.87 $38.95
3.89 $38.46
3.91 $37.98
3.93 $37.50
3.95 $37.03
3.97 $36.55
3.99 $36.09
4.01 $35.62
4.03 $35.16
4.05 $34.70
4.07 $34.24
4.09 $33.79
4.11 $33.34
4.13 $32.89
4.15 $32.45
4.17 $32.01
4.19 $31.57
4.21 $31.14
4.23 $30.71
4.25 $30.28
4.27 $29.85
4.29 $29.43
4.31 $29.01
4.32 $28.80
4.33 $28.59
4.34 $28.38
4.35 $28.17
4.36 $27.97
4.37 $27.76
4.38 $27.56
4.39 $27.35
4.41 $26.94
4.43 $26.54
4.45 $26.14
4.47 $25.74
4.49 $25.34
4.51 $24.95
4.53 $24.55
4.55 $24.16
4.57 $23.78
4.59 $23.39
4.61 $23.01
4.63 $22.63
4.65 $22.25
4.67 $21.88
4.69 $21.51
4.71 $21.13
4.73 $20.77
4.75 $20.40
4.77 $20.04
4.79 $19.68
4.81 $19.32
4.83 $18.96
4.85 $18.60
4.87 $18.25
4.89 $17.90
4.91 $17.55
4.93 $17.20
4.95 $16.86
4.97 $16.52
4.99 $16.18
5.01 $15.84
5.03 $15.50
5.05 $15.17
5.07 $14.83
5.09 $14.50
5.11 $14.17
5.13 $13.85
5.15 $13.52
5.17 $13.20
5.19 $12.88
5.21 $12.56
5.23 $12.24
5.25 $11.92
5.27 $11.61
5.29 $11.30
5.31 $10.99
5.33 $10.68
5.35 $10.37
5.37 $10.07
5.39 $9.76
5.40 $9.61
5.41 $9.46
5.42 $9.31
5.43 $9.16
5.44 $9.01
5.45 $8.86
5.46 $8.71
5.47 $8.56
5.48 $8.41
5.49 $8.27
5.51 $7.97
5.53 $7.68
5.55 $7.39
5.57 $7.10
5.59 $6.81
5.61 $6.53
5.63 $6.24
5.65 $5.96
5.67 $5.68
5.69 $5.40
5.71 $5.12
5.73 $4.84
5.75 $4.57
5.77 $4.29
5.79 $4.02
5.81 $3.75
5.83 $3.48
5.85 $3.21
5.87 $2.94
5.89 $2.68
5.91 $2.41
5.93 $2.15
5.95 $1.89
5.97 $1.63
5.99 $1.37
6.01 $1.11
6.03 $0.86
6.05 $0.60
6.07 $0.35
6.09 $0.10
6.11 -$0.15
6.13 -$0.40
6.15 -$0.65
6.17 -$0.90
6.19 -$1.15
6.21 -$1.39
6.23 -$1.63
6.25 -$1.88
6.27 -$2.12
6.29 -$2.36
6.31 -$2.60
6.33 -$2.83
6.35 -$3.07
6.37 -$3.31
6.39 -$3.54
6.41 -$3.77
6.43 -$4.01
6.45 -$4.24
6.47 -$4.47
6.49 -$4.69
6.50 -$4.81
6.51 -$4.92
6.52 -$5.04
6.53 -$5.15
6.54 -$5.26
6.55 -$5.37
6.56 -$5.49
6.57 -$5.60
6.59 -$5.82
6.61 -$6.04
6.63 -$6.26
6.65 -$6.48
6.67 -$6.70
6.69 -$6.92
6.71 -$7.14
6.73 -$7.35
6.75 -$7.57
6.77 -$7.78
6.79 -$8.00
6.81 -$8.21
6.83 -$8.42
6.85 -$8.63
6.87 -$8.84
6.89 -$9.05
6.91 -$9.25
6.93 -$9.46
6.95 -$9.67
6.97 -$9.87
6.99 -$10.07
7.01 -$10.28
7.03 -$10.48
7.05 -$10.68
7.07 -$10.88
7.09 -$11.08
7.11 -$11.27
7.13 -$11.47
7.15 -$11.67
7.17 -$11.86
7.19 -$12.06
7.21 -$12.25
7.23 -$12.44
7.25 -$12.64
7.27 -$12.83
7.29 -$13.02
7.31 -$13.21
7.33 -$13.40
7.35 -$13.58
7.37 -$13.77
7.39 -$13.96
7.41 -$14.14
7.43 -$14.33
7.45 -$14.51
7.47 -$14.69
7.49 -$14.88
7.51 -$15.06
7.53 -$15.24
7.55 -$15.42
7.57 -$15.60
7.58 -$15.69
7.59 -$15.77
7.60 -$15.86
7.61 -$15.95
7.62 -$16.04
7.63 -$16.13
7.64 -$16.22
7.65 -$16.30
7.66 -$16.39
7.67 -$16.48
7.69 -$16.65
7.71 -$16.83
7.73 -$17.00
7.75 -$17.17
7.77 -$17.35
7.79 -$17.52
7.81 -$17.69
7.83 -$17.86
7.85 -$18.03
7.87 -$18.19
7.89 -$18.36
7.91 -$18.53
7.93 -$18.69
7.95 -$18.86
7.97 -$19.02
7.99 -$19.19
8.01 -$19.35
8.03 -$19.51
8.05 -$19.68
8.07 -$19.84
8.09 -$20.00
8.11 -$20.16
8.13 -$20.32
8.15 -$20.48
8.17 -$20.64
8.19 -$20.79
8.21 -$20.95
8.23 -$21.11
8.25 -$21.26
8.27 -$21.42
8.29 -$21.57
8.31 -$21.73
8.33 -$21.88
8.35 -$22.03
8.37 -$22.18
8.39 -$22.34
8.41 -$22.49
8.43 -$22.64
8.45 -$22.79
8.47 -$22.94
8.49 -$23.08
8.51 -$23.23
8.53 -$23.38
8.55 -$23.53
8.57 -$23.67
8.59 -$23.82
8.61 -$23.96
8.63 -$24.11
8.65 -$24.25
8.67 -$24.40
8.68 -$24.47
8.69 -$24.54
8.70 -$24.61
8.71 -$24.68
8.72 -$24.75
8.73 -$24.82
8.74 -$24.89
8.75 -$24.97
8.77 -$25.11
8.79 -$25.25
8.81 -$25.39
8.83 -$25.53
8.85 -$25.66
8.87 -$25.80
8.89 -$25.94
8.91 -$26.08
8.93 -$26.21
8.95 -$26.35
8.97 -$26.49
8.99 -$26.62
9.01 -$26.76
9.03 -$26.89
9.05 -$27.02
9.07 -$27.16
9.09 -$27.29
9.11 -$27.42
9.13 -$27.55
9.15 -$27.69
9.17 -$27.82
9.19 -$27.95
9.21 -$28.08
9.23 -$28.21
9.25 -$28.33
9.27 -$28.46
9.29 -$28.59
9.31 -$28.72
9.33 -$28.85
9.35 -$28.97
9.37 -$29.10
9.39 -$29.22
9.41 -$29.35
9.43 -$29.47
9.45 -$29.60
9.47 -$29.72
9.49 -$29.85
9.51 -$29.97
9.53 -$30.09
9.55 -$30.21
9.57 -$30.34
9.59 -$30.46
9.61 -$30.58
9.63 -$30.70
9.65 -$30.82
9.67 -$30.94
9.69 -$31.06
9.71 -$31.18
9.73 -$31.30
9.75 -$31.41
9.76 -$31.47
9.77 -$31.53
9.78 -$31.59
9.79 -$31.65
9.80 -$31.71
9.81 -$31.77
9.82 -$31.82
9.83 -$31.88
9.84 -$31.94
9.85 -$32.00
9.87 -$32.11
9.89 -$32.23
9.91 -$32.34
9.93 -$32.46
9.95 -$32.57
9.97 -$32.69
9.99 -$32.80
10.01 -$32.91
10.03 -$33.02
10.05 -$33.14
10.07 -$33.25
10.09 -$33.36
10.11 -$33.47
10.13 -$33.58
10.15 -$33.69
10.17 -$33.80
10.19 -$33.91
10.21 -$34.02
10.23 -$34.13
10.25 -$34.24
10.27 -$34.35
10.29 -$34.45
10.31 -$34.56
10.33 -$34.67
10.35 -$34.78
10.37 -$34.88
10.39 -$34.99
10.41 -$35.09
10.43 -$35.20
10.45 -$35.30
10.47 -$35.41
10.49 -$35.51
10.51 -$35.62
10.53 -$35.72
10.55 -$35.82
10.57 -$35.93
10.59 -$36.03
10.61 -$36.13
10.63 -$36.23
10.65 -$36.34
10.67 -$36.44
10.69 -$36.54
10.71 -$36.64
10.73 -$36.74
10.75 -$36.84
10.77 -$36.94
10.79 -$37.04
10.81 -$37.14
10.83 -$37.24
10.85 -$37.34
10.86 -$37.38
10.87 -$37.43
10.88 -$37.48
10.89 -$37.53
10.90 -$37.58
10.91 -$37.63
10.92 -$37.68
10.93 -$37.73
10.94 -$37.77
10.95 -$37.82
10.96 -$37.87
10.97 -$37.92
10.98 -$37.97
10.99 -$38.02
11.00 -$38.06
11.01 -$38.11
11.02 -$38.16
11.03 -$38.21
11.04 -$38.26
11.05 -$38.30
11.06 -$38.35
11.07 -$38.40
11.08 -$38.45
11.09 -$38.49
11.10 -$38.54
11.11 -$38.59
11.12 -$38.64
11.13 -$38.68
11.14 -$38.73
11.15 -$38.78
11.16 -$38.82
11.17 -$38.87
11.18 -$38.92
11.19 -$38.96
11.20 -$39.01
11.21 -$39.06
11.22 -$39.10
11.23 -$39.15
11.24 -$39.20
11.25 -$39.24
11.26 -$39.29
11.27 -$39.33
11.28 -$39.38
11.29 -$39.43
11.30 -$39.47
PROBLEM 6.32
EOY CF GRAPHIC PRESENTATION OF PW VERSUS i
0 -$101.00
1$411.00 IPW
2 -$558.00 0 $1.00
3$253.00 0.01 $0.83
4$2.00 0.02 $0.68
5$8.00 0.03 $0.54
6 -$14.00 0.04 $0.43
0.05 $0.32
a BY EXAMINING THE GRAPH OF PW VS I, THREE ROOTS ARE APPARENT 0.06 $0.23
BY USING THE [GUESS] OPTION OF EXCEL’S IRR FUNCTION, 0.07 $0.16
THESE THREE ROOTS CAN BE LOCATED 0.08 $0.09
0.09 $0.04
IRR = IRR(CF_COLUMN, GUESS) 0.1 -$0.01
0.11 -$0.04
IRR = IRR(CF_COLUMN,10%) 0.12 -$0.07
IRR = 9.82% 0.13 -$0.09
0.14 -$0.11
IRR = IRR(CF_COLUMN,25%) 0.15 -$0.12
IRR = 25.67% 0.16 -$0.12
0.17 -$0.12
IRR = IRR(CF_COLUMN,60%) 0.18 -$0.12
IRR = 57.45% 0.19 -$0.11
0.2 -$0.10
b SINCE THE PW OF THE INVESTMENT AT MARR IS NEGATIVE 0.21 -$0.08
THE INVESTMENT IS NOT ATTRACTIVE 0.22 -$0.07
0.23 -$0.05
0.24 -$0.03
0.25 -$0.01
0.26 $0.01
0.27 $0.03
0.28 $0.05
0.29 $0.07
0.3 $0.09
0.31 $0.11
0.32 $0.13
0.33 $0.14
0.34 $0.16
0.39 $0.22
0.41 $0.23
0.42 $0.24
0.46 $0.23
0.48 $0.21
0.51 $0.17
0.52 $0.15
0.58 -$0.02
0.61 -$0.13
0.63 -$0.22
0.65 -$0.32
0.67 -$0.42
0.69 -$0.54
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0% 10% 20% 30% 40% 50% 60% 70% 80%
VALUDES OF PW
VALUES OF i
PW versus i
PROBLEM 8.33
a SOLUTION USING EXCEL’S IRR FUNCTION
EOY + CF – CF NET CF
0 -$1,400.00 -$1,400.00
1$0.00 $0.00
2$500.00 $500.00
3$500.00 $500.00
4$500.00 $500.00
5$500.00 $500.00
6$0.00 $0.00
7$500.00 $500.00
8$600.00 $600.00
9$700.00 $700.00
10 $800.00 $800.00
11 $900.00 $900.00
12 -$1,000.00 -$1,000.00
13 -$2,000.00 -$2,000.00
14 -$3,000.00 -$3,000.00
15 $1,400.00 $1,400.00
IRR = IRR(NET_CF_COLUMN)
IRR = 16.82%
b DECISION RULE
IF IRR >= MARR (13.5%), ACCEPT; OTHERWISE, REJECT
c QRU SHOULD INVEST
PROBLEM 6.34
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 15%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, AUBURN, LAGRANGE, ANNISTON
NULL BECOMES THE “CURRENT BEST” AND AUBURN THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR AUBURN – NULL ARE NEEDED
EOY AUBURN NULL INCR. CF
0 -$1,000,000.00 $0.00 -$1,000,000.00
1 $410,000.00 $0.00 $410,000.00
EOY LAGRANGE AUBURN INCR. CF
0 -$1,260,000.00 -$1,000,000.00 -$260,000.00
1 $480,000.00 $410,000.00 $70,000.00
2 $480,000.00 $410,000.00 $70,000.00
3 $480,000.00 $410,000.00 $70,000.00
4 $480,000.00 $410,000.00 $70,000.00
5 $480,000.00 $410,000.00 $70,000.00
6 $480,000.00 $410,000.00 $70,000.00
EOY ANNISTON LAGRANGE INCR. CF
0 -$1,620,000.00 -$1,260,000.00 -$360,000.00
1 $520,000.00 $480,000.00 $40,000.00
2 $520,000.00 $480,000.00 $40,000.00
3 $520,000.00 $480,000.00 $40,000.00
4 $520,000.00 $480,000.00 $40,000.00
5 $520,000.00 $480,000.00 $40,000.00
6 $520,000.00 $480,000.00 $40,000.00
7 $520,000.00 $480,000.00 $40,000.00
8 $520,000.00 $480,000.00 $40,000.00
9 $520,000.00 $480,000.00 $40,000.00
10 $520,000.00 $480,000.00 $40,000.00
11 $520,000.00 $480,000.00 $40,000.00
12 $520,000.00 $480,000.00 $40,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 4.73%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED
LAGRANGE REMAINS THE CURRENT BEST
SINCE THERE ARE NO MORE CHALLENGERS, LAGRANGE IS RECOMMENDED.
CONSIDER THE INVESTMENT ALTERNATIVES IN INCREASING ORDER OF THE
INITIAL INVESTMENT: CONSIDER A, THEN EITHER B OR B-A, DEPENDING ON
THE OUTCOME FOR A.
IRR(A) = 16.643% > MARR = 12%. CALCULATE IRR(B-A)USING EITHER EXCEL’S
RATE OR IRR FUNCTION.
CALCULATE IRR FOR THE RECOMMENDED INVESTMENT USING EITHER
EXCEL’S RATE OR IRR FUNCTION.
PROBLEM 6.36
MARR = 15%
n = 10
INVESTMENT ALTERNATIVE A B C A-C B-A
INITIAL INVESTMENT $600,000 $800,000 $470,000 $130,000 $200,000
SALVAGE VALUE $70,000 $130,000 $65,000 $5,000 $60,000
ANNUAL RECEIPTS $400,000 $600,000 $260,000 $140,000 $200,000
ANNUAL DISBURSEMENTS $130,000 $270,000 $70,000 $60,000 $140,000
NET ANNUAL REVENUE $270,000 $330,000 $190,000 $80,000 $60,000
ALT A B C FEASIBLE? WHY NOT?
1 0 0 0 YES
2 0 0 1 NO C CONTINGENT ON B
3 0 1 0 YES
4 0 1 1 NO EXCEEDS BUDGET LIMIT
5 1 0 0 YES
6 1 0 1 NO EXCEEDS BUDGET LIMIT
7 1 1 0 NO A&B MUTUALLY EXCLUSIVE
8 1 1 1 NO A&B MUTUALLY EXCLUSIVE
EOY NCF(1) NCF(3) NCF(5) NCF(5-1) NCF(3-5)
0$0 -$800,000 -$600,000 -$600,000 ########
1$0 $330,000 $270,000 $270,000 $60,000
2$0 $330,000 $270,000 $270,000 $60,000
3$0 $330,000 $270,000 $270,000 $60,000
4$0 $330,000 $270,000 $270,000 $60,000
5$0 $330,000 $270,000 $270,000 $60,000
6$0 $330,000 $270,000 $270,000 $60,000
7$0 $330,000 $270,000 $270,000 $60,000
8$0 $330,000 $270,000 $270,000 $60,000
9$0 $330,000 $270,000 $270,000 $60,000
10 $0 $460,000 $340,000 $340,000 $120,000
STEP 1:
STEP 2: SINCE IRR(1) DOES NOT EXIST, WE CALCULATE IRR(5-1) USING EXCEL’S IRR FUNCTION.
IRR(5-1) = 43.957% =IRR(F24:F34)
STEP 3: IS IRR(5-1) > MARR? IF SO, CALCULATE IRR(3-5); IF NOT, CALCULATE IRR(3)
IRR(3-5) = 28.204% =IRR(G24:G34)
STEP 4: DRAW CONCLUSION.
SINCE IRR(3-5) > MARR, RECOMMEND INVESTMENT ALTERNATIVE 3, WHICH IS PROPOSAL B.
STEP 5:
IRR(B) = 40.054% =IRR(D24:D34)
IRR(5-1) = 43.957% > MARR = 15%. CALCULATE IRR(3-5) USING EXCEL’S IRR
FUNCTION.
CONSIDER THE INVESTMENT ALTERNATIVES IN INCREASING ORDER OF THE INITIAL
INVESTMENT: CONSIDER 1, THEN EITHER 5 OR 5-1, DEPENDING ON THE OUTCOME FOR 1.
THEN EITHER 3-5 OR 3, DEPENDING ON THE OUTCOME OF 5-1 OR 5.
CALCULATE IRR FOR THE RECOMMENDED INVESTMENT USING EXCEL’S IRR FUNCTION.