PORTFOLIO PW
g CAP CONSTRAINT $280,000.00 1, 2 $46,000.00
$350,000.00 2, 5 $56,590.58
$420,000.00 1, 2, 3 $70,281.85
h MARR 9.60% 1, 5 $100,637.36
12.00% 2, 5 $56,590.58
14.40% 1, 2 $24,062.77 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00
ANNUAL RETURN $24,000.00 $22,000.00 $15,000.00 $25,000.00 $30,000.00
SALVAGE VALUE $150,000.00 $130,000.00 $100,000.00 $160,000.00 $200,000.00
PRESENT WORTH $10,167.37 $13,895.40 $2,541.84 $8,303.35 $5,083.68
INTERNAL RATE OF RETURN 16.00% 16.92% 15.00% 15.63% 15.00%
VALUE OF x 1 1 0 0 0
PORTFOLIO INVESTMENT $150,000.00 $130,000.00 $0.00 $0.00 $0.00 $280,000.00
PORTFOLIO PRESENT WORTH $10,167.37 $13,895.40 $0.00 $0.00 $0.00 $24,062.77
MARR 14.40%
CAP CONSTRA
$350,000.00
INVESTMENT PERIOD 7
REALIZED INITIAL INVESTMENT $150,000.00 $130,000.00 $0.00 $0.00 $0.00 $280,000.00
REALIZED ANNUAL RETURN $24,000.00 $22,000.00 $0.00 $0.00 $0.00 $46,000.00
REALIZED SALVAGE VALUE $150,000.00 $130,000.00 $0.00 $0.00 $0.00 $280,000.00
P’FOLIO IRR 16.43%
PROBLEM 12.6
a OPTIMUM PORTFOLIO 1, 3, 4
b PRESENT WORTH $90,978.88
c PORTFOLIO IRR 12.00%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00
SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
PRESENT WORTH $37,907.87 $22,744.72 $18,953.93 $34,117.08 $18,953.93
INTERNAL RATE OF RETURN 12.50% 12.00% 12.50% 11.50% 11.00%
VALUE OF x 1 0 1 1 0
PORTFOLIO INVESTMENT $400,000.00 $0.00 $200,000.00 $600,000.00 $0.00 $1,200,000.00
PORTFOLIO PRESENT WORTH $37,907.87 $0.00 $18,953.93 $34,117.08 $0.00 $90,978.88
MARR 10% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $0.00 $200,000.00 $600,000.00 $0.00 $1,200,000.00
REALIZED ANNUAL RETURN $50,000.00 $0.00 $25,000.00 $69,000.00 $0.00 $144,000.00
REALIZED SALVAGE VALUE $400,000.00 $0.00 $200,000.00 $600,000.00 $0.00 $1,200,000.00
PORTFOLIO IRR 12.00%
d OPTIMUM PORTFOLIO 1, 2, 3
e PRESENT WORTH $79,606.52
f PORTFOLIO IRR 12.33%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00
SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
PRESENT WORTH $37,907.87 $22,744.72 $18,953.93 $34,117.08 $18,953.93
INTERNAL RATE OF RETURN 12.50% 12.00% 12.50% 11.50% 11.00%
VALUE OF x 1 1 1 0 0
PORTFOLIO INVESTMENT $400,000.00 $300,000.00 $200,000.00 $0.00 $0.00 $900,000.00
PORTFOLIO PRESENT WORTH $37,907.87 $22,744.72 $18,953.93 $0.00 $0.00 $79,606.52
MARR 10% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $0.00 $0.00 $900,000.00
REALIZED ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $0.00 $0.00 $111,000.00
REALIZED SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $0.00 $0.00 $900,000.00
P’FOLIO IRR 12.33%
PORTFOLIO PW
g CAP CONSTRAINT $1,000,000.00 1, 2, 3 $79,606.52
$1,250,000.00 1, 3, 4 $90,978.88
$1,500,000.00 1, 2, 3, 4 $113,723.60
h MARR 8.00% 1, 3, 4 $191,650.08
10.00% 1, 3, 4 $90,978.88
12.00% 1, 3 $10,814.33 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $69,000.00 $55,000.00
SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $600,000.00 $500,000.00
PRESENT WORTH $7,209.55 $0.00 $3,604.78 -$10,814.33 -$18,023.88
INTERNAL RATE OF RETURN 12.50% 12.00% 12.50% 11.50% 11.00%
VALUE OF x 1 0 1 0 0
PORTFOLIO INVESTMENT $400,000.00 $0.00 $200,000.00 $0.00 $0.00 $600,000.00
PORTFOLIO PRESENT WORTH $7,209.55 $0.00 $3,604.78 $0.00 $0.00 $10,814.33
MARR 12% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $0.00 $200,000.00 $0.00 $0.00 $600,000.00
REALIZED ANNUAL RETURN $50,000.00 $0.00 $25,000.00 $0.00 $0.00 $75,000.00
REALIZED SALVAGE VALUE $400,000.00 $0.00 $200,000.00 $0.00 $0.00 $600,000.00
P’FOLIO IRR 12.50%
PROBLEM 12.7
a OPTIMUM PORTFOLIO 2, 4, 5
b PRESENT WORTH $20,604.13
c PORTFOLIO IRR 12.77%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
ANNUAL RETURN $4,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00
SALVAGE VALUE $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
PRESENT WORTH -$1,584.93 $3,169.87 $1,584.93 $6,339.73 $11,094.53
INTERNAL RATE OF RETURN 8.89% 11.67% 10.59% 12.00% 14.67%
VALUE OF x 0 1 0 1 1
PORTFOLIO INVESTMENT $0.00 $60,000.00 $0.00 $100,000.00 $75,000.00 $235,000.00
PORTFOLIO PRESENT WORTH $0.00 $3,169.87 $0.00 $6,339.73 $11,094.53 $20,604.13
MARR 10% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 4
REALIZED INITIAL INVESTMENT $0.00 $60,000.00 $0.00 $100,000.00 $75,000.00 $235,000.00
REALIZED ANNUAL RETURN $0.00 $7,000.00 $0.00 $12,000.00 $11,000.00 $30,000.00
REALIZED SALVAGE VALUE $0.00 $60,000.00 $0.00 $100,000.00 $75,000.00 $235,000.00
PORTFOLIO IRR 12.77%
d OPTIMUM PORTFOLIO 2, 3, 5
e PRESENT WORTH $15,849.33
f PORTFOLIO IRR 12.27%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
ANNUAL RETURN $4,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00
SALVAGE VALUE $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
PRESENT WORTH -$1,584.93 $3,169.87 $1,584.93 $6,339.73 $11,094.53
INTERNAL RATE OF RETURN 8.89% 11.67% 10.59% 12.00% 14.67%
VALUE OF x 0 1 1 0 1
PORTFOLIO INVESTMENT $0.00 $60,000.00 $85,000.00 $0.00 $75,000.00 $220,000.00
PORTFOLIO PRESENT WORTH $0.00 $3,169.87 $1,584.93 $0.00 $11,094.53 $15,849.33
MARR 10% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 4
REALIZED INITIAL INVESTMENT $0.00 $60,000.00 $85,000.00 $0.00 $75,000.00 $220,000.00
REALIZED ANNUAL RETURN $0.00 $7,000.00 $9,000.00 $0.00 $11,000.00 $27,000.00
REALIZED SALVAGE VALUE $0.00 $60,000.00 $85,000.00 $0.00 $75,000.00 $220,000.00
P’FOLIO IRR 12.27%
MUTUAL EXCLUSIVITH CONSTRAINT 1 F58+G58
PORTFOLIO PW
g CAP CONSTRAINT $200,000.00 4, 5 $17,434.26
$250,000.00 2, 4, 5 $20,604.13
$300,000.00 2, 4, 5 $20,604.13
h MARR 8.00% 2, 4, 5 $37,095.82
10.00% 2, 4, 5 $20,604.13
12.00% 4, 5 $6,074.70 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
ANNUAL RETURN $4,000.00 $7,000.00 $9,000.00 $12,000.00 $11,000.00
SALVAGE VALUE $45,000.00 $60,000.00 $85,000.00 $100,000.00 $75,000.00
PRESENT WORTH -$4,252.29 -$607.47 -$3,644.82 $0.00 $6,074.70
INTERNAL RATE OF RETURN 8.89% 11.67% 10.59% 12.00% 14.67%
VALUE OF x 0 0 0 1 1
PORTFOLIO INVESTMENT $0.00 $0.00 $0.00 $100,000.00 $75,000.00 $175,000.00
PORTFOLIO PRESENT WORTH $0.00 $0.00 $0.00 $0.00 $6,074.70 $6,074.70
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 4
REALIZED INITIAL INVESTMENT $0.00 $0.00 $0.00 $100,000.00 $75,000.00 $175,000.00
REALIZED ANNUAL RETURN $0.00 $0.00 $0.00 $12,000.00 $11,000.00 $23,000.00
REALIZED SALVAGE VALUE $0.00 $0.00 $0.00 $100,000.00 $75,000.00 $175,000.00
P’FOLIO IRR 13.14%
PROBLEM 12.8
a OPTIMUM PORTFOLIO 2, 4
b PRESENT WORTH $530,720.51
c PORTFOLIO IRR 21.99%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
ANNUAL RETURN $80,000.00 $100,000.00 $105,000.00 $125,000.00 $140,000.00
SALVAGE VALUE $50,000.00 $50,000.00 $60,000.00 $75,000.00 $75,000.00
PRESENT WORTH $210,842.53 $233,733.88 $218,312.14 $296,986.63 $289,155.14
PORTFOLIO IRR 21.99%
MARR 10% CAP CONSTRAINT $1,000,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $0.00 $400,000.00 $0.00 $0.00 $600,000.00 $1,000,000.00
REALIZED ANNUAL RETURN $0.00 $100,000.00 $0.00 $0.00 $140,000.00 $240,000.00
MUTUAL EXCLUSIVITY CONSTRAINT 1 D62+F62
PORTFOLIO PW
g CAP CONSTRAINT $800,000.00 1, 4 $507,829.17
$1,000,000.00 2, 4 $530,720.51
$1,200,000.00 1, 2, 4 $741,563.04
h MARR 8.00% 2, 5 $668,318.72
10.00% 2, 4 $530,720.51
12.00% 2, 4 $411,546.84 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $300,000.00 $400,000.00 $450,000.00 $500,000.00 $600,000.00
ANNUAL RECEIPTS $205,000.00 $230,000.00 $245,000.00 $260,000.00 $290,000.00
ANNUAL DISBURSEMENTS $125,000.00 $130,000.00 $140,000.00 $135,000.00 $150,000.00
PROBLEM 12.9
a OPTIMUM PORTFOLIO 1, 4, 6, 7, 9, 10
b PRESENT WORTH $1,025,054.50
c PORTFOLIO IRR 18.68%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6 7 8 9 10
INITIAL INVESTMENT $150,000.00 $200,000.00 $225,000.00 $275,000.00 $350,000.00 $400,000.00 $475,000.00 $500,000.00 $550,000.00 $600,000.00
ANNUAL RETURN $35,000.00 $38,000.00 $45,000.00 $60,000.00 $75,000.00 $95,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00
SALVAGE VALUE $25,000.00 $50,000.00 $22,500.00 $27,500.00 $55,000.00 $75,000.00 $50,000.00 $100,000.00 $75,000.00 $75,000.00
PRESENT WORTH $74,698.43 $52,770.71 $60,180.24 $104,276.47 $132,047.41 $212,649.62 $220,179.55 $60,842.53 $216,263.80 $196,986.63
INTERNAL RATE OF RETURN 20.15% 15.37% 15.72% 17.99% 17.81% 20.73% 19.65% 12.56% 18.18% 16.91%
VALUE OF x 1 0 0 1 0 1 1 0 1 1
PORTFOLIO INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $0.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,450,000.00
PORTFOLIO PRESENT WORTH $74,698.43 $0.00 $0.00 $104,276.47 $0.00 $212,649.62 $220,179.55 $0.00 $216,263.80 $196,986.63 $1,025,054.50
MARR 10% CAP CONSTRAINT $2,500,000.00
INVESTMENT PERIOD 10
d OPTIMUM PORTFOLIO 1, 2, 4, 5, 6, 7, 9
e PRESENT WORTH $1,012,885.99
f PORTFOLIO IRR 18.72%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6 7 8 9 10
INITIAL INVESTMENT $150,000.00 $200,000.00 $225,000.00 $275,000.00 $350,000.00 $400,000.00 $475,000.00 $500,000.00 $550,000.00 $600,000.00
ANNUAL RETURN $35,000.00 $38,000.00 $45,000.00 $60,000.00 $75,000.00 $95,000.00 $110,000.00 $85,000.00 $120,000.00 $125,000.00
MUTUAL EXCLUSIVITY CONSTRAINT 1 C58+E58
CONTINGENCY CONSTRAINT 2 D58+G58
VALUE OF x 1 0 0 1 0 1 1 0 1 1
PORTFOLIO INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $0.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,450,000.00
PORTFOLIO PRESENT WORTH $55,807.14 $0.00 $0.00 $72,867.65 $0.00 $160,919.18 $162,623.19 $0.00 $152,174.76 $130,425.87 $734,817.79
MARR 12% CAP CONSTRAINT $2,500,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $0.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $600,000.00 $2,450,000.00
PROBLEM 12.10
a OPTIMUM PORTFOLIO 2, 4, 5, 6
b PRESENT WORTH $9,950.82
c PORTFOLIO IRR 11.42%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17
INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70%
VALUE OF x 0 1 0 1 1 1
PORTFOLIO INVESTMENT $0.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $185,000.00
PORTFOLIO PRESENT WORTH $0.00 $947.70 $0.00 $2,937.86 $2,843.09 $3,222.17 $9,950.82
MARR 10% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $185,000.00
REALIZED ANNUAL RETURN $0.00 $3,750.00 $0.00 $4,775.00 $6,750.00 $5,850.00 $21,125.00
REALIZED SALVAGE VALUE $0.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $185,000.00
PORTFOLIO IRR 11.42%
d OPTIMUM PORTFOLIO 1, 2, 3, 4, 6
PRESENT WORTH $7,676.34
PORTFOLIO IRR 11.13%
e OPTIMUM PORTFOLIO 2, 4, 5, 6
PRESENT WORTH $9,950.82
PORTFOLIO IRR 11.42%
f OPTIMUM PORTFOLIO 2, 4, 5, 6
PRESENT WORTH $9,950.82
PORTFOLIO IRR 11.42%
g OPTIMUM PORTFOLIO 1, 2, 4, 6
PRESENT WORTH $7,486.80
PORTFOLIO IRR 11.32%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17
INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70%
VALUE OF x 1 1 0 1 0 1 4
PORTFOLIO INVESTMENT $25,000.00 $35,000.00 $0.00 $40,000.00 $0.00 $50,000.00 $150,000.00
PORTFOLIO PRESENT WORTH $379.08 $947.70 $0.00 $2,937.86 $0.00 $3,222.17 $7,486.80
MARR 10% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $35,000.00 $0.00 $40,000.00 $0.00 $50,000.00 $150,000.00
REALIZED ANNUAL RETURN $2,600.00 $3,750.00 $0.00 $4,775.00 $0.00 $5,850.00 $16,975.00
REALIZED SALVAGE VALUE $25,000.00 $35,000.00 $0.00 $40,000.00 $0.00 $50,000.00 $150,000.00
P’FOLIO IRR 11.32%
MUTUAL EXCLUSIVITY CONSTRAINT 1 F68+G68
PORTFOLIO PW
h CAP CONSTRAINT $160,000.00 4, 5, 6 $9,003.12
$200,000.00 2, 4, 5, 6 $9,950.82
$240,000.00 1, 2, 3, 4, 5, 6 $10,519.43
i MARR 8.00% 2, 4, 5, 6 $25,253.89
10.00% 2, 4, 5, 6 $9,950.82
12.00% NONE $0.00 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
PRESENT WORTH -$1,441.91 -$1,622.15 -$1,982.63 -$90.12 -$1,622.15 -$540.72
INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70%
VALUE OF x 0 0 0 0 0 0
PORTFOLIO INVESTMENT $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00
PORTFOLIO PRESENT WORTH $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00
MARR 12% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00
REALIZED ANNUAL RETURN $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00
REALIZED SALVAGE VALUE $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00
P’FOLIO IRR #NUM! THIS TABLE IS NOT AN ERROR – THE LAST ANALYSIS HAD NO PORTFOLIO
PROBLEM 12.11
a OPTIMUM PORTFOLIO
b PRESENT WORTH
c PORTFOLIO IRR
SEE BELOW FOR DETAILS
OVERALL
EOY CF(1) CF(2) CF(3) CF(4) P’FOLIO CF
0 -$50,000 -$125,000 -$200,000 -$250,000 -$425,000
1 -$100,000 -$75,000 $50,000 $75,000 -$100,000
2 $50,000 $70,000 $50,000 $75,000 $195,000
3 $50,000 $70,000 $50,000 $75,000 $195,000
4 $50,000 $70,000 $50,000 $75,000 $195,000
5 $50,000 $70,000 $75,000 $75,000 $195,000
6 $50,000 $70,000 $75,000 $85,000 $205,000
7 $50,000 $70,000 $75,000 $85,000 $205,000
8 $50,000 $70,000 $75,000 $85,000 $205,000
9 $50,000 $70,000 $75,000 $85,000 $205,000
10 $75,000 $100,000 $75,000 $100,000 $275,000
PRESENT WORTH $130,503 $184,868 $181,596 $240,163 $555,535
INTERNAL RATE OF RETURN 27.59% 26.85% 26.28% 28.51% 27.73%
VALUE OF x 1 1 0 1
PORTFOLIO INVESTMENT YR 0 $50,000.00 $125,000.00 $0.00 $250,000.00 $425,000.00
PORTFOLIO INVESTMENT YR 1 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00
PORTFOLIO PRESENT WORTH $130,503.30 $184,867.81 $0.00 $240,163.49 $555,534.60
MARR 10% CAP CONSTRAINT YR 0 $500,000.00
INVESTMENT PERIOD 10 CAP CONSTRAINT YR 1 $175,000.00
PORTFOLIO IRR 27.73%
d PORTFOLIO PW
CAP CONSTRAINT $400,000.00 1, 2, 3 $496,967.01
$500,000.00 1, 2, 4 $555,534.60
$600,000.00 2, 3, 4 $606,627.20
e MARR 8.00% 1, 2, 4 $669,914.98
10.00% 1, 2, 4 $555,534.60
12.00% 1, 2, 4 $456,393.23 ***
SEE BELOW FOR ONE SETUP ***
EOY CF(1) CF(2) CF(3) CF(4) P’FOLIO CF
0 -$50,000 -$125,000 -$200,000 -$250,000 -$425,000
1 -$100,000 -$75,000 $50,000 $75,000 -$100,000
2 $50,000 $70,000 $50,000 $75,000 $195,000
3 $50,000 $70,000 $50,000 $75,000 $195,000
4 $50,000 $70,000 $50,000 $75,000 $195,000
5 $50,000 $70,000 $75,000 $75,000 $195,000
6 $50,000 $70,000 $75,000 $85,000 $205,000
7 $50,000 $70,000 $75,000 $85,000 $205,000
8 $50,000 $70,000 $75,000 $85,000 $205,000
9 $50,000 $70,000 $75,000 $85,000 $205,000
10 $75,000 $100,000 $75,000 $100,000 $275,000
PRESENT WORTH $106,632 $150,711 $147,833 $199,051 $456,393
INTERNAL RATE OF RETURN 27.59% 26.85% 26.28% 28.51% 27.73%
VALUE OF x 1 1 0 1
PORTFOLIO INVESTMENT YR 0 $50,000.00 $125,000.00 $0.00 $250,000.00 $425,000.00
PORTFOLIO INVESTMENT YR 1 $100,000.00 $75,000.00 $0.00 $0.00 $175,000.00
PORTFOLIO PRESENT WORTH $106,631.91 $150,710.52 $0.00 $199,050.79 $456,393.23
MARR 12% CAP CONSTRAINT YR 0 $500,000.00
INVESTMENT PERIOD 10 CAP CONSTRAINT YR 1 $175,000.00
P’FOLIO IRR 27.73%
PROBLEM 12.12
INVESTMENT OPPORTUNITY A B C D E
INITIAL INVESTMENT $75,000.00 $60,000.00 $80,000.00 $55,000.00 $90,000.00
ANNUAL RETURN $8,750.00 $7,250.00 $9,750.00 $6,500.00 $10,750.00
SALVAGE VALUE $75,000.00 $60,000.00 $80,000.00 $55,000.00 $90,000.00
PRESENT WORTH $4,738.48 $4,738.48 $6,633.88 $3,790.79 $6,633.88
INTERNAL RATE OF RETURN 11.67% 12.08% 12.19% 11.82% 11.94%
VALUE OF x 0 1 0 0 1
PORTFOLIO INVESTMENT $0.00 $60,000.00 $0.00 $0.00 $90,000.00 $150,000.00
PORTFOLIO PRESENT WORTH $0.00 $4,738.48 $0.00 $0.00 $6,633.88 $11,372.36
MARR 10% CAP CONSTRAINT $150,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $60,000.00 $0.00 $0.00 $90,000.00 $150,000.00
REALIZED ANNUAL RETURN $0.00 $7,250.00 $0.00 $0.00 $10,750.00 $18,000.00
REALIZED SALVAGE VALUE $0.00 $60,000.00 $0.00 $0.00 $90,000.00 $150,000.00
PORTFOLIO IRR 12.00%
PROBLEM 12.13
a) INVESTMENT OPPORTUNITY A B C D E F
INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00
ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $5,950.00 $5,150.00 $4,250.00
SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $2,000.00 $2,100.00 $1,200.00
PRESENT WORTH $4,102.71 $3,115.68 $1,690.83 $2,583.27 $756.19 $4,001.21
INTERNAL RATE OF RETURN 30.40% 19.73% 18.34% 16.89% 13.52% 24.30%
VALUE OF x 1 1 1 0 0 1
PORTFOLIO INVESTMENT $8,000.00 $15,000.00 $10,000.00 $0.00 $0.00 $12,000.00 $45,000.00
PORTFOLIO PRESENT WORTH $4,102.71 $3,115.68 $1,690.83 $0.00 $0.00 $4,001.21 $12,910.44
MARR 12% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $0.00 $0.00 $12,000.00 $45,000.00
REALIZED ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $0.00 $0.00 $4,250.00 $15,270.00
REALIZED SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $0.00 $0.00 $1,200.00 $5,050.00
PORTFOLIO IRR 22.60%
INVEST IN A, B, C, AND F
b) INVESTMENT OPPORTUNITY A B C D E F
INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00
ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $5,950.00 $5,150.00 $4,250.00
SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $2,000.00 $2,100.00 $1,200.00
PRESENT WORTH $4,102.71 $3,115.68 $1,690.83 $2,583.27 $756.19 $4,001.21
INTERNAL RATE OF RETURN 30.40% 19.73% 18.34% 16.89% 13.52% 24.30%
VALUE OF x 1 0 1 0 1 1
PORTFOLIO INVESTMENT $8,000.00 $0.00 $10,000.00 $0.00 $19,000.00 $12,000.00 $49,000.00
PORTFOLIO PRESENT WORTH $4,102.71 $0.00 $1,690.83 $0.00 $756.19 $4,001.21 $10,550.95
MARR 12% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $8,000.00 $0.00 $10,000.00 $0.00 $19,000.00 $12,000.00 $49,000.00
REALIZED ANNUAL RETURN $3,200.00 $0.00 $3,070.00 $0.00 $5,150.00 $4,250.00 $15,670.00
REALIZED SALVAGE VALUE $1,000.00 $0.00 $1,100.00 $0.00 $2,100.00 $1,200.00 $5,400.00
PORTFOLIO IRR 20.03%
INVEST IN A, B, C, AND F
0B & D MUTUALLY EXCLUSIVE
PROBLEM 12.14
a) INVESTMENT OPPORTUNITY M N O P Q R
INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00
ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $5,950.00 $5,150.00 $4,250.00
SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $2,000.00 $2,100.00 $1,200.00
PRESENT WORTH $6,686.33 $6,886.86 $4,135.67 $7,353.37 $4,796.20 $7,463.40
INTERNAL RATE OF RETURN #NUM! 27.63% 26.45% 25.26% 22.12% 31.90%
VALUE OF x 1 0 1 1 0 1
PORTFOLIO INVESTMENT $8,000.00 $0.00 $10,000.00 $20,000.00 $0.00 $12,000.00 $50,000.00
PORTFOLIO PRESENT WORTH $6,686.33 $0.00 $4,135.67 $7,353.37 $0.00 $7,463.40 $25,638.76
MARR 15% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 8
REALIZED INITIAL INVESTMENT $8,000.00 $0.00 $10,000.00 $20,000.00 $0.00 $12,000.00 $50,000.00
REALIZED ANNUAL RETURN $3,200.00 $0.00 $3,070.00 $5,950.00 $0.00 $4,250.00 $16,470.00
REALIZED SALVAGE VALUE $1,000.00 $0.00 $1,100.00 $2,000.00 $0.00 $1,200.00 $5,300.00
PORTFOLIO IRR 29.06%
INVEST IN M, O, P, AND R
-8000
3200
3200
3200
3200
3200
3200
3200
4200
37.181%
b) INVESTMENT OPPORTUNITY M N O P Q R
INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00
ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $5,950.00 $5,150.00 $4,250.00
SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $2,000.00 $2,100.00 $1,200.00
PRESENT WORTH $6,686.33 $6,886.86 $4,135.67 $7,353.37 $4,796.20 $7,463.40
INTERNAL RATE OF RETURN #NUM! 27.63% 26.45% 25.26% 22.12% 31.90%
VALUE OF x 1 0 1 1 1 1
PORTFOLIO INVESTMENT $8,000.00 $0.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00 $69,000.00
PORTFOLIO PRESENT WORTH $6,686.33 $0.00 $4,135.67 $7,353.37 $4,796.20 $7,463.40 $30,434.96
MARR 15% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 8
REALIZED INITIAL INVESTMENT $8,000.00 $0.00 $10,000.00 $20,000.00 $19,000.00 $12,000.00 $69,000.00
REALIZED ANNUAL RETURN $3,200.00 $0.00 $3,070.00 $5,950.00 $5,150.00 $4,250.00 $21,620.00
REALIZED SALVAGE VALUE $1,000.00 $0.00 $1,100.00 $2,000.00 $2,100.00 $1,200.00 $7,400.00
NOTE: PROBLEMS 13 AND 14 ARE IDENTICAL EXCEPT FOR THE MARR AND THE LENGTH OF THE PLANNING HORIZON.
HOWEVER, VERY DIFFERENT SOLUTIONS ARE OBTAINED, DEMONSTRATING THE SENSITIVITY OF THE CAPITAL BUDGETING
SOLUTION TO SUCH CHANGES.
NOTICE: EXCEL’S RATE
FUNCTION DOES NOT WORK
FOR THESE VALUES. HOWEVER,
EXCEL’S IRR FUNCTION SHOWS
THAT THE IRR FOR INVESTMENT
M IS 37.181%.
PROBLEM 12.15
aI21 (H11) NOTE! CELL LETTERS AND NUMBERS DO NOT CORRESPOND TO THE
PICTURE IN THE TEXT BECAUSE OF FORMATTING IN THIS SOLUTION.
bC19:H19 (B9:G9)
IT IS THE SAME PROBLEM, HOWEVER.
cC19:H19 = BINARY (B9:G9 = BINARY)
I20<= I22 (H10<=H12)
SEE BELOW FOR DETAILS
LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00
SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64
INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08%
VALUE OF x 1 1 0 1 0 1
PORTFOLIO INVESTMENT $20,000.00 $40,000.00 $0.00 $50,000.00 $0.00 $60,000.00 $170,000.00
PORTFOLIO PRESENT WORTH $1,130.04 $1,271.30 $0.00 $4,378.92 $0.00 $3,672.64 $10,452.91
MARR 12% CAP CONSTRAINT $175,000.00
INVESTMENT PERIOD 10
`
dSET UP CELL C58 AS THE SUM OF X1+X2
REQUIRE CELL C58 TO BE <=1
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00
SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64
INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08%
VALUE OF x 1 0 1 1 0 1
PORTFOLIO INVESTMENT $20,000.00 $0.00 $30,000.00 $50,000.00 $0.00 $60,000.00 $160,000.00
PORTFOLIO PRESENT WORTH $1,130.04 $0.00 $847.53 $4,378.92 $0.00 $3,672.64 $10,029.15
MARR 12% CAP CONSTRAINT $175,000.00
INVESTMENT PERIOD 10
MUTUAL EXCLUSIVITY CONSTRAINT 1 C53+D53
e SET X2<=X3 AS A CONSTRAINT
THAT IS THE D89<=E89 CONSTRAINT LISTED
SEE BELOW FOR DETAILS
LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00
SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64
INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08%
VALUE OF x 1 0 1 1 0 1
PORTFOLIO INVESTMENT $20,000.00 $0.00 $30,000.00 $50,000.00 $0.00 $60,000.00 $160,000.00
PORTFOLIO PRESENT WORTH $1,130.04 $0.00 $847.53 $4,378.92 $0.00 $3,672.64 $10,029.15
MARR 12% CAP CONSTRAINT $175,000.00
INVESTMENT PERIOD 10
fSET SUM OF X’S TO <=4
AND SUM OF X’S >=3
THAT IS THE I125<=4
AND I25>=3
SEE BELOW FOR DETAILS
LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
ANNUAL RETURN $2,600.00 $5,025.00 $3,750.00 $6,775.00 $9,350.00 $7,850.00
SALVAGE VALUE $20,000.00 $40,000.00 $30,000.00 $50,000.00 $75,000.00 $60,000.00
PRESENT WORTH $1,130.04 $1,271.30 $847.53 $4,378.92 $1,977.58 $3,672.64
INTERNAL RATE OF RETURN 13.00% 12.56% 12.50% 13.55% 12.47% 13.08%
VALUE OF x 1 1 0 1 0 1 4
PORTFOLIO INVESTMENT $20,000.00 $40,000.00 $0.00 $50,000.00 $0.00 $60,000.00 $170,000.00
PORTFOLIO PRESENT WORTH $1,130.04 $1,271.30 $0.00 $4,378.92 $0.00 $3,672.64 $10,452.91
MARR 12% CAP CONSTRAINT $175,000.00
INVESTMENT PERIOD 10
PROBLEM 12.16
a I21 (H11) NOTE! CELL LETTERS AND NUMBERS DO NOT CORRESPOND TO THE
PICTURE IN THE TEXT BECAUSE OF FORMATTING IN THIS SOLUTION.
b C19:H19 (B9:G9)
IT IS THE SAME PROBLEM, HOWEVER.
c C19:H19 = BINARY (B9:G9 = BINARY)
I20<=I22 (H10<=H12)
SEE BELOW FOR DETAILS
LINEAR PROGRAMMING FORMULATION FOR A CAPITAL BUDGETING PROBLEM
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17
INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70%
VALUE OF x 1 0 0 1 1 1
PORTFOLIO INVESTMENT $25,000.00 $0.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $175,000.00
PORTFOLIO PRESENT WORTH $379.08 $0.00 $0.00 $2,937.86 $2,843.09 $3,222.17 $9,382.20
MARR 10% CAP CONSTRAINT $180,000.00
INVESTMENT PERIOD 5
d DETERMINE X4+X5
THEN, SET X4+X5<=1
THIS IS THE C57<=1 CONSTRAINT
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17
INTERNAL RATE OF RETURN 10.40% 10.71% 10.17% 11.94% 11.25% 11.70%
VALUE OF x 1 1 1 1 0 1
PORTFOLIO INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $0.00 $50,000.00 $180,000.00
PORTFOLIO PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $0.00 $3,222.17 $7,676.34
MARR 10% CAP CONSTRAINT $180,000.00
INVESTMENT PERIOD 5
MUTUAL EXCLUSIVITY CONSTRAINT 1 F51+G51
e SET THE CONSTRAINT X6<=X5
THIS IS THE H83<=G83 CONSTRAINT
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5 6
INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00
ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00
SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00