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
f DETERMINE THE SUM OF THE X‘S
SET THIS SUM = 3
THIS IS THE I115=3 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 0 0 0 1 1 1 3
PORTFOLIO INVESTMENT $0.00 $0.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $150,000.00
PORTFOLIO PRESENT WORTH $0.00 $0.00 $0.00 $2,937.86 $2,843.09 $3,222.17 $9,003.12
MARR 10% CAP CONSTRAINT $180,000.00
INVESTMENT PERIOD 5
PROBLEM 12.17
FALSE
A COUNTEREXAMPLE TO THIS IS SHOWN IN THE TEXT
PROBLEM 12.18
TRUE, IF THE INVESTMENTS HAVE THE SPECIAL STRUCTURE OF 100% SALVAGE VALUE AND UNIFORM ANNUAL RETURNS AND THERE ARE
NO MUTUALLY EXCLUSIVE, CONTINGENCY, OR OTHER CONSTRAINTS.
THIS IS BECAUSE WE ARE MAKING MULTIPLE INVESTMENTS AND EACH CAN BE ANY PERCENTAGE FROM 0% TO 100%
PROBLEM 12.19
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 2 4 5 3
PERCENT 100% 100% 100% 10%
TOTAL PW $44,158.51
TOTAL INVESTMENT $250,000.00
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
ANNUAL RETURN $10,800.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00
SALVAGE VALUE $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
PRESENT WORTH $6,488.60 $15,140.06 $5,407.16 $14,959.82 $13,517.91
INTERNAL RATE OF RETURN 14.40% 18.46% 15.00% 17.19% 15.75%
VALUE OF x 0 1 0.1 1 1
PORTFOLIO INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $0.00 $15,140.06 $540.72 $14,959.82 $13,517.91 $44,158.51
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
P’FOLIO IRR 16.90%
b PORTFOLIO PW
CAP CONSTRAINT $200,000.00 2, 4, 5(55.00%) $37,534.73
$250,000.00 2, 4, 5, 3(10.00%) $44,158.51
$300,000.00 2, 4, 5, 3, 1(6.67%) $49,457.53
c MARR 9.60% 2, 4, 5, 3(10.00%) $69,894.65
12.00% 2, 4, 5, 3(10.00%) $44,158.51 ***
14.40% 2, 4, 5, 3(10.00%) $21,252.08
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
ANNUAL RETURN $10,800.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00
SALVAGE VALUE $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
PRESENT WORTH $6,488.60 $15,140.06 $5,407.16 $14,959.82 $13,517.91
INTERNAL RATE OF RETURN 14.40% 18.46% 15.00% 17.19% 15.75%
VALUE OF x 0 1 0.1 1 1.000
PORTFOLIO INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $0.00 $15,140.06 $540.72 $14,959.82 $13,517.91 $44,158.51
MARR 12.00% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
P’FOLIO IRR 16.90%
d OPTIMAL PORTFOLIO 2 4 5 3
PERCENT 100% 100% 100% 10%
TOTAL PW $44,158.51
TOTAL INVESTMENT $250,000.00
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
ANNUAL RETURN $10,800.00 $12,000.00 $7,500.00 $13,750.00 $15,750.00
SALVAGE VALUE $75,000.00 $65,000.00 $50,000.00 $80,000.00 $100,000.00
PRESENT WORTH $6,488.60 $15,140.06 $5,407.16 $14,959.82 $13,517.91
INTERNAL RATE OF RETURN 14.40% 18.46% 15.00% 17.19% 15.75%
VALUE OF x 0 1 0.1 1 1
PORTFOLIO INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $0.00 $15,140.06 $540.72 $14,959.82 $13,517.91 $44,158.51
MARR 12.00% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $750.00 $13,750.00 $15,750.00 $42,250.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $5,000.00 $80,000.00 $100,000.00 $250,000.00
P’FOLIO IRR 16.90%
PROBLEM 12.21
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 1 2 5 3 4
PERCENT 100% 100% 100% 100% 35%
TOTAL PW $123,283.35
TOTAL INVESTMENT $250,000.00
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $22,000.00 $17,000.00
SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 $36,047.76 $33,163.94
INTERNAL RATE OF RETURN 30.00% 30.00% 23.53% 22.00% 26.15%
VALUE OF x 1 1 1 0.35 1
PORTFOLIO INVESTMENT $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 $12,616.72 $33,163.94 $123,283.35
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $7,700.00 $17,000.00 $64,200.00
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
P’FOLIO IRR 25.68%
b PORTFOLIO PW
CAP CONSTRAINT $200,000.00 1, 2, 5, 3(82.36% $104,432.49
$250,000.00 1, 2, 5, 3, 4(35%) $123,283.35
$300,000.00 1, 2, 5, 3, 4(85%) $141,307.23
c MARR 9.60% 1, 2, 5, 3, 4(35%) $153,959.71
12.00% 1, 2, 5, 3, 4(35%) $123,283.35
14.40% 1, 2, 5, 3, 4(35%) $95,889.39 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $22,000.00 $17,000.00
SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
PRESENT WORTH $13,261.30 $21,218.08 $26,386.58 $25,842.53 $25,978.54
INTERNAL RATE OF RETURN 30.00% 30.00% 23.53% 22.00% 26.15%
VALUE OF x 1 1 1 0.35 1
PORTFOLIO INVESTMENT $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $13,261.30 $21,218.08 $26,386.58 $9,044.89 $25,978.54 $95,889.39
MARR 14.40% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $7,700.00 $17,000.00 $64,200.00
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $35,000.00 $65,000.00 $250,000.00
P’FOLIO IRR 25.68%
d OPTIMAL PORTFOLIO 1 2 3 4
PERCENT 100% 100% 100% 100%
TOTAL PW $113,550.45
TOTAL INVESTMENT $250,000.00
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $22,000.00 $17,000.00
SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $100,000.00 $65,000.00
PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 $36,047.76 $33,163.94
INTERNAL RATE OF RETURN 30.00% 30.00% 23.53% 22.00% 26.15%
VALUE OF x 1 1 1 1 0
PORTFOLIO INVESTMENT $25,000.00 $40,000.00 $85,000.00 $100,000.00 $0.00 $250,000.00
PORTFOLIO PRESENT WORTH $16,221.49 $25,954.39 $35,326.81 $36,047.76 $0.00 $113,550.45
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $100,000.00 $0.00 $250,000.00
REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $22,000.00 $0.00 $61,500.00
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $100,000.00 $0.00 $250,000.00
P’FOLIO IRR 24.60%
PROBLEM 12.22
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 2 1 4
PERCENT 100% 100% 43.75%
TOTAL PW $68,171.11
TOTAL INVESTMENT $350,000.00
SEE BELOW FOR DETAILS
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 $27,382.54 $29,208.04 $13,691.27 $26,469.79 $27,382.54
INTERNAL RATE OF RETURN 16.00% 16.92% 15.00% 15.63% 15.00%
VALUE OF x 1 1 0 0.4375 0
PORTFOLIO INVESTMENT $150,000.00 $130,000.00 $0.00 $70,000.00 $0.00 $350,000.00
PORTFOLIO PRESENT WORTH $27,382.54 $29,208.04 $0.00 $11,580.53 $0.00 $68,171.11
MARR 12% CAP CONSTRAINT $350,000.00
INVESTMENT PERIOD 7
REALIZED INITIAL INVESTMENT $150,000.00 $130,000.00 $0.00 $70,000.00 $0.00 $350,000.00
REALIZED ANNUAL RETURN $24,000.00 $22,000.00 $0.00 $10,937.50 $0.00 $56,937.50
REALIZED SALVAGE VALUE $150,000.00 $130,000.00 $0.00 $70,000.00 $0.00 $350,000.00
P’FOLIO IRR 16.27%
PORTFOLIO PW
b CAP CONSTRAINT $280,000.00 2, 1 $56,590.58 ***
$350,000.00 2, 1, 4(43.75%) $68,171.11
$420,000.00 2, 1, 4(87.5%) $79,751.65
c MARR 9.60% 2, 1, 4(43.75%) $115,128.65
12.00% 2, 1, 4(43.75%) $68,171.11
14.40% 2, 1, 4(43.75%) $27,695.48
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 $27,382.54 $29,208.04 $13,691.27 $26,469.79 $27,382.54
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 $27,382.54 $29,208.04 $0.00 $0.00 $0.00 $56,590.58
MARR 12.00% CAP CONSTRAINT $280,000.00
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%
d OPTIMAL PORTFOLIO 2 4 1
PERCENT 100% 100% 40%
TOTAL PW $66,630.85
TOTAL INVESTMENT $350,000.00
SEE BELOW FOR DETAILS
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 $27,382.54 $29,208.04 $13,691.27 $26,469.79 $27,382.54
INTERNAL RATE OF RETURN 16.00% 16.92% 15.00% 15.63% 15.00%
VALUE OF x 0.4 1 0 1 0
PORTFOLIO INVESTMENT $60,000.00 $130,000.00 $0.00 $160,000.00 $0.00 $350,000.00
PORTFOLIO PRESENT WORTH $10,953.02 $29,208.04 $0.00 $26,469.79 $0.00 $66,630.85
MARR 12% CAP CONSTRAINT $350,000.00
INVESTMENT PERIOD 7
REALIZED INITIAL INVESTMENT $60,000.00 $130,000.00 $0.00 $160,000.00 $0.00 $350,000.00
REALIZED ANNUAL RETURN $9,600.00 $22,000.00 $0.00 $25,000.00 $0.00 $56,600.00
REALIZED SALVAGE VALUE $60,000.00 $130,000.00 $0.00 $160,000.00 $0.00 $350,000.00
P’FOLIO IRR 16.17%
PROBLEM 12.23
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 1 3 2 4
PERCENT 100% 100% 100.00% 58.33%
TOTAL PW $99,508.15
TOTAL INVESTMENT $1,250,000.00
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 1 1 0.583333333 0
PORTFOLIO INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
PORTFOLIO PRESENT WORTH $37,907.87 $22,744.72 $18,953.93 $19,901.63 $0.00 $99,508.15
MARR 10% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
REALIZED ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $40,250.00 $0.00 $151,250.00
REALIZED SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
P’FOLIO IRR 12.10%
LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
ALTERNATIVE
PERCENT
TOTAL PW
TOTAL INVESTMENT
b PORTFOLIO PW
CAP CONSTRAINT $1,000,000.00 1, 3, 2, 4(16.67%) $85,292.70
$1,250,000.00 1, 3, 2, 4(58.33%) $99,508.15
$1,500,000.00 1, 3, 2, 4 $113,723.60
c MARR 8.00% 1, 3, 2, 4(58.33%) $204,626.39 ***
10.00% 1, 3, 2, 4(58.33%) $99,508.15
12.00% 1, 3, 2 $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 $71,868.78 $47,912.52 $35,934.39 $83,846.91 $59,890.65
INTERNAL RATE OF RETURN 12.50% 12.00% 12.50% 11.50% 11.00%
VALUE OF x 1 1 1 0.583333333 0
PORTFOLIO INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
PORTFOLIO PRESENT WORTH $71,868.78 $47,912.52 $35,934.39 $48,910.70 $0.00 $204,626.39
MARR 8.00% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
REALIZED ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $40,250.00 $0.00 $151,250.00
REALIZED SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
P’FOLIO IRR 12.10%
d OPTIMAL PORTFOLIO 1 3 2 4
PERCENT 100% 100% 100% 58.33%
TOTAL PW $99,508.15
TOTAL INVESTMENT $1,250,000.00
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 1 1 0.583333333 0
PORTFOLIO INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
PORTFOLIO PRESENT WORTH $37,907.87 $22,744.72 $18,953.93 $19,901.63 $0.00 $99,508.15
MARR 10% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
REALIZED ANNUAL RETURN $50,000.00 $36,000.00 $25,000.00 $40,250.00 $0.00 $151,250.00
REALIZED SALVAGE VALUE $400,000.00 $300,000.00 $200,000.00 $350,000.00 $0.00 $1,250,000.00
P’FOLIO IRR 12.10%
PROBLEM 12.24
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 5 4 2 3
PERCENT 100% 100% 100.00% 17.65%
TOTAL PW $20,883.82
TOTAL INVESTMENT $250,000.00
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
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 0.764705882 1 1
PORTFOLIO INVESTMENT $0.00 $60,000.00 $65,000.00 $100,000.00 $75,000.00 $300,000.00
PORTFOLIO PRESENT WORTH $0.00 $3,169.87 $1,212.01 $6,339.73 $11,094.53 $21,816.13
MARR 10% CAP CONSTRAINT $300,000.00
d OPTIMAL PORTFOLIO 5 4 2 3
PERCENT 100% 100% 100% 17.65%
TOTAL PW $20,883.82
TOTAL INVESTMENT $250,000.00
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 0.176470588 1 1
PORTFOLIO INVESTMENT $0.00 $60,000.00 $15,000.00 $100,000.00 $75,000.00 $250,000.00
PORTFOLIO PRESENT WORTH $0.00 $3,169.87 $279.69 $6,339.73 $11,094.53 $20,883.82
MARR 10% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 4
REALIZED INITIAL INVESTMENT $0.00 $60,000.00 $15,000.00 $100,000.00 $75,000.00 $250,000.00
REALIZED ANNUAL RETURN $0.00 $7,000.00 $1,588.24 $12,000.00 $11,000.00 $31,588.24
REALIZED SALVAGE VALUE $0.00 $60,000.00 $15,000.00 $100,000.00 $75,000.00 $250,000.00
P’FOLIO IRR 12.64%
PROBLEM 12.25
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 1 4 2
PERCENT 100% 100% 50.00%
TOTAL PW $624,696.11
TOTAL INVESTMENT $1,000,000.00
SEE BELOW FOR DETAILS
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
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
INTERNAL RATE OF RETURN 24.04% 21.94% 19.99% 22.04% 19.96%
VALUE OF x 1 0.5 0 1 0
PORTFOLIO INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
PORTFOLIO PRESENT WORTH $210,842.53 $116,866.94 $0.00 $296,986.63 $0.00 $624,696.11
MARR 10% CAP CONSTRAINT $1,000,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
REALIZED ANNUAL RETURN $80,000.00 $50,000.00 $0.00 $125,000.00 $0.00 $255,000.00
REALIZED SALVAGE VALUE $50,000.00 $25,000.00 $0.00 $75,000.00 $0.00 $150,000.00
P’FOLIO IRR 22.62%
b PORTFOLIO PW
CAP CONSTRAINT $800,000.00 1, 4 $507,829.17
$1,000,000.00 1, 4, 2(50%) $624,696.11 ***
$1,200,000.00 1, 4, 2 $741,563.04
c MARR 8.00% 1, 4, 2(50%) $780,549.78
10.00% 1, 4, 2(50%) $624,696.11
12.00% 1, 4, 2(50%) $489,102.86
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
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
INTERNAL RATE OF RETURN 24.04% 21.94% 19.99% 22.04% 19.96%
VALUE OF x 1 0.5 0 1 0
PORTFOLIO INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
PORTFOLIO PRESENT WORTH $210,842.53 $116,866.94 $0.00 $296,986.63 $0.00 $624,696.11
MARR 10% CAP CONSTRAINT $1,000,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
REALIZED ANNUAL RETURN $80,000.00 $50,000.00 $0.00 $125,000.00 $0.00 $255,000.00
REALIZED SALVAGE VALUE $50,000.00 $25,000.00 $0.00 $75,000.00 $0.00 $150,000.00
P’FOLIO IRR 22.62%
d OPTIMAL PORTFOLIO 1 4 2
PERCENT 100% 100% 50%
TOTAL PW $624,696.11
TOTAL INVESTMENT $1,000,000.00
SEE BELOW FOR DETAILS
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
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
INTERNAL RATE OF RETURN 24.04% 21.94% 19.99% 22.04% 19.96%
VALUE OF x 1 0.5 0 1 0
VALUE IF X ROUNDED UP 1 1 0 1 0 3
PORTFOLIO INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
PORTFOLIO PRESENT WORTH $210,842.53 $116,866.94 $0.00 $296,986.63 $0.00 $624,696.11
MARR 10% CAP CONSTRAINT $1,000,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $300,000.00 $200,000.00 $0.00 $500,000.00 $0.00 $1,000,000.00
REALIZED ANNUAL RETURN $80,000.00 $50,000.00 $0.00 $125,000.00 $0.00 $255,000.00
REALIZED SALVAGE VALUE $50,000.00 $25,000.00 $0.00 $75,000.00 $0.00 $150,000.00
P’FOLIO IRR 22.62%
PROBLEM 12.26
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 6 1 7 9 4 5 10
PERCENT 100% 100% 100.00% 100% 100% 100.00% 50%
TOTAL PW $1,058,608.60
TOTAL INVESTMENT $2,500,000.00
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%
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 0.428571429 1 1 0 1 0
PORTFOLIO INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $150,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $0.00 $2,000,000.00
PORTFOLIO PRESENT WORTH $74,698.43 $0.00 $0.00 $104,276.47 $56,591.75 $212,649.62 $220,179.55 $0.00 $216,263.80 $0.00 $884,659.61
MARR 10% CAP CONSTRAINT $2,000,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $150,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $0.00 $2,000,000.00
d OPTIMAL PORTFOLIO 6 1 7 9 4 10 5
PERCENT 100% 100% 100% 100% 100% 100% 14.29%
TOTAL PW $1,043,918.42
TOTAL INVESTMENT $2,500,000.00
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%