e OPTIMAL PORTFOLIO 6 1 7 9 4 5 10
PERCENT 100% 100% 100% 100% 100% 100% 50.00%
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%
VALUE OF x 1 0 0 1 1 1 1 0 1 0.5
PORTFOLIO INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $350,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $300,000.00 $2,500,000.00
PORTFOLIO PRESENT WORTH $74,698.43 $0.00 $0.00 $104,276.47 $132,047.41 $212,649.62 $220,179.55 $0.00 $216,263.80 $98,493.32 $1,058,608.60
MARR 10% CAP CONSTRAINT $2,500,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $150,000.00 $0.00 $0.00 $275,000.00 $350,000.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $300,000.00 $2,500,000.00
REALIZED ANNUAL RETURN $35,000.00 $0.00 $0.00 $60,000.00 $75,000.00 $95,000.00 $110,000.00 $0.00 $120,000.00 $62,500.00 $557,500.00
REALIZED SALVAGE VALUE $25,000.00 $0.00 $0.00 $27,500.00 $55,000.00 $75,000.00 $50,000.00 $0.00 $75,000.00 $37,500.00 $345,000.00
P’FOLIO IRR 18.77%
f OPTIMAL PORTFOLIO 6 1 7 9 4 2 10
PERCENT 100% 100% 100% 100% 100% 100% 75.00%
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 1 0 1 0 1 1 0 1 0.75
VALUE OF X ROUNDED UP 1 1 0 1 0 1 1 0 1 1 7
PORTFOLIO INVESTMENT $150,000.00 $200,000.00 $0.00 $275,000.00 $0.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $450,000.00 $2,500,000.00
PORTFOLIO PRESENT WORTH $74,698.43 $52,770.71 $0.00 $104,276.47 $0.00 $212,649.62 $220,179.55 $0.00 $216,263.80 $147,739.98 $1,028,578.56
MARR 10% CAP CONSTRAINT $2,500,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $150,000.00 $200,000.00 $0.00 $275,000.00 $0.00 $400,000.00 $475,000.00 $0.00 $550,000.00 $450,000.00 $2,500,000.00
REALIZED ANNUAL RETURN $35,000.00 $38,000.00 $0.00 $60,000.00 $0.00 $95,000.00 $110,000.00 $0.00 $120,000.00 $93,750.00 $551,750.00
REALIZED SALVAGE VALUE $25,000.00 $50,000.00 $0.00 $27,500.00 $0.00 $75,000.00 $50,000.00 $0.00 $75,000.00 $56,250.00 $358,750.00
P’FOLIO IRR 18.52%
MUTUAL EXCLUSIVITY CONSTRAINT 1 C183+E183+G183
CONTINGENCY CONSTRAINT 1 D184+G184
PROBLEM 12.27
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 4 6 5 2 1
PERCENT 100% 100% 100% 100% 60%
TOTAL PW $10,178.26
TOTAL INVESTMENT $200,000.00
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 0.6 1 0 1 1 1
PORTFOLIO INVESTMENT $15,000.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $200,000.00
PORTFOLIO PRESENT WORTH $227.45 $947.70 $0.00 $2,937.86 $2,843.09 $3,222.17 $10,178.26
MARR 10% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $15,000.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $200,000.00
REALIZED ANNUAL RETURN $1,560.00 $3,750.00 $0.00 $4,775.00 $6,750.00 $5,850.00 $22,685.00
REALIZED SALVAGE VALUE $15,000.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $200,000.00
P’FOLIO IRR 11.34%
b PORTFOLIO PW
CAP CONSTRAINT $160,000.00 4, 6, 5, 2(28.57%) $9,273.89
$200,000.00 4, 6, 5, 2, 1(60%) $10,178.26
$240,000.00 4, 6, 5, 2, 1, 3 $10,519.43 ***
c MARR 8.00% 4, 6, 5, 2, 1(60%) $26,691.27
10.00% 4, 6, 5, 2, 1(60%) $10,178.26
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 $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 1 1
PORTFOLIO INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $240,000.00
PORTFOLIO PRESENT WORTH $379.08 $947.70 $189.54 $2,937.86 $2,843.09 $3,222.17 $10,519.43
MARR 10% CAP CONSTRAINT $240,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $240,000.00
REALIZED ANNUAL RETURN $2,600.00 $3,750.00 $3,050.00 $4,775.00 $6,750.00 $5,850.00 $26,775.00
REALIZED SALVAGE VALUE $25,000.00 $35,000.00 $30,000.00 $40,000.00 $60,000.00 $50,000.00 $240,000.00
P’FOLIO IRR 11.16%
d OPTIMAL PORTFOLIO 4 6 5 2 1
PERCENT 100% 100% 83% 100% 100%
TOTAL PW $9,856.05
TOTAL INVESTMENT $200,000.00
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 0.833333333 1
PORTFOLIO INVESTMENT $25,000.00 $35,000.00 $0.00 $40,000.00 $50,000.00 $50,000.00 $200,000.00
PORTFOLIO PRESENT WORTH $379.08 $947.70 $0.00 $2,937.86 $2,369.24 $3,222.17 $9,856.05
MARR 10% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $35,000.00 $0.00 $40,000.00 $50,000.00 $50,000.00 $200,000.00
REALIZED ANNUAL RETURN $2,600.00 $3,750.00 $0.00 $4,775.00 $5,625.00 $5,850.00 $22,600.00
REALIZED SALVAGE VALUE $25,000.00 $35,000.00 $0.00 $40,000.00 $50,000.00 $50,000.00 $200,000.00
P’FOLIO IRR 11.30%
e OPTIMAL PORTFOLIO 4 6 5 2 1
PERCENT 100% 100% 100% 100% 50%
TOTAL PW $10,140.35
TOTAL INVESTMENT $197,500.00
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 0.5 1 0 1 1 1
VALUE OF 4x 2 4 0 4 4 4
PORTFOLIO INVESTMENT $12,500.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $197,500.00
PORTFOLIO PRESENT WORTH $189.54 $947.70 $0.00 $2,937.86 $2,843.09 $3,222.17 $10,140.35
MARR 10% CAP CONSTRAINT $200,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $12,500.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $197,500.00
REALIZED ANNUAL RETURN $1,300.00 $3,750.00 $0.00 $4,775.00 $6,750.00 $5,850.00 $22,425.00
REALIZED SALVAGE VALUE $12,500.00 $35,000.00 $0.00 $40,000.00 $60,000.00 $50,000.00 $197,500.00
P’FOLIO IRR 11.35%
PROBLEM 12.28
a LOAD THE PORTFOLIO FROM HIGHEST IRR TO LOWEST IRR
OPTIMAL PORTFOLIO 4 1 2 3
PERCENT 100% 100% 100% 37.5%
TOTAL PW $623,633.06
TOTAL INVESTMENT $500,000.00 YEAR 0
$175,000.00 YEAR 1
SEE BELOW FOR DETAILS
OVERALL
EOY CF(1) CF(2) CF(3) CF(4) P’FOLIO CF
PORTFOLIO PRESENT WORTH $130,503.30 $184,867.81 $158,896.41 $240,163.49 $714,431.01
MARR 10% CAP CONSTRAINT YR 0 $600,000.00
INVESTMENT PERIOD 10 CAP CONSTRAINT YR 1 $175,000.00
P’FOLIO IRR 27.38%
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 $207,500
6 $50,000 $70,000 $75,000 $85,000 $217,500
7 $50,000 $70,000 $75,000 $85,000 $217,500
8 $50,000 $70,000 $75,000 $85,000 $217,500
9 $50,000 $70,000 $75,000 $85,000 $217,500
10 $75,000 $100,000 $75,000 $100,000 $275,000
PRESENT WORTH
$130,503 $184,868 $181,596 $240,163 $581,081
INTERNAL RATE OF RETURN 27.59% 26.85% 26.28% 28.51% 27.50%
VALUE OF x
0.50 1.00 0.50 1.00
PORTFOLIO INVESTMENT YR 0 $25,000.00 $125,000.00 $100,000.00 $250,000.00 $500,000.00
PORTFOLIO INVESTMENT YR 1 $50,000.00 $75,000.00 $0.00 $0.00 $125,000.00
PORTFOLIO PRESENT WORTH $65,251.65 $184,867.81 $90,797.95 $240,163.49 $581,080.90
MARR 10% CAP CONSTRAINT YR 0 $500,000.00
INVESTMENT PERIOD 10 CAP CONSTRAINT YR 1 $125,000.00
P’FOLIO IRR 27.50%
SOLVER COULD NOT FIND A SOLUTION TO THIS
FORMULATION. IT IS OFTEN THE CASE, PARTICULARLY
WITH DIVISIBLE INVESTMENTS, THAT SOLVER CANNOT
FIND A SOLUTION. THE CONSTRAINT THAT LIMITS FULL
OR PARTIAL INVESTMENT TO NO MORE THAN 3
INVESTMENTS IS THE SOURCE OF THE DIFFICULTY . IN
THIS CASE, IF YOU CAN ONLY CHOOSE 3 INVESTMENTS
AND CHOOSING THE 3 WITH THE GREATEST PRESENT
HERE, WE INTERPRET MUTUALLY EXCLUSIVE TO MEAN ABSOLUTE EXCLUSION. IN OTHER WORDS, IF EITHER INVESTMENT IS PURSUED PARTIALLY
OR FULLY, THE OTHER INVESTMENT CANNOT BE PURSUED AT ALL. FOR THAT REASON, CELL E87 IS THE PRODUCT OF THE DECISION VARIABLES
FOR INVESTMENTS D AND F. THE SOLVER CONSTRAINT IS THAT THE VALUE OF CELL E87 MUST EQUAL ZERO.
PROBLEM 12.30
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 p 100.00% 100.00% 100.00% 25.00% 0.00% 100.00%
PORTFOLIO INVESTMENT $8,000.00 $15,000.00 $10,000.00 $5,000.00 $0.00 $12,000.00 $50,000.00
PORTFOLIO PRESENT WORTH $6,686.33 $6,886.86 $4,135.67 $1,838.34 $0.00 $7,463.40 $27,010.60
MARR 15% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 8
REALIZED INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $5,000.00 $0.00 $12,000.00 $50,000.00
REALIZED ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $1,487.50 $0.00 $4,250.00 $16,757.50
REALIZED SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $500.00 $0.00 $1,200.00 $5,550.00
PORTFOLIO IRR 29.75%
INVEST IN 100% OF M, N, O, AND R; INVEST IN 25% OF P (SAME ANSWER AS OBTAINED FOR PROBLEM 12.29)
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 p 0.00% 100.00% 0.00% 100.00% 0.00% 100.00%
LET X = 1 IF p > 0; OTHERWISE, X = 0 0 1 0 1 0 1 3
PORTFOLIO INVESTMENT $0.00 $15,000.00 $0.00 $20,000.00 $0.00 $12,000.00 $47,000.00
PORTFOLIO PRESENT WORTH $0.00 $6,886.86 $0.00 $7,353.37 $0.00 $7,463.40 $21,703.62
MARR 15% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 8
REALIZED INITIAL INVESTMENT $0.00 $15,000.00 $0.00 $20,000.00 $0.00 $12,000.00 $47,000.00
REALIZED ANNUAL RETURN $0.00 $4,750.00 $0.00 $5,950.00 $0.00 $4,250.00 $14,950.00
REALIZED SALVAGE VALUE $0.00 $1,750.00 $0.00 $2,000.00 $0.00 $1,200.00 $4,950.00
PORTFOLIO IRR 27.73%
c) 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 p 100.00% 100.00% 100.00% 0.00% 26.32% 100.00%
PORTFOLIO INVESTMENT $8,000.00 $15,000.00 $10,000.00 $0.00 $5,000.00 $12,000.00 $50,000.00
PORTFOLIO PRESENT WORTH $6,686.33 $6,886.86 $4,135.67 $0.00 $1,262.16 $7,463.40 $26,434.41
SOLVER COULD NOT FIND A SOLUTION TO THIS
FORMULATION. IT IS OFTEN THE CASE, PARTICULARLY
WITH DIVISIBLE INVESTMENTS, THAT SOLVER CANNOT
FIND A SOLUTION. THE CONSTRAINT THAT LIMITS FULL
OR PARTIAL INVESTMENT TO NO MORE THAN 3
INVESTMENTS IS THE SOURCE OF THE DIFFICULTY . IN
THIS CASE, IF YOU CAN ONLY CHOOSE 3 INVESTMENTS
AND CHOOSING THE 3 WITH THE GREATEST PRESENT
WORTH VALUES DOES NOT VIOLATE THE CAPITAL
MARR 15% CAP CONSTRAINT $50,000.00
INVESTMENT PERIOD 8
REALIZED INITIAL INVESTMENT $8,000.00 $15,000.00 $10,000.00 $0.00 $5,000.00 $12,000.00 $50,000.00
REALIZED ANNUAL RETURN $3,200.00 $4,750.00 $3,070.00 $0.00 $1,355.26 $4,250.00 $16,625.26
REALIZED SALVAGE VALUE $1,000.00 $1,750.00 $1,100.00 $0.00 $552.63 $1,200.00 $5,602.63
PORTFOLIO IRR 29.45%
0.00% P & R MUTUALLY EXCLUSIVE
INVEST FULLY (100%) IN M, N, O, AND R. INVEST PARTIALLY (26.32%) IN Q (SAME ANSWER AS FOR PROBLEM 12.29)
HERE, WE INTERPRET MUTUALLY EXCLUSIVE TO MEAN ABSOLUTE EXCLUSION. IN OTHER WORDS, IF EITHER INVESTMENT IS PURSUED PARTIALLY OR
FULLY, THE OTHER INVESTMENT CANNOT BE PURSUED AT ALL. FOR THAT REASON, CELL E87 IS THE PRODUCT OF THE DECISION VARIABLES FOR
INVESTMENTS D AND F. THE SOLVER CONSTRAINT IS THAT THE VALUE OF CELL E87 MUST EQUAL ZERO.
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00
SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24
INTERNAL RATE OF RETURN 25.00% 20.00% 23.13% 22.50% 20.36%
VALUE OF x 0 0 1 1 0
PORTFOLIO INVESTMENT $0.00 $0.00 $40,000.00 $50,000.00 $0.00 $90,000.00
PORTFOLIO PRESENT WORTH $0.00 $0.00 $9,212.88 $10,111.69 $0.00 $19,324.57
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $0.00 $0.00 $40,000.00 $50,000.00 $0.00 $90,000.00
REALIZED ANNUAL RETURN $0.00 $0.00 $9,250.00 $11,250.00 $0.00 $20,500.00
REALIZED SALVAGE VALUE $0.00 $0.00 $40,000.00 $50,000.00 $0.00 $90,000.00
PORTFOLIO IRR 22.78%
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00
SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24
INTERNAL RATE OF RETURN 25.00% 20.00% 23.13% 22.50% 20.36%
VALUE OF x 1 1 0 1 0
PORTFOLIO INVESTMENT $15,000.00 $25,000.00 $0.00 $50,000.00 $0.00 $90,000.00
PORTFOLIO PRESENT WORTH $4,718.79 $2,247.04 $0.00 $10,111.69 $0.00 $17,077.53
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $15,000.00 $25,000.00 $0.00 $50,000.00 $0.00 $90,000.00
REALIZED ANNUAL RETURN $3,750.00 $5,000.00 $0.00 $11,250.00 $0.00 $20,000.00
REALIZED SALVAGE VALUE $15,000.00 $25,000.00 $0.00 $50,000.00 $0.00 $90,000.00
PORTFOLIO IRR 22.22%
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00
SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24
INTERNAL RATE OF RETURN 25.00% 20.00% 23.13% 22.50% 20.36%
VALUE OF x 1 1 1 0 0
PORTFOLIO INVESTMENT $15,000.00 $25,000.00 $40,000.00 $0.00 $0.00 $80,000.00
PORTFOLIO PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $0.00 $0.00 $16,178.71
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
MUTUALLY EXCLUSIVE CONSTRAINT 1
REALIZED INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $0.00 $0.00 $80,000.00
REALIZED ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $0.00 $0.00 $18,000.00
REALIZED SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $0.00 $0.00 $80,000.00
PORTFOLIO IRR 22.50%
EOY CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P’FOLIO)
0 -$15,000.00 -$18,000.00 -$20,000.00 –$25,000.00 -$30,000.00 -$40,000.00 -$100,000.00
1 $4,500.00 $3,000.00 $4,000.00 $6,500.00 $6,000.00 $15,000.00 $30,000.00
2 $4,500.00 $4,500.00 $5,000.00 $6,500.00 $9,000.00 $15,000.00 $31,000.00
3 $4,500.00 $6,000.00 $6,000.00 $6,500.00 $12,000.00 $25,000.00 $42,000.00
4 $4,500.00 $7,500.00 $7,000.00 $6,500.00 $15,000.00 $0.00 $18,000.00
5 $4,500.00 $9,000.00 $8,000.00 $12,500.00 $0.00 $0.00 $25,000.00
PW $2,058.54 $3,665.06 $2,024.95 $3,365.64 $2,153.54 $4,815.93 $12,265.06
VALUE OF X 1 0 1 1 0 1 4
P’FOLIO INV $15,000.00 $0.00 $20,000.00 $25,000.00 $0.00 $40,000.00 $100,000.00
P’FOLIO PW $2,058.54 $0.00 $2,024.95 $3,365.64 $0.00 $4,815.93 $12,265.06
MARR 10.00% CAPITAL LIMIT $100,000.00
INV PERIOD 5 P’FOLIO IRR 14.94%
MUTUALLY EXCLUSIVE CONSTRAINT 1 =B9+C9
EITHER/OR CONTINGENCY CONSTRAINT 2 =D9+E9
EOY CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P’FOLIO)
0 -$15,000.00 -$18,000.00 -$20,000.00 –$25,000.00 -$30,000.00 -$40,000.00 -$83,000.00
1 $4,500.00 $3,000.00 $4,000.00 $6,500.00 $6,000.00 $15,000.00 $24,500.00
2 $4,500.00 $4,500.00 $5,000.00 $6,500.00 $9,000.00 $15,000.00 $26,000.00
3 $4,500.00 $6,000.00 $6,000.00 $6,500.00 $12,000.00 $25,000.00 $37,500.00
4 $4,500.00 $7,500.00 $7,000.00 $6,500.00 $15,000.00 $0.00 $14,000.00
5 $4,500.00 $9,000.00 $8,000.00 $12,500.00 $0.00 $0.00 $21,500.00
PW $2,058.54 $3,665.06 $2,024.95 $3,365.64 $2,153.54 $4,815.93 $11,846.63
VALUE OF X 0 1 0 1 0 1 3
P’FOLIO INV $0.00 $18,000.00 $0.00 $25,000.00 $0.00 $40,000.00 $83,000.00
P’FOLIO PW $0.00 $3,665.06 $0.00 $3,365.64 $0.00 $4,815.93 $11,846.63
MARR 10.00% CAPITAL LIMIT $100,000.00
INV PERIOD 5 P’FOLIO IRR 15.70%
MUTUALLY EXCLUSIVE CONSTRAINT 1 =B9+C9
EITHER/OR CONTINGENCY CONSTRAINT 1 =D9+E9
EOY CF(1) CF(2) CF(3) CF(4) CF(5) CF(6) CF(P’FOLIO)
0 -$15,000.00 -$18,000.00 -$20,000.00 –$22,000.00 -$35,000.00 -$40,000.00 -$75,000.00
1 $4,500.00 $10,000.00 $4,000.00 $6,500.00 $6,000.00 $10,000.00 $25,000.00
2 $4,500.00 $7,500.00 $5,000.00 $6,000.00 $6,900.00 $10,000.00 $23,000.00
3 $4,500.00 $5,000.00 $6,000.00 $5,500.00 $7,935.00 $10,000.00 $21,000.00
4 $4,500.00 $2,500.00 $7,000.00 $5,000.00 $9,125.25 $10,000.00 $19,000.00
5 $4,500.00 $5,000.00 $8,000.00 $8,500.00 $15,494.04 $15,000.00 $26,000.00
PW $2,058.54 $5,857.97 $2,024.95 $1,692.90 -$2,028.04 $1,012.47 $11,634.36
VALUE OF X 1 1 1 1 0 0 4
P’FOLIO INV $15,000.00 $18,000.00 $20,000.00 $22,000.00 $0.00 $0.00 $75,000.00
P’FOLIO PW $2,058.54 $5,857.97 $2,024.95 $1,692.90 $0.00 $0.00 $11,634.36
MARR 10.00% CAPITAL LIMIT $100,000.00
INV PERIOD 5
P’FOLIO IRR
15.98%
MUTUALLY EXCLUSIVE CONSTRAINT 2 =B9+C9
EITHER/OR CONTINGENCY CONSTRAINT 2 =D9+E9
ECONOMICALLY VIABLE INVESTMENTS SORTED BY IRR
INVESTMENT OPPORTUNITY 1 3 4 5 2
INITIAL INVESTMENT $15,000.00 $40,000.00 $50,000.00 $70,000.00 $25,000.00
ANNUAL RETURN $3,750.00 $9,250.00 $11,250.00 $14,250.00 $5,000.00
SALVAGE VALUE $15,000.00 $40,000.00 $50,000.00 $70,000.00 $25,000.00
PRESENT WORTH $4,718.79 $9,212.88 $10,111.69 $7,415.24 $2,247.04
INTERNAL RATE OF RETURN 25.00% 23.13% 22.50% 20.36% 20.00%
VALUE OF x 1 1 0.9 0 0
PORTFOLIO INVESTMENT $15,000.00 $40,000.00 $45,000.00 $0.00 $0.00 $100,000.00
PORTFOLIO PRESENT WORTH $4,718.79 $9,212.88 $9,100.52 $0.00 $0.00 $23,032.19
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $15,000.00 $40,000.00 $45,000.00 $0.00 $0.00 $100,000.00
REALIZED ANNUAL RETURN $3,750.00 $9,250.00 $10,125.00 $0.00 $0.00 $23,125.00
REALIZED SALVAGE VALUE $15,000.00 $40,000.00 $45,000.00 $0.00 $0.00 $100,000.00
PORTFOLIO IRR 23.13%
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00
SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24
INTERNAL RATE OF RETURN 25.00% 20.00% 23.13% 22.50% 20.36%
VALUE OF x 1 0 1 0.9 0
PORTFOLIO INVESTMENT $15,000.00 $0.00 $40,000.00 $45,000.00 $0.00 $100,000.00
PORTFOLIO PRESENT WORTH $4,718.79 $0.00 $9,212.88 $9,100.52 $0.00 $23,032.19
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $15,000.00 $0.00 $40,000.00 $45,000.00 $0.00 $100,000.00
REALIZED ANNUAL RETURN $3,750.00 $0.00 $9,250.00 $10,125.00 $0.00 $23,125.00
REALIZED SALVAGE VALUE $15,000.00 $0.00 $40,000.00 $45,000.00 $0.00 $100,000.00
PORTFOLIO IRR 23.13%
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
ANNUAL RETURN $3,750.00 $5,000.00 $9,250.00 $11,250.00 $14,250.00
SALVAGE VALUE $15,000.00 $25,000.00 $40,000.00 $50,000.00 $70,000.00
PRESENT WORTH $4,718.79 $2,247.04 $9,212.88 $10,111.69 $7,415.24
INTERNAL RATE OF RETURN 25.00% 20.00% 23.13% 22.50% 20.36%
VALUE OF x 1 0 1 0 0.642857143
PORTFOLIO INVESTMENT $15,000.00 $0.00 $40,000.00 $0.00 $45,000.00 $100,000.00
PORTFOLIO PRESENT WORTH $4,718.79 $0.00 $9,212.88 $0.00 $4,766.94 $18,698.61
MARR 18% CAP CONSTRAINT $100,000.00
INVESTMENT PERIOD 10
REALIZED INITIAL INVESTMENT $15,000.00 $0.00 $40,000.00 $0.00 $45,000.00 $100,000.00
REALIZED ANNUAL RETURN $3,750.00 $0.00 $9,250.00 $0.00 $9,160.71 $22,160.71
REALIZED SALVAGE VALUE $15,000.00 $0.00 $40,000.00 $0.00 $45,000.00 $100,000.00
PORTFOLIO IRR 22.16%
MUTUALLY EXCLUSIVE CONSTRAINT 1 AND 2 1 B7+C7
MUTUALLY EXCLUSIVE CONSTRAINT 3 AND 4 1 D7+E7
CONTINGENT CONSTRAINT 1