FE PROBLEM 12.1
ANSWER: b
SINCE THE PRINTER SHOULD NOT BE PURCHASED IF THE COMPUTER IS NOT PURCHASED, THE PURCHASE OF THE
PRINTER IS CONTINGENT ON THE PURCHASE OF THE COMPUTER.
FE PROBLEM 12.2
ANSWER: a
MUTUALLY EXCLUSIVE MEANS BOTH CANNOT BE PURSUED. THE POSSIBLE VALUES FOR (X1, X2) ARE (0, 0), (1, 0), AND (0,
1). THE ONLY COMBINATION THAT IS NOT ALLOWED IS (1, 1). THEREFORE, THE SUM OF THE TWO MUST BE NO GREATER
THAN 1.
FE PROBLEM 12.3
ANSWER: b
CONTINGENT MEANS THAT AN INVESTMENT CANNOT BE PURSUED UNLESS ANOTHER INVESTMENT IS PURSUED. IF X2 IS
CONTINGENT ON X1, THEN THE POSSIBLE VALUES FOR (X1, X2) ARE (0, 0), (1, 0), AND (1, 1). THE ONLY COMBINATION
THAT IS NOT ALLOWED IS (0, 1). THEREFORE, THE VALUE OF X2 MUST BE NO GREATER THAN THE VALUE OF X1.
FE PROBLEM 12.4
ANSWER: c
THE REQUIREMENT THAT THE “DO NOTHING” ALTERNATIVE IS NOT FEASIBLE MEANS THAT AT LEAST ONE OF THE
INVESTMENTS MUST BE PURSUED. THE POSSIBLE VALUES FOR (X1, X2) ARE (1, 1), (1, 0), AND (0, 1). THE ONLY
COMBINATION THAT IS NOT ALLOWED IS (0, 0). THEREFORE, THE SUM OF THE VALUES OF X1 AND X2 MUST BE AT LEAST
EQUAL TO 1.
FE PROBLEM 12.5
ANSWER: d
INTERNAL RATE OF RETURN IS AN INCREMENTAL METHOD. RANKING MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVES
BASED ON IRR WILL NOT NECESSARILY YIELD A RANKING THAT IS THE SAME AS WILL BE OBTAINED WHEN RANKING
EITHER PW, FW, OR AW.
FE PROBLEM 12.6
IF A BINARY DECISION IS MADE FOR EACH OF N INVESTMENT PROPOSALS, THEN 2N INVESTMENT COMBINATIONS ARE POSSIBLE.
ANSWER: d
FE PROBLEM 12.7
THE BOX-JENKINS ALGORITHM IS USED FOR FORECASTING, NOT CAPITAL RATIONING
ANSWER: a
FE PROBLEM 12.8
ANSWER: c
WHEN THE INVESTMENTS HAVE THE SPECIAL PROPERTY OF A 100% SALVAGE VALUE AND A UNIFORM ANNUAL SERIES OF
RETURNS, THE “BUCKET FILLING” APPROACH CAN BE USED BY RANKING THE INVESTMENTS ON THE BASIS OF THEIR IRR
AND “ADDING INVESTMENTS TO THE BUCKET” UNTIL IT IS “FULL”
FE PROBLEM 12.9
ANSWER: b
THE BLP FORMULATION OF THE CAPITAL RATIONING PROBLEM INCLUDES PRESENT WORTH VALUES IN THE OBJECTIVE
FUNCTION AND THE INVESTMENT REQUIREMENTS IN THE CONSTRAINTS. INVESTMENT PROPOSAL 3 HAS A PRESENT
WORTH OF 950 AND AN INITIAL INVESTMENT OF 25,000.
FE PROBLEM 12.10
ANSWER: c
FROM THE CONSTRAINTS, INVESTMENTS 1 AND 2 ARE MUTUALLY EXCLUSIVE AND INVESTMENT 4 IS CONTINGENT ON
INVESTMENT 3 BEING PURSUED.
FE PROBLEM 12.11
ANSWER: b
THE BLP FORMULATION OF THE CAPITAL RATIONING PROBLEM INCLUDES PRESENT WORTH VALUES IN THE OBJECTIVE
FUNCTION AND THE INVESTMENT REQUIREMENTS IN THE CONSTRAINTS. THE SUM OF THE INITIAL INVESTMENT
REQUIREMENTS FOR THE INVESTMENTS PURSUED MUST BE NO GREATER THAN THE AMOUNT OF CAPITAL AVAILABLE.
THE RIGHT-HAND SIDE OF THE FIRST CONSTRAINT PROVIDES THE BUDGET LIMIT, 70,000.
PROBLEM 12.1
TRUE
PW AND AW AND FW ARE ALL CONSISTENT MEASURES
PROBLEM 12.2
a OPTIMUM PORTFOLIO 2, 4, 5
b PRESENT WORTH $43,617.79
c PORTFOLIO IRR 16.94%
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
PORTFOLIO INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
PORTFOLIO PRESENT WORTH $0.00 $15,140.06 $0.00 $14,959.82 $13,517.91 $43,617.79
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $0.00 $13,750.00 $15,750.00 $41,500.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
PORTFOLIO IRR 16.94%
d OPTIMUM PORTFOLIO 2, 4, 5
e PRESENT WORTH $43,617.79
f PORTFOLIO IRR 16.94%
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
PORTFOLIO INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
PORTFOLIO PRESENT WORTH $0.00 $15,140.06 $0.00 $14,959.82 $13,517.91 $43,617.79
MARR 12% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $0.00 $13,750.00 $15,750.00 $41,500.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
P’FOLIO IRR 16.94%
MUTUAL EXCLUSIVITY CONSTRAINT 1 C58+F58
g PORTFOLIO PW
CAP CONSTRAINT $200,000.00 2, 3, 4 $33,507.05
$250,000.00 2, 4, 5 $43,617.79
$300,000.00 2, 3, 4, 5 $49,000.00
h MARR 9.60% 2, 4, 5 $68,860.59
12.00% 2, 4, 5 $43,617.79
14.40% 2, 4, 5 $21,150.07 ***
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 $0.00 $8,976.88 $1,020.10 $7,582.74 $4,590.45
INTERNAL RATE OF RETURN 14.40% 18.46% 15.00% 17.19% 15.75%
VALUE OF x 0 1 0 1 1
PORTFOLIO INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
PORTFOLIO PRESENT WORTH $0.00 $8,976.88 $0.00 $7,582.74 $4,590.45 $21,150.07
MARR 14.40% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
REALIZED ANNUAL RETURN $0.00 $12,000.00 $0.00 $13,750.00 $15,750.00 $41,500.00
REALIZED SALVAGE VALUE $0.00 $65,000.00 $0.00 $80,000.00 $100,000.00 $245,000.00
P’FOLIO IRR 16.94%
PROBLEM 12.3
a OPTIMUM PORTFOLIO 2, 4, 5
b PRESENT WORTH $567,672.40
c PORTFOLIO IRR 27.50%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
ANNUAL RETURN $90,000.00 $85,000.00 $75,000.00 $130,000.00 $115,000.00
SALVAGE VALUE $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
PRESENT WORTH $141,918.10 $151,379.31 $141,918.10 $208,146.55 $208,146.55
INTERNAL RATE OF RETURN 25.71% 28.33% 30.00% 26.00% 28.75%
VALUE OF x 0 1 0 1 1
PORTFOLIO INVESTMENT $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
PORTFOLIO PRESENT WORTH $0.00 $151,379.31 $0.00 $208,146.55 $208,146.55 $567,672.40
MARR 15% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 6
REALIZED INITIAL INVESTMENT $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
REALIZED ANNUAL RETURN $0.00 $85,000.00 $0.00 $130,000.00 $115,000.00 $330,000.00
REALIZED SALVAGE VALUE $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
PORTFOLIO IRR 27.50%
d OPTIMUM PORTFOLIO 3, 4, 5
e PRESENT WORTH $558,211.20
f PORTFOLIO IRR 27.83%
SEE BELOW FOR DETAILS
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
ANNUAL RETURN $90,000.00 $85,000.00 $75,000.00 $130,000.00 $115,000.00
SALVAGE VALUE $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
PRESENT WORTH $141,918.10 $151,379.31 $141,918.10 $208,146.55 $208,146.55
INTERNAL RATE OF RETURN 25.71% 28.33% 30.00% 26.00% 28.75%
VALUE OF x 0 0 1 1 1 3
PORTFOLIO INVESTMENT $0.00 $0.00 $250,000.00 $500,000.00 $400,000.00 $1,150,000.00
PORTFOLIO PRESENT WORTH $0.00 $0.00 $141,918.10 $208,146.55 $208,146.55 $558,211.20
MARR 15% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 6
REALIZED INITIAL INVESTMENT $0.00 $0.00 $250,000.00 $500,000.00 $400,000.00 $1,150,000.00
REALIZED ANNUAL RETURN $0.00 $0.00 $75,000.00 $130,000.00 $115,000.00 $320,000.00
REALIZED SALVAGE VALUE $0.00 $0.00 $250,000.00 $500,000.00 $400,000.00 $1,150,000.00
P’FOLIO IRR 27.83%
MUTUAL EXCLUSIVITY CONSTRAINT 1 C58+D58+F58
g PORTFOLIO PW
CAP CONSTRAINT $1,000,000.00 2, 3, 5 $501,443.96
$1,250,000.00 2, 4, 5 $567,672.40
$1,500,000.00 2, 3, 4, 5 $709,590.51
h
MARR 12.00% 2, 4, 5 $764,721.76
15.00% 2, 4, 5 $567,672.40
18.00% 2, 4, 5 $398,726.69 ***
SEE BELOW FOR ONE SETUP ***
INVESTMENT OPPORTUNITY 1 2 3 4 5
INITIAL INVESTMENT $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
ANNUAL RETURN $90,000.00 $85,000.00 $75,000.00 $130,000.00 $115,000.00
SALVAGE VALUE $350,000.00 $300,000.00 $250,000.00 $500,000.00 $400,000.00
PRESENT WORTH $94,435.27 $108,425.68 $104,928.08 $139,904.10 $150,396.91
INTERNAL RATE OF RETURN 25.71% 28.33% 30.00% 26.00% 28.75%
VALUE OF x 0 1 0 1 1
PORTFOLIO INVESTMENT $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
PORTFOLIO PRESENT WORTH $0.00 $108,425.68 $0.00 $139,904.10 $150,396.91 $398,726.69
MARR 18% CAP CONSTRAINT $1,250,000.00
INVESTMENT PERIOD 6
REALIZED INITIAL INVESTMENT $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
REALIZED ANNUAL RETURN $0.00 $85,000.00 $0.00 $130,000.00 $115,000.00 $330,000.00
REALIZED SALVAGE VALUE $0.00 $300,000.00 $0.00 $500,000.00 $400,000.00 $1,200,000.00
P’FOLIO IRR 27.50%
PROBLEM 12.4
a OPTIMUM PORTFOLIO 1, 2, 3, 4
b PRESENT WORTH $113,550.45
c PORTFOLIO IRR 24.60%
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
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $100,000.00 $0.00 $250,000.00
PORTFOLIO IRR 24.60%
d OPTIMUM PORTFOLIO 1, 2, 4, 5
e PRESENT WORTH $111,387.58
f PORTFOLIO IRR 25.43%
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $0.00 $100,000.00 $65,000.00 $230,000.00
REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $0.00 $22,000.00 $17,000.00 $58,500.00
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $0.00 $100,000.00 $65,000.00 $230,000.00
P’FOLIO IRR 25.43%
g PORTFOLIO PW
CAP CONSTRAINT $200,000.00 2, 3, 5 $94,445.14
$250,000.00 1, 2, 3, 4 $113,550.45
$300,000.00 2, 3, 4, 5 $130,492.90
h MARR 9.60% 1, 2, 3, 4 $143,619.14
12.00% 1, 2, 3, 4 $113,550.45
14.40% 1, 2, 3, 5 $86,844.50 ***
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
MARR 14.40% CAP CONSTRAINT $250,000.00
INVESTMENT PERIOD 5
REALIZED INITIAL INVESTMENT $25,000.00 $40,000.00 $85,000.00 $0.00 $65,000.00 $215,000.00
REALIZED ANNUAL RETURN $7,500.00 $12,000.00 $20,000.00 $0.00 $17,000.00 $56,500.00
REALIZED SALVAGE VALUE $25,000.00 $40,000.00 $85,000.00 $0.00 $65,000.00 $215,000.00
PROBLEM 12.5
a OPTIMUM PORTFOLIO 2, 5
b PRESENT WORTH $56,590.58
c PORTFOLIO IRR 15.76%
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 1 0 0 1
PORTFOLIO INVESTMENT $0.00 $130,000.00 $0.00 $0.00 $200,000.00 $330,000.00
PORTFOLIO PRESENT WORTH $0.00 $29,208.04 $0.00 $0.00 $27,382.54 $56,590.58
MARR 12% CAP CONSTRAINT $350,000.00
INVESTMENT PERIOD 7
REALIZED INITIAL INVESTMENT $0.00 $130,000.00 $0.00 $0.00 $200,000.00 $330,000.00
REALIZED ANNUAL RETURN $0.00 $22,000.00 $0.00 $0.00 $30,000.00 $52,000.00
REALIZED SALVAGE VALUE $0.00 $130,000.00 $0.00 $0.00 $200,000.00 $330,000.00
PORTFOLIO IRR 15.76%
d OPTIMUM PORTFOLIO 1, 2
e PRESENT WORTH $56,590.58
f PORTFOLIO IRR 16.43%
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 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% CAP CONSTRAINT $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%
MUTUAL EXCLUSIVITY CONSTRAINT 1 D58+G58