PROBLEM 6.53
IRR COMPARISONS MUST BE DONE INCREMENTALLY
THIS SOLUTION ASSUMES THAT NULL IS NOT AN OPTION; THE PROBLEM CAN ALSO BE WORKED
ASSUMING THAT NULL IS AN OPTION.
MARR IS 10%; ALL CASH FLOWS ARE IN $K
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS FIRST SATELLITE ONLY, SECOND SATELLITE ONLY, BOTH SATELLITES
FIRST ONLY BECOMES THE “CURRENT BEST” AND SECOND ONLY THE “CHALLENGER“
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
SECOND ONLY – FIRST ONLY
EOY SECOND ONLY FIRST ONLY INCR CF
0 -$850.00 -$750.00 -$100.00
1 -$120.00 -$150.00 $30.00
2 -$120.00 -$150.00 $30.00
3 -$120.00 -$150.00 $30.00
4 -$120.00 -$150.00 $30.00
5 $2,105.00 $2,075.00 $30.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 15.24%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED
SECOND ONLY BECOMES THE NEW CURRENT BEST
BOTH BECOMES THE CHALLENGER
THUS THE CASH FLOWS OF BOTH – SECOND ONLY ARE NEEDED.
BOTH – SECOND ONLY
EOY BOTH SECOND ONLY INCR CF
0 -$1,750.00 -$850.00 -$900.00
1 -$400.00 -$120.00 -$280.00
2 -$400.00 -$120.00 -$280.00
3 -$400.00 -$120.00 -$280.00
4 -$400.00 -$120.00 -$280.00
5 $5,250.00 $2,105.00 $3,145.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 12.56%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (10%) THE INCREMENTAL INVESTMENT IS ACCEPTED
BOTH BECOMES THE NEW CURRENT BEST
THERE ARE NO MORE CHALLENGERS TO CONSIDER.
THUS CONTRACTING FOR BOTH SATELLITES IS PREFERRED.
PROBLEM 6.54
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 10%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS LEASE, PURCHASE
LEASE BECOMES THE “CURRENT BEST” AND PURCHASE THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
PURCHASE – LEASE
EOY PURCHASE LEASE INCR CF
0 -$60,000.00 -$21,000.00 -$39,000.00
1 $23,000.00 $2,000.00 $21,000.00
2 $23,000.00 $2,000.00 $21,000.00
3 $33,000.00 $23,000.00 $10,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 17.94%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED
PURCHASE BECOMES THE NEW CURRENT BEST
SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, PURCHASE IS RECOMMENDED
PROBLEM 6.55
a GOAL SEEK IS USED TO DETERMINE ERR
MARR IS 10%/YEAR
10.45% 10.00%
EOY – CF + CF NET CF (F|P i’,n-t) (F|P MARR,n-t) FW OF -CF FW OF +CF FW OF CF
0 -$100.00 -$100.00 1.81505 1.77156 -$181.50 $0.00 -$181.50
1 $800.00 $800.00 1.64339 1.61051 $0.00 $1,288.41 $1,288.41
2 -$750.00 -$750.00 1.48796 1.46410 -$1,115.97 $0.00 -$1,115.97
3 $900.00 $900.00 1.34724 1.33100 $0.00 $1,197.90 $1,197.90
4 -$950.00 -$950.00 1.21982 1.21000 -$1,158.83 $0.00 -$1,158.83
5 $700.00 $700.00 1.10446 1.10000 $0.00 $770.00 $770.00
6 -$800.00 -$800.00 1.00000 1.00000 -$800.00 $0.00 -$800.00
$0.00 <- FW
TO IMPLEMENT GOAL SEEK:
(1) SET CELL: FW SET THE FUTURE WORTH
(2) TO VALUE: ZERO TO A VALUE OF ZERO
(3) BY CHANGING CELL: (F|P i’,n-t) BY CHANGING THE i’ INTEREST RATE (THE ERR)
ERR = 10.45%
NOTE: EXCEL’S SOLVER RESULTS IN THE SAME SOLUTION (10.45%)
b ERR >= MARR (10%); THEREFORE, ATTRACTIVE
PROBLEM 6.56
MARR IS 10%/YEAR
a EOY CF
0 -$100.00
1$25.00
2$25.00
3$25.00
4$25.00
5$25.00
6$25.00
ERR = MIRR(CF_COLUMN,,MARR)
ERR = 11.57%
B ERR >= MARR (10%); THEREFORE, ATTRACTIVE
PROBLEM 6.57
a SOLUTIONS USES GOAL SEEK TO DETERMINE ERR
MARR IS 10%/YEAR
13.10% 10.00%
EOY – CF + CF NET CF (F|P i’,n-t) (F|P MARR,n-t) FW OF -CF FW OF +CF FW OF CF
0 -$100.00 -$100.00 2.09348 1.77156 -$209.35 $0.00 -$209.35
1 $25.00 $25.00 1.85093 1.61051 $0.00 $40.26 $40.26
2 $25.00 $25.00 1.63649 1.46410 $0.00 $36.60 $36.60
3 $60.00 $60.00 1.44689 1.33100 $0.00 $79.86 $79.86
4 -$30.00 -$30.00 1.27925 1.21000 -$38.38 $0.00 -$38.38
5 $60.00 $60.00 1.13104 1.10000 $0.00 $66.00 $66.00
6 $25.00 $25.00 1.00000 1.00000 $0.00 $25.00 $25.00
$0.00 <- FW
TO IMPLEMENT GOAL SEEK:
(1) SET CELL: FW SET THE FUTURE WORTH
(2) TO VALUE: ZERO TO A VALUE OF ZERO
(3) BY CHANGING CELL: (F|P i‘,n-t) BY CHANGING THE i‘ INTEREST RATE (THE ERR)
ERR = 13.10%
NOTE: EXCEL’S SOLVER RESULTS IN THE SAME SOLUTION (13.10%)
b ERR >= MARR (10%); THEREFORE, ATTRACTIVE
PROBLEM 6.58
a SOLUTIONS USES GOAL SEEK TO DETERMINE ERR
MARR IS 10%/YEAR
9.9997% 10.00%
EOY – CF + CF NET CF (F|P i’,n-t) (F|P MARR,n-t) FW OF -CF FW OF +CF FW OF CF
0 -$101.00 -$101.00 1.77153 1.77156 -$178.92 $0.00 -$178.92
1 $411.00 $411.00 1.61049 1.61051 $0.00 $661.92 $661.92
2 -$558.00 -$558.00 1.46408 1.46410 -$816.96 $0.00 -$816.96
3 $253.00 $253.00 1.33099 1.33100 $0.00 $336.74 $336.74
4 $2.00 $2.00 1.20999 1.21000 $0.00 $2.42 $2.42
5 $8.00 $8.00 1.10000 1.10000 $0.00 $8.80 $8.80
6 -$14.00 -$14.00 1.00000 1.00000 -$14.00 $0.00 -$14.00
$0.00 <- FW
TO IMPLEMENT GOAL SEEK:
(1) SET CELL: FW SET THE FUTURE WORTH
(2) TO VALUE: ZERO TO A VALUE OF ZERO
(3) BY CHANGING CELL: (F|P i’,n-t) BY CHANGING THE i’ INTEREST RATE (THE ERR)
ERR = 9.9997%
NOTE: ADDITIONAL DECIMAL POSITIONS ARE REQUIRED IN DISPLAYING i’ TO DETERMINE THAT IT IS, IN FACT, LESS THAN MARR
NOTE: EXCEL’S SOLVER RESULTS IN THE SAME SOLUTION (9.9997%)
b ERR < MARR (10%); THEREFORE, NOT ATTRACTIVE
PROBLEM 6.59
MARR IS 10%/YEAR
a EOY CF
0 -$100.00
1$15.00
2$15.00
3$15.00
4$15.00
5$15.00
6$15.00
ERR = MIRR(CF_COLUMN,,MARR)
ERR = 2.47%
b ERR < MARR (10%); THEREFORE, NOT ATTRACTIVE
PROBLEM 6.60
a SOLUTIONS USES GOAL SEEK TO DETERMINE ERR
MARR IS 10%/YEAR
10.35% 10.00%
EOY – CF + CF NET CF (F|P i’,n-t) (F|P MARR,n-t) FW OF -CF FW OF +CF FW OF CF
0 -$100.00 -$100.00 1.80529 1.77156 -$180.53 $0.00 -$180.53
1 $25.00 $25.00 1.63602 1.61051 $0.00 $40.26 $40.26
2 $200.00 $200.00 1.48262 1.46410 $0.00 $292.82 $292.82
3 -$100.00 -$100.00 1.34361 1.33100 -$134.36 $0.00 -$134.36
4 $250.00 $250.00 1.21763 1.21000 $0.00 $302.50 $302.50
5 -$200.00 -$200.00 1.10346 1.10000 -$220.69 $0.00 -$220.69
6 -$100.00 -$100.00 1.00000 1.00000 -$100.00 $0.00 -$100.00
$0.00 <- FW
TO IMPLEMENT GOAL SEEK:
(1) SET CELL: FW SET THE FUTURE WORTH
(2) TO VALUE: ZERO TO A VALUE OF ZERO
(3) BY CHANGING CELL: (F|P i’,n-t) BY CHANGING THE i’ INTEREST RATE (THE ERR)
ERR = 10.35%
NOTE: EXCEL’S SOLVER RESULTS IN THE SAME SOLUTION (10.35%)
b ERR >= MARR (10%); THEREFORE, ATTRACTIVE
PROBLEM 6.61
CASH FLOWS IN K$
MARR IS 20%/YEAR
EOY CF
0 -$70,000.00
1 $20,000.00
2 $19,000.00
3 $18,000.00
4 $17,000.00
5 $16,000.00
6 $15,000.00
7 $14,000.00
8 $13,000.00
9 $12,000.00
10 $11,000.00
11 $10,000.00
12 $9,000.00
13 $8,000.00
14 $7,000.00
15 $6,000.00
16 $5,000.00
17 $4,000.00
18 $3,000.00
19 $2,000.00
20 $1,000.00
ERR = MIRR(CF_COLUMN,,MARR)
ERR = 20.47%
(1) ERR = 20.47%
(2) INVESTMENT IS ATTRACTIVE; NU THINGS SHOULD INVEST IN THE BUSINESS VENTURE
(3) IF ERR >= MARR (20%), THEN ATTRACTIVE; OTHERWISE, UNATTRACTIVE
PROBLEM 6.62
MARR = 12%
EOY CF
0 -$80,000
1$10,000
2$16,000
3$22,000
4$28,000
5$28,000
6$22,000
7$16,000
8$10,000
ERR = 14.197% =MIRR(C6:C14,,C3)
SINCE ERR > MARR, RECOMMEND THE INVESTMENT
PROBLEM 6.63
MARR = 10%
EOY CF
0 -$70,000
1$20,000
2$19,000
3$18,000
4$17,000
5$16,000
6$15,000
7$14,000
8$13,000
9$12,000
10 $11,000
11 $10,000
12 $9,000
13 $8,000
14 $7,000
15 $6,000
16 $5,000
17 $4,000
18 $3,000
19 $2,000
20 $1,000
ERR = 12.758% =MIRR(C6:C26,,C3)
SINCE ERR > MARR, RECOMMEND THE INVESTMENT
ANNUAL EXPENSES
PROBLEM 6.65
MARR = 10%
EOY CF
0 -$50,000
1$7,500
2$7,500
3$7,500
4$7,500
5$7,500
6$7,500
7$7,500
8$7,500
9$7,500
10 $7,500
11 $0
12 $0
13 $0
14 $0
15 $50,000
ERR = 11.101% =MIRR(C6:C21,,C3)
SINCE IRR > MARR, RECOMMEND THE INVESTMENT