PROBLEM 6.37
ORDER OF COMPARISON: NULL, C, D, A, B
a MARR = 50%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL C C-NULL 39.20% NULL
NULL D D-NULL 36.00% NULL
NULL A A-NULL 44.00% NULL
NULL B B-NULL 40.00% NULL
PREFER NULL
b MARR = 41%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL C C-NULL 39.20% NULL
NULL D D-NULL 36.00% NULL
NULL A A-NULL 44.00% A
A B B-A 28.30% A
PREFER A
c MARR = 25%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL C C-NULL 39.20% C
C D D-C 18.40% C
C A A-C 61.00% A
A B B-A 28.30% B
PREFER B
PROBLEM 6.38
a MARR = 12%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL A A-NULL 10.00% NULL
NULL B B-NULL 9.00% NULL
NULL C C-NULL 8.00% NULL
NULL D D-NULL 7.00% NULL
NULL E E-NULL 6.00% NULL
NULL F F-NULL 5.00% NULL
NULL G G-NULL 7.00% NULL
PREFER NULL
A C C-A 2.00% A
A D D-A 9.00% A
A E E-A 5.00% A
A F F-A 8.00% A
A G G-A 3.00% A
PREFER A
A C C-A 2.00% A
A D D-A 9.00% D
D E E-D 3.00% D
D F F-D 5.00% D
D G G-D 4.00% D
B C C-B 0.10% B
B D D-B 5.00% D
D E E-D 3.00% D
D F F-D 5.00% F
F G G-F 2.00% F
PREFER F
e MARR = 1.5%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL A A-NULL 10.00% A
A B B-A 7.00% B
B C C-B 0.10% B
B D D-B 5.00% D
D E E-D 3.00% E
E F F-E 5.00% F
F G G-F 2.00% G
PREFER G
PROBLEM 6.39
IRR COMPARISONS MUST BE DONE INCREMENTALLY
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, T3, T4, T1, T2
a MARR IS 25%/YEAR
NULL BECOMES THE “CURRENT BEST” AND T3 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR T3 – NULL ARE NEEDED
EOY T3 NULL INCR. CF
0 -$470,000.00 $0.00 -$470,000.00
1 $190,000.00 $0.00 $190,000.00
2 $190,000.00 $0.00 $190,000.00
3 $190,000.00 $0.00 $190,000.00
4 $190,000.00 $0.00 $190,000.00
5 $190,000.00 $0.00 $190,000.00
6 $190,000.00 $0.00 $190,000.00
7 $190,000.00 $0.00 $190,000.00
8 $190,000.00 $0.00 $190,000.00
9 $190,000.00 $0.00 $190,000.00
10 $255,000.00 $0.00 $255,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 39.14%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (25%) THE INCREMENTAL INVESTMENT IS ACCEPTED.
T3 BECOMES THE NEW CURRENT BEST
T4 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T4 – T3 ARE NEEDED
EOY T4 T3 INCR. CF
0 -$540,000.00 -$470,000.00 -$70,000.00
1 $200,000.00 $190,000.00 $10,000.00
2 $200,000.00 $190,000.00 $10,000.00
3 $200,000.00 $190,000.00 $10,000.00
4 $200,000.00 $190,000.00 $10,000.00
5 $200,000.00 $190,000.00 $10,000.00
6 $200,000.00 $190,000.00 $10,000.00
7 $200,000.00 $190,000.00 $10,000.00
8 $200,000.00 $190,000.00 $10,000.00
9 $200,000.00 $190,000.00 $10,000.00
10 $400,000.00 $255,000.00 $145,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 18.20%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR (25%) THE INCREMENTAL INVESTMENT IS REJECTED.
T3 REMAINS THE CURRENT BEST
T1 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T1 – T3 ARE NEEDED
EOY T1 T3 INCR. CF
0 -$600,000.00 -$470,000.00 -$130,000.00
1 $270,000.00 $190,000.00 $80,000.00
2 $270,000.00 $190,000.00 $80,000.00
3 $270,000.00 $190,000.00 $80,000.00
4 $270,000.00 $190,000.00 $80,000.00
5 $270,000.00 $190,000.00 $80,000.00
6 $270,000.00 $190,000.00 $80,000.00
7 $270,000.00 $190,000.00 $80,000.00
8 $270,000.00 $190,000.00 $80,000.00
9 $270,000.00 $190,000.00 $80,000.00
10 $340,000.00 $255,000.00 $85,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 61.03%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (25%) THE INCREMENTAL INVESTMENT IS ACCEPTED.
T1 BECOMES THE NEW CURRENT BEST
T2 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T2 – T1 ARE NEEDED
EOY T2 T1 INCR. CF
0 -$800,000.00 -$600,000.00 -$200,000.00
1 $330,000.00 $270,000.00 $60,000.00
2 $330,000.00 $270,000.00 $60,000.00
3 $330,000.00 $270,000.00 $60,000.00
4 $330,000.00 $270,000.00 $60,000.00
5 $330,000.00 $270,000.00 $60,000.00
6 $330,000.00 $270,000.00 $60,000.00
7 $330,000.00 $270,000.00 $60,000.00
8 $330,000.00 $270,000.00 $60,000.00
9 $330,000.00 $270,000.00 $60,000.00
10 $460,000.00 $340,000.00 $120,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 28.20%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (25%) THE INCREMENTAL INVESTMENT IS ACCEPTED.
T2 BECOMES THE NEW CURRENT BEST
THERE ARE NO MORE CHALLENGERS SO T2 IS PREFERRED.
b MARR IS 42%/YEAR
NULL BECOMES THE “CURRENT BEST” AND T3 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR T3 – NULL ARE NEEDED
EOY T3 NULL INCR. CF
0 -$470,000.00 $0.00 -$470,000.00
1 $190,000.00 $0.00 $190,000.00
2 $190,000.00 $0.00 $190,000.00
3 $190,000.00 $0.00 $190,000.00
4 $190,000.00 $0.00 $190,000.00
5 $190,000.00 $0.00 $190,000.00
6 $190,000.00 $0.00 $190,000.00
7 $190,000.00 $0.00 $190,000.00
8 $190,000.00 $0.00 $190,000.00
9 $190,000.00 $0.00 $190,000.00
10 $255,000.00 $0.00 $255,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 39.14%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR (42%) THE INCREMENTAL INVESTMENT IS REJECTED.
NULL REMAINS THE NEW CURRENT BEST
T4 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T4 – T3 ARE NEEDED
EOY T4 NULL INCR. CF
0 -$540,000.00 $0.00 -$540,000.00
1 $200,000.00 $0.00 $200,000.00
2 $200,000.00 $0.00 $200,000.00
3 $200,000.00 $0.00 $200,000.00
4 $200,000.00 $0.00 $200,000.00
5 $200,000.00 $0.00 $200,000.00
6 $200,000.00 $0.00 $200,000.00
7 $200,000.00 $0.00 $200,000.00
8 $200,000.00 $0.00 $200,000.00
9 $200,000.00 $0.00 $200,000.00
10 $400,000.00 $0.00 $400,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 35.94%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR (42%) THE INCREMENTAL INVESTMENT IS REJECTED.
NULL REMAINS THE CURRENT BEST
T1 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T1 – T3 ARE NEEDED
EOY T1 NULL INCR. CF
0 -$600,000.00 $0.00 -$600,000.00
1 $270,000.00 $0.00 $270,000.00
2 $270,000.00 $0.00 $270,000.00
3 $270,000.00 $0.00 $270,000.00
4 $270,000.00 $0.00 $270,000.00
5 $270,000.00 $0.00 $270,000.00
6 $270,000.00 $0.00 $270,000.00
7 $270,000.00 $0.00 $270,000.00
8 $270,000.00 $0.00 $270,000.00
9 $270,000.00 $0.00 $270,000.00
10 $340,000.00 $0.00 $340,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 43.96%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR (42%) THE INCREMENTAL INVESTMENT IS ACCEPTED.
T1 BECOMES THE NEW CURRENT BEST
T2 BECOMES THE NEXT CHALLENGER
THUS THE CASH FLOWS FOR T2 – T1 ARE NEEDED
EOY T2 T1 INCR. CF
0 -$800,000.00 -$600,000.00 -$200,000.00
1 $330,000.00 $270,000.00 $60,000.00
2 $330,000.00 $270,000.00 $60,000.00
3 $330,000.00 $270,000.00 $60,000.00
4 $330,000.00 $270,000.00 $60,000.00
5 $330,000.00 $270,000.00 $60,000.00
6 $330,000.00 $270,000.00 $60,000.00
7 $330,000.00 $270,000.00 $60,000.00
8 $330,000.00 $270,000.00 $60,000.00
9 $330,000.00 $270,000.00 $60,000.00
10 $460,000.00 $340,000.00 $120,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 28.20%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR (42%) THE INCREMENTAL INVESTMENT IS REJECTED.
T1 REMAINS THE CURRENT BEST
THERE ARE NO MORE CHALLENGERS SO T1 IS PREFERRED.
NOTE: IF THE IRR FOR EACH ALTERNATIVE IS CALCULATED, T1 IS THE ONLY ALTERNATIVE WHOSE IRR VALUE
EXCEEDS 42%, HENCE, THE PREFERRENCE FOR T1 IN THE INCREMENTAL ANALYSIS IS AN EXPECTED OUTCOME.
PROBLEM 6.40
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 10%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, BAR, SPOT, BEAM
NULL BECOMES THE “CURRENT BEST” AND BAR THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
BAR – NULL
EOY BAR NULL INCR CF
0 -$6,000.00 $0.00 -$6,000.00
1 $2,000.00 $0.00 $2,000.00
2 $2,000.00 $0.00 $2,000.00
3 $2,000.00 $0.00 $2,000.00
4 $2,000.00 $0.00 $2,000.00
5 $2,000.00 $0.00 $2,000.00
6 $2,000.00 $0.00 $2,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 24.29%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED.
LIGHT BAR BECOMES THE NEW CURRENT BEST
SLIDING SPOTS BECOMES THE CHALLENGER
SPOTS – BAR
EOY SPOTS BAR INCR CF
0 -$14,000.00 -$6,000.00 -$8,000.00
1 $3,500.00 $2,000.00 $1,500.00
2 $3,500.00 $2,000.00 $1,500.00
3 $3,500.00 $2,000.00 $1,500.00
4 $3,500.00 $2,000.00 $1,500.00
5 $3,500.00 $2,000.00 $1,500.00
6 $3,500.00 $2,000.00 $1,500.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 3.47%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED
LIGHT BAR REMAINS THE CURRENT BEST
REFLECTED BEAM BECOMES THE CHALLENGER
BEAM – BAR
EOY BEAM BAR INCR CF
0 -$20,000.00 -$6,000.00 -$14,000.00
1 $0.00 $2,000.00 -$2,000.00
2 $2,300.00 $2,000.00 $300.00
3 $4,600.00 $2,000.00 $2,600.00
4 $6,900.00 $2,000.00 $4,900.00
5 $9,200.00 $2,000.00 $7,200.00
6 $11,500.00 $2,000.00 $9,500.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 9.35%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED
LIGHT BAR REMAINS THE CURRENT BEST
SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, LIGHT BAR IS RECOMMENDED
PROBLEM 6.41
SAVINGS CERTIFICATE
EOM + CF – CF NET CF
0 -$12,000.00 -$12,000.00
2$100.00 $100.00
4$100.00 $100.00
6$100.00 $100.00
8$100.00 $100.00
9$100.00 $100.00
10 $100.00 $100.00
11 $100.00 $100.00
12 $100.00 $100.00
13 $100.00 $100.00
24 $100.00 $100.00
25 $100.00 $100.00
26 $100.00 $100.00
27 $100.00 $100.00
28 $100.00 $100.00
39 $100.00 $100.00
40 $100.00 $100.00
41 $100.00 $100.00
42 $100.00 $100.00
43 $100.00 $100.00
54 $100.00 $100.00
55 $100.00 $100.00
56 $100.00 $100.00
57 $100.00 $100.00
58 $100.00 $100.00
IRR = 0.94%
ANNUALIZED IRR = 11.85%
PROBLEM 6.42
a A LIST OF POSSIBLE ALTERNATIVES WILL BE CREATED AND THEN THE INFEASIBLE
ALTERNATIVES WILL BE ELIMINATED. IN THE TABLE BELOW, A ONE INDICATES
THAT A PROPOSAL IS INCLUDED; A ZERO INDICATES THAT IT IS NOT. THERE
ARE A TOTAL OF 16 (2^4) POSSIBLE COMBINATIONS
10 0 1 0 1 YES
11 0 0 1 1 NO Y1 & Y2 ARE ME
12 1 1 1 0 NO X1 & X2 ARE ME
13 1 1 0 1 NO X1 & X2 ARE ME
14 1 0 1 1 NO Y1 & Y2 ARE ME
EOY X1 NULL INCR CF
0 -$10,000.00 $0.00 -$10,000.00
1 $1,600.00 $0.00 $1,600.00
2 $1,600.00 $0.00 $1,600.00
3 $1,600.00 $0.00 $1,600.00
IRR = 5.84%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED
NULL REMAINS THE CURRENT BEST
X2 BECOMES THE CHALLENGER
IRR = 7.90%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED
PROBLEM 6.43
MARR = 12%
n = 10
EOY NCF(A) NCF(B) NCF(A-B)
0 -$40,000 –$30,000 -$10,000
1 $8,000 $9,000 -$1,000
2 $8,000 $8,500 -$500
3 $8,000 $8,000 $0
4 $8,000 $7,500 $500
5 $8,000 $7,000 $1,000
6 $8,000 $6,500 $1,500
7 $8,000 $6,000 $2,000
8 $8,000 $5,500 $2,500
9 $8,000 $5,000 $3,000
10 $8,000 $4,500 $3,500
STEP 1:
STEP 2: CALCULATE IRR(B) USING EXCEL’S IRR FUNCTION.
IRR(B) = 21.423% =IRR(D8:D18)
STEP 3: IS IRR(B) > MARR? IF SO, CALCULATE IRR(A-B); IF NOT, CALCULATE IRR(A)
IRR(A-B) = 2.557% =IRR(E8:E18)
STEP 4: DRAW CONCLUSION.
SINCE IRR(A-B) < MARR, RECOMMEND INVESTMENT ALTERNATIVE B.
STEP 6:
IRR(B) = 21.423% =IRR(D8:D18)
CONSIDER THE INVESTMENT ALTERNATIVES IN INCREASING ORDER OF THE INITIAL
INVESTMENT: CONSIDER B, THEN EITHER A-B OR A, DEPENDING ON THE OUTCOME FOR B.
IRR(B) = 21.423% > MARR = 12%. CALCULATE IRR(A-B) USING EXCEL’S IRR
FUNCTION.
CALCULATE IRR FOR THE RECOMMENDED INVESTMENT USING EXCEL’S IRR FUNCTION.
=RATE(I4,C8,-C4,C9)
NOTICE, IF THE INCREMENTAL NET ANNUAL REVENUE WERE $28,588.75 , INSTEAD OF $30,000, THE RATE FUNCTION YIELDS A
IRR(9-1) = 20.454% > MARR = 10%. CALCULATE IRR(3-9).
CALCULATE IRR FOR THE RECOMMENDED INVESTMENT.
EXAMINING THE NET CASH FLOWS, ALTERNATIVE 9 DOMINATES ALTERNATIVE 5. BOTH REQUIRE THE SAME INITIAL INVESTMENT
CONSIDER THE INVESTMENT ALTERNATIVES IN INCREASING ORDER OF THE INITIAL INVESTMENT: 1, 9, 3, 6.
IRR(3-9) = 19.545% > MARR = 10%. CALCULATE IRR(6-3).
NOTE: IN MANY CASES, EXCEL’S RATE FUNCTION CAN BE USED TO CALCULATE IRR. HOWEVER, THERE ARE INSTANCES IN
SINCE IRR(6-3) > MARR, RECOMMEND INVESTMENT ALTERNATIVE 6, WHICH IS THE COMBINATION OF
THIS IS A CASE WHERE IRR EXISTS, BUT EXCEL’S RATE FUNCTION CANNOT
PROBLEM 6.45
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 20%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS GATE 1, GATE 2, GATE 3
GATE 1 BECOMES THE “CURRENT BEST” AND GATE 2 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR GATE 2 – GATE 1 ARE NEEDED
GATE 2 – GATE 1
EOY GATE 2 GATE 1 INCR CF
0 -$19,000.00 -$15,000.00 -$4,000.00
1 -$5,600.00 -$6,500.00 $900.00
2 -$5,600.00 -$6,500.00 $900.00
3 -$5,600.00 -$6,500.00 $900.00
4 -$5,600.00 -$6,500.00 $900.00
5 -$3,600.00 -$6,500.00 $2,900.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 15.10%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED.
GATE 1 REMAINS THE NEW CURRENT BEST
GATE 3 BECOMES THE CHALLENGER
THUS, THE CASH FLOWS FOR GATE 3 – GATE 1 ARE NEEDED
GATE 3 – GATE 1
EOY GATE 3 GATE 1 INCR CF
0 -$24,000.00 -$15,000.00 -$9,000.00
1 -$4,000.00 -$6,500.00 $2,500.00
PROBLEM 6.46
a INCREMENTAL CASH FLOW ARE A – C
EOY A C A – C
0 -$600,000.00 -$470,000.00 -$130,000.00
1 $270,000.00 $190,000.00 $80,000.00
2 $270,000.00 $190,000.00 $80,000.00
3 $270,000.00 $190,000.00 $80,000.00
4 $270,000.00 $190,000.00 $80,000.00
5 $270,000.00 $190,000.00 $80,000.00
6 $270,000.00 $190,000.00 $80,000.00
7 $270,000.00 $190,000.00 $80,000.00
8 $270,000.00 $190,000.00 $80,000.00
9 $270,000.00 $190,000.00 $80,000.00
10 $340,000.00 $255,000.00 $85,000.00
b IRR = IRR(A-C_COLUMN)
IRR = 61.03%
c MARR = 37%
CURRENT BEST CHALLENGER INCREMENT IRR OF INCREMENT WINNER
NULL C C-NULL 39.00% C
C D D-C 18.00% C
C A A-C 61.03% A
A B B-A 28.00% A
PREFER A
d IF MARR = 40%, PW(C) < 0 SINCE IRR(C) = 39%
PROBLEM 6.47
IRR COMPARISONS MUST BE DONE INCREMENTALLY
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS MACHINE A37Y, MACHINE 7745
NULL IS NOT AN OPTION SINCE THE PROBLEM STATES THAT A MACHINE MUST BE PURCHASED
MARR IS 6%/YEAR
A37Y BECOMES THE “CURRENT BEST” AND 7745 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR 7745 – A37Y ARE NEEDED
EOY 7745 A37Y INCR. CF
0 -$10,000.00 -$8,000.00 -$2,000.00
1 -$300.00 -$300.00 $0.00
2 -$300.00 -$300.00 $0.00
3 -$300.00 -$300.00 $0.00
4 -$300.00 -$300.00 $0.00
5 -$300.00 -$300.00 $0.00
6 -$300.00 -$300.00 $0.00
7 -$300.00 -$300.00 $0.00
8 -$300.00 -$300.00 $0.00
9 -$300.00 -$300.00 $0.00
10 $700.00 -$300.00 $1,000.00
IRR = IRR(INCR_CF_COLUMN)
IRR = -6.70%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR, THE INCREMENTAL INVESTMENT IS REJECTED.
A37Y REMAINS THE CURRENT BEST
SINCE THERE ARE NO MORE CHALLENGERS, A37Y IS RECOMMENDED.
PROBLEM 6.48
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 10%; ORDER OF INVESTMENTS: NULL, B, A
INCREMENTAL ANALYSIS OF B-NULL
EOY + CF – CF NET CF
0 -$280,000.00 -$280,000.00
1 $95,000.00 $95,000.00
2 $95,000.00 $95,000.00
3 $95,000.00 $95,000.00
4 $95,000.00 $95,000.00
IRR = IRR(NET_CF_COLUMN)
IRR = 13.44%
IRR OF INCREMENT IS GREATER THAN MARR (10%) SO B IS PREFERRED TO NULL
ANALYZE INCREMENTAL CASH FLOWS OF A-B
INCREMENTAL ANALYSIS OF A-B
EOY + CF – CF NET CF
0 -$100,000.00 -$100,000.00
1 $30,000.00 $30,000.00
2 $30,000.00 $30,000.00
3 $30,000.00 $30,000.00
4 $30,000.00 $30,000.00
IRR = IRR(NET_CF_COLUMN)
IRR = 7.71%
IRR OF INCREMENT A-B IS LESS THAN MARR (10%), SO REJECT THE INCREMENT; STAY WITH VENDOR B
SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, VENDOR B IS RECOMMENDED
PROBLEM 6.49
IRR COMPARISONS MUST BE DONE INCREMENTALLY
THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED
ASSUMING THAT NULL IS NOT AN OPTION.
MARR IS 15%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, 2, 3, 1
NULL BECOMES THE “CURRENT BEST” AND 2 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR 2 – NULL ARE NEEDED
0 -$10,000.00
1 $1,770.00
2 $1,770.00
3 $1,770.00
4 $1,770.00
5 $1,770.00
6 $1,770.00
7 $1,770.00
IRR = IRR(NET_CF_COLUMN)
IRR = 12.00%
THUS, THE CASH FLOWS FOR 3 – NULL ARE NEEDED
EOY 3
0 -$15,000.00
1 $3,580.00
2 $3,580.00
3 $3,580.00
4 $3,580.00
5 $3,580.00
6 $3,580.00
7 $3,580.00
IRR = IRR(NET_CF_COLUMN)
IRR = 20.02%
1 BECOMES THE CHALLENGER
THUS, THE CASH FLOWS FOR 1 – 3 ARE NEEDED
POLISHER 1 – POLISHER 3
EOY 1 3 INCR CF
0 -$20,000.00 -$15,000.00 -$5,000.00
1 $4,465.00 $3,580.00 $885.00
2 $4,465.00 $3,580.00 $885.00
3 $4,465.00 $3,580.00 $885.00
4 $4,465.00 $3,580.00 $885.00
5 $4,465.00 $3,580.00 $885.00
6 $4,465.00 $3,580.00 $885.00
7 $4,465.00 $3,580.00 $885.00
8 $4,465.00 $3,580.00 $885.00
9 $4,465.00 $3,580.00 $885.00
10 $4,465.00 $3,580.00 $885.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 12.00%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJESCTED
3 STAYS THE NEW CURRENT BEST
THERE ARE NO MORE CHALLENGERS, THUS POLISHER 3 IS RECOMMENDED
PROBLEM 6.50
IRR COMPARISONS MUST BE DONE INCREMENTALLY
THIS SOLUTION ASSUMES THAT NULL IS AN OPTION; THE PROBLEM CAN ALSO BE WORKED
ASSUMING THAT NULL IS NOT AN OPTION.
MARR IS 10%
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, B002, C003, A001
NULL BECOMES THE “CURRENT BEST” AND B002 THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR B002-NULL ARE NEEDED
B002 – NULL
EOY NET CF
0 -$110.00
1 $60.00
2 $60.00
3 $60.00
4 $70.00
IRR = IRR(NET_CF_COLUMN)
IRR = 42.11%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED.
B002 BECOMES THE NEW CURRENT BEST
C003 BECOMES THE CHALLENGER
THUS, THE CASH FLOWS FOR C003 – B002 ARE NEEDED
C003 – B002
EOY C003 B002 INCR CF
0 -$160.00 –$110.00 -$50.00
1 $80.00 $60.00 $20.00
2 $80.00 $60.00 $20.00
3 $80.00 $60.00 $20.00
4 $80.00 $70.00 $10.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 16.48%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED.
C003 BECOMES THE NEW CURRENT BEST
A001 BECOMES THE CHALLENGER
THUS, THE CASH FLOWS FOR A001 – C003 ARE NEEDED
C003 – B002
EOY A001 C003 INCR CF
0 -$210.00 –$160.00 -$50.00
1 $80.00 $80.00 $0.00
2 $90.00 $80.00 $10.00
3 $100.00 $80.00 $20.00
4 $110.00 $80.00 $30.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 5.65%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR THE INCREMENTAL INVESTMENT IS REJECTED.
SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, C003 IS RECOMMENDED
PROBLEM 6.51
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 10%/YEAR
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS NULL, 1-INCH, 2-INCH
NULL BECOMES THE “CURRENT BEST”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
THUS, THE CASH FLOWS FOR 1-INCH – NULL ARE NEEDED
EOY 1-INCH NULL INCR. CF
0 -$100,000.00 $0.00 -$100,000.00
1 -$41,250.00 -$375,000.00 $333,750.00
2 -$41,250.00 -$375,000.00 $333,750.00
3 -$41,250.00 -$375,000.00 $333,750.00
4 -$41,250.00 -$375,000.00 $333,750.00
5 -$41,250.00 -$375,000.00 $333,750.00
6 -$41,250.00 -$375,000.00 $333,750.00
7 -$41,250.00 -$375,000.00 $333,750.00
8 -$41,250.00 -$375,000.00 $333,750.00
9 -$41,250.00 -$375,000.00 $333,750.00
10 -$41,250.00 -$375,000.00 $333,750.00
IRR = IRR(INCR_CF_COLUMN)
IRR = 333.75%
SINCE THE IRR OF THE INCREMENT IS GREATEER THAN MARR, THE INCREMENTAL INVESTMENT IS ACCEPTED.
1-INCH BECOMES THE NEW CURRENT BEST
2-INCH BECOMES THE CHALLENGER
THUS, THE CASH FLOWS FOR 2-INCH – 1-INCH ARE NEEDED
EOY 2-INCH 1-INCH INCR. CF
0 -$212,500.00 -$100,000.00 -$112,500.00 1.00000 -$112,500.00
1 -$30,000.00 -$41,250.00 $11,250.00 0.90909 $10,227.27
2 -$30,000.00 -$41,250.00 $11,250.00 0.82645 $9,297.52
3 -$30,000.00 -$41,250.00 $11,250.00 0.75131 $8,452.29
4 -$30,000.00 -$41,250.00 $11,250.00 0.68301 $7,683.90
5 -$30,000.00 -$41,250.00 $11,250.00 0.62092 $6,985.36
6 -$30,000.00 -$41,250.00 $11,250.00 0.56447 $6,350.33
7 -$30,000.00 -$41,250.00 $11,250.00 0.51316 $5,773.03
8 -$30,000.00 -$41,250.00 $11,250.00 0.46651 $5,248.21
9 -$30,000.00 -$41,250.00 $11,250.00 0.42410 $4,771.10
10 -$30,000.00 -$41,250.00 $11,250.00 0.38554 $4,337.36
IRR = IRR(INCR_CF_COLUMN)
IRR = 0.00%
SINCE THE IRR OF THE INCREMENT IS LESS THAN MARR, THE INCREMENTAL INVESTMENT IS REJECTED.
1-INCH REMAINS THE CURRENT BEST
SINCE THERE ARE NO MORE CHALLENGERS, 1-INCH IS RECOMMENDED.
PROBLEM 6.52
IRR COMPARISONS MUST BE DONE INCREMENTALLY
MARR IS 6%; ALL DOLLAR VALUES ARE IN M$
FOR AN INCREMENTAL ANALYSIS, THE ORDER MUST BE DETERMINED.
ORDER IS EXTENDED, ONE-TIME
EXTENDED BECOMES THE “CURRENT BEST” AND ONE-TIME THE “CHALLENGER”
NEXT, THE INCREMENTAL CASH FLOWS FOR “CHALLENGER” – “CURRENT BEST” MUST BE DETERMINED
ONE-TIME – EXTENDED
EOY ONE-TIME EXTENDED INCR CF
0 -$14.40 -$1.00 -$13.40
1 $0.00 -$1.30 $1.30
2 $0.00 -$1.30 $1.30
3 $0.00 -$1.30 $1.30
4 $0.00 -$1.30 $1.30
5 $0.00 -$1.30 $1.30
6 $0.00 -$1.30 $1.30
7 $0.00 -$1.30 $1.30
8 $0.00 -$1.30 $1.30
9 $0.00 -$1.30 $1.30
10 $0.00 -$1.30 $1.30
11 $0.00 -$1.30 $1.30
12 $0.00 -$1.30 $1.30
13 $0.00 -$1.30 $1.30
14 $0.00 -$1.30 $1.30
15 $0.00 -$1.30 $1.30
16 $0.00 -$1.30 $1.30
17 $0.00 -$1.30 $1.30
18 $0.00 -$1.30 $1.30
19 $0.00 -$1.30 $1.30
20 $0.00 -$1.30 $1.30
IRR = IRR(INCR_CF_COLUMN)
IRR = 7.36%
SINCE THE IRR OF THE INCREMENT IS GREATER THAN MARR THE INCREMENTAL INVESTMENT IS ACCEPTED
ONE-TIME BECOMES THE NEW CURRENT BEST
SINCE THERE ARE NO MORE ALTERNATIVES TO BE CONSIDERED, ONE-TIME IS RECOMMENDED