Proposals A,B,C,D,E,F and G are being considered with money flows over 10 years
ID: 2597168 • Letter: P
Question
Proposals A,B,C,D,E,F and G are being considered with money flows over 10 years
Proposal (A and G) are mutually exclusive (C and D) are also mutually exclusive, and proposl B depends on C or D. The MARR is set at 9% a) Formulate the problem with integer programming b)which proposals should be selected if the amount of money avaible for investment is $100,000?
A B C D E F G Investment $35,000 $10,000 $65,000 $42,000 $12,000 $52,000 $27,000 Net Annual Benefit $7,000 $2,200 $13,000 $9,000 $2,4000 $11,000 $7,200 Salvage Value $3,000 $0 $5,000 $2,000 $500 0 $1,000Explanation / Answer
1. Calculation of Net Present Value of Each program.
A
B
C
D
E
F
G
Investment
$35,000
$10,000
$65,000
$42,000
$12,000
$52,000
$27,000
Net Annual Benefit
$7,000
$2,200
$13,000
$9,000
$2,4000
$11,000
$7,200
Present Value of 10 years (Cumulative)
(1/1.091+2+..+10)
6.417
6.417
6.417
6.417
6.417
6.417
6.417
Present Value of Benefits
(Net Annual x Present value of 10 years)
(A)
44919
14117
83421
57753
154008
70587
46202
Salvage Value
$3,000
$0
$5,000
$2,000
$500
0
$1,000
Present Value of 10th year
0.422
0.422
0.422
0.422
0.422
0.422
0.422
Present value of Salvage amount (B)
1266
0
2110
844
211
0
422
Total Present Value of cash inflows (A+B)
46185
14117
85531
58597
154219
70587
46624
Net Present Value
(Total Present Value of cash inflows – Investment)
11185
4117
20531
16597
142219
18587
19624
2. Selection of programs with investment amount of $100,000
1. Since the net present value of program E is highest, the company should select the same. Remaining amount for investment = (100,000 - 12,000) = 88,000.
2. Project C is having next best NPV and therefore it should be selected next. Since C & D are mutually exclusive, company cannot accept project D if G is selected. Remaning amount after selection of C = (88,000 - 65,000) = $23,000
3. Out of the remaining projects, G is having best NPV but the same cannot be accepted as it has investment amount of $27,000 which is not available. Similarly, F having next best NPV after G cannot be accepted as initial amount is $52,000. A can also be not accepted as it is having investment of $35,000.
4. Remaining project B can be accepted as it is dependent on C or D. Since we take up C, we can also take up B.
Overall NPV = 142219 + 20531 + 4117 = $166,867.
NOTE: in the given question, it appears to me that Annual Benefit in project E of $24,000 is mistakenly written by student as $24,000. I think it is $2,400. I have answered the question taking $24,000 and not $2,400. If the figure is not correct then my answer may vary to the actual. Kindly check the amount once.
A
B
C
D
E
F
G
Investment
$35,000
$10,000
$65,000
$42,000
$12,000
$52,000
$27,000
Net Annual Benefit
$7,000
$2,200
$13,000
$9,000
$2,4000
$11,000
$7,200
Present Value of 10 years (Cumulative)
(1/1.091+2+..+10)
6.417
6.417
6.417
6.417
6.417
6.417
6.417
Present Value of Benefits
(Net Annual x Present value of 10 years)
(A)
44919
14117
83421
57753
154008
70587
46202
Salvage Value
$3,000
$0
$5,000
$2,000
$500
0
$1,000
Present Value of 10th year
0.422
0.422
0.422
0.422
0.422
0.422
0.422
Present value of Salvage amount (B)
1266
0
2110
844
211
0
422
Total Present Value of cash inflows (A+B)
46185
14117
85531
58597
154219
70587
46624
Net Present Value
(Total Present Value of cash inflows – Investment)
11185
4117
20531
16597
142219
18587
19624
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