B D (15) 3. Proposals A, B, C, D, E, F and G are being considered with money flo

Question

B D (15) 3. Proposals A, B, C, D, E, F and G are being considered with money flows over 10 years. G Investment $25,000 $10,000 $40,000 $45,000 $15,000 $55,000 $25,000 Net Annual Benefit $7,000 $2,200 $10,000 $12,000 $2,800 $14,000 $8,000 Salvage Value $3,000 $O $5,000 $2,000 $500 $1,000 Proposal (A and E) are mutually exclusive, (C and D) are also mutually exclusive, and proposal B depends on Cor D. The MARR is set at 10%. a) Formulate the problem with Integer Programming. b) Which proposal(s) should be selected if the amount of money available for investment is $100,000?

Explanation / Answer

We are given investment which is cash outflow at year zero
Net annual benefit is operating cashflow
Salvage value will get added to the net annual benefit amount for the final year ie year 10.

Thus the NPVs for various projects at MARR of 10% is

Years

A

B

C

D

E

F

G

0

-25000

-10000

-40000

-45000

-15000

-55000

-25000

1

7000

2200

10000

12000

2800

14000

8000

2

7000

2200

10000

12000

2800

14000

8000

3

7000

2200

10000

12000

2800

14000

8000

4

7000

2200

10000

12000

2800

14000

8000

5

7000

2200

10000

12000

2800

14000

8000

6

7000

2200

10000

12000

2800

14000

8000

7

7000

2200

10000

12000

2800

14000

8000

8

7000

2200

10000

12000

2800

14000

8000

9

7000

2200

10000

12000

2800

14000

8000

10

10000

2200

15000

14000

3300

14000

9000

NPV at 10%

$17,426

$3,198

$21,249

$26,824

$2,180

$28,204

$22,311

So Project A and E are mutually exclusive thus only project with higher NPV can be selected which is project A
Project C and D are mutually exclusive thus only project with higher NPV can be selected which is project D

Thus to make investment into various project (excluding C and E) with available investment of $100,000
Project A
Project D
Project G to get maximum NPV of $66561 by investing $95000

Whereas by investing in project D and F we can get NPV of $55028 with full $100,000 but its less than the above one

Years

A

B

C

D

E

F

G

0

-25000

-10000

-40000

-45000

-15000

-55000

-25000

1

7000

2200

10000

12000

2800

14000

8000

2

7000

2200

10000

12000

2800

14000

8000

3

7000

2200

10000

12000

2800

14000

8000

4

7000

2200

10000

12000

2800

14000

8000

5

7000

2200

10000

12000

2800

14000

8000

6

7000

2200

10000

12000

2800

14000

8000

7

7000

2200

10000

12000

2800

14000

8000

8

7000

2200

10000

12000

2800

14000

8000

9

7000

2200

10000

12000

2800

14000

8000

10

10000

2200

15000

14000

3300

14000

9000

NPV at 10%

$17,426

$3,198

$21,249

$26,824

$2,180

$28,204

$22,311

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