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Question 1 (25 points): An investor has two investment alternatives, Project A and Project B, that are mutually exclusive. Ot
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Answer #1

Correct Answer:

A

B

C

D =A*C

E =B*C

F =D+E

year

Cash outflow

Cash inflow

PV of $1 @ 10%

PV of cash outflow

Pv of cash inflow

PV of net cash flow

0

$      (5,000.00)

$                                -  

1.0000

$       (5,000.00)

$                          -  

$             (5,000.00)

1

$      (3,500.00)

$                                -  

0.9091

$       (3,181.82)

$                          -  

$             (3,181.82)

2

$      (2,500.00)

$                   3,000.00

0.8264

$       (2,066.12)

$             2,479.34

$                   413.22

3

$                   3,000.00

0.7513

$                      -  

$             2,253.94

$                2,253.94

4

$                   3,000.00

0.6830

$                      -  

$             2,049.04

$                2,049.04

5

$                   3,000.00

0.6209

$                      -  

$             1,862.76

$                1,862.76

6

$                   2,500.00

0.5645

$                      -  

$             1,411.18

$                1,411.18

7

$                   2,500.00

0.5132

$                      -  

$             1,282.90

$                1,282.90

8

$                   2,500.00

0.4665

$                      -  

$             1,166.27

$                1,166.27

8

8500

0.46650738

$                      -  

$             3,965.31

$                3,965.31

NPV project A

$                6,222.81

Project A

NPV1

$      6,222.81

NPV2

$        (118.01)

NPV1-NPV2

          6,340.82

npv1/(npv1-npv2)

0.981389178

r1

10.0%

r2

23.0%

r2-r1

13.0%

IRR = r1+(npv1/(npv1-npv2) * (r2-r1)

22.76%

Working:

For the purpose of calculation of IRR, we have to assume a discount rate on which the npv of the project is less than zero .

A

B

C

D =A*C

E =B*C

F =D+E

year

Cash outflow

Cash inflow

PV of $1 @ 23%

PV of cash outflow

Pv of cash inflow

PV of net cash flow

0

$                                  (5,000.00)

$                   -  

1.0000

$              (5,000.00)

$               -  

$    (5,000.00)

1

$                                  (3,500.00)

$                   -  

0.8130

$              (2,845.53)

$               -  

$    (2,845.53)

2

$                                  (2,500.00)

$      3,000.00

0.6610

$              (1,652.46)

$ 1,982.95

$          330.49

3

$      3,000.00

0.5374

$                             -  

$ 1,612.15

$      1,612.15

4

$      3,000.00

0.4369

$                             -  

$ 1,310.69

$      1,310.69

5

$      3,000.00

0.3552

$                             -  

$ 1,065.60

$      1,065.60

6

$      2,500.00

0.2888

$                             -  

$      721.95

$          721.95

7

$      2,500.00

0.2348

$                             -  

$      586.95

$          586.95

8

$      2,500.00

0.1909

$                             -  

$      477.20

$          477.20

8

8500

0.1909

$                             -  

$ 1,622.48

$      1,622.48

NPV project A

$       (118.01)

Requirement 2:

A

B

C

D =A*C

E =B*C

F =D+E

year

Cash outflow

Cash inflow

PV of $1 @ 10%

PV of cash outflow

Pv of cash inflow

PV of net cash flow

0

$    (15,000.00)

$                                -  

1.0000

$    (15,000.00)

$                          -  

$           (15,000.00)

1

$      (4,000.00)

$                   4,500.00

0.9091

$       (3,636.36)

$             4,090.91

$                   454.55

2

$                     -  

$                   4,250.00

0.8264

$                      -  

$             3,512.40

$                3,512.40

3

$                   4,000.00

0.7513

$                      -  

$             3,005.26

$                3,005.26

4

$                   3,750.00

0.6830

$                      -  

$             2,561.30

$                2,561.30

5

$                   3,500.00

0.6209

$                      -  

$             2,173.22

$                2,173.22

6

$                   3,250.00

0.5645

$                      -  

$             1,834.54

$                1,834.54

7

$                   3,000.00

0.5132

$                      -  

$             1,539.47

$                1,539.47

8

$                   1,750.00

0.4665

$                      -  

$                 816.39

$                   816.39

8

$                11,000.00

0.4665

$                      -  

$             5,131.58

$                5,131.58

NPV project B

$                6,028.71

Working:

Project b

NPV1

$                6,028.71

NPV2

$                    (87.71)

NPV1-NPV2

                   6,116.42

NPV1/(NPV1-NPV2)

0.985660051

r1

0.1

r2

0.18

r2-r1

0.08

IRR = r1+(npv1/(npv1-npv2) * (r2-r1)

17.89%

Working:

A

B

C

D =A*C

E =B*C

F =D+E

year

Cash outflow

Cash inflow

PV of $1 @ 10%

PV of cash outflow

Pv of cash inflow

PV of net cash flow

0

$                                (15,000.00)

$                   -  

1.0000

$           (15,000.00)

$               -  

$ (15,000.00)

1

$                                  (4,000.00)

$      4,500.00

0.8475

$              (3,389.83)

$ 3,813.56

$          423.73

2

$                                                  -  

$      4,250.00

0.7182

$                             -  

$ 3,052.28

$      3,052.28

3

$      4,000.00

0.6086

$                             -  

$ 2,434.52

$      2,434.52

4

$      3,750.00

0.5158

$                             -  

$ 1,934.21

$      1,934.21

5

$      3,500.00

0.4371

$                             -  

$ 1,529.88

$      1,529.88

6

$      3,250.00

0.3704

$                             -  

$ 1,203.90

$      1,203.90

7

$      3,000.00

0.3139

$                             -  

$      941.78

$          941.78

8

$      1,750.00

0.2660

$                             -  

$      465.57

$          465.57

8

$    11,000.00

0.2660

$                             -  

$ 2,926.42

$      2,926.42

NPV project B

$          (87.71)

Project B should be accepted.

End of answer.

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