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# The investment detective case solutions

The investment Detective

We can rank the projects by simply inspecting the cash flows (mention bellow), yet it’s not a good measure to rank them.

We can’t rank the projects by only simple inspection of the cash flows because of the time value of money and cost of capital of companies. We use capital budgeting tools to measure financial performance of projects.

The Ranking by simply inspecting the cash flows:

Rank

1st

2nd

3rd

4th

5th

6th

7th

8th

Projects

3

5

8

4

1

7

6

2

Cash Flows

\$10,000

\$4,200

\$4,150

\$3,561

\$3,310

\$2,560

\$2,200

\$2,165

In order to rank these projects, in a purely quantitative manner, we used the following for the 8 projects:

A. Net Present Value (NPV)

B. Internal Rate of Return (IRR)

C. Payback Period (PP)

D. Profitability Index (PI)

A. Net Present Value (NPV)

Year

Project 1

Project 2

Project 3

Project 4

Project 5

Project 6

Project 7

Project 8

0

(\$2,000)

(\$2,000)

(\$2,000)

(\$2,000)

(\$2,000)

(\$2,000)

(\$2,000)

(\$2,000)

1

300.00

1,514.55

-

145.45

254.55

2,000.00

1,090.91

(318.18 )

2

272.73

276.03

-

165.29

231.40

-

743.80

(49.59)

3

247.93

123.97

-

262.96

210.37

-

225.39

45.08

4

225.39

-

-

269.79

191.24

-

61.47

239.05

5

204.90

-

-

268.24

173.86

-

43.46

434.64

6

186.28

-

-

248.37

158.05

-

-

677.37

7

169.34

-

-

226.82

143.68

-

-

1,154.61

8

466.51

-

-

207.13

130.62

-

-

-

9

-

-

-

189.15

118.75

-

-

-

10

-

-

-

172.72

107.95

-

-

-

11

-

-

-

157.72

98.14

-

-

-

12

-

-

-

143.70

89.22

-

-

-

13

-

-

-

130.64

81.11

-

-

-

14

-

-

-

119.03

73.73

-

-

-

15

-

-

-

-

67.03

-

-

-

S PV(CF)

2,073.086

1,914.545

2,393.920

2,228.222

2,129.702

2,000

2,165.041

2,182.984

NPV

73.086

(85.455)

393.920

228.222

129.702

0

165.041

182.984

Rank

6th

8th

1st

2nd

5th

7th

4th

3rd

B. Internal Rate of Return (IRR)

Projects

Project 1

Project 2

Project 3

Project 4

Project 5

Project 6

Project 7

Project 8

IRR

10.87%

6.31%

11.33%

12.33%

11.12%

10.00%

15.26%

11.41%

Rank

6th

8th

4th

2nd

5th

7th

1st

3rd

All of these projects are accepted except Project 2 because its cost of capital has higher percentage than the percentage project internal rate of return. Moreover, Project 6 will be a subject of be in different because the cost of capital equal to internal rate of return, which lead to break even project.

COC = 10%

C. Payback Period (PP)

In Payback Period there are two method, non-discounted cash flow and discounted cash flow. Drawback of non-discounted cash flow does not consider TVM and the rate of return, and the discounted cash flow does not examine all the cash flows.

Projects

Project 1

Project 2

Project 3

Project 4

Project 5

Project 6

Project 7

Project 8

Payback Year

7

2

15

6

8

1

2

7

Payback

2,310

2,000

10,000

1,977

2,240

2,200

2,100

4,150

Discounted Payback

1,606.58

1,790.58

2,393.92

1,360.10

1,493.78

2,000

1,834.71

2,182.98

Decision (DPP)

Reject

Reject

Accept

Reject

Reject

Be in different

Reject

Accept

Rank

6th

5th

1st

8th

7th

3rd

4th

2nd

D. Profitability Index (PI)

Projects

Project 1

Project 2

Project 3

Project 4

Project 5

Project 6

Project 7

Project 8

PI

1.037

0.957

1.197

1.092

1.065

1.000

1.083

1.0773

Rank

6th

8th

1st

2nd

5th

7th

3rd

4th

All the projects will be undertaken except for project 8 since it is mutually exclusive with project 7, and project 6 and 2 will not be undertaken since they have IRR that is less than the 10%, the discount rate. Project 1 also might not be taken since “certain officers of the company have recently asserted that the discount rate should be much higher.”

Rank

1st

2nd

Project

8

7

IRR

11.41%

15.26%

NPV

182.98

165.04

Since these two projects are mutually exclusive and have the IRR above 10%, Project 8 will be chosen because it has higher NPV.

Rank

1st

2nd

3rd

4th

5th

6th

7th

8th

Project

3

4

8

7

5

1

6

2

PI

1.197

1.092

1.083

1.0773

1.065

1.037

1.000

0.957

All the projects will be undertaken except for project 7 since it is mutually exclusive with project 8, and project 6 and 2 will not be undertaken since they have PI’s equal to 1 and 0.957, because they are not greater than 1.

Selected Projects as per the quantitative methods as follow:

Rank

1st

2nd

3rd

4th

Projects

Projects 3

Projects 4

Projects 8

Projects 5

• Comparing the quantitative methods, we noticed that project 3 scored 1st four times using simple inspections of cash flows, NPV, PP, and PI. Project 7 however, scored 1st only through using the IRR method. Looking on the last ranked projects, project 2 has scored last 4 times using simple inspections of cash flows, NPV, IRR, and PI.

• Net Present Value is considered the best approach since it:

i. Uses Cash Flows.

ii. Uses all the Cash Flows of the project.

iii. And discounts the Cash Flows properly.

And through using the NPV approach, Project 3 got the highest NPV, 393.92, and then comes 4, 8, 5 and 1.

Selected Projects as per the quantitative methods as follow:

Rank

1st

2nd

3rd

4th

Projects

Projects 3

Projects 4

Projects 8

Projects 5

The above table showing that it is absolutely the rank will be differ from the ranking obtain by simple inception of the cash flow

Project 1 Bonds

Project 2 Equipment Depreciation

Project 3 Land or real assets investments

Project 4 Diary factory that incur agricultural costs

Project 5 Car Loan

Project 6 Stock

Project 7 Trucks Depreciation

Project 8 Construction projects

0.10865030333732562 6.3088234267993482E-2 0.11326357684480115 0.12328333077501186 0.11121604343002223 0.10000000000000009 0.15257139008454979 0.1140642023834566

IRR

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