# Case Study The Investment Detective

1. Can you rank the projects simply by inspecting the cash flows?
2. What criteria might you use to rank the projects? Which quantitative ranking methods are better? Why?
3. What is the ranking you found by using quantitative methods? Does this ranking differ from the ranking obtained by simple inspection of the cash flows?
4. What kinds of real investment projects have cash flows similar to those in Exhibit 1?

The investment Detective

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

We canâ€™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

â€“

145.45

254.55

2,000.00

1,090.91

(318.18 )

2

272.73

276.03

â€“

165.29

231.40

â€“

743.80

(49.59)

3

247.93

123.97

â€“

262.96

210.37

â€“

225.39

45.08

4

225.39

â€“

â€“

269.79

191.24

â€“

61.47

239.05

5

204.90

â€“

â€“

268.24

173.86

â€“

43.46

434.64

6

186.28

â€“

â€“

248.37

158.05

â€“

â€“

677.37

7

169.34

â€“

â€“

226.82

143.68

â€“

â€“

1,154.61

8

466.51

â€“

â€“

207.13

130.62

â€“

â€“

â€“

9

â€“

â€“

â€“

189.15

118.75

â€“

â€“

â€“

10

â€“

â€“

â€“

172.72

107.95

â€“

â€“

â€“

11

â€“

â€“

â€“

157.72

98.14

â€“

â€“

â€“

12

â€“

â€“

â€“

143.70

89.22

â€“

â€“

â€“

13

â€“

â€“

â€“

130.64

81.11

â€“

â€“

â€“

14

â€“

â€“

â€“

119.03

73.73

â€“

â€“

â€“

15

â€“

â€“

â€“

â€“

67.03

â€“

â€“

â€“

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 â€œcertain officers of the company have recently asserted that the discount rate should be much higher.â€

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 PIâ€™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

â€¢    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.

â€¢    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

Survey of Finance and Engineering Economics

Presented by

Mohammed Ali Alsendi

Instructor

Professor Wajeeh Elali

Time Value of Money

Time value of money refers to the concept that a dollar today is worth more than a dollar tomorrow.

Case study

NATASHA, 30 years old and has Bachelor of science degree in computer science.

Working as Tier 2 field service representative for a telephony corporation located in Seattle, Washington.

She has \$75,000 that recently inherited from her aunt, and invested this money in 10 years treasury bond.

Terms of Common Inputs

Current Salary \$38,000/-

She donâ€™t expect to lose any income during the Certification or while she earning her MBA.

In both cases, she expect her salary differential will also grow at a rate of 3% per year, for as long as she keep working.

Keep using the interest rate as discount rate for the remainder of the problem

CAMPARISME SUMMARY

Option 1 â€œNetwork Designâ€ Option 2 â€œMBAâ€
Position Tier 3 Managerial Position
Cost \$5,000 \$25,000 / Year
Period 1 year 3 years
Salery Increasment \$10,000 \$20,000
Payment Due End of 1 year Begin of each year
Risk Above 80% on an exam at end of course Evening program which will take 3 years to complete

Summary

Timeline

Option 1

Option 2

t0

t1

t2

t3

\$38,000

\$39,140

\$50,614.20

\$52,132.62

\$38,000 x 3%

(\$39,140+\$10,000) x 3%

\$50,614.20 x 3%

(\$5,000)

(\$25,000)

(\$25,000)

(\$25,000)

\$39,140

\$40,314.20

\$41,523.626

\$38,000 x 3%

\$39,140x 3%

\$39,140 x 3%

t4

\$53,696.59

\$63,369.33

(\$41,523.626+\$20,000) x 3%

\$52,132.62x 3%

Timeline Graph

Current Sutation 38000 39140 40314.200000000004 41523.626000000004 42769.334780000005 44052.414823400009 45373.987268102013 46735.206886145075 Certificate 38000 39140 50614.200000000004 52132.626000000004 53696.604780000009 55307.50292340001 56966.728011102015 58675.729851435077 MBA 38000 39140 40314.200000000004 62123.625999999997 63987.334779999997 65906.954823399996 67884.163468101993 69920.688372145058

Yearly Income

Treasury Bond

Amount \$75,000

Period 10 years

Rate 3.52% (1st June, 2009)*

A marketable, fixed-interest government debt security with a maturity of more than 10 years. Treasury bond make interest payment annualy and the income that holders receive is only taxed the federal level.

t0

t1

t2

t10

(\$75,000)

Treasury Bond

\$9027.19

\$9027.19

\$9027.19

â€¦..

PVA(ordinary) = PMT 1 â€“ (1+k)-n

K

\$75,000 = x 1 â€“ (1+0.0352)-10

0.0352

PMT = \$9027.190

[ ]

[ ]

Certificate

PV4 = (FV4+TB) (1+r)-4

= (53,696.6+ 9027.19) (1+0.0352) -4

PV4 = \$54,617.934

NPV = PV â€“ Certificate cost

= 54.617.934â€“ 5000 = \$49,617.934

t0

t1

t2

t3

\$38,000

\$39,140

\$50,614.20

\$52,132.62

\$38,000 x 3%

(\$39,140+\$10,000) x 3%

\$50,614.20 x 3%

(\$5,000)

t4

\$53,696.60

\$52,132.62x 3%

MBA

PV4 = (FV4+TB) (1+r)-4

= (62,123.626+ 9027.19) (1+0.0352) -4

PV4 = \$71,151.686

1

PMT(due) = PMT 1-(1+r)-n (1+r)

r

= 25,000 1-(1+0.0352)-2 (1+0.352)

0.352

PMT(due) = \$49,149.91

[ ]

[ ]

2

t0

t1

t2

t3

\$38,000

(\$25,000)

(\$25,000)

(\$25,000)

\$39,140

\$40,314.20

\$41,523.626

\$38,000 x 3%

\$39,140x 3%

\$40,314.20 x 3%

PMT(MBA cost) = 25,000 + 49,149.91 = \$ 74,149.91

t4

\$62,123.626

(\$41.523.626+\$20,000) x 3%

From 1 , 2

NPV = PV3 â€“ Cost of MBA

= 71151.686 â€“ 74,149.91

NPV = \$(2,998.223)

MBA

I will suggest Natasha as a Financial Planning to enroll in the Certificate Program based on her desire that she is not expect to lose any income during the certificate. Moreover, its impossible to implement this condition if she choose the MBA program unless she sell a fraction of her future earning from her treasury bond or she could barrow money from other recourses.

Thank you

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