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
Answer Q1:
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
Answer Q2:
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.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 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.
Answer 3:
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
Answer 4:
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
Nadia Mohammed Daabis
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 don’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 “Network Design†Option 2 “MBAâ€
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
…..
PVA(ordinary) = PMT 1 – (1+k)-n
K
$75,000 = x 1 – (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 – Certificate cost
= 54.617.934– 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 – Cost of MBA
= 71151.686 – 74,149.91
NPV = $(2,998.223)
MBA
Financial Planning Advice
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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