- QUESTION
Please answer any ten of the twelve questions. Each question is weighted equally. If you answer more than ten questions, I will select the best ten. Note that the highest grade you can receive is 100 points.
In addition to posting this answer sheet, be sure to post an excel file that shows your calculations. DO NOT just insert Excel or CB derived answers in your answer sheet.
For CB output, you should paste the forecast output in your Excel calculations file. Show the split view in all CB output.
- Two investments (A and B, below) have been proposed to the Capital Investment committee of your organization;
- The required rate of return for your company is 6%. What is the NPV for each investment? Assume all costs and benefits occur at the beginning of the year indicated.
- What is the payback period for each investment?
- Which investment would you recommend and why?
|
Investment A |
Year 0 |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
|
Costs: |
$125,000 |
$10,000 |
$10,000 |
$10,000 |
$10,000 |
$10,000 |
|
Benefits: |
- |
$90,000 |
$55,000 |
$35,000 |
$20,000 |
$20,000 |
|
|
|
|
|
|
|
|
|
Investment B |
Year 0 |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
Year 5 |
|
Costs: |
$70,000 |
|
|
|
|
|
|
Benefits: |
|
$45,000 |
$15,000 |
$10,000 |
$10,000 |
$15,000 |
- Unfortunately, the Capital Investment Committee refused to approve your recommendation (Problem 1) since you did not consider the uncertainty inherent in these types of investments. You pull out your very dog-eared text from PMAN 635 and repeat your analysis, this time using Crystal Ball and the following information:
- Investment A:
- Year 0 Investment cost: Triangular distribution (optimistic: $100,000; most likely: $125,000; pessimistic: $200,000)
- Year 1-5 operating cost: Normal distribution (mean of $10,000, standard deviation of $2,000)
- Investment A:
- Year 1 Benefits: Normal distribution (mean of $90,000, standard deviation of $20,000)
- Year 2 Benefits: Normal distribution (mean of $55,000, standard deviation of $15,000)
- Year 3 Benefits: Normal distribution (mean of $35,000, standard deviation of $10,000)
- Year 4 Benefits: Normal distribution (mean of $20,000, standard deviation of $5000)
- Year 5 Benefits: Normal distribution (mean of $20,000, standard deviation of $5000)
- Investment B:
- Year 0 Investment cost: Uniform distribution (Minimum: $65,000; Maximum: $75,000)
- Year 1 Benefits: Normal distribution (mean of $45,000, standard deviation of $20,000)
- Year 2 Benefits: Normal distribution (mean of $15,000, standard deviation of $5,000)
- Year 3 Benefits: Normal distribution (mean of $10,000, standard deviation of $3,000)
- Year 4 Benefits: Normal distribution (mean of $10,000, standard deviation of $3,000)
- Year 5 Benefits: Normal distribution (mean of $15,000, standard deviation of $5,000)
If the IRR is still 6%, what is the NPV for each investment?
- Using the forward and backward pass method, identify the Critical Path and total duration for the following network. Show all work.
|
Task |
duration |
Pred |
|
a |
10 |
|
|
b |
5 |
a |
|
c |
8 |
a |
|
d |
3 |
b |
|
e |
5 |
c |
|
f |
5 |
d, e |
- For the network below:
- Calculate T-E and Variance for each activity.
- Calculate the expected duration of the network. Do not use Crystal Ball.
- What is the probability the network will take no more than 21 days? Use the Z-table or Excel’s NORMDIST function, not Crystal Ball. Be sure to show all work.
|
Task |
Optimistic Duration |
Most Likely duration |
Pessimistic Duration |
T-E |
Var |
Pred |
|
A |
8 |
10 |
14 |
|
|
|
|
B |
4 |
5 |
7 |
|
|
A |
|
C |
8 |
8 |
9 |
|
|
A |
|
D |
3 |
3 |
3 |
|
|
B, C |
- The first unit produced by a manufacturer required 6 hours. If the industry uses a 90 percent learning curve rate, how long should the following units take?
- Unit 2
- Unit 3
- Unit 4
- Please answer discussion question 6 at the end of Chapter 4 of Mantel. Limit your answer to 200 words or less.
- Enter the tasks and resources in the attached file (Midterm Question 7.doc) into MS Project. Note that there are two tables in this file. What is the total duration and cost for your project? Include your MSP project file with your submission.
- Please answer each of the following:
- What is the expected time to complete a task with an optimistic (a), most likely (m), and pessimistic (b) times of 3, 4 and 7 days respectively?
- What is the standard deviation of the same task, assuming that 99.7% of the outcomes fall between a and b?
- What is the standard deviation of the same task, assuming that 90% of the outcomes fall between a and b?
- There are three (and only three) paths through a network (project), each with a probability of completion in less than 24 months as indicated:
- S- a-b-F P1(<24) = .95
- S- d-e-F P2(<24) = .85
- S- g-h-F P3(<24) = .90
- If the tasks are independent, what is the probability of the project being completed within 24 months? Note: S is the start node, F is the finish node
- What is the probability the project being completed in 24 months or longer?
- You are a project manager who is reviewing the estimates for the cost of materials. You therefore begin tracking the estimated cost estimates of two procurement specialists and comparing their estimates with the actual costs of the materials once ordered. You obtain the information reflected in the attached tracking table.
- Does the data indicate that either of the two procurement specialists is biased? Which one? In which direction?
- Regardless of bias, does one procurement specialist appear to be more accurate in their estimates than the other? Which one?
Be sure to explain your answers. Hint, review the material in Section 4.3 of Mantel.
- Referring to the project in question 7:
- Using the information contained in the attached file (Midterm Question 11), what is the new duration and cost for the project? You do not have to use MSP to answer this question. Note, since the tasks are laddered, there is only one path through the network. Therefore, TEproject = ƩTE activities and the VARproject = ƩVAR
- Using Table 5-7 in Mantel, what is the probability that you can finish the project in 115 days?
- Referring back to Question 2, you have proudly submitted your analysis of investments A and B. You are called back in to the Capital Investment Committee for what you assume will be to receive their gracious thanks for a job well done. Unfortunately, you realize there is a new member on the committee and you recognize a former Professor of yours from UMUC. He is still wearing both a belt and suspenders, so you are not surprised at his first question: “And what is the 90% solution?” You realize he is really asking for the value that each investment will exceed 90% of the time? Fortunately, you still have access to crystal ball, so you whip out your laptop and…
- Well, what is the answer for Investment A?
- And, what is the answer for Investment B?
| Subject | Statistics | Pages | 13 | Style | APA |
|---|
Answer
-
- Two investments (A and B, below) have been proposed to the Capital Investment committee of your organization;
- The required rate of return for your company is 6%. What is the NPV for each investment? Assume all costs and benefits occur at the beginning of the year indicated.
- What is the payback period for each investment?
- Which investment would you recommend and why?
Investment A
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Costs:
$125,000
$10,000
$10,000
$10,000
$10,000
$10,000
Benefits:
-
$90,000
$55,000
$35,000
$20,000
$20,000
Investment B
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Costs:
$70,000
Benefits:
$45,000
$15,000
$10,000
$10,000
$15,000
ANSWER
- Net Present Value (NPV)
Where Ct is cash inflow during project period
C0 is the total investment cost
t is the number of time periods
r is the discount rate=6%
A
Cash inflow
$90000
$55000
$35000
$20000
$20000
$220000
Cash investment
$125000
$10000
$10000
$10000
$10000
$10000
$175000
B
Cash inflow
$45000
$15000
$10000
$10000
$15000
$95000
Cash investment
$70000
0
0
0
0
0
$70000
- Payback Period
For A is (125+10)-90=45
(45+10)-55=0
Hence the payback period is 2 years
For B is (70-(45+15+10)= 0
Hence payback period is three years
- Base on the NPV, the recommended project is project B since its value is positive.
Based on payback period I would still choose B since its cash inflow increases even after payback period.
- Using the forward and backward pass method to identify the Critical Path and total duration for the following network. Show all work.
Task
Duration
Pred
a
10
b
5
a
c
8
a
d
3
b
e
5
c
f
5
d, e
ANSWER
Critical path is the longest duration
- For the network below:
- Calculate T-E and Variance for each activity.
- Calculate the expected duration of the network. Do not use Crystal Ball.
- What is the probability the network will take no more than 21 days? Use the Z-table or Excel’s NORMDIST function, not Crystal Ball. Be sure to show all work.
Task
Optimistic Duration
Most Likely duration
Pessimistic Duration
T-E
Var
Pred
A
8
10
14
10.33
1
B
4
5
7
5.17
0.25
A
C
8
8
9
8.17
0.028
A
D
3
3
3
3
0
B, C
where o is the optimum time
m is the most likely duration
p is the pessimist duration
variance
- Expected duration of the network
This is same as the duration of the critical path
The probability that the network will take 21 days will be given by:
Using the Z-table,
- The first unit produced by a manufacturer required 6 hours. If the industry uses a 90 percent learning curve rate, how long should the following units take?
- Unit 2
- Unit 3
- Unit 4
ANSWER
where is direct labour hours for the first unit
is cumulative number of units produced
learning rate (as decimal)
- For unit 2;
- Please answer discussion question 6 at the end of Chapter 4 of Mantel. Limit your answer to 200 words or less.
ANSWER
QUESTION: Distinguish among highly probable risks, extremely serious risks, and highly vulnerable areas in risk identification.
Highly probable risks have a great chance of happening. The magnitudes of such risks can be insignificant to very serious.
Extremely serious risks are risks that have very momentous concerns while their chances of happening may be very low to very high.
Highly vulnerable areas refer to risks that are both highly possible and exceptionally serious.
- Please answer each of the following:
- What is the expected time to complete a task with an optimistic (a), most likely (m), and pessimistic (b) times of 3, 4 and 7 days respectively?
- What is the standard deviation of the same task, assuming that 99.7% of the outcomes fall between a and b?
- What is the standard deviation of the same task, assuming that 90% of the outcomes fall between a and b?
ANSWER
- Standard deviation σ
Recall,
If probability 99.7%, then it using tables; means is
If duration fall between a and b, then
Hence
- If probability is 90%, using tables,
Hence
- There are three (and only three) paths through a network (project), each with a probability of completion in less than 24 months as indicated:
S- a-b-F P1(<24) = .95
S- d-e-F P2(<24) = .85
S- g-h-F P3(<24) = .90
- If the tasks are independent, what is the probability of the project being completed within 24 months? Note: S is the start node, F is the finish node
- What is the probability the project being completed in 24 months or longer?
ANSWER
- If all are independent, then the probability of project being completed in 24 hours is
that is
.
- You are a project manager who is reviewing the estimates for the cost of materials. You therefore begin tracking the estimated cost estimates of two procurement specialists and comparing their estimates with the actual costs of the materials once ordered. You obtain the information reflected in the attached tracking table.
- Does the data indicate that either of the two procurement specialists is biased? Which one? In which direction?
- Regardless of bias, does one procurement specialist appear to be more accurate in their estimates than the other? Which one?
Be sure to explain your answers. Hint; review the material in Section 4.3 of Mantel.
ANSWER
- The data has indicated that the first procurement specialist is biased since his MAR and Tracking signal tend to drift away from zero. i.e are large. The biases are also positive.
- The first procurement officer is more accurate than the second since column and are exact (there is no variation in their values).
- Referring to the project in question 7:
- Using the information contained in the attached file (Midterm Question 11), what is the new duration and cost for the project? You do not have to use MSP to answer this question. Note, since the tasks are laddered, there is only one path through the network. Therefore, TEproject = ƩTE activities and the VARproject = ƩVAR
- Using Table 5-7 in Mantel, what is the probability that you can finish the project in 115 days?
ANSWER
Activities
Most Likely Duration (days)
Optimistic Duration (days)
Pessimistic Duration (days)
Expected Duration T E
Var
σ
Charter Approved
0
0
Phase 1
Work Package 1
Activity 1
0
3
7
5
0.444
0.667
Activity 2
5
4
7
5.167
1.25
1.118
Activity 3
5
4
8
5.333
0.444
0.667
Work Package 2
Activity 4
10
8
15
10.5
1.361
1.167
Activity 5
10
8
12
10
0.444
0.667
Activity 6
10
9
15
10.667
1
1
Work Package 3
Activity 7
5
3
8
5.167
0.694
0.833
Activity 8
10
8
15
10.5
1.361
1.167
Activity 9
15
10
22
15.333
4
2
Phase II
Work Package 4
Activity 10
5
4
8
5.333
0.444
0.667
Activity 11
5
4
10
5.667
1
1
Activity 12
10
10
15
10.833
0.694
0.833
Work Package 5
Activity 13
5
3
10
5.5
1.361
1.167
Activity 14
5
4
10
5.667
1
1
Completion
0
0
110.667
15.497
13.953
- New duration is 110.667 days
- P(<115)
Using table 5-7,
Hence P(<115)=0.6179
- Two investments (A and B, below) have been proposed to the Capital Investment committee of your organization;
References
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