Data Driven Decision Models 2
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53563633773 |
Type |
Essay |
Writer Level |
Masters |
Style |
APA |
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4 |
Perfect Number of Pages to Order |
5-10 Pages |
Description/Paper Instructions
Data Driven Decision Models 2
1
Data Driven Decision Models 2
Individual Assignment 5
Answer the two questions below.
Question 1: (50 points)
A Flexible Savings Account (FSA) plan allows you to put money into an account at the beginning of the calendar year that can be used for medical expenses. This amount is not subject to federal tax as you pay medical expenses during the year, you are reimbursed by the administrator of the FSA until the money is exhausted. From that point on, you must pay your medical expenses out of your own pocket. On the other hand, if you put more money into your FSA than the medical expenses you incur, this extra money is lost to you. The goal of this study is to identify the optimal amount of FSA contribution to maximize the expected salary after tax and medical expenses.
Your annual salary is $70,000 and your federal income tax rate is 30%. Assume that you put $2,000 into your FSA at the beginning of the year and that medical expenses in a year are normally distributed with mean $2,000 and a standard deviation of $500.
A static model is given in the IA5_Q1_FSA_template.xlsx. Note that the output is the amount of money left to you after i) putting money into the FSA, ii) paying tax, iii) paying out of pocket medical expenditure. Make sure you understand all the calculations in the model.
- a) (5 pts) Determine the input variables of this problem:
- What is(are) the input random variable(s)?
- What is(are) the decision variable(s)?
- b) (15 pts) Add the simulation functionality to the template to output the salary after tax and health care costs (add randomness to any random variables and designate the appropriate outputs). Run the simulation with 1000 replications. Copy and paste the graph of the distribution of salary after tax and health care costs. Explain the shape of the distribution. Particularly, can you explain the spike on the right and the smooth distribution on the left?
- c) (30 pts) Now use RiskSimTable to experiment with the amount of money put in the FSA. Set the range of the amount of FSA contribution to [$0, $4000]. The sections shaded in yellow are intended to assist you organize the information. Also, add RiskSimTable function to the model and update the number of simulations.
Copy and paste your table. Based on the simulation results, answer the following questions.
- If you are risk-neutral, how much would you contribute to your FSA? Explain your answer.
- If you are risk-averse, how much would you contribute to your FSA? Explain your answer.
Question 2: (50 points)
The Greatyear Tire Company has developed a new tire and wants to jump start the marketing of this tire. Based on their testing of the product, it has mean lifetime of 36,500 miles and a standard deviation of 5,000 miles. They also determined that the lifetime follows a normal distribution with those parameters quite well.
The marketing department decided on the following plan for promotion of the product: they are so sure that the product will wear well that they will promise to pay a rebate for any tire that needs replacement at a threshold. They are considering 5 thresholds: 28,000, 29,000, 30,000, 31,000 and 32,000 miles, respectively. They will pay the purchaser back $1 for each full 100 miles the tire is below this threshold. (For example, if the threshold is 29,000, and the tire is replaced at 27,430 miles, the below threshold mileage is 1,570 miles (= 29,000-27,430). Then, the below threshold mileage is divided by 100 (that yields 15.7), so the number of FULL 100s below is 15. This person would be paid $15 for that tire.)
- a) (5 pts) Determine the input variables of this problem:
- What is(are) the input random variable(s)?
- What is(are) the decision variable(s)?
- b) (30 pts) Set up a simulation model in @Risk for each of the 5 different thresholds. Use 1000 replications for each alternative threshold. Also, show the Mean, Standard Deviation, Max rebate, and the probability that a rebate will exceed $5.
Copy and paste your table. Discuss the results briefly (2-3 lines). HINTS:
- Use the spreadsheet titled IA5_Q2_Tire_template.xlsx as a starting point for this analysis.
- The sections shaded in yellow are intended to assist you organize the information.
- Add the simulation functionality to the template to output the rebate per tire (add randomness to any random variables and designate the appropriate outputs).
- To round the number FULL 100s down to the nearest integer, use ‘INT’ function in Excel.
- Use RiskSimTable to compute the summary statistics for all five thresholds simultaneously.
Management expects that the promotion will run for the initial 3 months after release and that sales will be approximately 2 million tires in that period. However, they do not want to invest more than $5 million in the rebate program.
- c) (5 pts) Based on the simulation results, compute the mean total cost for each alternative threshold assuming that sales will be 2 million tires.
- d) (10 pts) Based on the results in part (c), what threshold level would you recommend that Greatyear use so that they will have strong sales but not exceed the $5 million limit in rebate cost. Explain your answer. At that level, what percent of tires will see a greater than $5 rebate?
1
Data Driven Decision Models 2
Individual Assignment
5
Answer the t
wo
questions below.
Question 1: (50 points)
A
Flexible
Savings
Account
(FSA)
plan
allows
you
to
put
money
into
an
account
at
the beginning
of the calendar year that can be
used for medical expenses. This amount
is not subject to federal
tax as you pay medical expenses during the year, you are reimbursed by the administrator of the
FSA until the money is exhausted. From that point on, you must pay your medical expenses out
of
your own pocket. On the other hand, if you put more money into your FSA than the medical
expenses you incur, this extra money is lost to
you.
The
goal
of
this
study
is
to
identify
the
optimal
amount
of
FSA
contribution to maximize the expected salary afte
r tax and medical
expenses.
Your annual salary is $70,000 and your federal income tax rate is 30%.
Assume that you put
$2,000
into your FSA at the beginning of the year and that medical expenses in a year are
normally distributed with mean $2,000 and a standard deviation of $500.
A
static
model
is
given
in
the
IA5_Q1_
FSA_template
.xlsx
.
Note
that
the
output
is
the
amount
of
money
left to you after i) putting money into the FSA, ii) paying tax, iii) paying out of pocket
medical expenditure
.
Make sure you understand all
the
calculations
in the model
.
a)
(
5
pts) Determine
the input v
ariables
of this problem:
What is(are) the input
random
variable(s)?
What is(are) the
decision
variable(s)?
b)
(
15
pts) Add the simulation functionality to the template to output the salary after tax
and health care costs (add randomness to any random variables and designate the
appropriate outputs)
.
Run the
simulatio
n with
1000 replications
.
Copy and paste
the
graph of the
distribution of salary after tax and health care costs.
Explain the shape
of the distribution. Particularly, can you explain the spike on the
right
and the smooth
distribution on the
left
?
c)
(
3
0 pts)
Now
use
R
isk
S
im
T
able
to experiment with the
amount of money put in the FSA.
Set the range of the amount of FSA contribution to [$0, $
4000].
The sections
shaded in
yellow are intended to assist you organize the information
.
Also,
add
RiskSimTable
function to the model and update the number of simulations.
Copy and paste your table
.
Based on the simulation results, answer the following
questions.
i.
If you are risk
–
neu
t
ral, how much would
you
contribute to
your FSA? Explain your
answer.
ii.
If you are risk
–
averse, how much would
you
contribute to
your FSA? Explain your
answer.
1
Data Driven Decision Models 2
Individual Assignment 5
Answer the two questions below.
Question 1: (50 points)
A Flexible Savings Account (FSA) plan allows you to put money into an account at the beginning
of the calendar year that can be used for medical expenses. This amount is not subject to federal
tax as you pay medical expenses during the year, you are reimbursed by the administrator of the
FSA until the money is exhausted. From that point on, you must pay your medical expenses out
of your own pocket. On the other hand, if you put more money into your FSA than the medical
expenses you incur, this extra money is lost to you. The goal of this study is to identify the optimal
amount of FSA contribution to maximize the expected salary after tax and medical expenses.
Your annual salary is $70,000 and your federal income tax rate is 30%. Assume that you put
$2,000 into your FSA at the beginning of the year and that medical expenses in a year are
normally distributed with mean $2,000 and a standard deviation of $500.
A static model is given in the IA5_Q1_FSA_template.xlsx. Note that the output is the amount of
money left to you after i) putting money into the FSA, ii) paying tax, iii) paying out of pocket
medical expenditure. Make sure you understand all the calculations in the model.
- a) (5 pts) Determine the input variables of this problem:
- What is(are) the input random variable(s)?
- What is(are) the decision variable(s)?
- b) (15 pts) Add the simulation functionality to the template to output the salary after tax
and health care costs (add randomness to any random variables and designate the
appropriate outputs). Run the simulation with 1000 replications. Copy and paste the
graph of the distribution of salary after tax and health care costs. Explain the shape
of the distribution. Particularly, can you explain the spike on the right and the smooth
distribution on the left?
- c) (30 pts) Now use RiskSimTable to experiment with the amount of money put in the FSA.
Set the range of the amount of FSA contribution to [$0, $4000]. The sections shaded in
yellow are intended to assist you organize the information. Also, add RiskSimTable
function to the model and update the number of simulations.
Copy and paste your table. Based on the simulation results, answer the following
questions.
- If you are risk-neutral, how much would you contribute to your FSA? Explain your
answer.
- If you are risk-averse, how much would you contribute to your FSA? Explain your
answer.
RUBRIC
QUALITY OF RESPONSE |
NO RESPONSE |
POOR / UNSATISFACTORY |
SATISFACTORY |
GOOD |
EXCELLENT |
Content (worth a maximum of 50% of the total points) |
Zero points: Student failed to submit the final paper. |
20 points out of 50: The essay illustrates poor understanding of the relevant material by failing to address or incorrectly addressing the relevant content; failing to identify or inaccurately explaining/defining key concepts/ideas; ignoring or incorrectly explaining key points/claims and the reasoning behind them; and/or incorrectly or inappropriately using terminology; and elements of the response are lacking. |
30 points out of 50: The essay illustrates a rudimentary understanding of the relevant material by mentioning but not full explaining the relevant content; identifying some of the key concepts/ideas though failing to fully or accurately explain many of them; using terminology, though sometimes inaccurately or inappropriately; and/or incorporating some key claims/points but failing to explain the reasoning behind them or doing so inaccurately. Elements of the required response may also be lacking. |
40 points out of 50: The essay illustrates solid understanding of the relevant material by correctly addressing most of the relevant content; identifying and explaining most of the key concepts/ideas; using correct terminology; explaining the reasoning behind most of the key points/claims; and/or where necessary or useful, substantiating some points with accurate examples. The answer is complete. |
50 points: The essay illustrates exemplary understanding of the relevant material by thoroughly and correctly addressing the relevant content; identifying and explaining all of the key concepts/ideas; using correct terminology explaining the reasoning behind key points/claims and substantiating, as necessary/useful, points with several accurate and illuminating examples. No aspects of the required answer are missing. |
Use of Sources (worth a maximum of 20% of the total points). |
Zero points: Student failed to include citations and/or references. Or the student failed to submit a final paper. |
5 out 20 points: Sources are seldom cited to support statements and/or format of citations are not recognizable as APA 6th Edition format. There are major errors in the formation of the references and citations. And/or there is a major reliance on highly questionable. The Student fails to provide an adequate synthesis of research collected for the paper. |
10 out 20 points: References to scholarly sources are occasionally given; many statements seem unsubstantiated. Frequent errors in APA 6th Edition format, leaving the reader confused about the source of the information. There are significant errors of the formation in the references and citations. And/or there is a significant use of highly questionable sources. |
15 out 20 points: Credible Scholarly sources are used effectively support claims and are, for the most part, clear and fairly represented. APA 6th Edition is used with only a few minor errors. There are minor errors in reference and/or citations. And/or there is some use of questionable sources. |
20 points: Credible scholarly sources are used to give compelling evidence to support claims and are clearly and fairly represented. APA 6th Edition format is used accurately and consistently. The student uses above the maximum required references in the development of the assignment. |
Grammar (worth maximum of 20% of total points) |
Zero points: Student failed to submit the final paper. |
5 points out of 20: The paper does not communicate ideas/points clearly due to inappropriate use of terminology and vague language; thoughts and sentences are disjointed or incomprehensible; organization lacking; and/or numerous grammatical, spelling/punctuation errors |
10 points out 20: The paper is often unclear and difficult to follow due to some inappropriate terminology and/or vague language; ideas may be fragmented, wandering and/or repetitive; poor organization; and/or some grammatical, spelling, punctuation errors |
15 points out of 20: The paper is mostly clear as a result of appropriate use of terminology and minimal vagueness; no tangents and no repetition; fairly good organization; almost perfect grammar, spelling, punctuation, and word usage. |
20 points: The paper is clear, concise, and a pleasure to read as a result of appropriate and precise use of terminology; total coherence of thoughts and presentation and logical organization; and the essay is error free. |
Structure of the Paper (worth 10% of total points) |
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7 points out of 10: Research paper presents an above-average use of formatting skills. The paper has slight errors within the paper. This can include small errors or omissions with the cover page, abstract, page number, and headers. There could be also slight formatting issues with the document spacing or the font Additionally the paper might slightly exceed or undershoot the specific number of required written pages for the assignment. |
10 points: Student provides a high-caliber, formatted paper. This includes an APA 6th edition cover page, abstract, page number, headers and is double spaced in 12’ Times Roman Font. Additionally, the paper conforms to the specific number of required written pages and neither goes over or under the specified length of the paper. |
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