Category: Mathematics

How do you calculate the level of net working capital (NWC)? What is the value of NWC at the end of Year 0, 1, and 6?

Canyon Buff’s

In this case study: (go into debt details with each question)

1. When calculating incremental unlevered net income, should we include all the expenses mentioned in the case? If not, what expenses should we exclude and why.

2. Is there a big jump of unlevered net income from Year 5 to Year 6? Why?

3. How do you calculate the level of net working capital (NWC)? What is the value of NWC at the end of Year 0, 1, and 6?

Case – Canyon Buff’s Chemical Equipment

This case is a simple capital budgeting exercise of the following topics:

• Incremental unlevered net income
• Free cash flow
• Sensitivity analysis and scenario analysis

Introduction

Canyon Buff Corp. has developed a new construction chemical that greatly improves the durability and weatherability of cement-based materials. After spending $500,000 on the research of the potential market for the new chemical, Canyon Buff is considering a project that requires an initial investment of $9,000,000 in manufacturing equipment.

• The equipment must be purchased before the chemical production can begin. For tax purposes, the equipment is subject to a 5-year straight-line-depreciation schedule, with a projected zero salvage value. For simplicity, however, we will continue to assume that
• the asset can actually be use doubt into the indefinite future (i.e., the actual useful life is effectively infinite).

• Canyon Buff anticipates that the sales will be $30,000,000 in the first year (Year 1). They expect that sales will initially grow at an annual rate of 6% until the end of sixth year (e.g., Year 6 sales = (1+6%)* Year 5 sales). After that, the sales will grow at the estimated 2% annual rate of inflation in perpetuity (e.g., Year 7 sales = (1+2%)* Year 6 sales).

• The cost of goods sold is estimated to be 72% of sales for each year.

• The accounting department also estimates that at the introduction in Year 0, the new product’s required initial net working capital will be $6,000,000. In future years (e.g., Year 1 and beyond) accounts receivable are expected to be 15% of the next year sales, inventory is expected to be 20% of the next year’s cost of goods sold and accounts payable are expected to be 15% of the next year’s cost of goods sold.

• The selling, general and administrative expense is estimated to be $6,000,000 per year, but $1million of this amount is the overhead expense that will be incurred even if the project is not accepted.

• The market research to support the product was completed last month at a cost of $500,000 to be paid by the end of next year.

• The annual interest expense tied to the project is $1,000,000.

• Canyon Buff has a cost of capital of 20% and faces a marginal tax rate of 30% and an average tax rate is 20%.

Explain how generating a simple random sample of 20 candy bars off the production line would be different than generating a simple random sample of 20 employees.

stats hw

4.) Explain how to generate a simple random sample of 20 employees out of the 85 total
employees who are working at a candy bar factory.

5.) Explain how generating a simple random sample of 20 candy bars off the production line
would be different than generating a simple random sample of 20 employees.

6.) Explain why sampling without replacement is preferable to sampling with replacement

7.) Provide an example of when you might want to take a systematic random sample
instead of a simple random sample, and explain what the advantages of a systematic
random sample might be.

8.) Provide an example of when you might want to take a stratified random sample instead of
a simple random sample, and explain what the advantages of a stratified random sample
might be.

9.) Provide an example of when you might want to take a cluster random sample instead of a
simple random sample, and explain what the advantages of a cluster sample might be.
Also, explain how you would choose the cluster sample.

10.) A telephone survey evaluating unemployment claims asks the question, “Do you think
people should be paid not to work?” The survey was conducted during the hours of 8:00
am to 4:00 pm for homeowners with listed landlines.

What are some possible sources of
error that might arise in their effort to estimate the population proportion who would
answer “yes” or “no” to this question? (Be sure to both identify any relevant types of
error with one of your vocabulary words and explain why it might occur.)

11.) Define the concept of “sampling error”. (Note: Your definition should include the idea
of sample, population, statistic, parameter.)

What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.

Introduction
Your instructor will provide you with a data file that includes data on five variables:

SALES represents the number of sales made this week.

CALLS represents the number of sales calls made this week.

TIME represents the average time per call this week.

YEARS represents years of experience in the call center.

TYPE represents the type of training the employee received.
Part A:

Exploratory Data Analysis
Preparation

• Open the files for the course project and the data set.

• For each of the five variables, process, organize, present and summarize the data. Analyze each variable by itself using graphical and numerical techniques of summarization. Use Excel as much as possible, explaining what the results reveal. Some of the following graphs may be helpful:

stem-leaf diagram, frequency/relative frequency table, histogram, boxplot, dotplot, pie chart, bar graph. Caution: not all of these are appropriate for each of these variables, nor are they all necessary.

More is not necessarily better. In addition be sure to find the appropriate measures of central tendency, the measures of dispersion, and the shapes of the distributions (for the quantitative variables) for the above data. Where appropriate, use the five number summary (the Min, Q1, Median, Q3, Max). Once again, use Excel as appropriate, and explain what the results mean.

• Analyze the connections or relationships between the variables. There are ten possible pairings of two variables. Use graphical as well as numerical summary measures. Explain the results of the analysis. Be sure to consider all 10 pairings. Some variables show clear relationships, while others do not.

Report Requirements

• From the variable analysis above, provide the analysis and interpretation for three individual variables. This would include no more than 1 graph for each, one or two measures of central tendency and variability (as appropriate), the shapes of the distributions for quantitative variables, and two or three sentences of interpretation.

• For the 10 pairings, identify and report only on three of the pairings, again using graphical and numerical summary (as appropriate), with interpretations.  note that at least one pairing must include a qualitative variable and at least one pairing must not include a qualitative variable.

• Prepare the report in Microsoft Word, integrating graphs and tables with text explanations and interpretations. Be sure to include graphical and numerical back up for the explanations and interpretations. Be selective in what is included in the report to meet the requirements of the report without extraneous information.

• All DeVry University policies are in effect, including the plagiarism policy.

• Project Part A report is due by the end of Week 2.

• Project Part A is worth 100 total points. See grading rubric below.
Submission:

The report, including all relevant graphs and numerical analysis along with interpretations
Format for report:

A. Brief Introduction

B. Discuss 1st individual variable, using graphical, numerical summary and interpretation

C. Discuss 2nd individual variable, using graphical, numerical summary and interpretation

D. Discuss 3rd individual variable, using graphical, numerical summary and interpretation

E. Discuss 1st pairing of variables, using graphical, numerical summary and interpretation

F. Discuss 2nd pairing of variables, using graphical, numerical summary and interpretation

G. Discuss 3rd pairing of variables, using graphical, numerical summary and interpretation

H. Conclusion
Part B: Hypothesis Testing and Confidence Intervals
Complete the following four hypotheses, using α = 0.05 for each. The week 5 spreadsheet can be used in these analyses.

1. Mean sales per week exceed 42.5 per salesperson

2. Proportion receiving online training is less than 55%

3 Mean calls made among those with no training is at least 145

4. Mean time per call is 14.7 minutes

• Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager’s belief. Use the Eight Steps of a Test of Hypothesis from Section 9.1 of your text book as a guide. You can use either the p-value or the critical values to draw conclusions. Be sure to explain your conclusion and interpret that to the claim in simple terms

• Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals.

• Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical.

• All DeVry University policies are in effect, including the plagiarism policy.

• Project Part B report is due by the end of Week 6.

• Project Part B is worth 100 total points. See grading rubric below.
Format for report:

A. Summary Report (about one paragraph on each of the four speculations)

B. Appendix with the calculations of the Eight Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas or spreadsheet screen shots used in the calculations.
Final Project: Regression and Correlation Analysis

Use the dependent variable (labeled Y) and one of the independent variables (labeled X1, X2, and X3) in the data file. Select and use one independent variable throughout this analysis. Use Excel to perform the regression and correlation analysis to answer the following. The week

6 spreadsheet can be helpful in this work.

1. Generate a scatterplot for the specified dependent variable (Y) and the selected independent variable (X), including the graph of the “best fit” line. Interpret.

2. Determine the equation of the “best fit” line, which describes the relationship between the dependent variable and the selected independent variable.
3. Determine the correlation coefficient. Interpret.

4. Determine the coefficient of determination. Interpret.

5. Test the utility of this regression model by completing a hypothesis test of b=0 using α=0.10. Interpret results, including the p-value.

6. Based on the findings in steps 1-5, analyze the ability of the independent variable to predict the dependent variable.

7. Compute the confidence interval for b, using a 95% confidence level. Interpret this interval.

8. Compute the 99% confidence interval for the dependent variable, for a selected value of the independent variable. Each student can choose a value to use for the independent variable (use same value in the next step). Interpret this interval.

9. Using the same chosen value for part (8), estimate the 99% prediction interval for the dependent variable. Interpret this interval.

10. What can be said about the value of the dependent variable for values of the independent variable that are outside the range of the sample values? Explain.

11. Describe a business decision that could be made based on the results of this analysis. In other words, how might the business operations change based on these statistical results.

12. All DeVry University policies are in effect, including the plagiarism policy.

13. Final Project report is due by the end of Week 7.

14. Final Project is worth 130 total points. See grading rubric below.

Summarize your results from Steps 1-11 in a 3-page report. The report should explain and interpret the results in ways that are understandable to someone who does not know statistics.
Submission:

The Word document, summary report should be submitted for questions 1-11. The Excel output can be included as an appendix, if needed.

Format for report:

A. Summary Report

B. Steps 1-11 addressed with appropriate output, graphs and interpretations. Be sure to number each step 1-11.

What Probability Distribution ( for example: triangular distribution, discrete distribution, or shewed distribution etc.) could you apply to this working scenario or one that have not listed?

Scenario

1. How can a Simulation Model help with your work? For example, In the electrical industry (Electrician) a Simulation Model could be use to determine or used for etc

2. What Probability Distribution ( for example: triangular distribution, discrete distribution, or shewed distribution etc.) could you apply to this working scenario or one that have not listed?

Explain why you would use this particular probability distribution and how would you apply it.