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Unformatted text preview: Starting Mathematics for Business Decisions Part 1: Probability and Simulation (i) Click on Slide Show in the main menu. (ii) Click on From Beginning in the next ribbon. (iii) When you are done reading each F title page, move to the next page by clicking anywhere on the screen.
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Title page Published and Distributed by Probabilit y Mathematical Association of Am The and With Interdisciplinary Multimedia Projects Simulatio n cisions De Math siness cs for Bu emati
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Business Decisions Mathematical Models Computer s - f X ( x ) dx = 00 er 20 d Winn Awar M ICTC ellence xc for E ovation nn and I the ed at nt Prese CNSF 2003 tion, i Exhib on, DC gt ashin W Mathematics for Business Decisions Part AuthorsProbability & Simulation 1:
Written By Dr. Richard B. Thompson Department of Mathematics University of Arizona
Business Projects By Dr. Christopher G. Lamoureux Department of Finance University of Arizona
O For 2007 ffi ce Mathematics for Business Decisions Part 1 Release 2, 2009 2009 by The Arizona Board of Regents for The University of Arizona. All rights reserved. Contents
F F F F F F F F Contents What would you like to see? Are you new to PowerPoint? Click on Easy Start. About Mathematics for Business Decisions Part 1: Probability and Simulation Using The Electronic Text Course Activities Project 1. Loan Work Outs Project 2. Stock Option Pricing Solving Computer Problems Index What is NEW in Release 1.55? Check for Updates What Mathematical & Computer Skills Will You Need? Acknowledgements and Credits Stop You did not make a selection from the list of topics on the preceding page. In order to study this material effectively you need to use hyperlinks, not simply move to the next page. Please click on Contents and then select the material that you wish to view. Contents Business About Mathematics for Business Decisions
About Business Math Mathematics
Mathematics for Business Decisions is designed specifically for students majoring in business. It is the result of extensive collaboration between faculty members from the Eller College of Management and from the Department of Mathematics at the University of Arizona. C I (material continues) About Mathematics for Business Decisions: page 2 About Business Math Mathematics for Business Decisions is the foundation for your future career in business, showing you how to apply the language of mathematics to business problems, and how to use computers to help you do mathematics. The content, method of instruction, and computer software in this course are all carefully selected to prepare you for the job market and for future business courses. Top priority is given to the qualities that are desired by corporate recruiters. These include communication skills, creative problem solving skills, and the ability to work in teams. (material continues) C I About Mathematics for Business Decisions: page 3 About Business Math Part 1 of Mathematics for Business Decisions centers around two significant business problems and the tools, both mathematical and computer based, that are needed for their solutions. You will use the spreadsheet package Excel to assist you with the mathematics and with the presentation of your results. After the description of each project, teams of students make initial reports, indicating how they would attempt to solve the problem. These reports will be based upon common sense, intuition, and past business experience. (material continues) C I About Mathematics About Business Math for Business Decisions: page 4 For several weeks after the initial reports, you will learn mathematical tools and computer skills that can be applied to the business case studies. While working on these, you will complete homework assignments. Using the new tools, each team will develop its final analysis of the projects and prepare both written and oral reports on their solutions. Student presentations will be given in the current business style, using PowerPoint and Excel. (material continues) C I About Mathematics for Business Decisions: page 5 About Business Math Class meetings will be used for presentation of the projects, discussion of the tools for their solutions, student activities, team reports, and instructor comments on the solutions. You will use this electronic text and its associated computer links to study the needed material. This can be done on any computer that is equipped with Windows XP or Vista, Office 2007, a CD drive, and an internet connection. Click on "Mathematics in Business Programs," to access a report on the mathematics that is needed by business majors. This was prepared by a national panel of business college faculty members and administrators. (material ends) C I Using The Electronic Text
Using The Electronic Text The PowerPoint, Excel, Word, and Media files for Part 1 of Mathematics for Business Decisions form a complete ELECTRONIC TEXT. This has many advantages over a traditional print and paper textbook. Hyperlinks allow you to move easily between mathematical instruction, computer calculation, internet sites, and tutorial videos. Computer animations clarify mathematical concepts. Split screens allow you to view more than one page or application at the same time. Electronic searching can locate any given word or phrase. Use of the electronic text will prepare you for future electronic learning and will show you how to create your own business presentations. Bytes on a CD weigh much less, take up less space, and cost less than a printed book! (material continues) C I Using The Text: page Using The ElectronicElectronic Text 2 To realize the advantages of your electronic text, you must use it very differently than you would use a printed book. Here
are some suggestions for the efficient use of your text, and some tips for getting the most benefit from the course files. Obtaining And Running The Files Moving Around In The Material Finding Specific Topics, Words, Or Pages Running Media Animations Click here. Viewing More Than One Page Or Application "Ask a Tutor" Videos List Of Course Files What is the difference between an electronic text and a printed book? (material ends) C I Electronic Text, Running Using The Electronic Text.Running Files The Files RUNNING THE TEXT FILES The text files run on PC's with Microsoft Windows XP or Vista, and Office 2007. PowerPoint, Excel, and Word files in the text contain boxes showing the text name, file release number, and date. Be sure that this information matches the assigned material in your course. The PowerPoint file MBD Part 1.pptx, which you are now viewing, is the starting point for your course work. It contains project descriptions and a complete electronic index. Mathematical and computer instruction is given in the files MBD 1 Proj 1.pptx and MBD 1 Proj 2.pptx. As soon as a presentation is opened, you can view the material and move around easily within the pages. However, animations and links to other pages, files, and applications will not operate until you start running the presentation. At times it is more efficient to leave a presentation in an open, but non-running, mode. In other cases you will want to run the presentation in order to take full advantage of its electronic features. Using The Electronic (material continues) C I Using The Electronic Running Files Electronic Text, Text. Running The Files: page 2 The easiest way to run a PowerPoint presentation is to click on the slide show icon in the toolbar at the bottom of the screen. Once the presentation is running, each click of the mouse button or press of the space bar will introduce a new feature or advance the presentation to the next page. Slide Show End Show While a PowerPoint presentation is running, clicking the right mouse button will display a menu of options. Clicking on End Show will stop the presentation. You can also change to the non-running mode by pressing ESC. To end your viewing session, close all applications. Using The Electronic (material ends) C I Using The Electronic Text. Moving Around Electronic Text, Moving Around MOVING AROUND IN THE MATERIAL T C I Previous page Tools Contents Index Next page Most pages contain some or all of the above buttons. Clicking on one of these while the presentation is running will move the presentation to the indicated location. Tools moves to a list of mathematical and computer tools for the current project. Contents moves to the table of contents. Index moves to an index for the entire course. The above buttons are inactive samples. Practice with the buttons at the bottom of the page. With a presentation running, clicking on hot boxes or underlined hypertext will perform the indicated action. When you follow a link to another application, such as Excel, you may need to move around within that document in order to see the desired material. Using The Electronic (material continues) C I Using The Electronic Text. Moving Around: page 2 Electronic Text, Moving Around On some computers, you may need to open applications, such as Excel, Word, or a browser, before following links to them. To return to a PowerPoint presentation from another application, click on the colored border at the bottom of the screen, below the current application. In some versions of PowerPoint, you return by left clicking on the PowerPoint Slide button, located on the menu bar at the bottom of the screen. Try this by clicking on the Excel button, and then returning to this page. Excel If, for some reason, the Task Bar is not visible, pressing Ctrl-Esc will display both the Task Bar and the Start Menu. These can also be displayed by pressing one of the Windows keys that are located between the Ctrl and Alt keys at the bottom of your keyboard. Windows Using The Electronic (material continues) C I Using The Electronic Text. Moving Around: page 3 Electronic Text, Moving Around When an exercise refers to a preceding exercise or example, the reference is usually a hot link that will take you directly to the previous material. You can click on the hypertext to get the information or see the methods that will be needed for the current exercise. The following plan provides a convenient way to return to the exercise on which you are currently working. To return to a PowerPoint slide after following a link to another slide, right click anywhere in the screen to see a pull-down menu. Left click on Last Viewed. Using The Electronic (material ends) C I Using The Electronic Text. Finding Things Electronic Text, Finding FINDING SPECIFIC TOPICS, WORDS, OR PAGES While a presentation is running hyperlinks in the electronic index may be followed to locate specific topics in the PowerPoint text. When a presentation is in the non-running mode, all occurrences of individual words or phrases can be located with PowerPoint's built-in Find function. Select the Home tab and then click on Find. Enter the words for which you want to search, then click on Find Next. It said, "Press any key." Enter your word or topic. (material continues) Using The Electronic C I Using The Electronic Text, Finding Finding Things: page 2 Electronic Text. While a PowerPoint presentation is running, clicking the right mouse button will display a menu of options. To move to any given page, click on Go To Slide. This will display a list of slides that are close to your present location. To see other slides place the cursor over the carrot at the bottom of the list. The list will then scroll to the last slide in the presentation and display All Slides. Click on this to see a searchable list of all slides. Select the desired slide and click on Go To. Using The Electronic (material continues) C I Using TheElectronic Text, Finding Finding Things: page 3 Electronic Text. When a presentation is in the non-running mode, pressing Page Up or Page Down on the keyboard moves the file to the preceding or following page, respectively. The Slide Sorter allows you to view thumbnail sketches of the pages and move to any selected page. Clicking on the Slide Sorter View icon at the lower left corner of the screen shows sketches. Double clicking on any page in the sorter selects that page for normal viewing. The presence of distinctive graphic images makes it easy to recognize a desired page. Slide Sorter View (material continues) Using The Electronic C I Using TheElectronic Text, Finding Finding Things: page 4 Electronic Text. The Slide tab in the Normal View allows you to view thumbnails of slides in a side panel. When a presentation is in the non-running mode, click on the Normal View icon at the lower left corner of the screen. Placing the cursor over a thumbnail will display its title. Clicking on any thumbnail will display the given slide in the main panel. The size of the side panel can be adjusted to display larger or smaller thumbnails. Normal View Normal View (material continues) Using The Electronic C I Using TheElectronic Text, Finding Finding Things: page 5 Electronic Text. When a presentation is in Normal View in the non-running mode, clicking on the Outline tab will display a list of slide titles in the side panel. Clicking on any title selects that slide for full frame viewing. Choosing a suitable working window allows you to use all of the features that are available in the non-running mode. Outline Using The Electronic (material ends) C I Using The Electronic Electronic Text, Animations Text. Animations RUNNING MEDIA ANIMATIONS Set Windows Media Player as the default application to open *.avi files. When the player is opened, click on View and then select Skin Mode. To activate an animated media file (*.avi), while a PowerPoint presentation is running, click anywhere in the file picture area. This will launch Windows Medial Player and start the animation. To gain the most understanding from the mathematical animations, you will want to control the motion manually. To do this, click on the media player's Pause button, and then use the slider to control the animation. To resume automatic motion, click on the Play button. Slider Play Button Pause Button Using The Electronic Practice with the clock on the next page. (material continues) C I Using The Electronic Text. Animations Electronic Text, Animations: page 2 Run the animation automatically through its complete three hour cycle. Computer Problem? Pause the animation and use the slider to set the time for exactly 2:00 o'clock. Restart automatic operation. Using The Electronic (material ends) C I UsingElectronic Electronic Text. Viewing The Text, Viewing VIEWING MORE THAN ONE PAGE OR APPLICATION By reducing the size of their windows, you can view the mathematics on a PowerPoint page and simultaneously perform Excel computations. To do this, the presentation must be open, but not running. Click here to reduce size. Drag borders to adjust window size and shape. Using The Electronic (material continues) C I Using The Electronic Text. Viewing: page 2 Electronic Text, Viewing You can open two different PowerPoint presentations, or two different slides in the same presentation. Click on View and then on Arrange All. BONUS! The 20 point type used in this text allows small group viewing on monitors, large group viewing with projection, and easy reading on split screens and laptops. Using The Electronic (material ends) C I Using The Electronic Text. "Ask a Tutor" Electronic Text, Ask a Tutor "ASK A TUTOR" VIDEOS Several pages in the course files contain "Ask a Tutor" boxes with a frequently asked question. Clicking anywhere in the upper box will open a short video that discusses the indicated material. The videos give informal answers that are similar to what you would get in a office visit with your instructor, or at a tutoring session. Avoid Computer Problems. Set Windows Media Player as the default application to open *.wmv files. When the player is opened, click on View and then select Skin Mode. To activate a video, while a PowerPoint presentation is running, click anywhere in the upper box of the picture. Ask a tutor
How do these videos work? To avoid a cluttered screen, minimize your browser once the video is playing. Try a sample video! Click anywhere in the upper box. (material ends) Using The Electronic Text I C Using The Electronic Text. Course Files Electronic Text, Course Files Excel
Bank Customers.xlsm Binomial 1.xlsx Blank.xlsx Cars.xlsx Coding.xlsx Coins.xlsx Comp. Int.xlsx Comp. Solution 1.xlsx Daily Sales.xlsx Density 1.xlsx Exercise 2.xlsx Flowers.xlsx IF.xlsx Loan Focus.xlsx Loan Records.xlsx Option Data.xlsx Option Focus.xlsx LIST OF COURSE FILES Excel (cont.)
Phone Log.xlsx SAR.xlsx Sick Time.xlsx Skills 1.xlsx Stoppages.xlsx Sum.xlsx Tractors.xlsx PowerPoint
MBD Part 1.pptx MBD 1 Proj 1.pptx MBD 1 Proj 2.pptx Stock Data.pptx Word
Blank.docx Equations.docx Preliminary 1.docx Rep. Solution 1.docx Media
Bank.avi Practice 1.avi Using The Electronic (material ends) C I Course Activities
Course Activity There are many different activities in Part 1 of Mathematics for Business Decisions. Select the topic that you wish to view. Teams And Projects Preliminary Report Studying The Tools Final Oral Report Avoiding Computer Problems Written Report Homework Study Plan Working With Your Team
(material continues) C I Course Course Activity,Teams & Projects Activity. Teams & Projects TEAMS AND PROJECTS Each project will be introduced with a standard Class Project, which will be studied and solved as mathematical and computer tools are developed. During the first week of classes, small groups of students will be formed to work on Team Projects which are very similar to the Class Project. When a project is first introduced to the class, each team will be told how to obtain the details of its particular project. This information may be in the form of an Excel file, material to be downloaded from the Internet, or data which is supplied by the instructor. Project Introduction Teams Formed Class Project Team Projects Preliminary Reports Tools and Homework Solution Course Activities (material continues) Written Reports C Oral Reports I Course Activity. Teams & Projects Course Activity, Teams & Projects: page 2 Immediately after projects are introduced, teams give preliminary oral reports. The class then develops and studies both mathematical and computer tools that will lead to sound business decisions, and will assist in project solutions. Focus on the Project sections follow work on most of the tools. These show how the given concepts apply to the Class Project. Homework problems ask each team to make the corresponding applications to its own Team Project. The Class Project is solved completely in the final Focus on the Project section. Student teams prepare both oral and written final reports. These emphasize the use of mathematics in their business decisions. Following the solution of the Class Project, we present an additional application of the project tools. These illustrate the use of the new concepts in a business setting that is completely different from that of the Class Project. Study of these "shadow projects" is optional. They may be used as reading assignment, or covered in the classroom while teams prepare their final repots on the Team Projects. Course Activities (material ends) C I Course Activity, Preliminary Reports Course Activity. Preliminary Reports PRELIMINARY REPORT View Video clips from a preliminary report in Mathematics for Business Decisions. Shortly after a project is introduced each team will give a brief oral preliminary report on its project. After introducing its members to the class, a team will give a description of the team's particular project, a discussion of the problem, and tentative decisions on the main project questions. The preliminary report should clearly indicate that your team has started to function as a problem solving group. It should also show that you have thought carefully about the project, and that you are beginning to develop some intuition about the business aspects of the situation. Do not worry if your team does not yet have an effective way to solve or even to attack the project. This ability will come as you study the computer and mathematical tools. In particular, you should NOT try to "read ahead" in a rushed attempt to study the tools. The preliminary report should be based upon study of the problem, your common sense, and business considerations. Since the report will be brief, your team must be well organized. Any use of PowerPoint or Excel should be kept at a very simple level. Course Activities (material ends) C I Course Activity, Tools Course Activity. Studying The Tools STUDYING THE TOOLS To keep your team's work on track, the final homework problem in most sections requires that you apply the given tool to your team project. Successful completion of these steps assures you that you are making satisfactory progress toward your report. Occasionally a team may head off in an inappropriate or completely wrong direction while working on its project. This can become a major problem if it is not discovered until the team is making its final report. For this reason it is usually wise for a team to discuss its conclusions with their instructor, prior to the report day. All mathematical and computer tools that will be needed for your project solution will be presented prior to the final section in each project. These concluding sections are substantial examples which use the earlier tools in much the same ways that you will use them in your project solutions. You should use the study time during the final example to complete work on your team's project. Course Activities (material ends) C I Course Activity. Course Activity, Oral Report Oral Reports Click anywhere in the picture to view video clips from a final report from Mathematics for Business Decisions. Click on the pictures to view short excerpts from PowerPoint presentations.
Welcome to Acadia Bank
Presented by Jennifer Copenhaver Jennifer Copenhaver Cheryl Kleiman Kelly Peck Darby Sinding Darby Sinding Team 1 FINAL ORAL REPORT When all needed tools have been studied, each team will give a final report. This is to be a major presentation, given in the style that you will use in your future business career. Each team will prepare a written report and give an oral presentation, using a computer. The oral report should be built around a PowerPoint presentation, with links to Excel files, as needed for the project. All members of a team must actively participate in the report and every member must be able to explain any given mathematical or computer aspect of the report. C I Course Activities (material continues) Course Activity, Oral Report Course Activity. Oral Reports: page 2 Oral reports will be evaluated on (i) the correctness and completeness of their contents; (ii) the ability of all team members to answer questions and explain what they have done; (iii) the extent to which they explore the Team Project beyond the basic level of the Class Project; and (iv) the organization, style, and business-like manner of the presentation. Oral presentations should introduce the team members and provide full information on the team's project. All of the projects lead to one or more significant business decisions. Reports should clearly include the team's final decisions, and should outline all of the major steps that were used in reaching those conclusions. Relevant mathematical formulas should be displayed and discussed. Any spreadsheets used in computations should be presented and explained. Teamwork is critical. Plan ahead and hold group practice sessions before the time for class reports. Be sure that every team member understands all of the business and mathematical ideas in your report. Course Activities (material continues) C I Course Activity. Oral Reports: page 3 Course Activity, Oral Report Be professional, dressing and acting as you would in an important business meeting. Speak directly to your audience. Do not simply read from notes or your PowerPoint file. Avoid excessive use of sounds and animation in your report. Do not attempt to show every step that you used in making your decision. Highlight the broad outline of your work. Be prepared to explain any detail that might be needed to answer a question. Interpret all mathematical results in the business setting. Assume that you are talking to a group of people who are familiar with the project tools, but not with your particular situation. If you use the course Excel files as models for your work, modify them so that they apply to your team's project. Leaving in text boxes of general directions gives a very poor impression of your team's effort. Course Activities (material ends) C I AVOIDING COMPUTER PROBLEMS Preparing computer files which may have to be run on an unknown computer can be challenging. Here are some ideas that will help you avoid surprises when you give your reports. Course Activity, Computer Problems Activity. Course Avoiding Computer Problems When a computer encounters a type font which is not in its system, it substitutes one of its own fonts. This may, or may not resemble the original font. To prevent odd looking presentations, use only standard type fonts which are supplied with Windows. The Times New Roman or Arial fonts are very safe choices. For good screen visibility use at least 20 point type fonts. This applies to equations as well as standard text. File size can cause computer problems during your report. Huge files may not load quickly on a computer whose software differs from that which is on the machine that created the files. Limit the resolution of any graphics to at most 150 pixels per inch. The size of a PowerPoint file may increase each time that it is saved. Using Save As to save the file under a new name will correct this problem. Course Activities (material continues) C I Course Activity. Avoiding Computer Problems Course Activity, Computer Problems: page 2 If you want to copy sections of an Excel spreadsheet into your PowerPoint presentation, copy from Excel, then use Paste Special/Picture (Windows Metafile) to paste the object into PowerPoint. In particular, do not paste as a "Microsoft Excel Worksheet Object." Incorrect use of copy/paste can create a simple PowerPoint presentation that contains over 26 MB. This may take as long as 35 minutes to open under some earlier versions of Office. It is wise to avoid links to the internet in computer work for your reports. Such links are usually unnecessary, and only add to the risk of something going wrong. Bring your report files to the classroom on a CD-R, a CD-RW, or a USB Drive. If you will need it, be sure to check that the presentation computer has a CD drive that reads CD-RW's, or a USB port! Redundancy is essential. Have your presentation on at lease two different media. Course Activities (material ends) C I WRITTEN REPORT Each team will prepare a written report. This should be a self-contained document, describing the team's particular project, presenting all calculations, indicating the key steps in its solution, and stating the team's conclusions. It would also be appropriate to include any relevant details that were omitted from the oral report. Just as in a business report, the team's written report should be word processed, and designed to make a lasting, positive impression on its readers. Personality and the ability to think on one's feet are key points in an oral presentation. Completeness, correct writing, and attention to details are the hallmarks of an excellent written report. People may retain the written record of your work long after they have lost a clear recollection of your oral presentation. Successful teams often start by first preparing their written report. Once this is done, key points are extracted to form the basis for the computer files which will be used in the oral report.
1 PRO RE JECT PO RT Tea m Course Activity, Written Report Course Activity. Written Report Course Activities (material continues) C I Course Activity. Written Report: page 2 Course Activity, Get Started Really Great Idea! Your work on a project starts with the team's preliminary report. As each new tool is studied, apply it to your particular project and expand your report. If you wait until just before the final report to utilize the tools, your team will be badly rushed and there will be no time to correct any problems or misconceptions. Building the report as you progress through the material will take the pressure off of reporting. Use the assigned homework to help you prepare your reports. Using the tools with your project data is also one of the best ways to prepare for examinations over those tools. Click on the pictures to view short excerpts from Mathematics for Business Decisions written reports. PDF copy: requires Adobe Acrobat Reader. (material ends) C I Course Activities is er 6 w ans 401.3 The 729, e). $2, (mayb Course Activity, Homework Course Activity. Homework HOMEWORK Homework problems are spread throughout the PowerPoint files. Working all of these problems provides one of the best ways to master the mathematical and computer topics. Some of the problems ask you to explore or modify existing Excel files. Other questions ask you to create your own new spreadsheets. Many problems are to be solved with pencil and paper mathematics. Homework problems which are handed in for grading should be submitted as Word or Excel files, or as printout from such files. All work, including equations, must be computer generated or word processed. Complete sentences describing your solution must accompany the mathematical and computer work. (material ends) h mig it it, 1.95. Wa e $ b t Course Activities C I Course Activity, Study Plan Course Activity. Study Plan STUDY PLAN Read the project description and use Excel to look up the data. Take time to become familiar with the situation, to understand the data, and to find out exactly what you are asked to do with the project. You will need both mathematical and computer tools in order to make effective decisions. Such topics are presented, following each project. Study all of the tools thoroughly, watching for ways to apply them to the project. Both the mathematical and computer tools should be studied in the order in which they are presented in the PowerPoint file. Course Activities (material continues) C I Course Activity. Study Plan Course Activity, Study Plan: page 2 Each section contains examples. Read these carefully and be sure that you understand each one before continuing to work on the following material. Some of the examples have buttons that you can use to view Excel worksheets or other ancillary material. Take advantage of this help by using all of the extra aids. All sections contain several exercises. Stop and work each one of these (whether or not it is to be handed in) before continuing your study. Some of the homework exercises provide the steps needed for your team's preparation of its project reports. These are particularly important problems. Course Activities (material continues) C I CourseCourse Activity,Study Plan: page 3 Activity. Study Plan Pay particular attention to the pages labeled "FOCUS on the project." These show how each tool allows you to gain further insight into the problem that you are studying. Calculus, Mathematics, on the project Business Computers Tests, Homework, Decisions Course Activities (material ends) C I Course Activity. Activity, TeamsWith Your Team Course Working WORKING WITH YOUR TEAM The ability to work effectively within a group of people is a major asset in the business world. It is also an important part of Mathematics for Business Decisions. You may encounter team members with any of the following traits. The martyr: Willing to do all of the team work, with or without public complaint. The slacker: Tries to get away without doing any of the work, but is willing to share in the credit. The boss: Everything must be done in exactly his or her way. The busy person: Cannot possibly fit team meetings into his or her full schedule. The never follow through person: Promises to help, but never gets the job done. Course Activities (material continues) C I Course Activity.Course Activity,With Your Team: page 2 Working Teams The bright person: Seems to understand everything and be able to do any part of a project. The slow person: Never seems to catch on to what is happening in class or with the project. You will find exactly the same mix of people in the rest of your business career. Learning to create an effective team out of diverse individuals may be a real challenge. Here are a few suggestions. Do not let one member dominate the team. Assert your right to influence group decisions and to participate fully in team activities. Do not accept the willingness of a few members to do most of the team work. If team homework is accepted, one person may be willing to do the problems. In this case, other team members will be unprepared for tests. Look for strengths in each team member and actively encourage everybody to participate. During project reports, the instructor is most likely to ask questions of any member who does not seem to be actively involved. Poor answers from one person reflect badly on the entire team. Course Activities (material continues) C I Course Activity.Course Activity,With Your Team: page 3 Working Teams Schedule team meetings at times and places which are convenient for every team member. If a member has a problem getting to meetings, ask him or her to pick a time for the next meeting. If problems develop within your team, attempt to work things out as a group. In the event that this does not seem to be working, keep your instructor informed of what is happening. If, despite being given ample opportunity and encouragement, a member has not participated in the preparation of a team report, other members have the right to omit his or her name from a written report or to exclude him or her from an oral presentation. Such action must only be taken as a last resort. However, you should not be intimidated into giving credit to someone who did not contribute to the team effort. The good news is that most teams learn to work together effectively. Different people bring diverse skills to the projects, creating a team that is stronger than its individual members. Students often report that teamwork provided support for their work in Mathematics for Business Decisions. Course Activities (material ends) C I Project 1. Loan Work Outs
Project 1. Loan Work Outs Video introduction by Prof. Christopher Lamoureux Department of Finance University of Arizona. 1. Project Description A. Business Background Class Project B. 2. Mathematical Tools Basic Probability A. Summation Notation B. Expected Value C. Conditional Probability D. Bayes' Theorem E. Management Example 3. Computer Tools F. Word Processing Mathematics Database Functions and A. Filtering B. T C I Loan Work Outs. Business Background
Project 1. Background A bank is a financial institution that transforms savings into capital investment. People and companies deposit excess cash in banks, which in turn lend these funds to other people and companies. The money is then invested in productive capital. Banks make both personal and commercial loans. In a personal loan the borrower receives an amount of money which he or she pays back in monthly installments. The borrower also pays monthly interest on the outstanding principal. In a commercial or business loan the borrower keeps the entire amount of the loan for a fixed period of time, and then returns the principal as a lump sum payment. While he or she has the money the borrower must make regular payments of interest on the loan. We will only consider commercial loans. The most important problem that a bank confronts is to whom it should lend. It makes this decision by processing information about the prospective borrower, and the proposed investments. (material continues) T C I Loan WorkBackgroundBusiness Background: page 2 Project 1. Outs. Since commercial loans are risky, the bank continually monitors borrowers. Should a borrower fail to make expected interest payments, the bank has to decide whether or not it should foreclose on the loan. In many cases, foreclosure means that the bank takes over ownership of a particular asset (the collateral for the loan), and sells this asset in the market. If it does not foreclose, the bank can attempt to salvage the loan by setting up a new schedule of interest payments or by temporarily deferring such payments. These actions are called a loan work out. The choice of whether to work out a loan or foreclose is a complex one. In many cases, foreclosure would force the borrower into bankruptcy. The key issue in a work out decision is the long-run viability of the borrower. (material continues) T C I Loan 1. Background Project Work Outs. Business Background: page 3 No! Yes! The bank has to decide whether the borrower has missed his or her recent payments because of temporary illiquidity or if there is a permanent problem. If it is the former, a work out may be indicated. If it is the latter, foreclosure may be appropriate. Given the importance of the work out or foreclose decision, many banks that lend to smaller and medium size companies force the borrowers to have an exclusive borrowing relationship. This enables the lending bank to make the work out decision by itself. (The law requires that all lenders must agree to a work out plan.) To protect itself against litigation, a bank must base the decision about whether or not to attempt a work out arrangement on quantifiable considerations. This often involves the use of historical data on past borrowers. To be effective, the use of data must take into account specific information about an individual borrower and about the current economic conditions. (material continues) T C I Loan Work Outs. Class Project
Project 1. Description, Class Acadia Bank has a commercial loan with a full value of $4,000,000 outstanding to John Sanders' entrepreneurial venture. This loan has a 10% interest rate, is one year old, and is scheduled to terminate in four years. The last interest payment was due three weeks ago, and John was unable to make the payment. In fact, the bank has recently audited John's books, and discovered that, for the moment, the venture is illiquid, and will be unable to make interest payments for at least the next three months. Acadia has to decide whether to foreclose on the loan, which would put John out of business, or to work out a new schedule of payments. Acadia knows that if it forecloses on John's loan, it will only recover a foreclosure value of $2,100,000 on the $4 million loan. If it were to enter into a work out arrangement, there is some chance that the entire loan would be re-paid, and the on-going relationship with John would adequately compensate the bank for the costs of the work out and any lost interest. (material continues) T C I Loan Work Outs. Class Project: page 2 Project 1. Description, Class If Acadia Bank attempts a work out, and John's venture fails anyway, then the business will have further decreased in value and the bank will only recover a default value of $250,000 on its loan. The problem confronting the bank is whether or not to work out the loan with John. In order to make this decision, the bank would like to know the expected value of a work out. Acadia Bank is the result of a merger between three banks. Unfortunately, each of these banks kept different kinds of records on the success or failure of past work out attempts. The former BR Bank has work out records which include the number of years of experience that the entrepreneur had in his or her current line of business. The former Cajun Bank has work out records which include the entrepreneur's education status (whether the highest education level is: high school, a bachelor's degree, or a graduate degree). Finally, the former DuPont Bank has work out records which include the state of the economy at the time of the work out (whether the economy was in a recession, in normal times, or in a boom). Each of the three former banks made loans to very similar populations of borrowers. (material continues) T C I Project 1.Work Outs. Loan Description, Class Class Project: page 3 Each of the former banks had data on several thousand individual work outs. The combined records that are available to Acadia Bank are shown in the Excel file Loan Records.xlsx. Conventional wisdom in the banking business indicates that the number of years of business experience of a borrower, educational level of a borrower, and the current economic conditions are all independent of each other. Moreover, these factors are independent, even if only successful loan work outs or only failed work out attempts are considered. The following demographic and economic data characterize John's current situation. John has seven years of experience in this kind of business. John has a Bachelor's degree in Business Administration. The economy is currently in "normal times." Armed with this data, should Acadia Bank enter into a work out agreement with John, or should it foreclose on the loan? Loan Records.xlsx (material continues) T C I Loan Work Outs. Team Projects
Project 1. Description, Team Each team of students will receive information about a borrower who has fallen behind with interest payments on a commercial loan from Acadia bank. This information will include the full value of the loan, the foreclosure value, the default value, and properties of the borrower and current times. Specifically, teams will know the number of years experience that the borrower has in his or her type of business and the highest educational level of the borrower: High School, Bachelor's Degree, or Graduate Degree. Teams will also know the current economic conditions: Recession, Normal, or Boom. Each team must use the Acadia Bank records and all information about its particular borrower to decide if Acadia Bank should enter into a work out agreement with the borrower, or if it should foreclose on the loan now. Loan Records.xlsx (material ends) T C I Project 2. Stock Option Pricing
Project 2. Stock Option Pricing Video introduction by 1. Project Description Business Background A. Class Project B. 2. Mathematical Tools Compound Interest A. Probability Distributions B. Random Sampling C. Wholesale Ordering Example D. 3. Computer Tools Histograms Simulation A. B. Prof. Christopher Lamoureux Department of Finance University of Arizona. T C I Stock Option Pricing. Business Background
Project 2. Background STOCKS Many companies raise capital by selling partial corporate ownership to the general public. This is done via shares of stock. These shares are then available for trading on stock exchanges, such as the New York Stock Exchange. The price of a share on an exchange fluctuates continually during a trading day, as determined by its perceived value to buyers and sellers. In general, the price of a company's stock reflects the extent to which the company is prospering. Thus, the value of an investment in stock may rise or fall, based upon numerous factors involving the general economy and the individual business. In good times, a company uses part of its profits to pay dividends to its share holders. If the price per share of a company's stock becomes too high, the company may declare a stock split. For example, if a share of Intel stock is currently selling for $140 when the company makes a 2:1 split, then the holder of one share receives certificates for two shares, priced at $140/2 = $70 per share. (material continues) T C I Stock 2. Background Project Option Pricing. Business Background: page 2 OPTIONS Investors' desire to make money in both good and bad markets and to protect themselves from losses, have led to the development of many stock derivatives. These are financial instruments whose values are linked to the value of an underlying stock or stock index, such as the S & P 500. Derivatives allow an investor to place a bet on what the stock market will do, without having to own actual stock shares. Stock options are a common type of derivative. These are securities which give the owner the right, but not the obligation, to buy or sell the stock for a prespecified price, over a specified period of time. A call option is the right to buy a stock, and a put option is the right to sell a stock. An American option may be exercised at any time prior to its expiration, but a European option may be exercised only on its expiration date. The prespecified price at which the option holder may buy (in the case of a call) or sell (in the case of a put) is called the strike price or the exercise price. (material continues) T C I Stock 2. Background Project Option Pricing. Business Background: page 3 Options are often described by the number of weeks or months from the time of purchase until the end of the period during which the option may be exercised. Thus, we might discuss a 10-week option. If the period is given in weeks, it is assumed to end on Friday of the given week. If a month is given as the expiration date for an option, it is understood that that the option period ends on the third Friday of that month. Example 1. A European call option on IBM, with a strike price of $125 and an expiration of next March allows a person to buy IBM shares for $125 on the third Friday of next March. Of course, this right is worthless if, at that time, IBM is selling for less than $125. In this case, the holder loses all of the money that he or she paid for the option. On the other hand, if IBM is trading for $135 on the expiration date, then the owner of the call can exercise the option, buy shares at $125, and immediately sell them for $135. This would produce income of $135 $125 = $10 per share. CALL (material continues) T C I Stock 2. Background Project Option Pricing. Business Background: page 4 In general, if S is the strike price of a call option ($125 in our example) and C is the price of IBM on the expiration date, then the final value of the call will be the maximum of 0 and C S. Example 2. A European put option on IBM, with a strike price of $115 and an expiration of next March allows a person to sell IBM shares for $115 on the third Friday of next March. If, at that time, IBM is selling for more than $115, the option would not be exercised. If this happens, the holder loses the price that he or she paid for the option. But, if IBM is trading for $110 on the expiration date, the owner of the put can buy shares for $110 and immediately exercise the option to sell them for $115. This would produce income of $115 $110 = $5 per share. In general, if S is the strike price of a put option ($115 in our example) and C is the price of IBM on the expiration date, then the final value of the put will be the maximum of 0 and S C. PUT (material continues) T C I Stock Option Pricing. Business Background: page 5 Project 2. Background Why might you want to buy an option? Example 3. Consider the IBM call that we discussed in Example 1. Suppose that the option costs $10 per share and that IBM is now selling for $120 per share. You believe that the stock will be selling for $140 per share by the third week of next March. You have two choices: buy stock or buy an option. If you buy a share of IBM now for $120 and hold it until next March, you expect to sell the share for $140, realizing a net income of $20. Ignoring the potential for interest during the period of the option, this is a return of $20/$120 16.7% on your $120 investment. Instead of this, you could use the same $120 to buy twelve IBM call options with a strike price of $125. Next March, you expect to be able to buy twelve shares of IBM for $125 each and then immediately sell them at the market price of $140. (material continues) T C I Stock Option Pricing. Business Background: page 6 Project 2. Background Your income would be 12 $15 = $180. Since you paid $120 for the option, your net profit is $180 $120 = $60. Ignoring the potential for interest during the period of the option, this is a return of $60/$120 = 50% on your $120 investment. If IBM is really going to be priced at $140 next March, then you would be smart to buy a call option rather than stock. The advantage of call options in a rising market is often called leverage. Obviously, you could be wrong in estimating the future price of IBM as $140. Suppose, for example, that next March the price is actually $124 per share. If you had bought an IBM share for $120, it could be sold for $124, realizing a net income of $4. Ignoring the potential for interest during the period of the option, this is a return of $4/$120 3.3% on your $120 investment. Suppose that you purchased a call. Next March anyone will be able to buy IBM for $124, so the option to buy shares at $125 will be worthless. In this case you lose all of your original $120. If IBM is really going to be priced at $124 next March, then you would be foolish to buy a call option rather than stock. (material continues) T C I Stock Option Pricing. Business Background: page 7 Project 2. Background Example 4. Consider the IBM put that we discussed in Example 2. Suppose that you bought IBM seven years ago, and the stock went up from $80 to $120 per share. You are worried about the company's fortunes over the next few months, but to avoid heavy taxation, you do not want to sell your IBM shares now. However, you wish to lock in the gains which you have already made. You can hold onto your IBM stock and also buy a $115 put for next March. No matter what IBM is worth next March, you will be able to sell your shares for $115. If shares are worth more than this on the market, you can simply retain your stock. By holding onto the stock, and buying the put, you can participate in all of the upside movement of the stock, and at the same time limit your downside exposure. Suppose you believe that IBM will experience a large shock before next March, but that you do not know whether the news will be good or bad. In this case, you can buy both calls and puts. This position is called a straddle. (material continues) T C I OPTION PRICING Stock2.Option Pricing. Project Background Business Background: page 8 Options are bought and sold in open markets, in much the same way that stocks are traded. In fact, almost all options are eventually sold, rather than being exercised. Trading in options is a very important part of modern finance both for risk management and for speculative purposes. Visit the Chicago Board of Options Exchange web page for more information about options and the markets in which they are traded. The value of any option is 0 or a positive amount, hence, it would always be nice to hold a put or a call. Obviously, one must pay a price for any option. The problem of determining the present value of an option is of considerable interest and importance in the business world. We will limit our work to pricing European call options. The value of a call when it expires depends on the price of the underlying stock on that date. Since we cannot predict future stock prices exactly, we must use probability to consider what the normalized stock price might be on the expiration date of the option. Probability assumptions are usually based on the past history of stock prices. www.cboe.com (material continues) T C I Stock Option Pricing. Business Background: page 9 Project 2. Background Such historical information is readily available on the World Wide Web. For information on the site which you will be using click on the box Downloading Stock Records at the bottom of this page. Market experience and financial theory lead to several important assumptions which we will make for option pricing. 1. Past history cannot be used to predict the future price of a stock. If this could be done, all investors would move their money to the stock with the best predicted return. This would drive up the price of that stock, destroying its potential value. 2. The past history of prices for a given stock can be used to predict the amount of future variation in the price of that stock. Market history indicates that stocks whose price has fluctuated widely in the past will continue to show such fluctuation, those with limited variability will retain that trait. The extent of a stock price's variability is called its volatility. Downloading Stock Records (material continues) T C I Stock Option Pricing. Business Background: page 10 Project 2. Background 3. All investments, whose values can be predicted probabilistically, are assumed to give the same rate of return. If this was not so, then all smart investors would switch their money to the investment with the highest predicted rate of return. Such movement of capital is called arbitrage. This would raise the cost of the chosen investment, and destroy its predicted rate of return. 4. We will assume that the common growth rate for all investments whose future values can be predicted is the rate of return on a United States Treasury Bill. Since the rate for this investment is guaranteed by the federal government, it is called the risk-free rate. 5. All investments with the same expected rate of growth are considered to be of equal value to investors. Obviously, some people will prefer one type of investment over another. However, tastes will vary, so we will ignore it in our pricing. This is called the risk neutral assumption. (material continues) T C I Stock Option Pricing. Business Background: page 11 Project 2. Background Current business practice uses methods of considerable mathematical Current business practice uses methods of considerable mathematical sophistication for option pricing. Most of these are derived from the Black Scholes sophistication for option pricing. Most of these are derived from the Black Scholes Method. For more information on option pricing click on the box at the bottom of Method. For more information on option pricing click on the box at the bottom of this page. this page. We will develop a simple method, called bootstrapping, which uses our We will develop a simple method, called bootstrapping, which uses our assumptions to determine fair prices for call options. assumptions to determine fair prices for call options. Warning! Warning! Stock and Option trading could Stock and Option trading could damage your bank account. Your work in this damage your bank account. Your work in this project does not provide a sufficient project does not provide a sufficient background for actual investing. As they say, background for actual investing. As they say, "Don't try this at home!" "Don't try this at home!" See Using The Electronic Text for information on playing video. Ask a tutor
What does "bootstrapping" mean? More on Option Pricing Computer Problem? (material ends) T C I Stock Option Pricing. Class Project
Project 2. Description, Class We suppose that it is Friday, November 14, 2008. Our goal is to find the present value, per share, of a European call on General Electric Company stock. The call is to expire 20 weeks later, with a strike price of $14.50. Our work is to be based upon the stock's price record of weekly closes for the past 8 years. In practice, both a bid (what someone is willing to pay) and an asked (at which some one is willing to sell) price are quoted for options. To simplify things, we will assume that these are the same. Any brokerage fees that might be charged for transactions will also be ignored. General Electric trades on the New York Stock Exchange under the ticker symbol GE. Information downloaded from finance.yahoo.com/q/hp on February 27, 2009 is shown in the sheets Yahoo and DL of the Excel file Option Data.xlsx. Relevant data have been copied into the sheet Data of that file. One important fact is that General Electric closed at an actual value of $16.02 on November 14, 2008. Option Data.xlsx (material continues) T C I Project 2. Description, Class Stock Option Pricing. Class Project: page 2 We can use our historical data to gather information on volatility, as discussed in Assumption 2. Our interest is in the ratios of one weekly close to the comparable close for the preceding week. As discussed in the file Stock Data.pptx, these are exactly the same as the ratios of weekly adjusted closing prices. These ratios of adjusted closes are computed in the sheet Data of Option Data.xlsx. It will be assumed that these ratios are all independent of each other. Finally, we will suppose that on November 14, 2008 the annual interest rate for a 20 week United States Treasury Bill was 1.75%, compounded continuously. This will be used as the risk-free rate, which is discussed in Assumption 4. Our only goal is to determine a fair option price. We have no interest in the question of whether or not people should have bought such an option, or even whether or not they should have bought GE stock on November 14, 2008. Likewise, we have no interest in any attempt on November 14, 2008 to predict the closing value of GE stock at the expiration of the option. According to Assumption 1, this is completely impossible. Stock Data.pptx Option Data.xlsx (material continues) T C I Stock Option Pricing. Team Projects
Project 2. Description, Team Each team of students will visit a web site and download historical data on the past weekly closing prices of a given stock. Team assignments will provide the following information. The name and ticker symbol of its stock. The starting date for its option. The number of years of historical data that will be used in pricing the option. The number of weeks for which its option is to run, and its strike price. The starting date risk-free interest rate of a Treasury Bill for the same period as the option. Each team is to use the class method and its team data to determine the value per share, at the option's starting date, of a European call on its stock. Stock Data.pptx (material ends) T C I What Mathematical & Computer Skills Will You Need?
What Math & Computer Skills Will You Need? MATHEMATICAL BACKGROUND Successful study of Part 1 of Mathematics for Business Decisions requires a solid background in algebra. A typical College Algebra course or a very strong Intermediate Algebra course should serve as an adequate mathematical prerequisite. In addition to the usual manipulative skills in algebra, you should be familiar with elementary set notation and be experienced in translating real world problems into mathematical notation. Functions play a major role in Part 1 of Mathematics for Business Decisions. You will need to be comfortable with functional notation and with the graphing of functions. x(x 2) = x2 2x f(x) = 3x/2 + 1 ABB (material continues) C I What Mathematical & Computer Skills Will You Need? page 2 Skills COMPUTER SKILLS Part 1 of Mathematics for Business Decisions is not designed to serve as your first introduction to computers. You must have some prior experience with Microsoft Windows and with the applications Excel and Word in the Microsoft Office Suite. "Computer literacy" is a very elusive quantity. It is often difficult for a student to know if his or her background with computers is extensive or current enough to be adequate for Part 1 of Mathematics for Business Decisions. Anyone who is enrolled in the course, or is thinking of enrolling in it, should use the following simple exercise to assess his or her computer skills and readiness for Part 1 of Mathematics for Business Decisions. You should allow an uninterrupted period of 20-25 minutes for the exercise. (material continues) C I What Mathematical & Computer Skills Will You Need? page 3 Skills Computer Readiness Check 1. Load Word and Excel. Create a new folder, named Practice, on one of your computer drives. 2. Open the course file Skills 1.xlsx and save that file in the folder Practice. Rename the file Computation 1.xlsx. Open the course file Preliminary 1.dox and save that file in the folder Practice. Rename the file Report 1.docx. 3. Open the Excel file Computation 1.xlsx, that you have saved in the folder, and follow the instructions that are given in the file. This will involve working in Computation 1.xlsx, copying material into the Word file Report 1.docx, and then adding text to that file. When you are done, save both of your files. (material continues) C I What Computer Skills Will You Need? page 4 Skills 4. If you have trouble with some part of the exercise use the application's online help to see if you can solve the problem. If you cannot figure out how to do a step, try to work around it and complete the exercise. 5. When you are done with your work and have saved your files, open the course files Comp. Solution 1.xlsx and Rep. Solution 1.docx, to view the solutions. These files contain comments and notes that will help you evaluate your computer readiness for Part 1 of Mathematics for Business Decisions. Study the solutions carefully, noting how each step was performed. (material continues) C I How well did you do? What Skills Computer Skills Will You Need? page 5 You can grade yourself! If your files are quite similar to the solutions, and if you completed the project in a reasonable amount of time, then you are probably in good shape to start the computer parts in Part 1 of Mathematics for Business Decisions. On the other hand, if the exercise took you more than 40 minutes, or if you missed more than three of the nine main points, then it is very likely that you need more computer experience before you tackle the course. If you are unsure about how to evaluate the results of your exercise, or if you are not comfortable about your computer background, talk to your instructor. Attempting to learn the advanced computer skills that are taught in Part 1 of Mathematics for Business Decisions without a solid foundation in the basic aspects of Excel and Word would be very frustrating and time consuming. The most likely result of such an effort would be a low course grade, or outright failure. Do not miss out on the excitement of the business applications because you are having a continuing struggle with computers. (material ends) C I "No, thanks, I just had one!!!" Solving Computer Problems
Solving Computer Problems "Have a computer problem?" The course files will run well on computers with most combinations of Microsoft Windows XP or Vista, and Microsoft Office Suite 2007. When a computer problem does occur, it is usually caused by an incomplete installation of software or some software component. If you experience a computer problem with the course files, you will probably find it discussed in the following list. Follow the instructions which are given for solving the problem. , mark potential trouble Computer Problem? spots in the text files. Click on a box to find a solution for the problem. Although the course files may run in several combinations of Windows and Office, they are Office 2007 files. Saving a course file as Office 2003 may cause it to run improperly in Office 2007. (material continues) C I Blue boxes, such as Solving Computer Computer Problems Problem 1 Course files do not open or do not run. Problems: page 2 Causes. You may be trying to run the material on a computer whose operating system is not Windows XP or Vista and Office 2007. The course files are not intended for use with Macintosh, Linux, or UNIX systems. Solution. Use a computer with the appropriate software. A utility that allows Office 2007 files to run in Office 2003 can be downloaded from Microsoft. This will enable most of the course files features. Click on the Downloads tab, and then download the Microsoft Office Compatibility Pack. Problem 2to video clips do not work. Links Causes. You may not be connected to the Internet, your computer may not have a sound card, or you may not have set Windows Media Player as the default application to open *.wmv files. Solution. Connect to the Internet, install a sound card, or set Windows Medial Player as the default player. Hint: Minimize your browser once the video is playing. (material continues) C I Solving Computer Problems: page 3 Computer Problems Problem 3 An animation does not open or does not run properly when you click on it. Cause. There is a problem with your computer's default media player for *.avi files. The player may not work well in your system, or it may not be able to play this type of file. Solution. Select a Windows Medial Player as the default application to open *.avi files. In Computer or Windows Explorer right click on one of the *.avi course files. For example, use Practice 1.avi. Next, left click on Open With. This will display a pull down menu. Click on Choose Program and then select Windows Media Player. application. Check the Always use the selected program to open this kind of file box and then on OK. When you first open the player, click on View and then on Skin Mode. (material continues) C I Solving Computer Computer Problems Problems: page 4 Problem 4 You see odd symbols, such as , , or ; where you would expect to see mathematical symbols; or you can not open the Symbol Font. Causes. Various things, such as the installation of other software or hardware, can cause the failure of Microsoft Office applications to recognize the Windows font, Symbol. If this happens, applications commonly substitute the corresponding Wingdings characters for the mathematical characters in Symbol. For example, , , and may appear as , , and .. Solution. If Symbol is available, this problem can be corrected by reinstalling Office. Insert the Office CD, run Setup, and select Reinstall. If Symbol is not available on your computer, you can download the font from the Mathematics for Business Decisions server. Click on fonts.exe, then on Save File. Save the self-extracting Zip file, fonts.exe, to a temporary location, put PowerPoint into the non-running mode, use the desktop or Windows Explorer to locate the file, and then double click on fonts.exe. Follow the directions to extract the files SYMBOL.TTF and MTEXTRA.TTF. Use Control Panel/Fonts/File/Install New Font to make the SYMBOL.TTF available. (material continues) C I Solving Computer Computer Problems Problems: page 5 Problem 5 Microsoft Equation 3.0 does not appear on the Insert/Object pull down menu, or you see an error message and some large symbols are displayed incorrectly when you open the editor. Causes. Some installations of Microsoft Office Suite do not include Microsoft Equation 3.0. Your installation of Windows may not contain the TrueType font MT Extra. This seems to have been a common problem with the Millennium Edition of Windows. Solutions. Install the equation editor. For an initial installation of Office, run the Setup program on the Install CD and select a Custom installation. If you have a previous installation, choose the Install/Remove option. In either case, follow the directions to install the Equation Editor. Install the missing font. You can download the font from the Mathematics for Business Decisions server. Click on fonts.exe, then on Save File. Save the self-extracting Zip file, fonts.exe, to a temporary location, put PowerPoint into the non-running mode, use the desktop or Windows Explorer to locate the file, and then double click on fonts.exe. Follow the directions to extract the files SYMBOL.TTF and MTEXTRA.TTF. Use Control Panel/Fonts/File/ Install New Font to make the MTEXTRA.TTF available. (material continues) C I Solving Computer Problems: page 6 Computer Problems Problem 5 Problem 6 box is a solid black color. A label Cause. In some older versions of PowerPoint, repeated running of a presentation may cause a yellow label box to show a solid black fill. Solution. Select the box, then click on Format on the main PowerPoint ribbon. Click on Shape Fill, click on No Fill. This will remove the black fill and reveal the text. Finally, repeat the above steps, but select yellow fill. This will restore the original appearance of the box. Problem 6 Problem 6 If the box is grouped with other objects on a page, you must ungroup the items before you can correct the color problem. To ungroup objects, select the group or one of its components, click on the Format tab, then select Group. Click on Ungroup. Correct the color fill problem and then regroup the objects. (material continues) C I Solving Computer Problems: page 7 Computer Problems Problem 7 You are unable to save your work on an Excel file because it is labeled as Read Only. Causes. The file property has been set to Read Only. This may have happened when the file was copied from a read only CD Solution. In My Computer or in Windows Explorer right click on the name or icon for the problem file. Select Properties from the pull down menu, and then click on General. Remove the check from Read-only, and then click on OK. If you copied the course files from a CD, you can select all of the files and remove all of their read only properties at the same time. Remove the check. (material continues) C I SolvingComputer Problems Computer Problems: page 8 Problem 8 You do not find Data Analysis or the function RANDBETWEEN on the Excel menus, an Excel file behaves oddly, or Histogram returns an error message. Causes. These Excel features are not loaded or are not operative. In such cases, an Excel file which uses Random Number Generation or RANDBETWEEN cannot be computed. In some systems, files whose names contain blank spaces cause a problem. The Histogram function can only be used in the same worksheet that contains its input range. Solutions. Click on the Office Button, then on Excel Options/Add-Ins. Select Manage Excel Add-Ins, then Go. Check the Analysis Tool Pack and Analysis Tool Pack - VBA boxes and then click on OK. If Analysis Tool Pack and Analysis Tool Pack - VBA do not appear on the pull down menu, under Add-Ins, you do not have a full installation of Excel. Reinstall the application. Avoid error messages by using Histogram in the same worksheet as its input range, or rename the file with a single name. (material continues) C I Solving Computer Problems: page 9 Computer Problems Problem 9 You do not find the utility Solver on the Excel Tools menu. Causes. This Excel features is not loaded or is not operative. Solution. Follow the Add-In directions that are given in Problem 8 to enable the Solver Add-In. Problem 10 While working in one of the Office applications, characters change after you type them. For example, i becomes I, f(x) becomes F(x), or 2nd becomes 2nd. Cause. The application is using its AutoComplete or AutoCorrect features. Solution. Click on the Office Button then on Excel Options. Select Proofing/AutoCoreect Options or Advanced. Disable any automatic changes which you do not want the application to make for you. (material continues) C I Solving Computer Problems: page 10 Computer Problems Problem 11 An Excel macro button does not run its macro. Cause. The Macro Security Level is set at high or medium. Solution. Change the Macro Security Level. If there is one, close the security message and close any open Excel or PowerPoint files. Click on the Office Button. Office Button Select Excel Options from the bottom of the dialog box. (material continues) C I Solving Computer Computer Problems Problems: page 11 Trust Center Settings Trust Center Click on Trust Center in the sidebar, then on Trust Center Settings under the Microsoft Office Excel Trust Center heading. Finally, select Enable all macros. (material continues) C I Solving Computer Problems: page 12 Computer Problems If the Developer tab is displayed, the security level can also be set by clicking on that tab, then on Macro Security/Macro Settings. If you are concerned about security problems with macros, other than those in Mathematics for Business Decisions, you may wish to reset the security level when you are not running course files. (material ends) C I D-G H-L M-P Q-S T-Z A Alternative 1-140 Assembly line stoppages example 2-104, 2-106, 2-109, 2-112 AVERAGE 2-39 B Bank customer example 1-4 Bayes' theorem 1-145 Binomial Random Variable 2-67, density 2-68 distribution 2-68 mean 2-93 Box and ball example 1-143 Index
Index C Car example 1-70, 1-82, 1-88, 1-94 chart.yahoo.com/d Stock Data Chicago Board of Options Exchange 64 Coding example 2-134, 2-142 Coin examples 1-52, 1-53, 1-55, 1-56, 1-59, 1-110, 2-138 Complement 1-16 Conditional probability, definition 1-106 properties 1-106 Continuous compounding 2-12 Control buttons 15 Course files needed 28 T1 T2 C (C continues) A-C H-L M-P Q-S T-Z C (continued) Cumulative distribution function 2-57 D Data Analysis, running 83 DAVERAGE 1-81 DCOUNT 1-70 De Morgan's Laws 1-18 E e 2-10 Effective annual yield 2-4 Equation editor 1-34 problems with running 80 Index: page 2 Index Events 1-2, independent 1-109 mutually exclusive 1-12 Executive Level Thinking 2-170 Expected value 1-58, 2-94 Exponential function 2-15 Exponential random variable 2-88, density 2-88 distribution 2-88 mean 2-97 F-G Files needed 28 Final reports oral 34 written 39 (F-G continues) T2 T1 C A-C D-G M-P Q-S T-Z F-G (continued) Focus sections, Basic Probability 1-26 Bayes' Theorem 1-151 Compound Interest 2-30 Conditional Probability 1-118 Database Functions and Filtering 1-103 Expected Value 1-67 Histograms 2-52 Probability Distributions 2-99 Random Sampling 2-119 Simulation 2-149 Free offer 1-174 Future value 2-22 Index: page 3 Index H Histogram 2-43 I-J-K IF 2-138 Independent events 1-109, conditioned 1-112 Intersection 1-11 Intervals 2-73 L Loan work outs, class project 52 team projects 55 Logarithms, definition 2-15 properties 2-16 T1 T2 C A-C D-G H-L Q-S T-Z M Mean, random variable 1-58, 2-94 sample 2-105 Mutually exclusive events 1-12 N Normalized Ratios 2-101 O Option Outcome 2-163 P Parameter 1-58 Partitions 1-131 Index: page 4 Index Phone calls example 2-122 Preliminary reports 32 Present value 2-24 Probability density function 2-79 Probability mass function 2-56 Probability, conditional 1-106 definition 1-2 properties 1-10, 1-12, 1-16, 1-18 Project 1, class project 52 team projects 55 Project 2, class project 68 team projects 70 T1 T2 C A-C D-G H-L M-P T-Z Q Quotation 2-162 R RAND 2-136 RANDBETWEEN 2-124 Random variable, continuous 2-74 definition 1-52 expected value of 1-58, 2-94 finite 2-56 mean of 1-58, 2-94 Ratios, normalized 2-101 Range 2-38 Relative frequency 2-110 Index: page 5 Index Reports, final 34 preliminary 32 Running animations 23 S Sample mean 2-105 Sample space 1-10 Search model, simple 1-159 cost and time model 1-166 Security guard example 2-77, 2-81 Sick time example 2-33, 2-43 Small business example 1-17 Sorting 2-33 T1 T2 (S continues) C A-C D-G H-L M-P Q-S S (continued) Stock option pricing, class project 68 team projects 70 Strange 2-117 Summation notation, definition 1-44 properties 1-48 Symbols 1-28 T Tractor example 1-134, 1-145 Tree diagrams 1-129 Index: page 6 Index U Uniform random variable 2-82 Union 1-11 V-W VLOOKUP 2-126 X-Y-Z Yield 2-4 T1 T2 C I would like to express Acknowledgements my appreciation to the following people who have been of great help with the writing, teaching, and publication of Mathematics for Business Decisions Part 1a and its companion e-texts Mathematics for Business Decisions Parts 1 and 2, and Calculus for Business Decisions. Robert Condon, former Computer System Manager for the Mathematics Department at the University of Arizona, provided excellent computer support during the early stages of the project. Acknowledgements & Credits Edward Alexander, Donald Barkouskas, Tina Deemer, Gregory Hartman, Deborah Hughes Hallett, Robert Indik, Thomas Kennedy, Joceline Lega, William McCallum, Nicholas Rogers, Eugene Smith, and Douglas Ulmer, University of Arizona; John Hagood and Janet McShane, Northern Arizona University; Darci Kracht, Frank Smith, and George Tonge, Kent State University; Mufid Abudiab, George Tintera, and Natalya Warner, Texas A & M University at Corpus Christi; John Grima, Glendale Community College; Julie Tarr and Yvonne Brown, Pima Community College; and Lawrence Morales, Seattle Central Community College; have provided many helpful comments and suggestions on the material. (material continues) Back to Contents Acknowledgements & Credits: page 2 Acknowledgements Marilou Mendel has served as course coordinator for the entire program at the University of Arizona during its later years. Her contributions have been of great value. Much of the success that the e-texts have enjoyed at the University of Arizona has been due to strong support from the Eller College of Management. Particular appreciation is owed to the Associate Dean for Undergraduate Programs, Pamela Perry. It has been a pleasure to work with The Mathematical Association of America. In particular, former Associate Executive Director, Donald J. Albers, has provided strong support and encouragement. Staff members Tonya Hahn, Kara Keller, Elaine Pedreira, Martha Pennigar, and Beverly Ruedi, have been very helpful. My wife, Shari Thompson, has contributed both great patience and much tangible assistance while this material was developed. Thank you, Richard B. Thompson (material continues) Back to Contents Acknowledgements & Credits: page 3 Acknowledgements Some of the photographic images in Mathematics for Business Decisions are taken from Hemera Photo-Objects Premium Image Collection, Version 1.0 by Hemera Technologies, Inc., P. O. Box 79093, Hull, Quebec, Canada J8Y6V2. Some of the clip-art graphics in Mathematics for Business Decisions are taken from Arts & Letters by Computer Support Corporation, 15926 Midway Road, Dallas, Texas 75244. The authors express their appreciation to those students at the University of Arizona who have permitted the use of, and links to, their work in Mathematics for Business Decisions. Development and dissemination of this material has been partially supported by a grant from the National Science Foundation. (material ends) Back to Contents Easy Start
Easy Start Getting around in PowerPoint is as easy as 1 - 2 - 3 - 4! If the cursor is hidden, wiggle the mouse, or right click and select Arrow under Pointer Options. 1. To advance to the next page, or to introduce the next effect on a page: Place the cursor in any blank area of the screen and left click. 2. To move to the preceding page: Left click on . Try it now. Move to the next page and then return. 3. To move to another page in the presentation, to another PowerPoint presentation, or to an application (such as an Excel file): Left click on action boxes, such as , or on underlined text. Excel 4. To return to PowerPoint from an application: Left Click on the strip of the PowerPoint screen that appears below the application screen. In some versions, you return by left clicking on the button PowerPoint Slide, located on the menu bar at the bottom of the screen. Try it now. Go to Excel and then return. (material continues) Back to Contents Easy Start: page 2 Easy Start Now that you have practiced the basic maneuvers, you are ready to learn the more sophisticated techniques which will help you study Part 1 of Mathematics for Business Decisions. To return to the regular course material, click on the red "Back to Contents box" at the bottom of this page. Once at the contents page, you might want to click on the hand next to About Mathematics for Business Decisions Part 1: Probability and Simulation. That section gives general information about the purpose and content of the course. After that, you should click on the hand next to Using The Electronic Text. That will display detailed instructions for using all of the course materials. Good luck with your work! (material ends) Back to Contents Option Pricing
Option Pricing The pricing of an option is a complicated matter, and one which is still under active consideration in both theory and practice. Most current pricing uses some variation of the "Black Scholes Method," which was first developed by Fischer Black and Myron S Scholes in papers published during 1973. After Black's death in 1995, work on option values earned the 1997 Nobel Prize in Economics for Scholes and Robert C. Merton Our bootstrapping method is easy to understand, and does not require the sophisticated mathematical tools that are used in the Black Scholes plans. In one example, the put and call prices determined by bootstrapping differed by less than 1% from the Black Scholes prices. Almost all options on individual stocks are now American options. However, European options are traded for options on some stock indices. www.cboe.com Back to Business Background (material continues) T C I OptionOption Pricing page 2 Pricing: The web site for the Chicago Board of Options Exchange provides a tremendous amount of information about options and their trading. This includes a glossary of terms that are used in discussing options. For example, a call is in-the-money or outof-the-money, depending upon whether its strike price is below or above the current market price of the underlying security. A put is in-the-money or out-of-the-money, depending upon whether its strike price is above or below the current market price of the underlying security. The intrinsic value of an option is the amount by which it is in-the-money and the time value of an option is the portion of the option price that is attributable to the amount of time remaining until the expiration of the option contract. This constitutes whatever value the option has in addition to its intrinsic value. The General Electric call in our class project is in-the-money by $1.52, which is its intrinsic value. www.cboe.com Back to Business Background (material continues) T C I OptionOption Pricing page 3 Pricing: A visit to the CBOE web site will allow you to discover whether or not you should be, or could even become, a naked writer. www.cboe.com A recent Public Broadcasting System NOVA program, Trillion Dollar Bet, featured the work of Myron Scholes and Robert Merton on options and hedge portfolios. Visit the PBS web site for information on this video and a wealth of other ideas on option trading. www.pbs.org/wgbh/nova/stockmarket You can download a two page Word document, OPTION VALUES: A Primer for Non-Experts, that gives a non-mathematical introduction to the concept of a hedge portfolio that is the central tool in current methods of option pricing. OPTION VALUES Back to Business Background (material continues) T C I OptionOption Pricing page 4 Pricing: Warning! Our discussion of options is only a brief introduction to derivatives, and provides inadequate preparation for any trading in stock options. The bootstrapping method which you will use in your team projects is an instructive educational tool, that provides a great deal of insight into the workings of options. It is not intended to provide professional accuracy in option pricing. More advanced work in finance is necessary for a solid foundation in the pricing and trading of derivatives. Back to Business Background www.cboe.com (material ends) T C I What Is The Difference?
Difference What are the differences between a paper and print book and an electronic text? Weight: 4 pounds, 12 ounces Volume: 165 cubic inches Cost: Weight: 2 ounces Volume: 3 cubic inches Cost:
$$$$$ $$$$$ You Can: Riffle through the pages to find a topic. Use the index and then turn pages to find a topic. Flip back and forth between two pages. Put it down and find a computer for computation. You Can: View thumbnails and click to see a page. Click on a topic in the electronic index. Split the screen to view two pages at the same time. Click on a link to compute in Excel. Back To Using The Electronic Text What Is New?
What Is New? NEW IN THE STANDARD EDITION, RELEASE 2 All files are in the Office 2007 formats: *.pptx, *.xlsx, *.xlsm, or *.docx. Screen captures and Excel directions apply to Office 2007. A new edition of the file Stock Data.pptx is included in the 2 releases. This reflects changes made in the web sites for historical stock price data. The Class Project for Stock Option Pricing has been updated to reflect current stock prices. All video clips are now in the *.wmv file format. These play conveniently in Windows Media Player and eliminate the need for RealPlayer. New advanced level observations have been added to the Class Project for Stock Option Pricing. Any ambiguities or typographical errors that have been found in Release 1.55 have been removed. Back to Contents (material ends) C I Update Text Files
Updates CHECK FOR POSSIBLE UPDATES Future changes in linked web sites and modifications made in new versions of Office and Windows may require adjustments in the electronic text files of Mathematics for Business Decisions. If this occurs, new files will be posted on the Mathematics for Business Decisions web site. Click on the Download Free Updates box and then follow the link to Free Downloads to see if there are any available updates and to download the most current files for your electronic text. ew N
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This note was uploaded on 03/27/2012 for the course MISY 2331 taught by Professor Changchit during the Spring '10 term at Texas A&M University, Corpus Christi.
- Spring '10