Business Math: A Step-by-Step Handbook Abridged Instructor Resources by Jelena Loncar-Vines is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
Business math is the study of mathematics required by the field of business. By the fact that you are reading this textbook, you must be interested in a business field such as accounting, marketing, human resources, or economics.
Regardless of your path, you cannot avoid dealing with money and numbers. Both personally and in your career you certainly use elementary arithmetic such as addition, subtraction, multiplication, and division. However, there is a whole field of mathematics that deals specifically with money. You will work with taxes, gross earnings, product prices, and currency exchange; you will be offered loans, lines of credit, mortgages, leases, savings bonds, and other financial tools. Do you know what these are and how these financial tools can maximize your earnings and minimize your costs? Do you have what it takes to execute smart monetary decisions both personally and for your business? Do you know how interest works and how it gets calculated? If you can answer “yes” to these questions, then you are already off to a great start. If not, by the end of this textbook you will have a better understanding of all of these topics and more.
Let’s be realistic. In some areas of life and business, you can achieve a reasonable degree of understanding just by reading. However, reading about business mathematics without doing it would be disastrous. To succeed, you must follow a structured approach:
This textbook covers topics from Chapters 8 to 13 inclusive adapted from the original Business Math: A Step-by-Step Handbook by J. Olivier and Lyryx Learning Inc. View the original text for free at Business Math: A Step-by-Step Handbook . Reused under a CC BY-NC-SA license.
Author: J. Olivier
Publisher: Lyryx Learning Inc.
Book title: Business Math: A Step-by-Step Handbook
Book version: 2021B
Publication date: July 19, 2021
Location: Calgary, Alberta, Canada
Book URL: https://lyryx.com/subjects/business/business-mathematics/
Sanja Kraishnik, BA, BEd, MMath
Sanja, the lead on this OER project, has taught math in the Business School at Conestoga College ITAL, in Kitchener, Ontario, for ten years. Sanja’s dedication to ensuring that math is accessible to all students is demonstrated by using LaTex and the MathJax plug-in for Pressbooks to render math formulas and her dedication to ensuring this OER met accessibility requirements. To learn more about using Latex and Pressbooks, review Using LaTex in Pressbooks by Sanja Krajisnik and Jelena Loncar.
Jelena Loncar-Vines, OCT, MSc, BEd
Jelena is a faculty member in the School of Business at Conestoga College ITAL and can be reached at jloncarvines@conestogac.on.ca. Jelena has been a mathematics educator for 14 years, 11 of which have been at the post-secondary level. Jelena’s career focus is to help make mathematics relatable and accessible to students. In addition to teaching, Jelena has volunteered on mathematics education-focused organizations, both provincial and local. Jelena is a life-long learner and enjoys active participation in professional development opportunities geared toward mathematics, post-secondary education, and effective use of technology in the classroom. The development of this OER, and the opportunity for close collaborations with colleagues, has been a very rewarding experience.
Carol Leppinen, Honours BMath, BEd, Honours Specialist Mathematics
Carol is a faculty member in the Business School at Conestoga College ITAL, in Kitchener Ontario and can be reached at cleppinen@conestogac.on.ca. Carol has been a full-time professor at Conestoga College ITAL since 1998 where she has taught Business Mathematics, Statistics, and Quantitative Methods. Prior to that, Carol taught Mathematics and Computer Science at the secondary school level for 5 years. Carol has been a career teacher and is passionate about her students. Carol is grateful for all that her students have taught her over the years.
Cover image created with Canva. Photos reused under the Canva Free Media License Agreement.
This Instructor Resources book was created to accompany Business Math: A Step-By-Step Approach Abridged by Krajisnik et al., which focuses on Chapters 8 through 13, inclusive. The content in this resource can be used with original Business Math: A Step-by-Step Handbook by J. Olivier as well for the relevant chapters.
This resource introduces the concept of using a story for your Business Math class, guidelines to get you started, as well at the case studies themselves. The solutions to the case studies contained herein can be accessed by emailing eCampusOntario.
Best wishes to you as you endeavour in an alternative approach to teaching and learning Business Math!
This project is made possible with funding by the Government of Ontario and through eCampusOntario’s support of the Virtual Learning Strategy. To learn more about the Virtual Learning Strategy visit: https://v ls.ecampusontario.ca .
Humans have a natural disposition for interpreting our experiences as stories. Using a “story” to deliver course content has been used in K-12 classrooms, as well as in the form of case studies in professional programs such as law (McNett, 2016).
With a Case Study approach in mind, this Instructor Resource to Business Math: A Step-by-Step Approach Abridged was created to facilitate the use of story in teaching Business Math concepts. The original Business Math: A Step-by-Step Handbook was designed with a Case Study for each chapter. To build the storyline concept for the text, the following contributions were made:
Using a story in your class can be a fun way to engage your students, create connections between concepts that can otherwise seem disjointed, and incorporate industry-based examples.
The idea of using a story to deliver your math content may be new to you. The How To, Tips, and Goals section provides a starting point. Please incorporate your own ideas and tweak as needed for your students. We hope that you enjoy exploring new avenues of teaching your students Business Mathematics!
McNett, G. (2016). Using Stories to Facilitate Learning. College Teaching, 64(4), 184–193. https://doi.org/10.1080/87567555.2016.1189389
This section discusses some guidelines to consider if you are adopting a storytelling approach to your Business Math class. Please note that the terms “story”, “storyline”, and “case study” are used synonymously.
It is recommended that the objectives and reasoning is shared with students. This can help with student buy-in and engagement as a story approach may be new way of learning math for students.
Once you have decided on your objectives, the next step is to decide how you will incorporate the story in your class. Some options to consider:
The “Introduction to Lightning Wholesale” introduces the premise of the story. This section introduces the company, its functions, its characters, and summarizes its challenges. Remember to include only the information from the Introduction that is relevant to your course. Add in any extra anecdotes to make it more interesting and fun. It is important for students to have a proper introduction to the story so that they have an idea of the main elements.
Each chapter’s case study can be found in this resource. The structure of each case study is as follows:
When considering how and where within a lesson plan the Lightning Warehouse story can be incorporated, you may consider the “BOPPPS” Lesson Plan framework (Brillinger, 2022):
For full details on each, visit Conestoga College’s Creating a BOPPPPS Lesson Plan.Brillinger, K. (2022, January 27). Creating a BOPPPPS lesson plan. Faculty Learning Hub, Conestoga College Teaching and Learning. https://tlconestoga.ca/creating-a-bopppps-lesson-plan/
McNett, G. (2016). Using Stories to Facilitate Learning. College Teaching, 64(4), 184–193. https://doi.org/10.1080/87567555.2016.1189389
Note: If there is any content that does not apply to your course, please make sure to edit the “Introduction to Lightning Wholesale” to only include the relevant information.
Lightning Wholesale is a mid- to large-size company that specializes in working directly with manufactures to bring sporting goods and equipment to mid- to small-sized retailers. The company is located in Southern Ontario, Canada. Lightning Wholesale acquires the goods, stores them in their warehouses, and distributes to retailers, who then sell to sporting enthusiasts across the province. Suppliers are global, including from the United States.
There are a few main concerns for Lightning Wholesale management at the moment: payroll needs review, revenues, costs and expenses need forecasting for the next fiscal year, the ski product line is considering reducing their line, cash flow and investment management, and it is time to negotiate a new contract with some unionized employees that is not going well, which could result in a three-month strike.
On their payroll, Lightning Wholesales has employees that are paid on a salary, hourly, commission, and overtime basis.
Lightning Wholesale cares about its employees and retailers. Where mangers can assist their employees, they try to. Where retailers need guidance, Lightning Wholesales tries to fill this gap as best they can.
More recently, Quentin, Manager of Human Resources, was approached by an employee, Katherine. Katherine needed some extra cash and asked for advanced pay. Although against company policy to provide an advance on pay, Quentin was able to have a chat with Katherine on other options to her current plan of working with a PayDay Loan company.
In working with its small retailers, many of which are owned and operated by sole proprietors, Lightning Wholesale assists the owners with their pricing to help develop promotional pricing plans and the amounts of the payments that can be advertised. Lightning Wholesale freely offers the help, since it means more sales and increased profits for the company. Typically, retailers will sell the skis at their list price.
Lighting Wholesale has a strong Registered Retirement Savings Plan (RRSP) program, with dollar-to-dollar matching, which they encourage their employees to take advantage of. Where they can, they try to educate their employees on the ins-and-outs of RRSPs so that their employees have awareness and can manage their RRSPs appropriately.
The Finance Department is responsible to effectively manage the company’s money. Due to its size, Lightning Wholesale, has a separate bank account for each of its departments from which all expenses, purchases, and charges are deducted. This account has all revenues and interest deposited into it. Currently, the manager of the sporting good department wants a summary of all interest amounts earned or charged to her department for current fiscal year. This allows her to better understand and assess the financial policies of the company and make any necessary change for the next fiscal year. Lightning Wholesale invests in Treasury Bills (T-Bills) as part of their financial strategy.
In the warehouse, the forklifts need replacing. The Purchasing Manager is working with Combilift to develop a payment structure. Although Lightning Wholesale has the cash on hand, it is trying to figure out it is in their best interest to take out a loan instead.
With year-end approaching, Lighting Wholesale has many processes that they are wrapping up. It is important that all departments are executing their responsibilities as accurately and seamlessly as possible.
As with most mid-size to large companies, Lightning Wholesale has a finance department to manage its money. The structure of Lightning Wholesale’s financial plan allows each department to have its own bank account from which all expenses, purchases, and charges are deducted. This same account has all revenues and interest deposited into it.
The manager of the sporting goods department wants a summary of all interest amounts earned or charged to her department for the year 2013. This will allow her to better understand and assess the financial policies of the company and make any necessary changes for 2014.
Month
(Year 2013)
Total Sales Revenue
(‘000s)
Cost of Goods Sold
(‘000s)
Operating Expenses
(‘000s)
| Select Dates | T-bill Yields | Prime Rate |
|---|---|---|
| December 31, 2012 | 2.85% | 4.25% |
| January 31, 2013 | 2.90% | 4.25% |
| February 28, 2013 | 2.87% | 4.25% |
| March 31, 2013 | 3.04% | 4.75% |
| April 30, 2013 | 3.09% | 4.75% |
| May 31, 2013 | 3.11% | 4.75% |
| June 20, 2013 | 3.07% | 4.75% |
| July 31, 2013 | 2.95% | 4.50% |
| August 31, 2013 | 2.92% | 4.50% |
| September 30, 2013 | 3.40% | 5.00% |
| October 31, 2013 | 3.45% | 5.00% |
| November 30, 2013 | 3.47% | 5.00% |
The manager wants a report that summarizes the following information from December 31, 2012, to December 31, 2013:
In order to meet the manager’s requirements, work through 2013 month by month starting from December 31, 2012, by following the steps below. Once arriving at December 31, 2013, use the answers to provide the four pieces of information requested by the manager.
Using the opening balance, determine the face value of T-bills that can be purchased. If the balance is negative, no T-bills are purchased, so skip to step 4.
Quentin is the human resources manager for Lightning Wholesale. Recently, he was approached by Katherine, who is one of the employees in the sporting goods department. She enquired about the possibility of getting an advance on her next paycheque. Quentin informed her that Lightning Wholesale’s payroll policy is not to provide advances on paycheques. Katherine indicated that she was having some financial problems, did not have a very good credit rating, and would be forced on her way home to stop in at a payday loan company to take out an advance.
Concerned for his employee, Quentin visited Katherine later in the day and sat down with her to show her the true costs of using a payday loan company. He also wanted to show her a better alternative to get some short-term financing.
Canadian payday loan companies generally operate under one of three structures:
The table below summarizes a sample of charges that could be imposed under each model.
| Charges | Traditional Model | Broker Model | Insurance Model |
|---|---|---|---|
| Effective Rate of Interest | 59% | 21% | 48% |
| Per Transaction Fee | $9.99 | $10.00 | N/A |
| Cheque Cashing Fee | 7.99% of principal and interest combined | $8.00 | N/A |
| Insurance Fee | N/A | N/A | 19% of principal and interest combined |
| Brokerage Fee | N/A | 29.5% of principal and interest combined | N/A |
Observe that under Section 347 of the Criminal Code, any charges related to the borrowing of money are considered interest. This includes any types of fees and charges, although in name they may not be called interest.
Sharon works for Lightning Wholesale, which strongly encourages its employees to save up for retirement. After learning on June 1, 2006, that the company matches dollar for dollar any employee investments into their RRSPs, she has been pursuing her RRSP actively.
Sharon soon figured out one important and often misunderstood fact about RRSPs. Though many people think of an RRSP as a financial tool, like a savings account, into which money is invested, she realized that an RRSP is actually a tax-sheltered environment. Within the RRSP you can invest your money into various financial tools to save your retirement income, and any interest or capital gains that are earned on these investments are not taxable. This is in contrast to investments held outside an RRSP environment; for the latter, all earnings are subject to annual income taxes. The financial tools available to an RRSP could include GICs, mutual funds, bonds, securities, trusts, gold bullion, and stocks, just to name a few. Sharon’s portfolio happens to include CSBs, GICs, and strip bonds.
She is interested in learning how much money she has saved up by June 1, 2010, and how much of that money is actually real, inflation-adjusted growth in her savings. In other words, she wants to account for inflation and get an understanding of how much real interest beyond cost of living adjustments she has earned in her RRSP.
| Contribution Date | Amount | Frequency | Interest Rates |
|---|---|---|---|
| December 1, 2006 | $1,000 | Annual on December 1 | 3%, 3.25%, 1.85%, and 0.4002% |
| February 1, 2007 | $1,000 | One-time lump sum | 2.95%, 3%, 3.05%, and 1.003% |
| March 1, 2007 | $1,000 | Annual on March 1 | 3.1%, 2.5%, 1%, and 0.4004% |
| December 1, 2007 | $1,000 | One-time lump sum | 3.3%, 3.4%, and 3.5308% |
| February 1, 2009 | $1,000 | One-time lump sum | 1.75% and 1.9117% |
| December 1, 2009 | $1,000 | One-time lump sum | 1.75% and 1.9117% |
| Contribution Date | Amount | Frequency | Interest Rates |
|---|---|---|---|
| September 1, 2006 | $5,000 | One-time lump sum | 2%, 2.4%, 3%, 4.5%, and 7% |
| Purchase Date | Face Value | Term | Market Yield |
|---|---|---|---|
| December 1, 2006 | $20,000 | 20-year | 7.053% |
| June 1, 2007 | $25,000 | 25-year | 6.5425% |
| December 1, 2008 | $15,000 | 25-year | 5.9067% |
Lightning Wholesale works very closely with some of its smaller retailers, many of which are owned and operated by sole proprietors. These owners generally need assistance with their pricing and call on the staff at Lightning Wholesale to help develop promotional pricing plans and the amounts of the payments that can be advertised. Lightning Wholesale freely offers the help, since it means more sales and increased profits for the company.
Many of the requests are identical in nature, so the staff at Lightning Wholesale want to develop a payment plan chart for their ski product line. This chart is to illustrate both the three-month and six-month payment plan amounts that can be advertised at various interest rates.
It is time to negotiate a new contract with some of Lightning Wholesale’s unionized employees. The company believes in dealing fairly with its employees. Based on the current economic environment, cost of living increases, and the financial health of the organization, management feels that the best it can offer is a 3% wage increase. From its own analysis, the union believes that the company is holding out and that a 5.5% wage increase is more than possible. Unfortunately, negotiations have broken down, and the union has turned to its employee group seeking strike action. The union is certain of achieving its wage increase through the strike action, though it advises the employees that they may need to go on strike for three months to achieve the goal. The employees are trying to figure out their best course of action—should they vote to go on strike or not?
The employees are uncertain of the time value of money, so they need to run a few scenarios. Perform steps 1 through 3 below using EACH of the time value of money estimates as a different scenario. Determine the outcome of the strike vote (go on strike or not go on strike).
Pay cash or take out a loan? That is the question the purchasing manager for Lightning Wholesale faces today. Lightning Wholesale needs to replace its fleet of 10 forklifts for its warehouse operations. After shopping around and putting out a request for quotes, it has chosen Combilift as its supplier. The purchasing manager for Lightning Wholesale has been informed that the company does have the cash available to pay off the debt immediately. Alternatively, Lightning Wholesale could take out a loan and finance the purchase. The purchasing manager wonders what recommendation she should make — pay cash or take the loan? She knows she will need to support this decision with facts to her superiors.
Solutions to the case studies can be found in the ancillary resources only available to instructors. Please contact eCampusOntario to access these solutions.
