The Art of Mathematics in Business. Dr Jae K Shim
of sections that discuss such important areas as predicting sales and costs, cash flow analysis, the allocation of financial resources, and finding the payback period. This book also contains illustrative and practical mathematical formulas, equations, models, ratios, and other statistical techniques that can be used to make sound and profitable business decisions. The examples in each section focus on financial problems and highlight the importance of using mathematical and financial management principles.
Other topics covered in The Art of Business Math include the methods used to find the correct level of inventory, determining the amount and rate of production, computing profits, finding the rate of return, monitoring and controlling costs, allocating financial resources, analyzing the financial position of the business, identifying trends, comparing performance to that of competitors, evaluating supervisors and employee productivity, using human and physical resources efficiently, determining how much and when to reorder, computing the necessary amount of merchandise safety stock, whether to offer a discount to customers, computing the cost of financing, determining cash requirements, computing the breakeven point, calculating the debt level, finding the variances between budgeted and actual revenues and/or costs, forecasting sales accurately, calculating adequate insurance coverage, finding the tax liability, computing the potential cash flows for projects, analyzing floor space, evaluating the effects of inflation, appraising customer relationships and transactions such as average order size and the number of backorders, computing the value of the business, and identifying potential bankruptcy so steps may be taken to avoid it. The business operator will also learn am how to use a computer to assemble data and perform rapid calculations which will promote the effective use of the mathematical procedures. There are also in-depth discussions of both simple and complex mathematical applications that may be applicable to a particular problem. Each quantitative approach is described clearly and concisely. In some cases, the reader will be directed to the use of financial calculators, spreadsheet programs such as Excel, Lotus 1-2-3 add-ins, stand-alone specialized computer software, accounting software, and cash management software.
The author does not assume that the reader has any mathematical expertise. Thus both the novice and the experienced businessperson will profit from the methodology contained in this action-oriented book. The applications will make the business manager competent in the use of the most up-to-date managerial tools. The presentation is easy to understand and is user-friendly. This book shows what the mathematical technique measures, why it is important, when it should be used, how it should be used, and what the numbers mean.
The field of financial management has recently witnessed a dangerous period of rapid change, stagnation, and contraction. Uncertainty about the future growth of the economy has forced the business operator to be more prudent and sophisticated in the allocation of financial resources. It is therefore imperative that business owners employ new mathematical and financial management techniques to aid their decision making. The author is aware of these vital and complex techniques and cover them in clear and concise detail.
The business manager must also be aware of both the usefulness and the limitations of the particular mathematical technique employed to solve a problem. This book points out, when required, that a particular technique may be appropriate in one situation but not in others. This book also contains hundreds of filled-in examples, illustrations, practical applications, measures, procedures, rules of thumb, statistical data, exhibits, tables, graphs, and diagrams. They are presented to aid in the comprehension and successful solution of a particular problem. The reader will also learn when and how to use the appropriate computational method, why it is used, when computer techniques such as spreadsheets should be used, and how to read and analyze the computer printout. Typical questions of concern to business managers are answered, such as: How much sales are needed to justify the cost of a proposed advertising program? How many factory workers are required to meet production needs? Is the business growing, and how does it compare to competition?
In today’s marketplace, economic downturns force business managers to face new challenges. This book will minimize the effects of these potentially disastrous periods. It is designed to maximize both the profits and the value of the firm for its owners. This is a central objective of this book, and each financial procedure discussed is linked to the impact it has on the value of the firm. The reader will find this book useful, practical, comprehensive, and profitable. Keep it handy as an easy-to-use reference. There is cross-referencing of topics and mathematical techniques. The index can be used to find a specific area of interest. The glossary defines important mathematical terms.
In summation, this book is an invaluable addition to any library and will provide quick and accurate answers to the business entrepreneur and manager. It will make an individual “savvy,” comfortable, and proficient in both the business math and the financial applications required for the successful operation of any business.
Jae K Shim
Los Alamitos, California
I wish to express my deep gratitude to Mike Jeffers of Glenlake for this edition. The input and efforts are much recognized and appreciated. Many thanks also go to Lana Murillo and Christina Ramos of California State University, Long Beach for their excellent editorial contribution in the production stage.
Evaluating the Cost of Bank Loans, Business Loans, Trade Credit, and Other Financing
1. Understanding Simple Interest
Introduction
The fee charged for the use of money, or principal, is called interest. It is the amount charged by a lender to a borrower. The interest rate is usually stated on an annual basis. The sum of the principal and the interest due is called the accumulated value, amount due, or maturity value. Compound interest is discussed in Sec. 60, How Do You Calculate Future Values? How Money Grows?
How is it Computed?
The amount of interest due is based on three factors: the principal, the rate of interest, and the time period during which the principal is used. One year is generally used as the time period. Simple interest is calculated on original principal only. The formula for simple interest is:
Interest = principal × rate × time
I = Prt
The maturity value S is given as:
Maturity value = principal + interest
Although the time span of a loan may be given in days, months, or years, the rate of interest is an annual rate. Thus, when the duration of a loan is given in months or days, the time must be converted to years. When the time is given in months, the formula is:
Example 1
A business owner obtains a 2-year loan of $10,000 from the Amalgamated Bank. The bank charges an annual simple interest rate of 10 percent. The rate of interest charged for 1 year is $1,000, calculated as follows:
$10,000 × 10% × 1 year = $1,000
The total simple interest for the 2-year period is $2,000, calculated as follows:
$1,000 × 2 years = $2,000
The maturity value (S) of the loan is $12,000, calculated as follows:
I = Prt
S = P + 1 = $10,000 + $2,000 = $12,000
Example 2
A business owner obtains a 3-month loan of $10,000 from Fidelity Bank. The bank charges an annual simple interest rate of 10 percent. The interest charged for the 3-month period is $250, and the maturity value of the loan is $10,250, calculated as follows:
P = $10,000r = 10% or 0.10t = 3/12 month
I=Prt