What Kind of Mathematics is Used in Business?

Hey friends. Some time back I asked myself what kind of mathematics is actually required to do business. I continuously researched on this topic until I found these 2 books
  1. Business math demystified
  2. Business math for dummies
I have read business math demystified till now. It is written by Allan G. Bluman. I have also gone through the contents of the 2nd book, business math for dummies. However, the contents of each book are pretty much the same.

To my surprise, I found that there is no need for learning higher mathematics for doing business. You can do business without learning calculus, matrix and determinants, geometry, trigonometry etc. 

Then what? The one word answer to what kind of mathematics is used in business is ARITHMETIC.

A Little Overview of Arithmetic

Arithmetic is the branch of mathematics which includes numbers and calculations. The main topics discussed in arithmetic are as follows:
  1. Basic Operations such as addition, subtraction, multiplication and division
  2. Ratio and Proportion
  3. Percentages
  4. Profit and Loss
  5. Simple and Compound interest
  6. Averages etc.

Actually, if you know addition, subtraction, multiplication and division, you can do business pretty well. 

Apart from these basic operations, you should also learn about fractions, decimals and percentages.

I told you that there is no need to learn unnecessary things that they teach you in mathematics. If you want to excel in business, all you need to learn is the basic operations of mathematics.

Most of the times in business, mathematics is used while giving a change of money. All you need to know is addition and subtraction here, and you are well to go.

Now comes the difficult part, the heart and soul of business mathematics, that is accounting.

In business, the transactions happen more frequently. It is always better for a businessman to keep an account of it. It will help to remove your fear of loss of money.

Checking accounts

Here is an example of an account book, and how you should record the transactions

Recording the Transactions, business mathematics, account register, payee, credit transaction, debit transaction, balance

Recording the Transactions, business mathematics, account register, payee, credit transaction, debit transaction, balance

Next, come payroll and commission.

Payroll and commission 

If you are starting a business you might have employees working for you. You have to pay them for their work. It is very necessary to learn about payroll. Payroll is broadly categorized into 3 types
  1. Yearly salary and hourly wages
  2. Piecework wages 
  3. Commission

Payroll deductions

It means when you pay your employee's taxes as an employer, you deduct this amount and, what you offer is your employee's net pay.

Mark-up

When you sell a product, you do not sell it at its cost price. What you do is mark up. Mark up means you sell your products more than its cost price. Markups are mainly divided into the 2 categories

1) Mark up on cost price, example;
Selling price = Cost price + Markup
      160%      =      100%   +    60%

2) Mark upon selling price, example;
Selling price = Cost price + Markup
      100%      =     75%      +    25%

In businesses, the mark up on selling price is used more frequently than mark up on cost price.

Relationship between both the markups

A mark-up of 20 percent on selling price is equivalent to a 25 percent markup rate on the cost price

Markdown and shrinkage

As a businessman, we sometimes need to mark-down from our selling price. This is mostly because of off-season selling.

Shrinkage means, from the past experience sellers, know that all of the items they purchased are not going to sell, because some of the items are going to be ruined before selling. So sellers have to mark up on each of the remaining items to adjust the shrinkage. Examples of such products are fragile toys, flowers and fruits etc.

Discounts

There are mainly 2 types of discounts in business
  1. Trade discount: Manufacturers or wholesalers give a discount on the listing price of products
  2. Cash discount: It is very necessary when a business owner wants the payment quickly. This type of discount mostly works in B2B businesses. These discounts are written as, 
3/15, n/30
It means if the customer pays the bill within 15 days, he will get a discount of 3%. If he pays after 15 days to 30 days, he won't get any discount. Payment of the bill after 30 days may lead to a fine.

Simple interest and promissory notes

Simple interest is very necessary when you are working with loans and investments in your business. 

Promissory notes and discounting

Promissory note means a document signed by the maker of loan to pay back the amount to the investor.

Discounting, in this case, means involving the third party to collect payment from the maker on the maturity date. And, the third party will issue cash to the investor now and charge some fees. This fee is called a discount.

Compound interest

Warren Buffett says that one of the greatest gifts of mathematics is the principle of compounding.

With the help of compound interest formula, we can determine the future value of present money and the present value of the future money.

Future value = Principal (1+r)N

Annuities and sinking funds

If you know in advance how much money you will need in the future, you can purchase an ordinary annuity and determine by a sinking fund payment how much will be required to achieve that amount in future.

Annuities means a fixed amount of investment every year. It is also known as the retirement fund. The formula for determining the future value of of an ordinary annuity is as follows

Future value = Present money ((1+r)N-1) / r

And, the sinking fund's formula

Present money= Future value*r / (1+r)N-1)

Consumer Credit

Some business allows their customers to buy an item now and pay for it later with equal monthly installments. This generally involves a down-payment with an EMI.

There are some important concepts in consumer credit, for example, the annual percentage rate and rule of 78s. These concepts are formula based. If you know their formulas then you can solve their questions easily.

What is the use of credit cards? Credit cards are used to 'buy now pay later' purposes. Some businesses allow this to maximize sales. There are mainly 2 ways to calculate the balance to be paid on credit cards.
  1. Unpaid balance
  2. Average daily balance
Next topic is a mortgage.

Mortgages

A loan for buying a home is called a mortgage.

Collateral

Collateral serves as a security for your lender. It may be gold, land or your income. If you are unable to pay your mortgage then your lender can sue your property.

Some terms you may encounter while solving mortgage problems are as follows
  1. Fixed-rate mortgage
  2. Monthly payments and amortization schedule
Next, we will learn about insurance

Insurance

There are many kinds of insurance. Insurance means to ensure future income. Mainly there are 3 types of insurance.
  1. Fire insurance and coinsurance
  2. Automobile insurance
  3. Life insurance
Insurance is for difficult times. 

How does insurance work?

As an insured, you have to pay the insurance company a premium. Premium means a fixed amount of money to be paid to the insurance company in order to get insurance.

On an accident or the end of the term, the company pays you the insured value.

What is the insured value?

The maximum amount of money the insurance company will disburse for your loss. For example, if you bought a house for 90000$, you can get a maximum of 90000$ for your loss.

Insurance rate

As an insured, we pay the insurance company a profit per unit coverage. This can be easily understood by the following formula to check fire insurance.

Annual premium= insured value*R / 100

Where R is the insurance rate.

Coinsurance

Coinsurance means when the insurance company doesn't insure the whole value, instead, it ensures a percentage of the whole value, say 80%. 

This happens because you insure your home, that is, you pay the company less than the coinsurance clause (<80%). 

When you incur a loss of some amount due to fire,

Amount received from the insurance company = loss * (the actual amount of insurance / required amount of insurance)

The application of this formula could be seen in the questions at the end of this post.

Automobile insurance

Most of the automobile insurance has a deductible clause. It means that on the occasion of complete loss of your vehicle, the insurance company will not pay the whole amount for the loss. It will deduct or subtract a part and pay the rest. When deductibles are more the premium is less.

Automobile insurance looks something like this, 25/50/10. Which means that the insurance company will pay at most 25000$ for a single person injury, 50000$ for the injury of all people involved in an accident, and 10000$ for the property loss, that is damage to the vehicle.

Taxes

There are many types of taxes. The basic 3 are as follows.
  1. Sales tax
  2. Property tax (on assessed value)
  3. Income tax

What is a tax? What do you need to learn in this chapter of taxes? Tax means a part of the money that the government takes for itself from your earnings. This money is used to pay the salary of government servants and to the welfare of the society.

The part that the government takes is generally in percentage. For example, 5% of your sales are used to pay taxes.

Stocks and bonds

When you buy a stock of a company, you buy its ownership. For example, Warren Buffett has 17% shares of Apple, meaning that Warren Buffett has 17% ownership of the company. A few things to keep in mind,
  • Stocks can be bought and sold
  • A dividend means when a company makes money, it distributes part of the profit to its shareholders
  • It depends on the company whether it wants to share dividends or to bootstrap its profit
Stock listing example, Dividend, PE ratio,Closing price, High, low
Stock listing example - 52 weeks

A stock listing looks something like the above picture. Most of the terms are easy to understand. I will tell you about PE ratio,

Price to earning ratio = (yesterday's closing price / annual earning per share)

And,

Annual earning per share = (company's total earning / number of shares owned by the stockholders)

1$/PE will give us the amount that the company will pay (dividend) for our 1 $ investment.

Current stock yield

Yield= annual dividend per share/closing price of the stock

ROI

ROI= (total gain / original cost of stock) * 100

Where, total gain = proceeds + dividends - original cost

Here, proceeds mean selling price of a stock and, original cost means the cost of stock + broker's commission

Next up we will discuss about bonds.

An example of Bond Listing

Example - 52 weeks bond listing
Bonds have a specific rate of interest and maturity date. Their face value is normally 1000$, as in the above example. Just like stocks, bonds can be bought and sold.

Next up we will learn the important concept of depreciation.

Depreciation

It is so obvious that equipment will lose its value after its daily use. Thus the equipment undergoes depreciation.

Common terms related to the depreciation are as follows.
  1. The estimated lifetime of an equipment
  2. Book value at the end of a specific period
  3. Scrap value at the end of its lifetime
There are 4 types of methods to determine depreciation.
  1. The straight-line method
  2. Sum-of-the-years-digits method
  3. Declining-balance method
  4. The units of production method
The straight-line methods will be explained in the Challenge section below.

Inventory

In simple words, the inventory means the stock of goods that is available to be sold. Every shopkeeper/businessman wants to sell his inventory as soon as possible. This is because on every turnover of the inventory the shopkeeper earns a profit. This profit plus the cost can again be used to buy the new inventory. Thus on every rotation or turnover, a businessman makes money.

There are 4 methods to compute the cost of goods sold to date.

Formula: Cost of goods sold= cost of good purchased - the cost of goods remaining

Methods:
  1. Specific identification inventory method
  2. Weighted average inventory method
  3. First-in, first-out method (FIFO)
  4. Last-in, first-out method (LIFO)
We will see the application of each of these methods in the Challenge section below.

Financial statements

Financial statements include balance sheets and income statements. A balance sheet gives owner's net-worth while income statement gives us net profit after sales. You must have read about these terms in the book Rich Dad Poor Dad. 

In simple words, the balance sheet includes assets and liabilities, while the income statement includes income and expenses. What is the difference between the asset and income? While an asset refers to the value, income refers to revenue.

Theory apart, let's understand the practical version of this.

The balance sheet

Suppose you own a clothing factory. In that case, assets mean cash, accounts receivable, merchandise cost, equipment cost, building cost etc. And liabilities mean wages payable, accounts payable, mortgage etc.

In this case, the owner's net-worth can be found out by subtracting liabilities from assets.

The income statement

As I have already told you that the income statement is related to the company's net profit or loss. The net profit can be found out by the following formula.

Net profit = Net sales - Cost of goods sold - Operating expenses

Note: the operating expenses means salaries paid, rent, utilities, insurance, maintenance etc.

Statistics and graphs

You might have seen this in movies that a businessman gives a business presentation with the help of graphs. Why is it so? Because it is a lot easier to understand when we try to display big data in the form of a graph.

Histogram

Steps to draw a histogram out of big data:
  1. Calculate the whole range (greatest number - smallest number)
  2. Divide the range in the number of groups and find units per group
  3. The smallest number of a group is called a lower limit and the largest number of the group is called the upper limit
  4. Tally the data and calculate frequency in each group
  5. Draw a histogram of Frequency vs Group
A histogram looks something like this,

Histogram on a notebook, histogram range, upper limit and lower limit in a histogram, tally and frequency in a histogram


Next up we will learn about the mean, median and mode in statistics.

Measures of average

  1. Mean and weighted mean
  2. Median means a middle number
  3. Mode means a frequent number in a group of data  

Measure of variability

With the help of variability, we can determine the deflection of data within the group. Take for example the following sets of data:

Set A: 5, 10, 15, 20, 25
Set B: 13, 14, 15, 16, 17 

Though the mean is the same for each of the above data-set. But in the set, A data values vary from 5 to 25, while in set B the data value varies from 13 to 17.

We will see its numerical application in the Challenge section below.

Graphs

As I have told you before that graphs help us to analyze the data quickly. There are many types of graphs.

Bar graph

This can be of 3 types - Horizontal, vertical and Pareto

An example of a horizontal bar graph is as follows:


Horizontal bar graph drawing, X and Y axis in a bar graph


To draw a vertical bar graph is simple and similar.

What's a Pareto bar graph? It looks something like the below picture. Note that in a Pareto graph, the data starts plotting from the high to low and the bars should touch each other.

Pareto bar graph, bar graphs example

The pie graph

To draw a pie graph, the following formula is used:

(Given quantity / Total quantity) * 360

A pie graph looks something like this:

Pie chart, pie graph, division in pie graph, 360 in pie graph

The time-series graph

It is a simple line graph with reference to time, that is, X-axis represents time. 

An example of a time-series graph is shown below.

Time series graph. Time series graph with respect to time, Time series graph with respect to years


There is another type of graph too, that is scatter diagrams. These scatter diagrams are easy to understand.

The stem and leaf plot

These can be easily understood by the image illustration below.

the stem and leaf plot, stem values, leaf values

That's all in business mathematics. I hope that you enjoyed this. 

P.S. All the information above is based on the book, Business maths demystified by Alan Bluman.

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