Chapter 02

2-*Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e

Chapter 2

PercentagesIntroductory Mathematics & Statistics

Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e


Learning ObjectivesUnderstand and use percentagesApply percentages to common commercial situationsCalculate commission (including brokerage)Calculate discounts (including chain, trade and cash discounts)Calculate tax (including GST, personal tax, company tax, FBT and land tax)Calculate profit and lossCalculate stamp duty



2.1 Conversion to and from percentagesConversion of a fraction to a percentageMultiply by 100 and use % signE.g.

Conversion of a decimal to a percentageMultiply by 100 by moving the decimal point 2 places to the right and then add a % signE.g.



Conversion to and from percentages (cont)Conversion of a percentage to a fractionDivide by 100 and remove % sign, then simplifyE.g.

Conversion of a percentage to a decimalDivide the percentage by 100 by moving the decimal point 2 places to the left, and then remove the % signE.g.



2.2 CommissionAn agent is paid a commission when he or she sells goods and services

Commission can be paid by looking at a eitherfixed amount (irrespective of sales)

straight commission with no fixed amount

Where:S = sale amountR = rate of commission per saleF= fixed amount paid (irrespective of sales)C= commission earned



2.2 Commission (cont)Brokerage

Brokerage is commission paid to a stockbroker who acts on a clients behalf

Brokerage rates vary according to the type of transaction, but general rules that apply are:

When selling, brokerage is subtracted from the proceeds of the sale

When buying, brokerage is added to the amount that you must pay for the stock or shares



2.3 DiscountsDiscount is an inducement for the customer to make a purchaseE.g.two for the price of onean advertised special with an expiry datea fixed amount off the pricea reduction in the unit price if large quantities are purchased

On some occasions there may be more than one discount on an item. These multiple discounts are called chain discounts

A reduction in price is referred to as a discount and is often expressed in the form of a percentage



2.3 Discounts (cont)To calculate the amount of discount,Where:L = list priceD = amount of discountR = rate of discountDP = discount price

The rate of discount is:

The amount of discount

The discount price (or net price) is:



2.3 Discounts (cont)Trade discountA special discount when goods and services are purchased from one business by another business.E.g.a builder purchasing timber from a timber yarda service station obtaining tyres from a manufacturer an electrician purchasing cables and switches from an electrical supplier

A typical trade discount would range between 10% and 25%, depending on the trade and the itemThe method for calculating trade discounts is the same as in the previous examples



2.3 Discounts (cont)Cash discountA form of discount that is given if the purchaser pays in cash or by chequeThe percentage of the discount may depend on how quickly the bill is paid.E.g. A supplier of electrical goods informs retailers that the following discounts are available for early payment of purchases: Within 7 days 10.0 % Within 14 days 7.5 % Within 28 days 2.5 %



2.4 Goods and Services Tax (GST)An Australian broad-based tax of 10% on most supplies of goods and servicesThe GST replaced a number of other taxes, including wholesale sales tax, that were applied at varying rates to a range of productsThe amount of GST payable can be calculated easily by working out 10% of the cost of the goods or serviceTo work out how much a customer has paid in GST, divide the final price by 11



2.5 Personal income taxIndividuals who receive income are liable for personal income

DefinitionsGross income is the total amount received or accruedAssessable income is gross income less exempt incomeAllowable deductions are costs of producing income and certain concessional deductionsTaxable income is assessable income less allowable deductionsTax payable is tax according to the table on taxable income less rebates



2.5 Personal income tax (cont)The tax-free threshold for most resident individuals is $6000

Taxpayers are subject to a Medicare levy, normally calculated at the rate of 1.5% of your taxable income



2.6 Company taxA company is a distinct legal entity with its own income tax liability that is separate from personal income tax

The income tax of companies is calculated on taxable income, which is the income earned by the company less any allowable deductions

The amount of tax to be paid is reduced by any PAYG (pay as you go) instalments paid during the year

The general rate of tax payable by companies on 200910 income is 30%



2.7 Fringe Benefits Tax (FBT)FBT is an Australian government tax paid on certain benefits employers provide to their employees in place of, or in addition to, salary

FBT is separate from income tax

FBT is payable by the employer and is based on the taxable value of the various fringe benefits provided

The rate of FBT is currently aligned with the top marginal income tax rate and was set at 46.5% in 200910



2.8 Land taxLand tax is a state tax levied on the owners of land in various states of Australia

A principal place of residence (your home) or land used for primary production (a farm) is exempt from land tax

You may be liable for land tax if you own or part-own:vacant land, including vacant rural landa holiday homeinvestment propertiescompany title unitsresidential, commercial or industrial units



2.8 Land tax (cont)Land tax is calculated on the combined value of all the taxable land you own

The land tax threshold varies from state to state

For example, for 2009 it was $368 000 in New South Wales$250 000 in Victoria$110 000 in South Australia$600 000 in Queensland



2.9 Profit and lossThe actual profit is the difference between the price the item is sold for (the selling price) and the cost of that item (the cost price)

An item may be sold for an amount that is less than the cost price. The profit is therefore negative and is referred to as a loss

The actual cost of an item is often difficult to calculate, since it involves not only the cost of obtaining the item from the supplier but other costs as well. These include the general costs of running a business, e.g.wagesinsurancetaxesstationeryequipment electricityrentother overhead expenses



2.9 Profit and loss (cont)The following definitions will be useful for profits:

SP = selling price (not including any applicable GST)CP = cost priceP = actual profit (when the value of SP exceeds the value of CP)Ps = profit rate (or mark-up rate) expressed as a fraction of selling pricePc = profit rate (or mark-up rate) expressed as a fraction of cost price

(The profit rates expressed as percentages are 100 Ps and 100 Pc, respectively)



2.9 Profit and loss (cont)The following definitions will be useful for loss:

L = actual loss (when the value of CP exceeds the value of SP)Ls = loss rate (or mark-down rate) expressed as a fraction of selling priceLc = loss rate (or mark-down rate) expressed as a fraction of cost price

(The loss rates expressed as percentages are 100 Ls and 100 Lc , respectively)



2.9 Profit and loss (cont)The following relationships hold:



2.10 Stamp dutyStamp duty is a tax on transactions that is levied by the individual states in AustraliaStamp duty is really a tax on the document of transfer (the title transfer), and not on the property itself

Stamp duty on vehiclesStamp duty is based on the market value of the vehicle or the price that was paid, whichever is greater

Stamp duty on real estateStamp duty is payable on the purchase price of propertyThe amount payable depends on the price of the property and which state it was bought in



SummaryThe application of percentages in modern business practice is widespread and this chapter has presented some of the more common examples

The introduction of the GST into Australia was part of significant tax reform including substantial personal income tax cuts and the removal of a number of indirect taxes

In using the taxation tables and related information, it is important to be aware that rates charged may vary from year to year


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