2-1 Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e Chapter 2 Percentages

2-1Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e

Chapter 2

Percentages

Introductory Mathematics

& Statistics


Learning Objectives

Understand and use percentages

Apply percentages to common commercial situations

Calculate 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 loss

Calculate stamp duty


2.1 Conversion to and from percentages• Conversion of a fraction to a percentage

– Multiply by 100 and use % sign

E.g.

• Conversion of a decimal to a percentage

– Multiply by 100 by moving the decimal point 2 places to the

right and then add a % sign

E.g.

%5.621008

5

percentageaas8

5Express

%9.26100269.0

percentageaas269.0Express


Conversion to and from percentages (cont…)• Conversion of a percentage to a fraction

– Divide by 100 and remove % sign, then simplify

E.g.

• Conversion of a percentage to a decimal

– Divide the percentage by 100 by moving the decimal point 2

places to the left, and then remove the % sign

E.g.

25

18

100

72

fractionaas72%Express

453.01003.45

decimalaas%3.45Express


2.2 Commission• An agent is paid a commission when he or she sells goods and

services

• Commission can be paid by looking at a either– fixed amount (irrespective of sales)

– straight commission with no fixed amount

• Where: S = sale amount R = rate of commission per sale F= fixed amount paid (irrespective of sales) C= commission earned

RSC

RSFC


2.2 Commission (cont…)

• Brokerage

– Brokerage is commission paid to a stockbroker who acts on a client’s 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 Discounts

• Discount is an inducement for the customer to make a purchase

E.g. two for the price of one an advertised special with an expiry date a fixed amount off the price a 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 price D = amount of discount R = rate of discount DP = discount price

– The rate of discount is:

– The amount of discount

– The discount price (or net price) is:

L

DR

DLDP

LRD



• Trade discount– A special discount when goods and services are purchased

from one business by another business.

E.g. a builder purchasing timber from a timber yard a 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 item

– The method for calculating trade discounts is the same as in the previous examples



• Cash discount– A form of discount that is given if the purchaser pays in cash

or by cheque– The 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 %




2.4 Goods and Services Tax (GST)

• An Australian broad-based tax of 10% on most supplies of goods and services

• The GST replaced a number of other taxes, including wholesale sales tax, that were applied at varying rates to a range of products

• The amount of GST payable can be calculated easily by working out 10% of the cost of the goods or service

• To work out how much a customer has paid in GST, divide the final price by 11

GST11priceinclusiveGST


2.5 Personal income tax

• Individuals who receive income are liable for personal income

• Definitions– Gross income is the total amount received or accrued– Assessable income is gross income less exempt income– Allowable deductions are costs of producing income and

certain concessional deductions– Taxable income is assessable income less allowable

deductions– Tax 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 tax

• A 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 2009–10 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 2009–10


2.8 Land tax

• Land 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 land– a holiday home– investment properties– company title units– residential, 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 loss• The 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.

wages insurance taxes stationery equipment electricity rent other 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 price

P = 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 price

Pc = 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)



• 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 price

Lc = 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)



• The following relationships hold:

CP

LL

SP

LL

SPCPL

c

s

CP

PP

SP

PP

CPSPP

c

s


2.10 Stamp duty• Stamp duty is a tax on transactions that is levied by the

individual states in Australia• Stamp duty is really a tax on the document of transfer (the title

transfer), and not on the property itself

• Stamp duty on vehicles– Stamp duty is based on the market value of the vehicle or

the price that was paid, whichever is greater

• Stamp duty on real estate– Stamp duty is payable on the purchase price of property– The amount payable depends on the price of the property

and which state it was bought in


Summary

• The 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

Documents

2-1 Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e Chapter 2 Percentages