Chapter 04

4-1Copyright 2010 McGraw-Hill Australia Pty Ltd PowerPoint slides to accompany Croucher, Introductory Mathematics and Statistics, 5e

Chapter 4

Ratios and Proportions

Introductory Mathematics & Statistics for Business


Learning Objectives

• Calculate ratios and proportions

• Calculate and apply profit ratios

• Calculate and apply efficiency ratios

• Calculate and apply liquidity ratios


4.1 Ratios and Proportions• A ratioratio is a method of comparing two or more numbers or rates.

• A proportionproportion represents the relativerelative contribution of a quantity to the whole.

• The value of a proportion should lie between 0 and 1.

• Ratios are often reduced to proportions.– If two quantities X and Y occur in the ratio a:b respectively, then

X occurs in the proportion of the time

Y occurs in the proportion of the time

baa

bab


Ratios and Proportions (cont…)

• Similarly, suppose that the three quantities X, Y and Z occur in the ratio a : b : c, respectively. This means that the

– proportion that X occurs is

– the proportion that Y occurs is

– proportion that Z occurs is

• This notion is easily extended to as many quantities as desired.

cbaa

cbab

cbac


Ratios and Proportions (cont…)• Rates• When comparisons involving large numbers are made, ratios

are used to express the rate at which events take place – E.g. The rate at which a car uses fuel is expressed as a rate

in the form:

number of kilometres : 100 litres

• In the case above the first number is a non-integer and the second number in the ratio is a base figure such as a standard unit of measurement.

• Hence, a rate is really a ratio expressed with a specified base.


Ratios and Proportions (cont…)

• Ratios with common first numbers may also be used to compare several items to indicate the percentage difference between one figure and another.

• For example: The first driver drove 1125 kilometres and the second driver only 1068.2 kilometres, using 100 litres of petrol

• We can therefore use these ratios as a basis of comparison for fuel economy


4.2 Profit Ratios• Profit ratios express the relationship of profit to some financial quantity

(e.g. total assets or sales)..

• The financial position of a company is indicated by a balance sheet.

• A balance sheet lists the resources of value (assets) and liabilities. An important issue is whether the company has the assets to cover its liabilities.

• The components of a profit and loss statement (or income statement) for a business produce the ratio of net profit to sales.


Profit Ratios (cont…)• Asset Turnover

– An asset is a resource of value controlled by a business e.g. cash, bank deposits, inventory, receivables

– This ratio measures sales to total assets and is known as the total asset turnover,

– For example – total asset turnover equals 283.3%. This means that there was a 283.3% turnover in sales in relation to assets.

assetstotalsalesturnoverassetTotal


Profit Ratios (cont…)Example

A company that sells mainframe computers has total sales of $3 400 000 in a period and assets of $1 200 000. Find the total asset turnover.

Solution

833.2000,200,1$000,400,3$

assetstotalsalesturnoverassetTotal


Profit Ratios (cont…)

– The aim of any asset management is to determine the use being made of assets to an organisation and to uncover any trend in the make-up of the total asset base.

– The total turnover measures the overall effectiveness of a company’s current management.

– A company with a low net profit margin should have a larger total asset turnover than a company with a high net profit margin


Profit Ratios (cont…)

• The return on investment for a company may be broken down into its profit margin and asset turnover components as follows

turnoverassettotalsales

profitnetassetstotal

salessales

profitnetassetstotalprofitnetinvestmentonReturn


4.3 Efficiency Ratios

• An efficiency ratio of a company reflects its ability to achieve the maximum return for the lowest possible level of assets. .

• A measure of the efficiency of a company’s stock control is given by the stock turnover (or inventory turnover), where:

where the cost of goods sold is found from the profit and loss statement

and

stock Averagesoldgoodsofcost over Stock turn

2stockclosingstockopeningstockAverage


Efficiency Ratios (cont…)

• Debtor TurnoverDebtor Turnover

– A measure of the operating efficiency of the credit policy of a business is the debtor turnover (or accounts receivable turnover).

– The debtor turnover uses gross figures and any bad debts are not deducted

receivableaccountsgrossaveragesalescreditgross rnover Debtors tu


Efficiency Ratios (cont…)

• The debtor turnover may also be expressed in terms of the average collection period (in days).

• The debtor turnover measures the effectiveness of credit control

• This ratio also indicates whether a company may be extending its credit facilities beyond an acceptable limit

turnoverdetor365periodcollectionAverage


4.4 Liquidity Ratios• Liquidity—the ability of a company to pay its immediate debts.

• There are two methods to measure this ability. They are Current-asset ratio and Acid-test ratio

• Current-asset ratioCurrent-asset ratio– indicates how well current liabilities are covered by current

assets – Defined as

• If a company has a high current-asset ratio, may indicate that it is able to meet its obligations

abilitiescurrent lisetscurrent as set ratio Current-as


Liquidity Ratios (cont…)

• Whether a current-asset ratio is acceptable or not depends on how readily stock and accounts receivable can be converted into cash and how quickly cash flows in from sales

• This ratio can be used to compare companies of varying sizes as well as to measure the liquidity of the same company from year to year


Liquidity Ratios (cont…)• Acid-test ratio

– The acid-test ratio includes assets that are expected to be turned into cash and liabilities that are due to be repaid within 12 months.

– Liquidity may be more immediately measured by excluding the less liquid current assets and less urgent current liabilities.

For example• current assets that may be excluded include

inventory and hire-purchase debtors.

• current liabilities excluded include bank overdrafts


Liquidity Ratios (cont…)

• The acid-test ratio (or quick-test ratio) is defined as

• The acid-test ratio gives an indication of a company’s ability to use its own liquid assets to meet its immediate financial commitments.

• It also provides a better indication than the current-asset ratio of the company’s ability to pay short-term debts.

overdraftbanksliabilitiecurrentinventoryassestscurrentratiotestAcid


Other Ratios

• Other ratios that reveal trends over time:

– Debt/equityDebt/equity - tests the leverage of an entity

– Proprietary ratioProprietary ratio - indicates long-term financial stability

– Return on investmentReturn on investment - interest to current and potential shareholders

– Rate of returnRate of return - indicates that the dollar value of profits is less important than the rate of return


Summary

• We have looked at Calculating ratios and proportions which included rates

Calculating and apply profit ratios, which included asset turnover and returns on investment

Calculating and apply efficiency ratios like debtor turnover. Also included was stock turnover and average stock

Calculating and apply liquidity ratios such as current-asset ratio and the acid-test ratio

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Chapter 04