{"id":52,"date":"2020-04-17T15:15:20","date_gmt":"2020-04-17T19:15:20","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=52"},"modified":"2025-01-15T15:29:52","modified_gmt":"2025-01-15T20:29:52","slug":"ratios","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/ratios\/","title":{"raw":"1.1 Ratios","rendered":"1.1 Ratios"},"content":{"raw":"This chapter uses ratios to analyze basic business concepts such as [pb_glossary id=\"70\"]profits[\/pb_glossary], [pb_glossary id=\"1142\"]expenses[\/pb_glossary] and [pb_glossary id=\"210\"]revenues[\/pb_glossary].\r\n
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Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

If only two quantities are involved, they are referred to as amount and base.<\/div>\r\n<\/div>\r\nA ratio expresses the relative sizes of quantities. If only two quantities are involved, they are referred to as amount <\/em>and base.<\/em>\r\n

[latex]\r\nRatio = \\frac{Amount}{Base}\r\n[\/latex]<\/p>\r\nA frequently used ratio is the ratio of profit to sales. In this case the base is sales and the amount is profit.\r\n\r\nThus you have\r\n

[latex]Ratio = \\frac{Amount}{Base}=\\frac{Profit}{Sales}=\\frac{\\$8,000}{\\$32,000}=0.25=25\\%[\/latex]<\/p>\r\nThis ratio is also written as\r\n

[latex]Amount: Base = \\$8,000:\\$32,000 =1:4 =0.25:1[\/latex]<\/p>\r\n\r\n

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Key Takeaways<\/p>\r\n\r\n<\/header>\r\n

It is common to express a pure ratio in percent.<\/div>\r\n<\/div>\r\nSince both the amount and base are in dollars, this is a pure ratio or fraction, and it is common in business to express it in percent.\r\n\r\nPercent is a ratio in which the base is 100. Thus, for the above example,\r\n

[latex]Ratio = 0.25 = \\frac{25}{100}=25\\%[\/latex]<\/p>\r\nwhere the symbol % signifies that the amount 25 is to be divided by 100.\r\n\r\nA ratio of 30% is thus:\r\n

[latex] 30\\% = \\frac{30}{100}=0.30[\/latex]<\/p>\r\nPercent is used so much in business analysis that you must become completely familiar with its meaning and be able to change back and forth between percent and decimals.\r\n\r\nThe profit-to-sales ratio expressed this way is called the [pb_glossary id=\"84\"]percent net margin[\/pb_glossary]. <\/em>It is used to compare the profitability of different companies or branches of companies.\r\n

\u00a0Example 1.1.1<\/h2>\r\nConsider a company that has three branches, A, B and C, operating in small, medium-sized and large towns. Suppose the branches have the following performances during a month:\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nA<\/th>\r\nB<\/th>\r\nC<\/th>\r\nTotal<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Sales<\/th>\r\n$12,500<\/td>\r\n$46,500<\/td>\r\n$63,200<\/td>\r\n$122,200<\/td>\r\n<\/tr>\r\n
Expenses<\/th>\r\n$9,550<\/td>\r\n$38,750<\/td>\r\n$48,850<\/td>\r\n$97,150<\/td>\r\n<\/tr>\r\n
Profit<\/th>\r\n$2,950<\/td>\r\n$7,750<\/td>\r\n$14,350<\/td>\r\n$25,050<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nFrom these raw figures it is not easy to assess the performance of the branches. It is clear that C's profit is greater than B's, and that B's is greater than A's, but you would expect that to occur because of the size of their markets and the volume of their sales. If you take the percent net margin, however, you get the following:\r\n

For A: [latex]\\frac{\\$2,950}{\\$12,500} = 0.236 = 23.6\\%[\/latex]<\/p>\r\nFor all branches and the company total:\r\n

\r\n
\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nA<\/strong><\/td>\r\nB<\/strong><\/td>\r\nC <\/strong><\/td>\r\nTOTAL<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
Percent Net Margin<\/strong><\/td>\r\n23.6%<\/td>\r\n16.7%<\/td>\r\n22.7%<\/td>\r\n20.5%<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nFrom those percentages, you can see that, in a sense, branch A has the best performance (for its size), and that branch B is farthest out of place. Although there may be good reasons for this, the ratios provide a reasonable place to start looking for improvements.\r\n\r\n<\/div>\r\nExamining profits on graphs illustrates the situation. First look at the graph of the dollar values of the profits (Figure 1.1).\r\n\r\n \r\n\r\n[caption id=\"attachment_3894\" align=\"aligncenter\" width=\"300\"]\"Bar Figure 1.1: Profits in Dollars[\/caption]\r\n\r\nThen look at the graph of profits as a percent of sales (Figure 1.2 below).\r\n\r\n \r\n\r\n[caption id=\"attachment_3895\" align=\"aligncenter\" width=\"300\"]\"Bar Figure 1.2: Profits as a Percent of Sales[\/caption]\r\n\r\nOn the last graph you can see that branch B is noticeably lower.\r\n\r\nRatios are frequently used in business analysis. Two examples:\r\n