{"id":58,"date":"2020-04-17T15:32:06","date_gmt":"2020-04-17T19:32:06","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&#038;p=58"},"modified":"2024-10-29T14:05:45","modified_gmt":"2024-10-29T18:05:45","slug":"topic-1","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/topic-1\/","title":{"raw":"1.3 Ratios With More Than Two Quantities","rendered":"1.3 Ratios With More Than Two Quantities"},"content":{"raw":"In some business situations, it is desirable to examine the relative sizes of a number of quantities. In such cases, ratios of the quantities are used.\r\n\r\nConsider, for example, the expenses of a merchandising company. These expenses can be usefully broken down into two major components:\r\n<ul>\r\n \t<li>the [pb_glossary id=\"1147\"]cost of the goods sold (COGS)[\/pb_glossary]<\/li>\r\n \t<li>all other expenses, called operating expenses.<\/li>\r\n<\/ul>\r\nWhen analyzing merchandising companies, it is customary to first deduct the cost of goods sold from sales revenue, and to call the result the gross profit.\r\n<p style=\"text-align: center\">[latex]Sales - COGS = Gross \\; Profit[\/latex]<\/p>\r\n[pb_glossary id=\"1148\"]Operating expenses[\/pb_glossary] are then deducted from the gross profit to get net profit.\r\n<p style=\"text-align: left;padding-left: 120px\">SALES\r\n<span style=\"text-decoration: underline\">- COGS<\/span>\r\nGROSS PROFIT\r\n<span style=\"text-decoration: underline\">- OPERATING EXPENSES<\/span>\r\nNET PROFIT<\/p>\r\nAll of these quantities are commonly compared with the sales revenue as the base.\r\n<h2>Example 1.3.1<\/h2>\r\nSuppose that in our opening example, in which the company had sales of $32,000 in a period, the cost of these goods was $20,000 and operating expenses were $4,000. You would arrange the analysis as follows:\r\n<table class=\"aligncenter\" border=\"0\">\r\n<thead>\r\n<tr>\r\n<td><\/td>\r\n<td>$<\/td>\r\n<td>% Sales<\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>\u00a0 Sales<\/td>\r\n<td>$32,000<\/td>\r\n<td>100.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>- COGS<\/td>\r\n<td>20,000<\/td>\r\n<td>62.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0 Gross Profit<\/td>\r\n<td>12,000<\/td>\r\n<td>37.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>- Operating Expenses<\/td>\r\n<td>4,000<\/td>\r\n<td>12.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\u00a0 Net Profit<\/td>\r\n<td>8,000<\/td>\r\n<td>25.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis has the format of a (very) simple Income Statement.\r\n\r\n&nbsp;\r\n\r\nWhen gross profit is compared with sales it is called [pb_glossary id=\"102\"]percent gross margin[\/pb_glossary]. Net profit compared with sales is called [pb_glossary id=\"84\"]percent net margin[\/pb_glossary].\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Key Takeaways<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\"><em>Gross profit compared with sales is called [pb_glossary id=\"102\"]percent gross margin[\/pb_glossary]; Net profit compared with sales is called [pb_glossary id=\"84\"]percent net margin[\/pb_glossary].<\/em><\/div>\r\n<\/div>\r\nSuppose now that a similar company was expected to perform with the same ratios but to have sales of $50,000 in a period. Then each of the other entries could be calculated by using the above ratios. For example:\r\n<p style=\"text-align: center\">[latex]\\frac{COGS}{Sales} = \\frac{COGS}{\\$50,000}=\\frac{62.5}{100}= 0.625[\/latex]<\/p>\r\nSo\r\n<p style=\"text-align: center\">[latex]COGS = Sales \\times 0.625 =\\$ 50,000 \\times 0.625 = \\$ 31,250[\/latex]<\/p>\r\nNotice that while the ratio was stated as a percent, it was necessary to replace it with the decimal equivalent in order to do the calculations. You should check that the other quantities come out, as in the following table:\r\n<table class=\"aligncenter\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 150px\"><\/td>\r\n<td style=\"width: 70px\"><\/td>\r\n<td style=\"width: 79px\">% <strong>Sales<\/strong><strong>\u00a0\u00a0 <\/strong><\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 150px\">Sales<\/td>\r\n<td style=\"width: 70px\">$50,000<\/td>\r\n<td style=\"width: 79px\">100.0<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 150px\">COGS<\/td>\r\n<td style=\"width: 70px\">31,250<\/td>\r\n<td style=\"width: 79px\">62.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 150px\">Gross Profit<\/td>\r\n<td style=\"width: 70px\">18,750<\/td>\r\n<td style=\"width: 79px\">37.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 150px\">Operating Expenses<\/td>\r\n<td style=\"width: 70px\">6,250<\/td>\r\n<td style=\"width: 79px\">12.5<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 150px\">Net Profit<\/td>\r\n<td style=\"width: 70px\">12,500<\/td>\r\n<td style=\"width: 79px\">25.0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAnother use of ratios is to allocate resources according to some measure of need or performance in an organization. For example, bonuses may be given as a percent of sales; budgeted expenses may be a percent of the previous year's expenses.\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Knowledge Check 1.3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA merchandising company finds that its COGS is 65% of sales and its monthly operating expenses are $14,000.\r\n\r\nWhat would be the COGS and the gross and net profits on sales of $90,000 in a month?\r\n\r\nWhat would be its percent gross margin and percent net margin?\r\n\r\n<a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/learning-activities-answer-key\/\"><em>Answers at the end of chapter.<\/em><\/a>\r\n\r\n<\/div>\r\n<\/div>\r\n<h2>Your Own Notes<\/h2>\r\n<ul>\r\n \t<li>Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t<li>These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t<li>Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]","rendered":"<p>In some business situations, it is desirable to examine the relative sizes of a number of quantities. In such cases, ratios of the quantities are used.<\/p>\n<p>Consider, for example, the expenses of a merchandising company. These expenses can be usefully broken down into two major components:<\/p>\n<ul>\n<li>the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_1147\">cost of the goods sold (COGS)<\/a><\/li>\n<li>all other expenses, called operating expenses.<\/li>\n<\/ul>\n<p>When analyzing merchandising companies, it is customary to first deduct the cost of goods sold from sales revenue, and to call the result the gross profit.<\/p>\n<p style=\"text-align: center\">[latex]Sales - COGS = Gross \\; Profit[\/latex]<\/p>\n<p><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_1148\">Operating expenses<\/a> are then deducted from the gross profit to get net profit.<\/p>\n<p style=\"text-align: left;padding-left: 120px\">SALES<br \/>\n<span style=\"text-decoration: underline\">&#8211; COGS<\/span><br \/>\nGROSS PROFIT<br \/>\n<span style=\"text-decoration: underline\">&#8211; OPERATING EXPENSES<\/span><br \/>\nNET PROFIT<\/p>\n<p>All of these quantities are commonly compared with the sales revenue as the base.<\/p>\n<h2>Example 1.3.1<\/h2>\n<p>Suppose that in our opening example, in which the company had sales of $32,000 in a period, the cost of these goods was $20,000 and operating expenses were $4,000. You would arrange the analysis as follows:<\/p>\n<table class=\"aligncenter\">\n<thead>\n<tr>\n<td><\/td>\n<td>$<\/td>\n<td>% Sales<\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u00a0 Sales<\/td>\n<td>$32,000<\/td>\n<td>100.00<\/td>\n<\/tr>\n<tr>\n<td>&#8211; COGS<\/td>\n<td>20,000<\/td>\n<td>62.5<\/td>\n<\/tr>\n<tr>\n<td>\u00a0 Gross Profit<\/td>\n<td>12,000<\/td>\n<td>37.5<\/td>\n<\/tr>\n<tr>\n<td>&#8211; Operating Expenses<\/td>\n<td>4,000<\/td>\n<td>12.5<\/td>\n<\/tr>\n<tr>\n<td>\u00a0 Net Profit<\/td>\n<td>8,000<\/td>\n<td>25.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This has the format of a (very) simple Income Statement.<\/p>\n<p>&nbsp;<\/p>\n<p>When gross profit is compared with sales it is called <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_102\">percent gross margin<\/a>. Net profit compared with sales is called <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_84\">percent net margin<\/a>.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Key Takeaways<\/p>\n<\/header>\n<div class=\"textbox__content\"><em>Gross profit compared with sales is called <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_102\">percent gross margin<\/a>; Net profit compared with sales is called <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_58_84\">percent net margin<\/a>.<\/em><\/div>\n<\/div>\n<p>Suppose now that a similar company was expected to perform with the same ratios but to have sales of $50,000 in a period. Then each of the other entries could be calculated by using the above ratios. For example:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{COGS}{Sales} = \\frac{COGS}{\\$50,000}=\\frac{62.5}{100}= 0.625[\/latex]<\/p>\n<p>So<\/p>\n<p style=\"text-align: center\">[latex]COGS = Sales \\times 0.625 =\\$ 50,000 \\times 0.625 = \\$ 31,250[\/latex]<\/p>\n<p>Notice that while the ratio was stated as a percent, it was necessary to replace it with the decimal equivalent in order to do the calculations. You should check that the other quantities come out, as in the following table:<\/p>\n<table class=\"aligncenter\">\n<tbody>\n<tr>\n<td style=\"width: 150px\"><\/td>\n<td style=\"width: 70px\"><\/td>\n<td style=\"width: 79px\">% <strong>Sales<\/strong><strong>\u00a0\u00a0 <\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 150px\">Sales<\/td>\n<td style=\"width: 70px\">$50,000<\/td>\n<td style=\"width: 79px\">100.0<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 150px\">COGS<\/td>\n<td style=\"width: 70px\">31,250<\/td>\n<td style=\"width: 79px\">62.5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 150px\">Gross Profit<\/td>\n<td style=\"width: 70px\">18,750<\/td>\n<td style=\"width: 79px\">37.5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 150px\">Operating Expenses<\/td>\n<td style=\"width: 70px\">6,250<\/td>\n<td style=\"width: 79px\">12.5<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 150px\">Net Profit<\/td>\n<td style=\"width: 70px\">12,500<\/td>\n<td style=\"width: 79px\">25.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Another use of ratios is to allocate resources according to some measure of need or performance in an organization. For example, bonuses may be given as a percent of sales; budgeted expenses may be a percent of the previous year&#8217;s expenses.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Knowledge Check 1.3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>A merchandising company finds that its COGS is 65% of sales and its monthly operating expenses are $14,000.<\/p>\n<p>What would be the COGS and the gross and net profits on sales of $90,000 in a month?<\/p>\n<p>What would be its percent gross margin and percent net margin?<\/p>\n<p><a href=\"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/learning-activities-answer-key\/\"><em>Answers at the end of chapter.<\/em><\/a><\/p>\n<\/div>\n<\/div>\n<h2>Your Own Notes<\/h2>\n<ul>\n<li>Are there any notes you want to take from this section? Is there anything you&#8217;d like to copy and paste below?<\/li>\n<li>These notes are for you only (they will not be stored anywhere)<\/li>\n<li>Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n<div id=\"h5p-1\">\n<div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-1\" class=\"h5p-iframe\" data-content-id=\"1\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Key takeaways, notes and comments from this section document tool.\"><\/iframe><\/div>\n<\/div>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_58_1147\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_58_1147\"><div tabindex=\"-1\"><p>Total Variable expenses, or all the costs that go into making your item.<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_58_1148\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_58_1148\"><div tabindex=\"-1\"><p>Fixed Costs<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_58_102\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_58_102\"><div tabindex=\"-1\"><\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_58_84\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_58_84\"><div tabindex=\"-1\"><\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":883,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-58","chapter","type-chapter","status-publish","hentry"],"part":3,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/58","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/users\/883"}],"version-history":[{"count":24,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/58\/revisions"}],"predecessor-version":[{"id":3947,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/58\/revisions\/3947"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapters\/58\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/media?parent=58"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/pressbooks\/v2\/chapter-type?post=58"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/contributor?post=58"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/wp-json\/wp\/v2\/license?post=58"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}