{"id":20046,"date":"2021-08-20T12:50:51","date_gmt":"2021-08-20T12:50:51","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=20046"},"modified":"2024-04-05T07:07:40","modified_gmt":"2024-04-05T07:07:40","slug":"price-multiples-based-on-forecasted-fundamentals","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/price-multiples-based-on-forecasted-fundamentals\/","title":{"rendered":"Price Multiples Based on Forecasted Fundamentals"},"content":{"rendered":"<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/0kMmbenpFuo\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\">\ufeff<\/span><\/iframe><\/p>\r\n\r\n<h2>Justified Leading P\/E Multiple based on Fundamentals<\/h2>\r\n<p>$$\\text{Justified leading}\\ \\frac{\\text{P}_{0}}{\\text{E}_1} =\\frac{\\text{D}_{1}\u2044\\text{E}_1}{\\text{r}-\\text{g}}=\\frac{1-\\text{b}}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(1-\\text{b}=\\) Payout Ratio<\/p>\r\n<p>$$\\begin{align*}\\text{Justified leading}\\ \\frac{\\text{P}_{0}}{\\text{E}_0} &amp;=\\frac{\\frac{\\text{D}_{0}(1+\\text{g})}{\\text{E}_0}}{\\text{r}-\\text{g}}=\\frac{(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}=\\bigg(\\frac{1-\\text{b}}{\\text{r}-\\text{g}}\\bigg)(1+\\text{g})\\\\ \\text{Justified trailing}&amp;=\\text{Justified leading}\\ \\frac{\\text{P}}{\\text{E}}\\times(1+\\text{g})\\end{align*}$$<\/p>\r\n<ul>\r\n\t<li>If earnings are expected to grow by \\(g\\), next year\u2019s earnings will be greater than last year\u2019s earnings by the growth rate, and the justified trailing P\/E ratio will be greater than the justified, leading P\/E ratio by (\\(1 + g\\)).<\/li>\r\n\t<li>A higher justified P\/E ratio indicates relative overvaluation.<\/li>\r\n<\/ul>\r\n<h4>Example: <span lang=\"EN-US\">Calculating <\/span>Justified P\/E <span lang=\"EN-US\">Based on Fundamentals<\/span><\/h4>\r\n<p>Given the following forecasted fundamentals:<\/p>\r\n<ul>\r\n\t<li>Retention ratio = 40%<\/li>\r\n\t<li>Required rate of return = 10%<\/li>\r\n\t<li>Dividend growth rate = 3%<\/li>\r\n<\/ul>\r\n<p>Calculate the justified trailing and justified leading multiples based on the above-forecasted fundamentals.<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$\\begin{align*}\\text{Justified trailing P\/E} &amp;= \\frac{(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}\\\\\u00a0 &amp;=\\frac{(1-40\\%)(1.03)}{0.10-0.03}\\\\&amp;=8.83\\\\ \\\\ \\text{Justified leading P\/E}&amp;=\\frac{1-0.40}{0.10-0.03}\\\\&amp;=8.57\\end{align*}$$<\/p>\r\n<h2>Justified P\/B Multiple based on Fundamentals<\/h2>\r\n<p>$$\\text{Justified}\\ \\frac{\\text{P}_{0}}{\\text{B}_{0}}=\\frac{\\text{ROE}-\\text{g}}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\u00a0\\(\\text{ROE}=\\) Return on equity.<\/p>\r\n<p>\u00a0\\(\\text{r}=\\) Required return on equity.<\/p>\r\n<p>\u00a0\\(\\text{g}=\\) Sustainable growth rate.<\/p>\r\n<h4>Example: Calculating P\/B Multiple Based on Fundamentals<\/h4>\r\n<p>The following information relates to ABC Ltd:<\/p>\r\n<ul>\r\n\t<li>ROE = 16%<\/li>\r\n\t<li>Required rate of return = 12%<\/li>\r\n\t<li>Expected growth rate = 10%<\/li>\r\n<\/ul>\r\n<p>The firm&#8217;s justified P\/B based on the above fundamentals is <em>closest<\/em> to:<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$\\begin{align*}\\text{Justified}\\ \\frac{\\text{P}_{0}}{\\text{B}_{0}}&amp;=\\frac{\\text{ROE}-\\text{g}}{\\text{r}-\\text{g}}\\\\&amp;=\\frac{0.16-0.10}{0.12-0.10}\\\\&amp;=3\\end{align*}$$<\/p>\r\n<p>All else equal, P\/B is positively related to ROE.<\/p>\r\n<ul>\r\n\t<li>The bigger the spread between ROE and \\(r\\), the higher the P\/B ratio, all else equal.<\/li>\r\n\t<li>A higher justified P\/B ratio indicates relative overvaluation.<\/li>\r\n<\/ul>\r\n<h2><span lang=\"EN-US\">Justified P\/S Multiple Based on Fundamentals<\/span><\/h2>\r\n<p>$$\\text{Justified P\/S}=\\frac{(\\text{E}_{0}\/\\text{S}_{0})(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}$$<\/p>\r\n<p>Where:<\/p>\r\n<p>\\(\\text{E}\/\\text{S}_{0}=\\) Net profit margin.<\/p>\r\n<p>\\(1-\\text{b}=\\) Payout ratio.<\/p>\r\n<p>P\/S ratio increases with an:<\/p>\r\n<ul>\r\n\t<li>Increase in profit margin<\/li>\r\n\t<li>Increase in earnings growth rate<\/li>\r\n<\/ul>\r\n<h4><span lang=\"EN-US\">Example: Calculating P\/S Multiple Based on Fundamentals<\/span><\/h4>\r\n<p>Consider the following information:<\/p>\r\n<p>$$\\small{\\begin{array}{l|r}\\text{Dividend payout ratio} &amp; 30\\% \\\\ \\hline\\text{ROE} &amp; 12\\% \\\\ \\hline\\text{EPS} &amp; \\$6 \\\\ \\hline\\text{Sales per share} &amp; \\$328 \\\\ \\hline{\\text{Expected growth rate in}\\\\ \\text{dividend and earnings}} &amp; 7.50\\% \\\\ \\hline\\text{Required rate of return} &amp; 15\\%\\\\ \\end{array}}$$<\/p>\r\n<p>Calculate justified P\/S based on these fundamentals.<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$\\begin{align*}\\text{Justified P\/S}&amp;=\\frac{(\\text{E}_{0}\/\\text{S}_{0})(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}\\\\&amp;=\\frac{(\\frac{6}{328})(0.30)(1.075)}{0.15-0.075}=0.0786\\end{align*}$$<\/p>\r\n<p>A low justified P\/S ratio may indicate the stock is\u00a0undervalued, while a significantly above-average ratio may suggest overvaluation.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>Consider the following information:<\/p>\r\n<ul>\r\n\t<li>Earnings growth ratio = 12%<\/li>\r\n\t<li>Required rate of return = 13%<\/li>\r\n\t<li>Long term profit margin = 6.5%<\/li>\r\n\t<li>Dividend payout ratio = 30%<\/li>\r\n<\/ul>\r\n<p>The justified P\/S ratio is <em>closest to:<\/em><\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>2.184.<\/li>\r\n\t<li>2.451.<\/li>\r\n\t<li>2.662.<\/li>\r\n<\/ol>\r\n<h3>Solution<\/h3>\r\n<p><strong>The correct answer is A.\u00a0<\/strong><\/p>\r\n<p>$$\\begin{align*}\\text{Justified P\/S}&amp;=\\frac{(\\text{E}_{0}\/\\text{S}_{0})(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}\\\\&amp;=\\frac{(0.065)(0.30)(1.12)}{0.13-0.12}= 2.184\\end{align*}$$<\/p>\r\n<\/blockquote>\r\n<p>Reading 25: Market-Based Valuation: Price and Enterprise Value Multiples<\/p>\r\n<p><em>LOS 25 (h) Calculate and interpret the justified price-to-earnings ratio (P\/E), price-to-book ratio (P\/B), and price-to-sales ratio (P\/S) for a stock, based on forecasted fundamentals.<\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\ufeff\ufeff Justified Leading P\/E Multiple based on Fundamentals $$\\text{Justified leading}\\ \\frac{\\text{P}_{0}}{\\text{E}_1} =\\frac{\\text{D}_{1}\u2044\\text{E}_1}{\\text{r}-\\text{g}}=\\frac{1-\\text{b}}{\\text{r}-\\text{g}}$$ Where: \\(1-\\text{b}=\\) Payout Ratio $$\\begin{align*}\\text{Justified leading}\\ \\frac{\\text{P}_{0}}{\\text{E}_0} &amp;=\\frac{\\frac{\\text{D}_{0}(1+\\text{g})}{\\text{E}_0}}{\\text{r}-\\text{g}}=\\frac{(1-\\text{b})(1+\\text{g})}{\\text{r}-\\text{g}}=\\bigg(\\frac{1-\\text{b}}{\\text{r}-\\text{g}}\\bigg)(1+\\text{g})\\\\ \\text{Justified trailing}&amp;=\\text{Justified leading}\\ \\frac{\\text{P}}{\\text{E}}\\times(1+\\text{g})\\end{align*}$$ If earnings are expected to grow by \\(g\\), next year\u2019s earnings will be greater than last&#8230;<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[102,401],"tags":[216,402,482,474],"class_list":["post-20046","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-equity-valuation","tag-cfa-level-2","tag-equity-valuation","tag-price-multiples-based-on-forecasted-fundamentals","tag-reading-29-market-based-valuation","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Price Multiples Based on Forecasted Fundamentals - CFA, FRM, and Actuarial Exams Study Notes<\/title>\n<meta name=\"description\" content=\"Explore the relationships between payout ratios, earnings growth rates, ROE, profit margins, and required rates of return in 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