{"id":15711,"date":"2021-05-27T19:59:45","date_gmt":"2021-05-27T19:59:45","guid":{"rendered":"https:\/\/analystprep.com\/study-notes\/?p=15711"},"modified":"2024-04-10T06:43:07","modified_gmt":"2024-04-10T06:43:07","slug":"effects-of-repurchases-on-earnings-per-share","status":"publish","type":"post","link":"https:\/\/analystprep.com\/study-notes\/cfa-level-2\/effects-of-repurchases-on-earnings-per-share\/","title":{"rendered":"Effects of Repurchases on Earnings per Share"},"content":{"rendered":"<p><iframe loading=\"lazy\" src=\"\/\/www.youtube.com\/embed\/hn2pw6Mx4OQ\" width=\"611\" height=\"343\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\r\n\r\n<p>Share repurchase may increase, decrease, or have no effect on EPS depending on how the repurchase is financed.<\/p>\r\n<p>$$\\text{EPS}=\\frac{\\text{Net income (NI)}}{\\text{Shares outstanding}}$$<\/p>\r\n<p>If the net income is constant, a smaller number of shares after the buyback leads to a higher EPS. If the buyback is financed with borrowed funds, both net income and outstanding shares will be decreased. This results in a lower EPS.<\/p>\r\n<h2>Internal Financing<\/h2>\r\n<p>The post-repurchase EPS will be higher than the pre-repurchase EPS if the rate of return on retained earnings is less than the cost of capital.<\/p>\r\n<h2>External Financing (Borrowed funds)<\/h2>\r\n<p>If repurchase is made with borrowed funds, the EPS will:<\/p>\r\n<ul>\r\n\t<li>increase if the After-tax cost of debt &lt; Earnings yield of the shares before the repurchase.<\/li>\r\n\t<li>decrease if the After-tax cost of debt &gt; Earnings yield of the shares before the repurchase.<\/li>\r\n\t<li>remain unchanged if the After-tax cost of debt = Earnings yield of the shares before the repurchase.<\/li>\r\n<\/ul>\r\n<h4>Example 1: Share Repurchases using Idle Cash<\/h4>\r\n<p>Grino Ltd. has the following information:<\/p>\r\n<ul>\r\n\t<li>Outstanding shares worth $12 million.<\/li>\r\n\t<li>Net income of $150 million.<\/li>\r\n\t<li>Grino&#8217;s share price is $40<\/li>\r\n\t<li>Cash worth $200 million is invested in government treasury bills at a zero percent interest.<\/li>\r\n\t<li>Grino&#8217;s analysts estimate that the shares could be bought in the open market at $50.<\/li>\r\n<\/ul>\r\n<p>Calculate the impact on EPS if Grino buys back the shares at $50 using idle cash.<\/p>\r\n<h4>Solution<\/h4>\r\n<p>$$\\text{Current EPS}=\\frac{$150\\ \\text{million}}{$12\\ \\text{million}}=$12.5$$<\/p>\r\n<p>After a share repurchase at $50, the number of shares outstanding reduces by 4 million \\(\\frac{$200,000,000}{$50}\\), and the new shares outstanding is \\(12,000,000-4,000,000=8\\ \\text{million}\\).<\/p>\r\n<p>EPS after repurchasing shares is \\(\\frac{$150,000,000}{8,000,000 \\text{ shares}}=$18.75\/ \\text{share}\\).<\/p>\r\n<p>EPS has increased by 50% because Grino used idle cash to repurchase the shares.<\/p>\r\n<h4>Example 2: Share Repurchases using Borrowed Funds<\/h4>\r\n<p>Jefferson Systems will borrow $16 million to finance a share repurchase. The following information is given:<\/p>\r\n<ul>\r\n\t<li>Earnings after-tax is $9 million.<\/li>\r\n\t<li>EPS before share repurchase is $3.<\/li>\r\n\t<li>Shares outstanding is 3 million.<\/li>\r\n\t<li>Planned share repurchase is 300,000 shares.<\/li>\r\n<\/ul>\r\n<p>Calculate the EPS after the share buyback and after-tax cost of borrowing as 6%.<\/p>\r\n<h5>Solution<\/h5>\r\n<p>$$\\begin{align*}\\text{EPS after repurchasing}&amp;=\\frac{(\\text{Earnings}-\\text{After-tax cost of funds})}{\\text{Shares outstanding after buyback}}\\\\ \\\\ &amp;=\\frac{[$9,000,000-($16,000,000\\times0.06)]}{2,700,000 \\text{ shares}}\\\\&amp;=$2.98\/ \\text{share}\\end{align*}$$<\/p>\r\n<p>We can see that with an after-tax cost of debt of 6%, the EPS decreased from $3 to $2.98.<\/p>\r\n<blockquote>\r\n<h2>Question<\/h2>\r\n<p>A firm has 3 million outstanding shares and earnings of \u20ac6 million. It has \u20ac12 million in idle cash that it plans to use to repurchase shares in the open market. The firm&#8217;s current share price is \u20ac60. The firm is planning to use the entire \u20ac12 million to finance the purchase.<\/p>\r\n<p>The firm&#8217;s EPS after the repurchase will be <em>closes<\/em>t to:<\/p>\r\n<ol style=\"list-style-type: upper-alpha;\">\r\n\t<li>\u20ac2.00.<\/li>\r\n\t<li>\u20ac2.14.<\/li>\r\n\t<li>\u20ac3.00.<\/li>\r\n<\/ol>\r\n<h4>Solution<\/h4>\r\n<p><strong>The correct answer is B.<\/strong><\/p>\r\n<p>The company can repurchase 200,000 shares \\(\\bigg(\\frac{\u20ac12,000,000}{\u20ac60}\\bigg)\\). After the repurchase, the number of outstanding shares would be 2.8 million shares (3,000,000 \u2013 200,000 shares).<\/p>\r\n<p>$$\\text{EPS after repurchasing the shares}=\\frac{\u20ac6,000,000}{2,800,000 \\text{ shares}}=\u20ac2.14\/ \\text{share}$$<\/p>\r\n<p><strong>A is incorrect. <\/strong>This is the earnings before the share buyback.<\/p>\r\n<p>$$\\text{EPS before repurchasing the shares}=\\frac{\u20ac6,000,000}{3,000,000 \\text{ shares}}=\u20ac2\/ \\text{share}$$<\/p>\r\n<\/blockquote>\r\n<p><em>Reading 18: Analysis of Dividends and Share Repurchases\u00a0<\/em><\/p>\r\n<p><em>LOS 18 (i) Calculate and compare the effect of a share repurchase on earnings per share when 1) the repurchase is financed by the company&#8217;s surplus cash and 2) the company uses debt to finance the repurchase.<\/em><\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>Share repurchase may increase, decrease, or have no effect on EPS depending on how the repurchase is financed. $$\\text{EPS}=\\frac{\\text{Net income (NI)}}{\\text{Shares outstanding}}$$ If the net income is constant, a smaller number of shares after the buyback leads to a higher&#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":[102,346],"tags":[216,344,377,368],"class_list":["post-15711","post","type-post","status-publish","format-standard","hentry","category-cfa-level-2","category-corporate-finance-cfa-level-2","tag-cfa-level-2","tag-corporate-finance","tag-effects-of-repurchases-on-earnings-per-share","tag-reading-21analysis-of-dividends-and-share-repurchases","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.9 - 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