{"id":18535,"date":"2025-06-13T07:22:31","date_gmt":"2025-06-13T07:22:31","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=18535"},"modified":"2025-06-13T07:22:33","modified_gmt":"2025-06-13T07:22:33","slug":"suppose-g-0-for-t-1-to-3-and-then-g-is-a-constant-6","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/suppose-g-0-for-t-1-to-3-and-then-g-is-a-constant-6\/","title":{"rendered":"Suppose g = 0 for t = 1 to 3, and then g is a constant 6%"},"content":{"rendered":"\n<p>Suppose g = 0 for t = 1 to 3, and then g is a constant 6%, Do = $2.00 and k is 13%. What is P.?<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>To find the <strong>price of a stock (P\u2080)<\/strong> under a <strong>non-constant growth model<\/strong>, we can use the <strong>dividend discount model (DDM)<\/strong>, adjusting for variable growth. Here&#8217;s the given information:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>g = 0%<\/strong> from <strong>t = 1 to 3<\/strong>, then <strong>g = 6%<\/strong> starting from <strong>t = 4<\/strong>.<\/li>\n\n\n\n<li><strong>D\u2080 = $2.00<\/strong><\/li>\n\n\n\n<li><strong>k (required rate of return) = 13%<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find Dividends for Years 1\u20133 (Zero Growth)<\/h3>\n\n\n\n<p>Since <strong>g = 0%<\/strong> for the first 3 years:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D\u2081 = D\u2082 = D\u2083 = $2.00<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find D\u2084 (Growth Starts at t = 4)<\/h3>\n\n\n\n<p>From year 4 onward, dividend grows at <strong>6%<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>D\u2084 = D\u2083 \u00d7 (1 + g) = 2.00 \u00d7 1.06 = $2.12<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find the Price at Year 3 (P\u2083)<\/h3>\n\n\n\n<p>From <strong>year 4 onward<\/strong>, growth is constant, so we can use the <strong>Gordon Growth Model<\/strong> to find <strong>P\u2083<\/strong>, the present value of all future dividends <strong>starting at year 4<\/strong>: P3=D4k\u2212g=2.120.13\u22120.06=2.120.07=30.29P_3 = \\frac{D_4}{k &#8211; g} = \\frac{2.12}{0.13 &#8211; 0.06} = \\frac{2.12}{0.07} = 30.29<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the Present Value (P\u2080)<\/h3>\n\n\n\n<p>Now discount <strong>D\u2081<\/strong>, <strong>D\u2082<\/strong>, <strong>D\u2083<\/strong>, and <strong>P\u2083<\/strong> to the present: P0=2.00(1.13)1+2.00(1.13)2+2.00+30.29(1.13)3P_0 = \\frac{2.00}{(1.13)^1} + \\frac{2.00}{(1.13)^2} + \\frac{2.00 + 30.29}{(1.13)^3} P0=2.001.13+2.001.2769+32.291.443P_0 = \\frac{2.00}{1.13} + \\frac{2.00}{1.2769} + \\frac{32.29}{1.443} P0=1.7699+1.5661+22.37=25.71P_0 = 1.7699 + 1.5661 + 22.37 = \\boxed{25.71}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words)<\/h3>\n\n\n\n<p>This problem requires using a <strong>multi-stage Dividend Discount Model (DDM)<\/strong>. Initially, the dividend does <strong>not grow<\/strong> for the first three years, remaining at <strong>$2.00<\/strong> annually. After that, it begins to grow perpetually at <strong>6%<\/strong>, creating a hybrid scenario: no-growth followed by constant growth.<\/p>\n\n\n\n<p>We begin by identifying the dividends for each of the first three years. Since growth is zero, each dividend from <strong>t = 1 to t = 3<\/strong> is simply <strong>$2.00<\/strong>.<\/p>\n\n\n\n<p>Starting in year 4, growth begins at 6%. Thus, we calculate the year 4 dividend as <strong>D\u2084 = $2.00 \u00d7 1.06 = $2.12<\/strong>.<\/p>\n\n\n\n<p>To find the value of all future dividends from <strong>t = 4 onward<\/strong>, we use the <strong>Gordon Growth Model<\/strong>, which assumes dividends grow at a constant rate indefinitely. This gives us <strong>P\u2083<\/strong>, the present value of all future dividends at <strong>t = 3<\/strong>, using: P3=D4k\u2212gP_3 = \\frac{D_4}{k &#8211; g}<\/p>\n\n\n\n<p>The final step is to discount all cash flows\u2014<strong>D\u2081<\/strong>, <strong>D\u2082<\/strong>, <strong>D\u2083<\/strong>, and <strong>P\u2083<\/strong>\u2014back to the present using the required rate of return (13%). The result, <strong>P\u2080 = $25.71<\/strong>, represents the <strong>intrinsic value<\/strong> of the stock based on its expected future dividends.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u2705 <strong>Final Answer: $25.71<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Suppose g = 0 for t = 1 to 3, and then g is a constant 6%, Do = $2.00 and k is 13%. What is P.? The correct answer and explanation is: To find the price of a stock (P\u2080) under a non-constant growth model, we can use the dividend discount model (DDM), adjusting [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-18535","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18535","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=18535"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18535\/revisions"}],"predecessor-version":[{"id":18536,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/18535\/revisions\/18536"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=18535"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=18535"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=18535"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}