{"id":61657,"date":"2026-07-22T05:54:34","date_gmt":"2026-07-22T05:54:34","guid":{"rendered":"https:\/\/analystprep.com\/cfa-level-1-exam\/?p=61657"},"modified":"2026-10-09T17:05:30","modified_gmt":"2026-10-09T17:05:30","slug":"implied-return-required-return-and-implied-growth-in-bond-and-equity-valuation","status":"publish","type":"post","link":"https:\/\/analystprep.com\/cfa-level-1-exam\/uncategorized\/implied-return-required-return-and-implied-growth-in-bond-and-equity-valuation\/","title":{"rendered":"Implied Return, Required Return, and Implied Growth in Bond and Equity Valuation"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"QAPage\",\n  \"mainEntity\": {\n    \"@type\": \"Question\",\n    \"name\": \"Edmund Company\u2019s stock trades at USD 50.00. The company pays an annual dividend to its shareholders, and its most recent payment of USD 2.00 occurred yesterday. Analysts following the company expect its dividend to grow at a constant rate of 4 percent per year. What is the company\u2019s required return?\",\n    \"text\": \"Options:\\n1. 8.16%.\\n2. 8.48%.\\n3. 9.16%.\",\n    \"answerCount\": 1,\n    \"acceptedAnswer\": {\n      \"@type\": \"Answer\",\n      \"text\": \"The correct answer is A. Using the Gordon Growth Model, the required return is calculated as r = D1\/P0 + g, where D1 is the expected dividend next year, P0 is the current stock price, and g is the constant dividend growth rate. The expected next dividend is D1 = $2.00 \u00d7 1.04 = $2.08. Therefore, r = $2.08 \u00f7 $50.00 + 0.04 = 0.0816, or 8.16%. Option B is incorrect because it does not correctly apply the expected next-year dividend. Option C is incorrect because it results from an incorrect calculation of the required return.\"\n    }\n  }\n}\n<\/script>\n\n\n\n<p class=\"wp-block-paragraph\">The growth rate is the rate at which the market expects an asset to grow. On the other hand, implied return is based on the current price and future security cash flows.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">When investors know the price and future value of an instrument, along with its associated cash flows, they can derive both the implied return and the growth rate. In essence, if we are given the price of an instrument and its associated cash flows, we can analyze whether it&#8217;s appropriately valued.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Implied Return for Fixed-Income Instruments<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Consider a fixed-income instrument. If we have the present value and assume all future cash flows occur as expected, the discount rate r, or yield-to-maturity (YTM), shows the implied return for the cash flow pattern under these assumptions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, take an equity investment. If we have the present value, future value, and discount rate, we can find the implied growth rate that aligns with these values.<br>\nThe implied return or growth rate reflects the market expectations incorporated into an asset&#8217;s market price. Understanding these expectations is critical for investors when making investment decisions.<\/p>\n\n\n\n<div style=\"margin: 18px 0;\">\n  <a style=\"display: block; text-align: center; padding: 14px 18px; border: 2px solid #2F5BFF; border-radius: 9999px; color: #ffffff; font-weight: 600; font-size: 16px; text-decoration: none; background-color: #1a73e8;\"\n     href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\">\n     Master CFA Level I required return and growth concepts with a Free Trial.\n  <\/a>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading\">Calculating the Implied Return for Fixed-Income Instruments<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Discount Bond<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">In the case of a discount bond or instrument, recall that an investor receives a single principal cash flow \\((FV_t)\\) at maturity, with \\((FV_t \u2013 PV_0)\\) representing the implied return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve for the implied return earned over the life of an instrument (N periods), we can rearrange the single cash flow present value formula.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that the single cash flow present value formula is:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_0 =\\frac{FV_t} {(1+r)^{-t}} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(FV_t\\) = Future value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(PV_0\\) = Present value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r\\) = Stated discount rate per period.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(t\\) = Number of compounding periods.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To solve for \\(r\\), we can rearrange this formula as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\sqrt[t]{\\frac {FV_t}{PV_0}}-1= \\left( \\frac {FV_t}{PV_0}\\right)^{\\frac {1}{t}}-1 $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We use this formula to calculate the implied periodic return earned over the instrument&#8217;s life (t periods) based on its present value (or price) and its future value.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Calculating the Implied Return for a Discount Bond<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider a zero-coupon bond with a price of $900, a future value of $1,000, and a maturity of 5 years. Calculate the implied annualized return \\(r\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\left( \\frac {FV_t}{PV_0} \\right)^{\\frac {1}{t}}-1 $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this case, \\(t\\)=5, \\(FV_t\\)=$1,000, \\(PV_0\\)=$900<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r= \\left(\\frac {1000}{900} \\right)^{\\frac {1}{5}}-1=2.13\\% $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means that an investor who purchases this zero-coupon bond at $900 and holds it for 5 years would earn an annualized implied return of 2.13%.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Coupon Bonds<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that fixed-income instruments that pay periodic interest have cash flows throughout their life until maturity. The <strong>yield-to-maturity (YTM)<\/strong> is a single implied market discount rate for all cash flows, irrespective of the timing of the cash flows implied by the market. It assumes an investor expects to receive all promised cash flows through maturity and reinvest any cash received at the same YTM.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The present value of a fixed-income instrument with periodic interest can be calculated using the following formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_{\\text{Coupon Bond}} =\\frac{PMT}{r}\\times \\left[1-\\frac{1}{(1+r)^T}\\right]+\\frac{FV_T}{(1+r)^T }$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\( PV_{\\text{Coupon Bond}} \\) = Present value (or price) of the instrument.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(PMT\\) = Periodic payment.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(FV_T\\) = Bond&#8217;s principal.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(T\\) = Number of periods to maturity.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r\\) = Discount rate (or internal rate of return) (YTM).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Implied Return for Fixed-income Instruments With Periodic Interest<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider a five-year corporate bond issued in 2023 with a 4.00 percent annual coupon and a price of USD110.00 per USD100 principal three years later. If an investor can reinvest periodic interest at the original YTM of 4.00 percent, the implied three-year return is <em>closest to<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We can calculate the future value (FV) after three years, including the future price of 110.00 and all cash flows reinvested to that date:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*}<br>\nFV_3 &amp; =PMT_1 (1+r)^2+PMT_2 (1+r)+PMT_3+PV_3 \\\\<br>\n&amp;=4 \\times (1.04)^2+4 \\times (1.04)+4+110.00 \\\\<br>\n&amp;= \\$122.49<br>\n\\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We can then solve for Milka&#8217;s annualized return, r, using the formula for implied return since we have \\(PV\\)=100, \\(FV\\)=122.49, \\(N\\)= 3 as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\sqrt[t]{\\frac {FV_t}{PV}}-1=\\sqrt[3]{\\frac {122.49}{110}}-1=3.65\\% $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means that Milka, who purchased the corporate bond at 100 and held it for 3 years, would earn an annualized implied return of 3.65%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Calculating the Yield-to-Maturity of a Coupon Bond<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">CityGroup Corp. issued a corporate bond 7 years ago with a face value of $1,000 and a 20-year maturity. The bond pays annual interest at a coupon rate of 6%. Currently, the bond is trading at $1,120. The yield to maturity (YTM) of CityGroup Corp.&#8217;s bond is <em>closest to<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Using the BA II Plus calculator, we solve the question as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We have<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{array}{l|c|c}<br>\n\\textbf{Steps} &amp; \\textbf{Explanation} &amp; \\textbf{Display} \\\\ \\hline<br>\n{[\\text{2nd}] [\\text{QUIT}] }&amp; \\text{Return to standard calc Mode} &amp; 0 \\\\ \\hline<br>\n{[\\text{2nd}] [\\text{CLR TVM}] } &amp; \\text{Clears TVM Worksheet} &amp; 0 \\\\ \\hline<br>\n13[N] &amp; \\text{Years\/periods} &amp; N = 13 \\\\ \\hline<br>\n-1,120[PV] &amp; \\text{Set the present value} &amp; PV = -1,120 \\\\<br>\n&amp; \\text{of the bond} &amp; \\\\ \\hline<br>\n60[PMT] &amp; \\text{Set the periodic} &amp; PMT = 3.90 \\\\<br>\n&amp; \\text{coupon payment} &amp; \\\\ \\hline<br>\n1,000[FV] &amp; \\text{Set the face value} &amp; FV = 1000.00 \\\\<br>\n&amp; \\text{of the bond} &amp; \\\\ \\hline<br>\n[CPT][I\/Y] &amp; \\text{Compute the YTM} &amp; I\/Y = 4.74\\%<br>\n\\end{array} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the YTM is 4.74%.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Implied Return and Growth for Equity Instruments<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The value of a stock is determined by both the expected return and the growth of its cash flows. By assuming a constant dividend growth rate, we can use the formula for the present value of an equity investment to calculate the stock&#8217;s implied return or growth rate.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Implied Return<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that the present value of a stock for constant growth of dividends is given by:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_t=\\frac {Div_t(1+g)}{r-g}=\\frac {Div_{t+1}}{r-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(PV_t\\) = Present value at time \\(t\\).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(Div_{t+1}\\) = Expected Dividend in the next period.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r\\) = Required rate of return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(g\\) = Constant growth rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r-g \\gt 0\\)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, we can calculate the implied return on a stock given its expected dividend yield and implied growth by rearranging the above formula as follows:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\frac {Div_t(1+g)}{PV_t }+g=\\frac {Div_{t+1}}{PV_t}+g $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In simple terms, if we assume a stock&#8217;s dividends will grow at a steady rate forever, the implied return is the sum of its expected dividend yield and the constant growth rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Implied Return and Growth<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assume Apple Inc. stock is trading at a share price of USD150.00, and its annualized expected dividend per share during the next year is USD2.00.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Moh, an analyst, projects that Apple&#8217;s dividend per share will increase at a constant rate of 5% per year indefinitely. The required return expected by investors on the stock is <em>closest to<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that the implied return formula is,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r= \\frac {Div_t(1+g)}{PV_t}+g=\\frac {Div_{t+1}}{PV_t}+g $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In this case, \\( Div_{t+1}\\)=$2.00, \\(PV_t\\)=$150, \\(g\\)=5%<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\frac {2.00(1.05)}{150}+0.05=6.4\\% $$<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Implied Growth<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">We can also solve for a stock&#8217;s implied growth rate, which is given by the following formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ g= r-\\frac {Div_t(1+g)}{PV_t }=r-\\frac {Div_{t+1}}{PV_t } $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The above formula implies that if we are certain of the expected dividend, we can compute the implied growth rate by subtracting the expected dividend yield from the required return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Calculating the Implied<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consider the previous example. Suppose Moh believes that Apple stock investors should expect a return of 8%, calculate the implied dividend growth rate for Apple Inc.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that the formula for calculating implied growth is as follows.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ g= r-\\frac {Div_t(1+g)}{PV_t }=r-\\frac {Div_{t+1}}{PV_t } $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ g=0.08-\\frac {2.00 \\times 1.05}{150}=0.066=6.60\\% $$<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Price-to-Earnings Ratio<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In equity instruments, it is common practice to compare the price-to-earnings ratio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>price-to-earnings (P\/E) ratio<\/strong> is a valuation metric that compares a stock&#8217;s current share price to its earnings per share. Investors and analysts use it to determine the relative value of a company&#8217;s shares compared to other companies or the market.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A stock with a higher price-to-earnings ratio is more expensive than a lower one, as investors are willing to pay more for each unit of earnings. This ratio is also a valuation metric for stock indexes, such as the S&amp;P 500.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Relating P\/E Ratio to Expected Future Cash Flows<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">The P\/E ratio relates to our earlier discussion of a stock&#8217;s price (\\(PV_t\\)) relative to its expected future cash flows. Recall the following equation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_t=\\frac {Div_t \\times (1+g)}{r-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By dividing both sides of the equation by \\(E_t\\), which represents earnings per share for period \\(t\\), we get the following equation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\frac {PV_t}{E_t} =\\frac { \\frac {Div_t}{E_t} \\times (1+g)}{r-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac {PV_t}{E_t}\\) = Price-to-earnings (P\/E) ratio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(\\frac {D_t}{E_t}\\) = Dividend payout ratio.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(g\\) = Growth rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r\\) = Required rate of return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The dividend payout ratio is the percentage of a company&#8217;s earnings paid out to shareholders as dividends.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Typically, the <strong>forward P\/E ratio<\/strong>, which is based on a projection of a company&#8217;s earnings per share for the next period \\((t+1)\\), is used.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the equation:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_t=\\frac {Div_t \\times (1+g)}{r-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">can be simplified by dividing both sides by \\(E_{t+1}\\)as below to find the forward P\/E ratio:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\begin{align} \\frac{PV_t}{E_{t+1}} &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ \\Rightarrow \\text{Forward price-to-earnings ratio} &amp;= \\frac{\\text{Expected Dividend payout ratio}}{r-g} \\end{align} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Intuitively, the forward P\/E ratio is positively correlated with higher expected dividend payouts and growth rates but negatively correlated with the required return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Solving for Implied Dividend Growth Rate<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose a company has a forward P\/E ratio of 15, a dividend payout ratio of 40%, and a required return of 10%. The implied dividend growth rate for this company is <em>closest to<\/em>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">First, we can use the formula for the forward P\/E ratio to solve for the implied dividend growth rate:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\begin{align} \\frac{PV_t}{E_{t+1}} &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ \\Rightarrow \\text{Forward price-to-earnings ratio} &amp;= \\frac{\\text{Expected Divided payout ratio}}{r-g} \\end{align}$$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the given values into the formula, we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ 15=\\frac {0.4}{0.1-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solving for \\(g\\), we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ g=0.1-\\frac {0.4}{15}=0.0733 $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the implied dividend growth rate for this company is 7.33%.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example: Solving for Required Return<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s assume you are not given the required rate of return in the question above, so that the company has a forward P\/E ratio of 15, a dividend payout ratio of 40%, and an implied dividend growth rate of 7.33%. What is the required return for this company?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall the formula for the forward P\/E ratio to solve for the required return:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$\\begin{align} \\frac{PV_t}{E_{t+1}} &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ &amp;= \\frac{\\frac{Div_{t+1}}{E_{t+1}}}{r-g} \\\\ \\Rightarrow \\text{Forward price-to-earnings ratio} &amp;= \\frac{\\text{Expected Divided payout ratio}}{r-g} \\end{align} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the given values into the formula, we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ 15=\\frac {0.4}{r-0.0733} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solving for \\(r\\), we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ r=\\frac {0.4}{15}+0.0733=0.1000 $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the required return for this company is 10%.<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<h2 class=\"wp-block-heading\">Question<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Edmund Company&#8217;s stock trades at USD 50.00. The company pays an annual dividend to its shareholders, and its most recent payment of USD 2.00 occurred yesterday. Analysts following the company expect its dividend to grow at a constant rate of 4 percent per year. What is the company&#8217;s required return?<\/p>\n\n\n\n<ol style=\"list-style-type:upper-alpha\" class=\"wp-block-list\">\n<li>8.16%.<\/li>\n\n\n\n<li>8.48%.<\/li>\n\n\n\n<li>9.16%.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The correct answer is A.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Recall that:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ PV_t=\\frac { Div_{t+1} \\times (1+g)}{r-g} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(PV_t\\) = Current stock price.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(Div_{t+1}\\) = Recent dividend payout.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(g\\) = Expected dividend growth rate.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\\(r\\) = Required return.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Substituting the given value into the formula, we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ 50=\\frac {2\\times (1+0.04)}{r-0.04} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solving for \\(r\\), we get:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$$ \\begin{align*}<br>\nr &amp; =\\frac {2 \\times (1+0.04)}{50}+0.04=0.0816 \\\\<br>\nr &amp; =0.0816 \\end{align*} $$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Edmund&#8217;s required return is 8.16%.<\/p>\n<\/blockquote>\n\n\n\n<div style=\"text-align: center; margin: 30px 0;\">\n  <a style=\"display: inline-flex; align-items: center; justify-content: center; padding: 12px 26px; border-radius: 9999px; background: #1e5bd8; color: #ffffff; font-weight: bold; text-decoration: none;\"\n     href=\"https:\/\/analystprep.com\/free-trial\/\"\n     target=\"_blank\"\n     rel=\"noopener noreferrer\">\n     Start Free Trial \u2192\n  <\/a>\n\n  <p style=\"margin-top: 12px; font-size: 16px; line-height: 1.5;\">\n    Strengthen your understanding of implied return, required return, implied growth, and bond and equity valuation in CFA Level I with study notes, practice questions, and mock exams.\n  <\/p>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The growth rate is the rate at which the market expects an asset to grow. On the other hand, implied return is based on the current price and future security cash flows. When investors know the price and future value&#8230;<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-61657","post","type-post","status-publish","format-standard","hentry","category-uncategorized","blog-post","no-post-thumbnail","animate"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Implied Return &amp; Growth | AnalystPrep CFA Level I Guide<\/title>\n<meta name=\"description\" content=\"Learn implied return, required return, and implied growth in bond and equity valuation for CFA Level 1 exam preparation and study.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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