0
텍스트 바로 아래의 방정식에서 "다음 방정식에서"r "을 계산해야합니다."vinculum이 분수로 표시되지 않는 경우를 제외하고는 올바르게 나타납니다. 다른 모든 분수는 제대로 작동/나타나고 있습니다.Vinculum이 XML 방정식에 나타나지 않습니다.
사내 도구를 사용하여 올바르게 검증하고 렌더링합니다.
도움이 필요하시면 도움을 주시면 감사하겠습니다.
<?xml version="1.0" encoding="UTF-8"?>
<component
xmlns="http://www.wiley.com/namespaces/wiley"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" guid="63ecc7d6-987a-4edb-819d-6a8b0dfb2518" type="studyText" version="4.0" xml:id="ST-L2EQ-3004-MultistageDividend-1608" xml:lang="en">
<header>
</header>
<body sectionsNumbered="no">
<section xml:id="sec-0033">
<feature xml:id="fea-0030">
<titleGroup>
<title type="featureName">Example</title>
<title type="main">Estimating Expected Return with the Two‐Stage DDM</title>
</titleGroup>
<section xml:id="sec-1009">
<p>Omega Industries recently paid a dividend of $1.50. The dividend is expected to grow at 13% for the next 3 years and 7% thereafter into perpetuity. Given that the stock's current market price equals $33, calculate the implied required return on equity.</p>
<p>
<b>Solution</b>:
</p>
<p>First we calculate the dividend payments for each year of the first stage, and for the first year of the constant growth phase.</p>
<p>D
<sub>1</sub> = 1.50 × 1.13 = $1.695
</p>
<p>D
<sub>2</sub> = 1.50 × 1.13
<sup>2</sup> = $1.915
</p>
<p>D
<sub>3</sub> = 1.50 × 1.13
<sup>3</sup> = $2.164
</p>
<p>D
<sub>4</sub> = 2.164 × 1.07 = $2.316
</p>
<p>We basically need to calculate “r” in the following equation:
<displayedItem numbered="no" type="mathematics" xml:id="disp-00AN">
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mn>33</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.695</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mi mathvariant="normal">r</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>1</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>1.915</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mi mathvariant="normal">r</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>2.164</mn>
</mrow>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mi mathvariant="normal">r</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mrow>
<mo>[</mo>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mn>2.316</mn>
</mrow>
<mrow>
<mi mathvariant="normal">r</mi>
<mo>−</mo>
<mn>0.07</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mn>1</mn>
<mrow>
<msup>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>+</mo>
<mi mathvariant="normal">r</mi>
<mo stretchy="false">)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mo>]</mo>
</mrow>
</mrow>
</math>
</displayedItem>
</p>
<p>Our financial calculators are of little help here, so we will have to adopt a trial‐and‐error approach. We start by estimating a certain discount rate and then calculate the present value based on it. If the present value based on that discount rate differs from the fair value of the stock, we will alter the discount rate accordingly.</p>
<p>Let's assume that the terminal value in Year 3 is $38. In that case, r is calculated as follows:
<displayedItem numbered="no" type="mathematics" xml:id="disp-00AO">
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mtable columnalign="left">
<mtr>
<mtd columnalign="left">
<mrow>
<mn>38</mn>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>3</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>07</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mi mathvariant="normal">r</mi>
<mo>−</mo>
<mn>0</mn>
<mo>.</mo>
<mn>07</mn>
</mrow>
</mfrac>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="right" columnspan="1">
<mrow>
<mi mathvariant="normal">r</mi>
<mo>=</mo>
<mn>13</mn>
<mo>.</mo>
<mn>09</mn>
<mi>%</mi>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd columnalign="right" columnspan="1">
<mrow/>
</mtd>
</mtr>
</mtable>
</mrow>
</math>
</displayedItem>
</p>
<p>Based on a cost of equity of 13.09%, the value of the stock is calculated as follows:
<displayedItem numbered="no" type="mathematics" xml:id="disp-00AP">
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi mathvariant="normal">NPV</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>.</mo>
<mn>695</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>1309</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>.</mo>
<mn>915</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>1309</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>.</mo>
<mn>164</mn>
<mo>+</mo>
<mn>38</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>1309</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mi>$</mi>
<mn>30</mn>
<mo>.</mo>
<mn>77</mn>
</mrow>
</math>
</displayedItem>
</p>
<p>
<b>TI BA II Plus Calculator keystrokes</b>:
</p>
<p>[CF] [2
<sup>ND</sup>] [CE|C]
</p>
<p>[ENTER] [↓]</p>
<p>1.695 [ENTER] [↓] [↓]</p>
<p>1.915 [ENTER] [↓] [↓]</p>
<p>40.164 [ENTER]</p>
<p>[NPV] 13.09 [ENTER] [↓] [CPT]</p>
<p>NPV =
<b>$30.77</b>
</p>
<p>The stock's estimated value of $30.77 is lower than the market price of the stock ($33). Therefore, we must lower our estimate of required rate of return.</p>
<p>Now let's assume a required rate of return of 12.70%. The terminal value in Year 3 can be calculated as:
<displayedItem numbered="no" type="mathematics" xml:id="disp-00AQ">
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msub>
<mi mathvariant="normal">V</mi>
<mrow>
<mn>3</mn>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>5</mn>
<mo stretchy="false">)</mo>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>13</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>3</mn>
</mrow>
</msup>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>07</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>0</mn>
<mo>.</mo>
<mn>127</mn>
<mo>−</mo>
<mn>0</mn>
<mo>.</mo>
<mn>07</mn>
</mrow>
</mfrac>
<mo>=</mo>
<mi>$</mi>
<mn>40</mn>
<mo>.</mo>
<mn>63</mn>
</mrow>
</math>
</displayedItem>
</p>
<p>The value of the stock can be calculated as:
<displayedItem numbered="no" type="mathematics" xml:id="disp-00AR">
<math
xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi mathvariant="normal">NPV</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>.</mo>
<mn>695</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>127</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>1</mn>
<mo>.</mo>
<mn>915</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>127</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>+</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mo>.</mo>
<mn>164</mn>
<mo>+</mo>
<mn>40</mn>
<mo>.</mo>
<mn>63</mn>
</mrow>
<mrow>
<mo stretchy="false">(</mo>
<mn>1</mn>
<mo>.</mo>
<mn>127</mn>
<mo stretchy="false">)</mo>
<msup>
<mi/>
<mrow>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>=</mo>
<mi>$</mi>
<mn>32</mn>
<mo>.</mo>
<mn>91</mn>
</mrow>
</math>
</displayedItem>
</p>
<p>
<b>TI BA II Plus Calculator keystrokes</b>:
</p>
<p>[CF] [2
<sup>ND</sup>] [CE|C]
</p>
<p>[ENTER] [↓]</p>
<p>1.695 [ENTER] [↓] [↓]</p>
<p>1.915 [ENTER] [↓] [↓]</p>
<p>42.79 [ENTER]</p>
<p>[NPV] 12.70 [ENTER] [↓] [CPT]</p>
<p>NPV =
<b>$32.91</b>
</p>
<p>A required rate of return of 12.70%
<b>approximately</b> makes the present value of the cash flows equal to the market price of the stock. The exact value for the required return can be calculated using a spreadsheet (Excel Solver). Note that this LOS does not ask you to be able to calculate the required return based on the two‐stage DDM, just that you should be able to explain how to do so.
</p>
</section>
</feature>
</section>
</body>
>
어떻게 렌더링됩니까? –