0
在等式正下方的文本「我們基本上需要計算」r「在下面的等式中：」正確顯示，除了vinculum沒有出現在任何分數上。所有其他分數正在工作/正確顯示。Vinculum不出現在XML公式中
使用我們的室內工具，它驗證並正確呈現。
任何幫助讓它出現，將不勝感激。
<?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>
>
它是如何呈現？ –