在文本正下方的等式中，我们基本上需要在下面的等式中计算“r”：＆＃34;出现正确但除了任何分数没有出现vinculum。所有其他分数都正常工作/出现。
使用我们的内部工具，它可以正确验证和渲染。
任何帮助它出现都会受到赞赏。
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<header>
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<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>
＆GT;
答案 0 :(得分：0)
我认为MathML没有任何问题。它在3种不同的工具中为我带来了好处。