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implement errata
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13 changes: 9 additions & 4 deletions modules/m00031/index.cnxml
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<section id="sect-00006">
<title>EBITDA (Earnings before Interest, Taxes, Depreciation, and Amortization)</title>
<para id="para-00021">Now that we have a full income statement, we can look at another commonly used measure of financial performance called EBITDA. <term class="no-emphasis" id="term-00009">EBITDA</term> stands for earnings before interest, taxes, depreciation, and amortization. Amortization is similar to depreciation. It is the spreading of the cost of an intangible asset over the course of its useful life. Intangible assets are long-term assets that lack physical substance, such as patents and copyrights.</para>
<para id="para-00022">Since EBITDA removes noncash items from the net income equation, it is considered a useful measure in assessing the cash flows provided by operating activities. We will assess cash flows using the <term id="term-00010">statement of cash flows</term> and various other cash flow measures later in this chapter as well.</para>
<para id="para-00022">Since EBITDA removes the effects of noncash items from the net income equation, it is considered a useful measure in assessing the cash flows provided by operating activities. We will assess cash flows using the <term id="term-00010">statement of cash flows</term> and various other cash flow measures later in this chapter as well.</para>
<para id="para-00023">As shown in <link target-id="fig-00004" document="m00031"/>, Clear Lake Sporting Goods’ EBITDA in the prior year was</para>
<equation id="eq-00003"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>19,500</mn><mo> </mo><mo>(</mo><mo>$</mo><mn>30,000</mn><mo>-</mo><mo>$</mo><mn>3,000</mn><mo>-</mo><mo>$</mo><mn>5,000</mn><mo>-</mo><mo>$</mo><mn>2,500</mn><mo>)</mo></math></equation>
<equation class="unnumbered" id="eq-00005"><label/>
<m:math><m:mrow><m:mtext>EBITDA</m:mtext><m:mo>=</m:mo><m:mtext>Net Income</m:mtext><m:mo>+</m:mo><m:mtext>Interest</m:mtext><m:mo>+</m:mo><m:mtext>Taxes</m:mtext><m:mo>+</m:mo><m:mtext>Depreciation</m:mtext><m:mo>+</m:mo><m:mtext>Amortization</m:mtext></m:mrow></m:math>
</equation>
<equation id="eq-00003">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<m:mrow><mo>$</mo><mn>40,500</mn><mo>=</mo><mo>(</mo><mo>$</mo><mn>30,000</mn><mo>+</mo><mo>$</mo><mn>3,000</mn><mo>+</mo><mo>$</mo><mn>5,000</mn><mo>+</mo><mo>$</mo><mn>2,500</mn><mo>)</mo></m:mrow></math></equation>
<para id="para-00036" xmlns="http://cnx.rice.edu/cnxml">and in the current year was</para>
<equation id="eq-00004"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>23,400</mn><mo> </mo><mo>(</mo><mo>$</mo><mn>35,000</mn><mo>-</mo><mo>$</mo><mn>2,000</mn><mo>-</mo><mo>$</mo><mn>6,000</mn><mo>-</mo><mo>$</mo><mn>3,600</mn><mo>)</mo><mo>.</mo></math></equation>
<equation id="eq-00004"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>46,600</mn><mo>=</mo><mo>(</mo><mo>$</mo><mn>35,000</mn><mo>+</mo><mo>$</mo><mn>2,000</mn><mo>+</mo><mo>$</mo><mn>6,000</mn><mo>+</mo><mo>$</mo><mn>3,600</mn><mo>)</mo><mo>.</mo></math></equation>
<figure id="fig-00004" xmlns="http://cnx.rice.edu/cnxml" class="scaled-down">
<title>EBITDA (Earnings before Interest, Taxes, Depreciation, and Amortization)</title>
<media alt="Full comparative year-end income statement for Clear Lake Sporting Goods for the prior and current years. The EBITA for Clear Lake Sporting Goods can be calculated using information in this figure. As shown in Figure 5.5, Clear Lake Sporting Goods EBITA in the prior year was $19,500. This is calculated by subtracting the interest expense ($3000), Income tax expense ($5000) and depreciation expense ($2500) from the net income ($30,000). The EBITA for current year was $23,400. This is calculated by subtracting the interest expense ($2000), Income tax expense ($6000) and depreciation expense ($3600) from the net income ($35,000)."><image mime-type="image/png" src="../../media/FINAN_Figure_05_01_005.png"/></media>
<media alt="Full comparative year-end income statement for Clear Lake Sporting Goods for the prior and current years. The EBITA for Clear Lake Sporting Goods can be calculated using information in this figure. As shown in Figure 5.5, Clear Lake Sporting Goods EBITA in the prior year was $40,500. This is calculated by adding the interest expense ($3000), Income tax expense ($5000) and depreciation expense ($2500) to the net income ($30,000). The EBITA for current year was $46,600. This is calculated by adding the interest expense ($2000), Income tax expense ($6000) and depreciation expense ($3600) to the net income ($35,000)."><image mime-type="image/png" src="../../media/FINAN_Figure_05_01_005.png"/></media>
</figure>
<note class="think-through" id="note-00003">
<title>Net Income</title>
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</section>
<section id="sect-00002">
<title>Operating Cash Flow</title>
<para id="para-00002">Now that we have a statement of cash flows prepared, we can move on to a few key elements of the statement used to assess organizational cash management performance. Operating cash flow, or net cash flow from operating activities, is calculated in the first section of the statement of cash flows. It depicts the cash generated (or used by) the primary business activities. Remember, operating cash flow is calculated under the indirect method by adjusting net income for noncash expenses like depreciation and adjustments for changes in current asset and liability accounts (changes in working capital).</para>
<equation id="eq-00001"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Operating</mi><mi>Cash</mi><mi>Flow</mi><mo>=</mo><mi>Operating</mi><mi>Income</mi><mo>+</mo><mi>Depreciation</mi><mo>-</mo><mi>Taxes</mi><mo>+</mo><mi>Change</mi><mi>in</mi><mi>Working</mi><mi>Capital</mi></math></equation>
<para id="para-00002">Now that we have a statement of cash flows prepared, we can move on to a few key elements of the statement used to assess organizational cash management performance. Operating cash flow, or net cash flow from operating activities, is calculated in the first section of the statement of cash flows. It depicts the cash generated (or used by) the primary business activities. Remember, operating cash flow is calculated under the indirect method by adjusting net income for noncash expenses like depreciation and adjustments for changes in current asset and liability accounts (changes in net working capital).</para>
<equation id="eq-00001"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Operating</mi><mi>Cash</mi><mi>Flow</mi><mo>=</mo><mi>Operating</mi><mi>Income</mi><mo>+</mo><mi>Depreciation</mi><mo>-</mo><mi>Taxes</mi><mo>+</mo><mi>Change</mi><mi>in</mi><mi>Net</mi><mi>Working</mi><mi>Capital</mi></math></equation>
<para id="para-00003" xmlns="http://cnx.rice.edu/cnxml">Operating cash flow is helpful in assessing organizational cash management performance as it relates to the core business function—operations. Key management practices in this area can have a profound impact on the firm’s cash flow. Practices and policies include customer payment terms, collection policies and practices, and vendor payment terms. Though changing a customer or vendor payment terms will not change the profit or loss for the firm, it will have an impact on the timing to cash flows. This is a key element of managing operational cash flow.</para>
</section>
<section id="sect-00003">
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<para id="para-00008">The <term id="term-00004">debt-to-equity ratio</term> shows the relationship between debt and equity as it relates to business financing. A company can take out loans, issue stock, and retain earnings to be used in future periods to keep operations running. A key difference in debt and equity is the interest expense repayment that a loan carries as opposed to equity, which does not have this requirement. Therefore, a company wants to know how much debt and equity contribute to its financing. The formula for the debt-to-equity ratio is</para>
<equation id="eq-00003"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Debt-to-Equity Ratio</mtext><mo>=</mo><mfrac><mtext>Total Liabilities</mtext><mtext>Total Stockholder Equity</mtext></mfrac></math></equation>
<para id="para-00009" xmlns="http://cnx.rice.edu/cnxml">The information needed to compute the debt-to-equity ratio for Clear Lake Sporting Goods in the current year can be found on the balance sheet.</para>
<equation id="eq-00004"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Debt-to-Equity Ratio</mtext><mo>=</mo><mfrac><mrow><mo>$</mo><mn>150,000</mn><mo> </mo><mo>+</mo><mo>$</mo><mn>50,000</mn></mrow><mrow><mo>$</mo><mn>100,000</mn></mrow></mfrac><mo>=</mo><mn>1.5</mn><mo> </mo><mtext>or</mtext><mo> </mo><mn>1.5:1</mn></math></equation>
<equation id="eq-00004"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Debt-to-Equity Ratio</mtext><mo>=</mo><mfrac><mrow><mo>$</mo><mn>150,000</mn></mrow><mrow><mo>$</mo><mn>100,000</mn></mrow></mfrac><mo>=</mo><mn>1.5</mn><mo> </mo><mtext>or</mtext><mo> </mo><mn>1.5:1</mn></math></equation>
<para id="para-00010" xmlns="http://cnx.rice.edu/cnxml">This means that for every one dollar of equity contributed toward financing, $1.50 is contributed from lenders. Recall that total assets equal total liabilities plus total equity. Both the debt-to-assets and debt-to-equity ratio have total liabilities in the numerator. The difference in the two ratios is the denominator. The denominator for the debt-to-equity ratio is total stockholder equity. The denominator for the debt-to-assets ratio is total assets, or total liabilities plus total equity. Thus, the two ratios contain the same information, making calculating both ratios redundant. A financial analyst may prefer to calculate one ratio over the other because of the format of readily available industry data to use for comparison purposes or for consistency with other calculations the analyst is performing.</para>
<note class="think-through" id="note-00002">
<title>Financing a Business Expansion</title>
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<note class="think-through" id="note-00008">
<title>Nonconstant Growth Dividends</title>
<exercise class="unnumbered" id="exer-00003"><problem id="prob-00003"><para id="para-00119">One final issue to address in this section is how we price a stock when dividends are neither constant nor growing at a constant rate. This can make things a bit more complicated. When a future pattern is not an annuity or the modified annuity stream of constant growth, there is no shortcut. You have to estimate every future dividend and then discount each individual dividend back to the present. All is not lost, however. Sometimes you can see patterns in the dividends. For example, a firm might shift into a dividend stream pattern that will allow you to use one of the dividend models to take a shortcut for pricing the stock. Let’s look at an example.</para>
<para id="para-00120">JM and Company is a small start-up firm that will institute a dividend payment—a $0.25 dividend—for the first time at the end of this year. The company expects rapid growth over the next four years and will increase its dividend to $0.50, then to $1.50, and then to $3.00 before settling into a constant growth dividend pattern with dividends growing at 5% every year (see <link target-id="table-00006" document="m00068"/>). If you believe that JM and Company will deliver this dividend pattern and you desire a 13% return on your investment, what price should you pay for this stock?</para>
<para id="para-00120">JM and Company is a small start-up firm that will institute a dividend payment—a $0.25 dividend—for the first time at the end of this year. The company expects rapid growth over the next four years and will increase its dividend to $0.50 at the end of the second year, then to $1.50 at the end of the third year, and then to $3.00 thereafter, settling into a constant growth dividend pattern with dividends growing at 5% every year (see <link target-id="table-00006" document="m00068"/>). If you believe that JM and Company will deliver this dividend pattern and you desire a 13% return on your investment, what price should you pay for this stock?</para>
<table summary="Some cells are left blank for visual design purposes." id="table-00006" class="timeline-table">
<tgroup cols="6">
<colspec colnum="1" colname="c1"/>
<colspec colnum="2" colname="c2"/>
<colspec colnum="3" colname="c3"/>
<colspec colnum="4" colname="c4"/>
<colspec colnum="5" colname="c5"/>
<colspec colnum="6" colname="c6"/>
<thead>
<row>
<entry align="center">T0</entry>
<entry align="center">T1</entry>
<entry align="center">T2</entry>
<entry align="center">T3</entry>
<entry align="center">T4</entry>
<entry align="center">T5</entry>
</row>
</thead>
<tbody>
<row>
<entry align="center">$0.25</entry>
<entry align="center">$0.50</entry>
<entry align="center">$1.50</entry>
<entry align="center">$1.275</entry>
<entry align="center">$3.00</entry>
<entry align="center"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>3.00</mn><mo> </mo><mo>×</mo><mo> </mo><mn>1.05</mn></math></entry>
</row>
</tbody>
</tgroup>
</table></problem>
<solution id="sol-00003" xmlns="http://cnx.rice.edu/cnxml"><para id="para-00121"><emphasis>Solution:</emphasis> To price this stock, we will need to discount the first four dividends at 13% and then discount the constant growth portion of the dividends, the first payment of which will be received at the end of year 5. Let’s calculate the first four dividends:</para>
<equation id="eq-00032"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnspacing="0px" columnalign="right center left"><mtr><mtd><mi>PV</mi><mo> </mo></mtd><mtd><mo>=</mo></mtd><mtd><mo> </mo><mfrac><mrow><mo>$</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfenced><mn>1</mn></msup></mfrac><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mo>$</mo><mn>0</mn><mo>.</mo><mn>50</mn></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfenced><mn>2</mn></msup></mfrac><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mo>$</mo><mn>1</mn><mo>.</mo><mn>50</mn></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfenced><mn>3</mn></msup></mfrac><mo> </mo><mo>+</mo><mo> </mo><mfrac><mrow><mo>$</mo><mn>3</mn><mo>.</mo><mn>00</mn></mrow><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfenced><mn>4</mn></msup></mfrac></mtd></mtr><mtr><mtd/><mtd><mo>=</mo></mtd><mtd><mo> </mo><mo>$</mo><mn>0.22</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>0.39</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>1.04</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>1.84</mn><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>3.49</mn></mtd></mtr></mtable></math></equation>
<solution id="sol-00003" xmlns="http://cnx.rice.edu/cnxml"><para id="para-00121"><emphasis>Solution:</emphasis> To price this stock, we will need to discount the first three dividends at 13% and then discount the constant growth portion of the dividends, the first payment of which will be received at the end of the 6th year. Let’s calculate the first three dividends:</para>
<equation id="eq-00032"><math xmlns="http://www.w3.org/1998/Math/MathML">
<mtable columnspacing="0px" columnalign="right center left">
<mtr>
<mtd><mi>PV</mi><mo> </mo></mtd><mtd><mo>=</mo></mtd>
<mtd><mo> </mo>
<mfrac><mrow><mo>$</mo><mn>0</mn><mo>.</mo><mn>25</mn></mrow>
<mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfrac>
<mo> </mo><mo>+</mo><mo> </mo>
<mfrac><mrow><mo>$</mo><mn>0</mn><mo>.</mo><mn>50</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfrac>
<mo> </mo><mo>+</mo><mo> </mo>
<mfrac><mrow><mo>$</mo><mn>1</mn><mo>.</mo><mn>50</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>13</mn></mrow></mfrac>
</mtd></mtr>
<mtr>
<mtd/><mtd><mo>=</mo></mtd>
<mtd><mo> </mo><mo>$</mo><mn>0.22</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>0.39</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>1.04</mn><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>1.65</mn></mtd>
</mtr></mtable></math></equation>
<para id="para-00122" xmlns="http://cnx.rice.edu/cnxml">We now turn to the constant growth dividend pattern, where we can use our infinite horizon constant growth model as follows:</para>
<equation id="eq-00033"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow><mn>4</mn></msub><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>$</mo><mn>3.00</mn><mo> </mo><mo>×</mo><mo> </mo><mo>(</mo><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mn>0.05</mn><mo>)</mo></mrow><mrow><mn>0.13</mn><mo> </mo><mo>-</mo><mo> </mo><mn>0.05</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>$</mo><mn>3.15</mn></mrow><mrow><mn>0.08</mn></mrow></mfrac><mo>=</mo><mo>$</mo><mn>39.375</mn></math></equation>
<equation id="eq-00033"><math xmlns="http://www.w3.org/1998/Math/MathML">
<msub><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow><mn>6</mn></msub><mo> </mo><mo>=</mo>
<mo> </mo><mfrac><mrow><mo>$</mo><mn>3.00</mn><mo> </mo><mo>×</mo><mo> </mo><mo>(</mo><mn>1</mn><mo> </mo><mo>+</mo><mo> </mo><mn>0.05</mn><mo>)</mo></mrow><mrow><mn>0.13</mn><mo> </mo><mo>-</mo><mo> </mo><mn>0.05</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>$</mo><mn>3.15</mn></mrow><mrow><mn>0.08</mn></mrow></mfrac><mo>=</mo><mo>$</mo><mn>39.375</mn></math></equation>
<para id="para-00123" xmlns="http://cnx.rice.edu/cnxml">This figure is the price of the constant growth portion at the end of the fourth period, so we still need to discount it back to the present at the 13% required rate of return:</para>
<equation id="eq-00034"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Price</mi><mo> </mo><mo>=</mo><mo> </mo><mfrac><mrow><mo>$</mo><mn>39.375</mn></mrow><msup><mfenced><mrow><mn>1.13</mn></mrow></mfenced><mn>4</mn></msup></mfrac><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>24.15</mn></math></equation>
<para id="para-00124" xmlns="http://cnx.rice.edu/cnxml">So, the price of this stock with a nonconstant dividend pattern is</para>
<equation id="eq-00035"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Price</mi><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>3.49</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>24.15</mn><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>27.64</mn></math></equation>
<equation id="eq-00035"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Price</mi><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>1.65</mn><mo> </mo><mo>+</mo><mo> </mo><mo>$</mo><mn>24.15</mn><mo> </mo><mo>=</mo><mo> </mo><mo>$</mo><mn>25.80</mn></math></equation>
</solution></exercise></note>
</section>
</section>
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