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Valuation Methods Employed in Investment Bank Fairness Opinion Letters
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Valuation Methods Employed in Investment Bank Fairness Opinion Letters

Background

A fairness opinion letter is a written third-party certification of the appropriateness of the price of a proposed transaction such as a merger, acquisition, leveraged buyout, or tender offer. A typical fairness opinion provides a range of what is believed to be fair values, with a presumption that the actual deal price should fall within this range. The data used in this case study is found in SunGard’s Schedule 14A Proxy Statement submitted to the SEC in May 2005.

On March 27, 2005, the investment banking behemoth Lazard Freres (Lazard) submitted a letter to the board of directors of SunGard Corporation pertaining to the fairness of a $10.9 billion bid to take the firm private made by an investor group. Lazard employed a variety of valuation methods to evaluate the offer price. These included the comparable company approach, the recent transactions method, discounted cash flow analysis, and an analysis of recent transaction premiums. The analyses were applied to each of the firm’s major businesses: software services and recovery availability services. The software services’ business provides software systems and support for application and transaction processing to financial services firms, universities, and government agencies. The recovery availability services business provides businesses and government agencies with backup and recovery support in the event their data processing systems are disrupted.

Comparable Company Analysis

Using publicly available information, Lazard reviewed the market values and trading multiples of the selected publicly held companies for each business segment. Multiples were based on stock prices as of March 24, 2005 and specific company financial data on publicly available research analysts’ estimates for 2005. In the case of SunGard’s software business, Lazard reviewed the market values and trading multiples of four publicly traded financial services companies and three publicly traded securities trading companies. In the case of SunGard’s recovery availability services business, Lazard reviewed the market values and trading multiples of the six selected publicly traded business continuity services (i.e., recoverability services firms) companies. These firms were believed to be representative of these segments of SunGard’s operations.

Lazard calculated enterprise values for these comparable companies as equity value plus debt, preferred stock, and all out-of-the-money convertibles (i.e., convertible debt whose conversion price exceeded the merger offer price), less cash and cash equivalents (i.e., short-term liquid securities). Estimated enterprise value multiples of earnings before interest, taxes, depreciation and amortization (i.e., EBITDA) were created for 2005 by dividing enterprise values by publicly available estimates of EBITDA for each comparable company. Similarly, price-to-earnings ratios were created by dividing equity values per share by earnings per share for each comparable company for calendar 2005. See Tables 8-1 and 8.2.
\quad \quad \quad \quad \quad \quad \quad  Table 8-1 Enterprise Value Multiples for\text { Table 8-1 Enterprise Value Multiples for}
\quad \quad \quad \quad \quad \quad  Comparable Recovery Availability Companies\text { Comparable Recovery Availability Companies}
 Enterprise Value as a Multiple of  EBITDA  Price-to-Earnings  Multiple (P/E) 2005E2005E High 9.0x38.1x Mean 6.7x18.2x Median 6.5x15.3x Low 3.8x12.6xE= estimate. \begin{array}{|l|c|c|}\hline & \begin{array}{c}\text { Enterprise Value as a Multiple of } \\\text { EBITDA }\end{array} & \begin{array}{c}\text { Price-to-Earnings } \\\text { Multiple (P/E) }\end{array} \\\hline& 2005 \mathrm{E} & 2005 \mathrm{E} \\\hline \text { High } & 9.0 \mathrm{x} & 38.1 \mathrm{x} \\ \hline \text { Mean } & 6.7 \mathrm{x} & 18.2 \mathrm{x} \\\hline \text { Median }& 6.5 \mathrm{x} & 15.3 \mathrm{x} \\\hline \text { Low } & 3.8 \mathrm{x} & 12.6 \mathrm{x} \\\hline \mathrm{E}=\text { estimate. } \\\hline \end{array}

Based on this analysis, Lazard determined an enterprise value to estimated 2005 EBITDA multiple range for SunGard’s recovery availability services business of 5.5x to 7.0x. Lazard also determined a 2005 estimated P/E range for this segment of 14.0x to 16.0x. Multiplying SunGard’s projected EBITDA and earnings per share for 2005 by these ranges, Lazard calculated an enterprise value range for SunGard’s recovery availability services business of approximately $3.1 billion to $3.7 billion. Financial projections for SunGard were provided by SunGard’s management.
 Table 8-2. Enterprise Value Multiples for Comparable Software Companies  Enterprise Value as a Multiple of  EBITDA  Price-to-Earnings  Multiple (P/E) High 13.8x21.5x Mean 9.7x18.8x Median 9.0x18.1x Low 7.3x16.9x\begin{array}{l}\text { Table 8-2. Enterprise Value Multiples for Comparable Software Companies }\\\begin{array} { | l | c | c | } \hline & \begin{array} { c } \text { Enterprise Value as a Multiple of } \\\text { EBITDA }\end{array} & \begin{array} { c } \text { Price-to-Earnings } \\\text { Multiple } ( \mathrm { P } / \mathrm { E } )\end{array} \\\hline \text { High } & 13.8 \mathrm { x } & 21.5 \mathrm { x } \\\hline \text { Mean } & 9.7 \mathrm { x } & 18.8 \mathrm { x } \\\hline \text { Median } & 9.0 \mathrm { x } & 18.1 \mathrm { x } \\\hline \text { Low } & 7.3 \mathrm { x } & 16.9 \mathrm { x } \\\hline\end{array}\end{array}
Based on the results in Table 8-2, Lazard determined an enterprise value to estimated 2005 EBITDA multiple range for SunGard’s software business of 7.5x to 9.5x. Lazard also determined a 2005 estimated P/E range for SunGard’s software business of 17.0 to 19.0x. Multiplying SunGard’s projected EBITDA and earnings per share for 2005 by these ranges, Lazard calculated an enterprise value range for SunGard’s software business of approximately $4.3 billion to $5.2 billion.

Lazard then summed the enterprise value ranges for SunGard’s software business and recovery availability services business to calculate a consolidated enterprise value range for SunGard of approximately $7.4 billion to $8.9 billion. Using this consolidated enterprise value range and assuming net debt (i.e., total debt less cash and cash equivalents on the balance sheet) of $273 million, Lazard calculated an implied price per share range for SunGard common stock of $24.20 to $29.00 by dividing the enterprise value less net debt by the SunGard shares outstanding.

Recent Transactions Method

For the recovery availability services business, Lazard reviewed ten merger and acquisition transactions since October 2001 for companies in the information technology outsourcing business. To the extent publicly available, Lazard reviewed the transaction enterprise values of the recent transactions as a multiple of the last twelve months EBITDA for the period ending on the recent transaction announcement date. See Table 8-3.
 Table 8-3. Enterprise Value as a Multiple of Last Twelve Months EBITDA \text { Table 8-3. Enterprise Value as a Multiple of Last Twelve Months EBITDA }
\quad \quad \quad \quad  for Recovery Availability Business \text { for Recovery Availability Business }
 High 10.8x Mean 7.37x Median 6.4x Low 5.4x\begin{array}{|l|c|}\hline \text { High } \quad\quad\quad\quad\quad& 10.8 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\\hline \text { Mean } & 7.37 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\\hline \text { Median } & 6.4 \mathrm{x}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \\\hline \text { Low } & 5.4 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\\hline\end{array}
Based on Table 8-3, Lazard determined an EBITDA multiple range of 6.5x to 7.5x and multiplied this range by the last twelve months EBITDA for SunGard’s recovery availability business to calculate an implied enterprise value range of approximately $3.4 billion to $4.0 billion.

Lazard reviewed 21 merger and acquisition transactions since February 2003 with a value greater than approximately $100 million for companies in the software business. To the extent publicly available, Lazard examined the transaction enterprise values of the recent transactions as a multiple of EBITDA for the last twelve months prior to the public announcement of the relevant recent transaction. See Table 8-4.
Table 8-4. Enterprise Value as a Multiple of Last Twelve Months EBITDA\text {Table 8-4. Enterprise Value as a Multiple of Last Twelve Months EBITDA}
\quad \quad \quad \quad  for the Software Business\text { for the Software Business}
 High 11.6x Mean 9.8x Median 9.9x Low 6.8x\begin{array}{|l|c|}\hline \text { High } \quad\quad\quad\quad\quad\quad\quad\quad\quad& 11.6 \mathrm{x} \quad\quad\quad\quad\quad\\\hline \text { Mean } & 9.8 \mathrm{x} \quad\quad\quad\quad\quad\\\hline \text { Median } & 9.9 \mathrm{x} \quad\quad\quad\quad\quad\\\hline \text { Low } & 6.8 \mathrm{x} \quad\quad\quad\quad\quad\\\hline\end{array}
Based on the information contained in Table 8-5, Lazard determined an EBITDA multiple range of 9.0x to 11.0x and multiplied this range by the last twelve month EBITDA for SunGard’s software business to calculate an implied enterprise value range for this business segment of approximately $5.0 billion to $6.1 billion.

Lazard then summed the enterprise value ranges for SunGard’s software business and recovery availability services business to calculate a consolidated enterprise value range for SunGard of approximately $8.4 billion to $10.1 billion. Using this consolidated enterprise value range and assuming net debt of $273 million, Lazard calculated the value per share of SunGard common stock of $27.60 to $32.70 by dividing the estimated consolidated enterprise value less net debt by common shares outstanding.

Discounted Cash Flow Analysis

Using projections provided by SunGard’s management, Lazard performed an analysis of the present value, as of March 31, 2005, of the free cash flows that SunGard could generate annually from calendar year 2005 through calendar year 2009. Lazard analyzed separately the cash flows for SunGard’s software business and recovery availability services business.

For SunGard’s software business, in calculating the terminal value, Lazard assumed perpetual growth rates (i.e., constant growth model) of 3.5% to 4.5% for the projected free cash flows for the periods subsequent to 2009. The projected annual cash flows through 2009 and beyond were then discounted to present value using discount rates ranging from 10.0% to 12.0%. Based on this analysis, Lazard calculated an implied enterprise value range for the software business of approximately $5.6 billion to $7.4 billion.

For SunGard’s recovery availability services business, in calculating the terminal value Lazard assumed perpetual growth rates of 2.0% to 3.0% for the projected free cash flows for periods subsequent to 2009. The projected cash flows were then discounted to present value using discount rates ranging from 10.0% to 12.0%. Lazard then calculated an implied enterprise value range for SunGard’s recovery availability business of approximately $2.6 billion to $3.3 billion.

Lazard then aggregated the enterprise value ranges for SunGard’s two business segments to calculate a consolidated enterprise value range for SunGard of approximately $8.2 billion to $10.7 billion. Using this consolidated enterprise value range and assuming net debt of $273 million, Lazard calculated an implied price per share range for SunGard common stock of $26.70 to $34.60.

Premiums Paid Analysis

Lazard performed a premiums paid analysis based upon the premiums paid in 73 recent transactions (not involving “mergers of equals” transactions) that were announced from January 2004 through March 2005 and involved transaction values in excess of $1 billion. In conducting its analysis, Lazard analyzed the premiums paid for recent transactions over $1 billion and those over $5 billion, since premiums paid may vary with the size of the transaction.

The analysis was based on the one day, one week and four week implied premiums for the transactions examined. The implied premiums were calculated by comparing the offer price for the target firm on the announcement date with the per share price of the target firm one day, one week, and four weeks prior to the announcement of the transaction. The results of these calculations are given in Table 8-5.
Valuation Methods Employed in Investment Bank Fairness Opinion Letters Background A fairness opinion letter is a written third-party certification of the appropriateness of the price of a proposed transaction such as a merger, acquisition, leveraged buyout, or tender offer. A typical fairness opinion provides a range of what is believed to be fair values, with a presumption that the actual deal price should fall within this range. The data used in this case study is found in SunGard’s Schedule 14A Proxy Statement submitted to the SEC in May 2005. On March 27, 2005, the investment banking behemoth Lazard Freres (Lazard) submitted a letter to the board of directors of SunGard Corporation pertaining to the fairness of a $10.9 billion bid to take the firm private made by an investor group. Lazard employed a variety of valuation methods to evaluate the offer price. These included the comparable company approach, the recent transactions method, discounted cash flow analysis, and an analysis of recent transaction premiums. The analyses were applied to each of the firm’s major businesses: software services and recovery availability services. The software services’ business provides software systems and support for application and transaction processing to financial services firms, universities, and government agencies. The recovery availability services business provides businesses and government agencies with backup and recovery support in the event their data processing systems are disrupted. Comparable Company Analysis Using publicly available information, Lazard reviewed the market values and trading multiples of the selected publicly held companies for each business segment. Multiples were based on stock prices as of March 24, 2005 and specific company financial data on publicly available research analysts’ estimates for 2005. In the case of SunGard’s software business, Lazard reviewed the market values and trading multiples of four publicly traded financial services companies and three publicly traded securities trading companies. In the case of SunGard’s recovery availability services business, Lazard reviewed the market values and trading multiples of the six selected publicly traded business continuity services (i.e., recoverability services firms) companies. These firms were believed to be representative of these segments of SunGard’s operations. Lazard calculated enterprise values for these comparable companies as equity value plus debt, preferred stock, and all out-of-the-money convertibles (i.e., convertible debt whose conversion price exceeded the merger offer price), less cash and cash equivalents (i.e., short-term liquid securities). Estimated enterprise value multiples of earnings before interest, taxes, depreciation and amortization (i.e., EBITDA) were created for 2005 by dividing enterprise values by publicly available estimates of EBITDA for each comparable company. Similarly, price-to-earnings ratios were created by dividing equity values per share by earnings per share for each comparable company for calendar 2005. See Tables 8-1 and 8.2. \quad \quad \quad \quad \quad \quad \quad \text { Table 8-1 Enterprise Value Multiples for} \quad \quad \quad \quad \quad \quad \text { Comparable Recovery Availability Companies} \begin{array}{|l|c|c|} \hline & \begin{array}{c} \text { Enterprise Value as a Multiple of } \\ \text { EBITDA } \end{array} & \begin{array}{c} \text { Price-to-Earnings } \\ \text { Multiple (P/E) } \end{array} \\ \hline& 2005 \mathrm{E} & 2005 \mathrm{E} \\ \hline \text { High } & 9.0 \mathrm{x} & 38.1 \mathrm{x} \\ \hline \text { Mean } & 6.7 \mathrm{x} & 18.2 \mathrm{x} \\ \hline \text { Median }& 6.5 \mathrm{x} & 15.3 \mathrm{x} \\ \hline \text { Low } & 3.8 \mathrm{x} & 12.6 \mathrm{x} \\ \hline \mathrm{E}=\text { estimate. } \\ \hline \end{array} Based on this analysis, Lazard determined an enterprise value to estimated 2005 EBITDA multiple range for SunGard’s recovery availability services business of 5.5x to 7.0x. Lazard also determined a 2005 estimated P/E range for this segment of 14.0x to 16.0x. Multiplying SunGard’s projected EBITDA and earnings per share for 2005 by these ranges, Lazard calculated an enterprise value range for SunGard’s recovery availability services business of approximately $3.1 billion to $3.7 billion. Financial projections for SunGard were provided by SunGard’s management. \begin{array}{l} \text { Table 8-2. Enterprise Value Multiples for Comparable Software Companies }\\ \begin{array} { | l | c | c | } \hline & \begin{array} { c } \text { Enterprise Value as a Multiple of } \\ \text { EBITDA } \end{array} & \begin{array} { c } \text { Price-to-Earnings } \\ \text { Multiple } ( \mathrm { P } / \mathrm { E } ) \end{array} \\ \hline \text { High } & 13.8 \mathrm { x } & 21.5 \mathrm { x } \\ \hline \text { Mean } & 9.7 \mathrm { x } & 18.8 \mathrm { x } \\ \hline \text { Median } & 9.0 \mathrm { x } & 18.1 \mathrm { x } \\ \hline \text { Low } & 7.3 \mathrm { x } & 16.9 \mathrm { x } \\ \hline \end{array} \end{array} Based on the results in Table 8-2, Lazard determined an enterprise value to estimated 2005 EBITDA multiple range for SunGard’s software business of 7.5x to 9.5x. Lazard also determined a 2005 estimated P/E range for SunGard’s software business of 17.0 to 19.0x. Multiplying SunGard’s projected EBITDA and earnings per share for 2005 by these ranges, Lazard calculated an enterprise value range for SunGard’s software business of approximately $4.3 billion to $5.2 billion. Lazard then summed the enterprise value ranges for SunGard’s software business and recovery availability services business to calculate a consolidated enterprise value range for SunGard of approximately $7.4 billion to $8.9 billion. Using this consolidated enterprise value range and assuming net debt (i.e., total debt less cash and cash equivalents on the balance sheet) of $273 million, Lazard calculated an implied price per share range for SunGard common stock of $24.20 to $29.00 by dividing the enterprise value less net debt by the SunGard shares outstanding. Recent Transactions Method For the recovery availability services business, Lazard reviewed ten merger and acquisition transactions since October 2001 for companies in the information technology outsourcing business. To the extent publicly available, Lazard reviewed the transaction enterprise values of the recent transactions as a multiple of the last twelve months EBITDA for the period ending on the recent transaction announcement date. See Table 8-3. \text { Table 8-3. Enterprise Value as a Multiple of Last Twelve Months EBITDA } \quad \quad \quad \quad \text { for Recovery Availability Business } \begin{array}{|l|c|} \hline \text { High } \quad\quad\quad\quad\quad& 10.8 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \hline \text { Mean } & 7.37 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \hline \text { Median } & 6.4 \mathrm{x}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \\ \hline \text { Low } & 5.4 \mathrm{x} \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\\ \hline \end{array} Based on Table 8-3, Lazard determined an EBITDA multiple range of 6.5x to 7.5x and multiplied this range by the last twelve months EBITDA for SunGard’s recovery availability business to calculate an implied enterprise value range of approximately $3.4 billion to $4.0 billion. Lazard reviewed 21 merger and acquisition transactions since February 2003 with a value greater than approximately $100 million for companies in the software business. To the extent publicly available, Lazard examined the transaction enterprise values of the recent transactions as a multiple of EBITDA for the last twelve months prior to the public announcement of the relevant recent transaction. See Table 8-4. \text {Table 8-4. Enterprise Value as a Multiple of Last Twelve Months EBITDA} \quad \quad \quad \quad \text { for the Software Business} \begin{array}{|l|c|} \hline \text { High } \quad\quad\quad\quad\quad\quad\quad\quad\quad& 11.6 \mathrm{x} \quad\quad\quad\quad\quad\\ \hline \text { Mean } & 9.8 \mathrm{x} \quad\quad\quad\quad\quad\\ \hline \text { Median } & 9.9 \mathrm{x} \quad\quad\quad\quad\quad\\ \hline \text { Low } & 6.8 \mathrm{x} \quad\quad\quad\quad\quad\\ \hline \end{array} Based on the information contained in Table 8-5, Lazard determined an EBITDA multiple range of 9.0x to 11.0x and multiplied this range by the last twelve month EBITDA for SunGard’s software business to calculate an implied enterprise value range for this business segment of approximately $5.0 billion to $6.1 billion. Lazard then summed the enterprise value ranges for SunGard’s software business and recovery availability services business to calculate a consolidated enterprise value range for SunGard of approximately $8.4 billion to $10.1 billion. Using this consolidated enterprise value range and assuming net debt of $273 million, Lazard calculated the value per share of SunGard common stock of $27.60 to $32.70 by dividing the estimated consolidated enterprise value less net debt by common shares outstanding. Discounted Cash Flow Analysis Using projections provided by SunGard’s management, Lazard performed an analysis of the present value, as of March 31, 2005, of the free cash flows that SunGard could generate annually from calendar year 2005 through calendar year 2009. Lazard analyzed separately the cash flows for SunGard’s software business and recovery availability services business. For SunGard’s software business, in calculating the terminal value, Lazard assumed perpetual growth rates (i.e., constant growth model) of 3.5% to 4.5% for the projected free cash flows for the periods subsequent to 2009. The projected annual cash flows through 2009 and beyond were then discounted to present value using discount rates ranging from 10.0% to 12.0%. Based on this analysis, Lazard calculated an implied enterprise value range for the software business of approximately $5.6 billion to $7.4 billion. For SunGard’s recovery availability services business, in calculating the terminal value Lazard assumed perpetual growth rates of 2.0% to 3.0% for the projected free cash flows for periods subsequent to 2009. The projected cash flows were then discounted to present value using discount rates ranging from 10.0% to 12.0%. Lazard then calculated an implied enterprise value range for SunGard’s recovery availability business of approximately $2.6 billion to $3.3 billion. Lazard then aggregated the enterprise value ranges for SunGard’s two business segments to calculate a consolidated enterprise value range for SunGard of approximately $8.2 billion to $10.7 billion. Using this consolidated enterprise value range and assuming net debt of $273 million, Lazard calculated an implied price per share range for SunGard common stock of $26.70 to $34.60. Premiums Paid Analysis Lazard performed a premiums paid analysis based upon the premiums paid in 73 recent transactions (not involving “mergers of equals” transactions) that were announced from January 2004 through March 2005 and involved transaction values in excess of $1 billion. In conducting its analysis, Lazard analyzed the premiums paid for recent transactions over $1 billion and those over $5 billion, since premiums paid may vary with the size of the transaction. The analysis was based on the one day, one week and four week implied premiums for the transactions examined. The implied premiums were calculated by comparing the offer price for the target firm on the announcement date with the per share price of the target firm one day, one week, and four weeks prior to the announcement of the transaction. The results of these calculations are given in Table 8-5. Based on this analysis, Lazard determined an applicable premium range of 20% to 30% for SunGard and applied this range to SunGard’s share price of $24.95 on March 18, 2005. Using this information, Lazard calculated an implied price per share range for SunGard common stock of $29.94 (i.e., 1.2 x $24.95) to $32.44 (1.3 x $24.95). Summary and Conclusions Table 8-6 summarizes the estimated valuation ranges based on the alternative valuation methods employed by Lazard Freres. Note that the $36 per offer price compares favorably to the estimated average valuation range, representing a premium of 12% (i.e., $36/$27.11) to 33% (i.e., $36/$32.19). Consequently, Lazard Freres viewed the investor group’s offer price for SunGard as fair. \begin{array}{l} \text { Table 8-6. Valuation Range Summary }\\ \begin{array} { | l | c | c | } \hline { \text { Valuation Method } } & \begin{array} { c } \text { Valuation Range (\$/Common } \\ \text { Share) } \end{array} & \begin{array} { c } \text { (Max. Valuation less Min. } \\ \text { Valuation)/Min. Valuation } \end{array} \\ \hline \text { Comparable Companies } & 24.20 - 29.00 & 19.8 \% \\ \hline \text { Recent Transactions } & 27.60 - 32.70 & 18.5 \% \\ \hline \text { Discounted Cash Flow } & 26.70 - 34.60 & 29.6 \% \\ \hline \text { Premiums Paid } & 29.94 - 32.44 & 8.4 \% \\ \hline \text { Average } & 27.11 - 32.19 & 18.7 \% \\ \hline \end{array} \end{array} -Discuss the strengths and weaknesses of each valuation method employed by these investment banks in constructing estimates of SunGard's value for the Fairness Opinion Letter. Be specific.
Based on this analysis, Lazard determined an applicable premium range of 20% to 30% for SunGard and applied this range to SunGard’s share price of $24.95 on March 18, 2005. Using this information, Lazard calculated an implied price per share range for SunGard common stock of $29.94 (i.e., 1.2 x $24.95) to $32.44 (1.3 x $24.95).

Summary and Conclusions

Table 8-6 summarizes the estimated valuation ranges based on the alternative valuation methods employed by Lazard Freres. Note that the $36 per offer price compares favorably to the estimated average valuation range, representing a premium of 12% (i.e., $36/$27.11) to 33% (i.e., $36/$32.19). Consequently, Lazard Freres viewed the investor group’s offer price for SunGard as fair.
 Table 8-6. Valuation Range Summary  Valuation Method  Valuation Range ($/Common  Share)  (Max. Valuation less Min.  Valuation)/Min. Valuation  Comparable Companies 24.20−29.0019.8% Recent Transactions 27.60−32.7018.5% Discounted Cash Flow 26.70−34.6029.6% Premiums Paid 29.94−32.448.4% Average 27.11−32.1918.7%\begin{array}{l}\text { Table 8-6. Valuation Range Summary }\\\begin{array} { | l | c | c | } \hline { \text { Valuation Method } } & \begin{array} { c } \text { Valuation Range (\$/Common } \\\text { Share) }\end{array} & \begin{array} { c } \text { (Max. Valuation less Min. } \\\text { Valuation)/Min. Valuation }\end{array} \\\hline \text { Comparable Companies } & 24.20 - 29.00 & 19.8 \% \\\hline \text { Recent Transactions } & 27.60 - 32.70 & 18.5 \% \\\hline \text { Discounted Cash Flow } & 26.70 - 34.60 & 29.6 \% \\\hline \text { Premiums Paid } & 29.94 - 32.44 & 8.4 \% \\\hline \text { Average } & 27.11 - 32.19 & 18.7 \% \\\hline\end{array}\end{array}
-Discuss the strengths and weaknesses of each valuation method employed by these investment banks in constructing estimates of SunGard's value for the Fairness Opinion Letter. Be specific.

Definitions:

Upper-Middle-Class

A socio-economic group characterized by high income, professional employment, and a high level of education.

Thriving Suburb

A suburban area experiencing growth and prosperity, often marked by an increase in population and improvements in quality of life.

Rated

Evaluated or assigned a level of quality, importance, or performance.

Culturally Responsive

Refers to pedagogy that recognizes the importance of including students' cultural references in all aspects of learning.

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