Financial Statement Analysis © Pearson Education Limited 2004 Fundamentals of Financial Management, 12/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI

Financial Statement Analysis u Financial Statements u A Possible Framework for Analysis u Balance Sheet Ratios u Income Statement and Income Statement/Balance Sheet Ratios u Trend Analysis u Common-Size and Index Analysis u Financial Statements u A Possible Framework for Analysis u Balance Sheet Ratios u Income Statement and Income Statement/Balance Sheet Ratios u Trend Analysis u Common-Size and Index Analysis

Examples of External Uses of Statement Analysis u Trade Creditors u Trade Creditors -- Focus on the liquidity of the firm. u Bondholders u Bondholders -- Focus on the long-term cash flow of the firm. u Shareholders u Shareholders -- Focus on the profitability and long-term health of the firm. u Trade Creditors u Trade Creditors -- Focus on the liquidity of the firm. u Bondholders u Bondholders -- Focus on the long-term cash flow of the firm. u Shareholders u Shareholders -- Focus on the profitability and long-term health of the firm.

Examples of Internal Uses of Statement Analysis u Plan u Plan -- Focus on assessing the current financial position and evaluating potential firm opportunities. u Control u Control -- Focus on return on investment for various assets and asset efficiency. u Understand u Understand -- Focus on understanding how suppliers of funds analyze the firm. u Plan u Plan -- Focus on assessing the current financial position and evaluating potential firm opportunities. u Control u Control -- Focus on return on investment for various assets and asset efficiency. u Understand u Understand -- Focus on understanding how suppliers of funds analyze the firm.

Primary Types of Financial Statements Income Statement u A summary of a firm’s revenues and expenses over a specified period, ending with net income or loss for the period. Income Statement u A summary of a firm’s revenues and expenses over a specified period, ending with net income or loss for the period. Balance Sheet u A summary of a firm’s financial position on a given date that shows total assets = total liabilities + owners’ equity. Balance Sheet u A summary of a firm’s financial position on a given date that shows total assets = total liabilities + owners’ equity.

Basket Wonders’ Balance Sheet (Asset Side) a. How the firm stands on a specific date. b. What BW owned. c. Amounts owed by customers. d. Future expense items already paid. e. Cash/likely convertible to cash within 1 year. f. Original amount paid. g. Acc. deductions for wear and tear. a. How the firm stands on a specific date. b. What BW owned. c. Amounts owed by customers. d. Future expense items already paid. e. Cash/likely convertible to cash within 1 year. f. Original amount paid. g. Acc. deductions for wear and tear. c d Current Assets e $1,195 f g Net Fix. Assets $ 701 Total Assets b $2,169 Cash and C.E. $ 90 Acct. Rec. c 394 Inventories 696 Prepaid Exp d 5 Accum Tax Prepay 10 Current Assets e $1,195 Fixed Assets f 1030 Less: Acc. Depr. g (329) Net Fix. Assets $ 701 Investment, LT 50 Other Assets, LT 223 Total Assets b $2,169 Basket Wonders Balance Sheet (thousands) Dec. 31, 2007 Basket Wonders Balance Sheet (thousands) Dec. 31, 2007 a

Basket Wonders’ Balance Sheet (Liability Side) a. Note, Assets = Liabilities + Equity. b. What BW owed and ownership position. c. Owed to suppliers for goods and services. d. Unpaid wages, salaries, etc. e. Debts payable < 1 year. f. Debts payable > 1 year. g. Original investment. h. Earnings reinvested. a. Note, Assets = Liabilities + Equity. b. What BW owed and ownership position. c. Owed to suppliers for goods and services. d. Unpaid wages, salaries, etc. e. Debts payable < 1 year. f. Debts payable > 1 year. g. Original investment. h. Earnings reinvested. c d d Current Liab. e $ 500 f g g h Total Equity $1,139 Notes Payable $ 290 Acct. Payable c 94 Accrued Taxes d 16 Other Accrued Liab. d 100 Current Liab. e $ 500 Long-Term Debt f 530 Shareholders’ Equity Com. Stock ($1 par) g 200 Add Pd in Capital g 729 Retained Earnings h 210 Total Equity $1,139 Total Liab/Equity a,b $2,169 Basket Wonders Balance Sheet (thousands) Dec. 31, 2007

Basket Wonders’ Income Statement a. Measures profitability over a time period. b. Received, or receivable, from customers. c. Sales comm., adv., officers’ salaries, etc. d. Operating income. e. Cost of borrowed funds. f. Taxable income. g. Amount earned for shareholders. a. Measures profitability over a time period. b. Received, or receivable, from customers. c. Sales comm., adv., officers’ salaries, etc. d. Operating income. e. Cost of borrowed funds. f. Taxable income. g. Amount earned for shareholders. b c f Increase in RE $ 53 Net Sales $ 2,211 Cost of Goods Sold b 1,599 Gross Profit $ 612 SG&A Expenses c 402 EBIT d $ 210 Interest Expense e 59 EBT f $ 151 Income Taxes 60 EAT g $ 91 Cash Dividends 38 Increase in RE $ 53 Basket Wonders Statement of Earnings (in thousands) for Year Ending December 31, 2007 Basket Wonders Statement of Earnings (in thousands) for Year Ending December 31, 2007 a

Use of Financial Ratios Types of Comparisons Internal Comparisons External Comparisons Types of Comparisons Internal Comparisons External Comparisons A Financial Ratio is an index that relates two accounting numbers and is obtained by dividing one number by the other.

External Comparisons and Sources of Industry Ratios Examples: Risk Management Association Dun & Bradstreet Almanac of Business and Industrial Financial Ratios Examples: Risk Management Association Dun & Bradstreet Almanac of Business and Industrial Financial Ratios similar This involves comparing the ratios of one firm with those of similar firms or with industry averages. Similarity Similarity is important as one should compare “apples to apples.”

Liquidity Ratios Current Current Assets Current Liabilities For Basket Wonders December 31, 2007Current Current Assets Current Liabilities For Basket Wonders December 31, 2007 Shows a firm’s ability to cover its current liabilities with its current assets. Balance Sheet Ratios Liquidity Ratios $1,195$ = 2.39

Liquidity Ratio Comparisons BW Industry BW Industry Year Current Ratio Ratio is stronger than the industry average.

Liquidity Ratios Acid-Test (Quick) Current Assets - Inv Current Liabilities For Basket Wonders December 31, 2007 Acid-Test (Quick) Current Assets - Inv Current Liabilities For Basket Wonders December 31, 2007 Shows a firm’s ability to meet current liabilities with its most liquid assets. Balance Sheet Ratios Liquidity Ratios $1,195 - $696 $ = 1.00

Liquidity Ratio Comparisons BW Industry BW Industry Year Acid-Test Ratio Ratio is weaker than the industry average.

Summary of the Liquidity Ratio Comparisons u Strong current ratio and weak acid-test ratio indicates a potential problem in the inventories account. u Note that this industry has a relatively high level of inventories. u Strong current ratio and weak acid-test ratio indicates a potential problem in the inventories account. u Note that this industry has a relatively high level of inventories. RatioBWIndustry RatioBWIndustry Current Acid-Test

Current Ratio -- Trend Analysis Comparison

Acid-Test Ratio -- Trend Analysis Comparison

Summary of the Liquidity Trend Analyses industry u The current ratio for the industry has been rising slowly at the same time the acid-test ratio has been relatively stable. inventories BW u This indicates that inventories are a significant problem for BW. industry u The current ratio for the industry has been rising slowly at the same time the acid-test ratio has been relatively stable. inventories BW u This indicates that inventories are a significant problem for BW. BW u The current ratio for BW has been rising at the same time the acid-test ratio has been declining.

Financial Leverage Ratios Debt-to-Equity Total Debt Shareholders’ Equity For Basket Wonders December 31, 2007Debt-to-Equity Total Debt Shareholders’ Equity For Basket Wonders December 31, 2007 Shows the extent to which the firm is financed by debt. Balance Sheet Ratios Financial Leverage Ratios $1,030$1, =.90

Financial Leverage Ratio Comparisons BW Industry BW Industry Year Debt-to-Equity Ratio BW has average debt utilization relative to the industry average.

Financial Leverage Ratios Debt-to-Total-Assets Total Debt Total Assets For Basket Wonders December 31, 2007Debt-to-Total-Assets Total Debt Total Assets For Basket Wonders December 31, 2007 Shows the percentage of the firm’s assets that are supported by debt financing. Balance Sheet Ratios Financial Leverage Ratios $1,030$2, =.47

Financial Leverage Ratio Comparisons BW Industry BW Industry Year Debt-to-Total-Asset Ratio BW has average debt utilization relative to the industry average.

Financial Leverage Ratios Total Capitalization Long-term Debt Total Capitalization For Basket Wonders December 31, 2007 Total Capitalization Long-term Debt Total Capitalization For Basket Wonders December 31, 2007 Shows the relative importance of long-term debt to the long-term financing of the firm. Balance Sheet Ratios Financial Leverage Ratios $530 $530$1, =.32 (i.e., LT-Debt + Equity)

Financial Leverage Ratio Comparisons BW Industry BW Industry Year Total Capitalization Ratio BW has average long-term debt utilization relative to the industry average.

Coverage Ratios Interest Coverage EBIT Interest Charges For Basket Wonders December 31, 2007 Interest Coverage EBIT Interest Charges For Basket Wonders December 31, 2007 Indicates a firm’s ability to cover interest charges. Income Statement Ratios Coverage Ratios $210$ = 3.56

Coverage Ratio Comparisons BW Industry BW Industry Year Interest Coverage Ratio BW has below average interest coverage relative to the industry average.

Coverage Ratio -- Trend Analysis Comparison

Summary of the Coverage Trend Analysis low earnings BW u This indicates that low earnings (EBIT) may be a potential problem for BW. debt levels industry u Note, we know that debt levels are in line with the industry averages. low earnings BW u This indicates that low earnings (EBIT) may be a potential problem for BW. debt levels industry u Note, we know that debt levels are in line with the industry averages. BW industry u The interest coverage ratio for BW has been falling since It has been below industry averages for the past two years.

Activity Ratios Receivable Turnover Annual Net Credit Sales Receivables For Basket Wonders December 31, 2007 Receivable Turnover Annual Net Credit Sales Receivables For Basket Wonders December 31, 2007 Indicates quality of receivables and how successful the firm is in its collections. Income Statement / Balance Sheet Ratios Activity Ratios $2,211$ = 5.61 (Assume all sales are credit sales.)

Activity Ratios Avg Collection Period Days in the Year Receivable Turnover For Basket Wonders December 31, 2007 Avg Collection Period Days in the Year Receivable Turnover For Basket Wonders December 31, 2007 Average number of days that receivables are outstanding. (or RT in days) Income Statement / Balance Sheet Ratios Activity Ratios days = 65 days

Activity Ratio Comparisons BW Industry BW Industry Year Average Collection Period BW has improved the average collection period to that of the industry average.

Activity Ratios Payable Turnover (PT) Annual Credit Purchases Accounts Payable For Basket Wonders December 31, 2007 Payable Turnover (PT) Annual Credit Purchases Accounts Payable For Basket Wonders December 31, 2007 Indicates the promptness of payment to suppliers by the firm. Income Statement / Balance Sheet Ratios Activity Ratios $1551$ = 16.5 (Assume annual credit purchases = $1,551.)

Activity Ratios PT in Days Days in the Year Payable Turnover For Basket Wonders December 31, 2007 PT in Days Days in the Year Payable Turnover For Basket Wonders December 31, 2007 Average number of days that payables are outstanding. Income Statement / Balance Sheet Ratios Activity Ratios days = 22.1 days

Activity Ratio Comparisons BW Industry BW Industry Year Payable Turnover in Days BW has improved the PT in Days. Is this good?

Activity Ratios Inventory Turnover Cost of Goods Sold Inventory For Basket Wonders December 31, 2007 Inventory Turnover Cost of Goods Sold Inventory For Basket Wonders December 31, 2007 Indicates the effectiveness of the inventory management practices of the firm. Income Statement / Balance Sheet Ratios Activity Ratios $1,599$ = 2.30

Activity Ratio Comparisons BW Industry BW Industry Year Inventory Turnover Ratio BW has a very poor inventory turnover ratio.

Inventory Turnover Ratio -- Trend Analysis Comparison

Activity Ratios Total Asset Turnover Net Sales Total Assets For Basket Wonders December 31, 2007 Total Asset Turnover Net Sales Total Assets For Basket Wonders December 31, 2007 Indicates the overall effectiveness of the firm in utilizing its assets to generate sales. Income Statement / Balance Sheet Ratios Activity Ratios $2,211$2, = 1.02

Activity Ratio Comparisons BW Industry BW Industry Year Total Asset Turnover Ratio BW has a weak total asset turnover ratio. Why is this ratio considered weak?

Profitability Ratios Gross Profit Margin Gross Profit Net Sales For Basket Wonders December 31, 2007 Gross Profit Margin Gross Profit Net Sales For Basket Wonders December 31, 2007 Indicates the efficiency of operations and firm pricing policies. Income Statement / Balance Sheet Ratios Profitability Ratios $612$2, =.277

Profitability Ratio Comparisons BW Industry 27.7%31.1% BW Industry 27.7%31.1% Year Gross Profit Margin BW has a weak Gross Profit Margin.

Gross Profit Margin -- Trend Analysis Comparison

Profitability Ratios Net Profit Margin Net Profit after Taxes Net Sales For Basket Wonders December 31, 2007 Net Profit Margin Net Profit after Taxes Net Sales For Basket Wonders December 31, 2007 Indicates the firm’s profitability after taking account of all expenses and income taxes. Income Statement / Balance Sheet Ratios Profitability Ratios $91$2, =.041

Profitability Ratio Comparisons BW Industry 4.1%8.2% BW Industry 4.1%8.2% Year Net Profit Margin BW has a poor Net Profit Margin.

Net Profit Margin -- Trend Analysis Comparison

Profitability Ratios Return on Investment Net Profit after Taxes Total Assets For Basket Wonders December 31, 2007 Return on Investment Net Profit after Taxes Total Assets For Basket Wonders December 31, 2007 Indicates the profitability on the assets of the firm (after all expenses and taxes). Income Statement / Balance Sheet Ratios Profitability Ratios $91$2, =.042

Profitability Ratio Comparisons BW Industry 4.2% 9.8% BW Industry 4.2% 9.8% Year Return on Investment BW has a poor Return on Investment.

Return on Investment – Trend Analysis Comparison

Profitability Ratios Return on Equity Net Profit after Taxes Shareholders’ Equity For Basket Wonders December 31, 2007 Return on Equity Net Profit after Taxes Shareholders’ Equity For Basket Wonders December 31, 2007 Indicates the profitability to the shareholders of the firm (after all expenses and taxes). Income Statement / Balance Sheet Ratios Profitability Ratios $91$1, =.08

Profitability Ratio Comparisons BW Industry 8.0%17.9% BW Industry 8.0%17.9% Year Return on Equity BW has a poor Return on Equity.

Return on Equity -- Trend Analysis Comparison

Summary of the Profitability Trend Analyses BW industry u The profitability ratios for BW have ALL been falling since Each has been below the industry averages for the past three years. COGS administrative costs BW u This indicates that COGS and administrative costs may both be too high and a potential problem for BW. u Note, this result is consistent with the low interest coverage ratio. BW industry u The profitability ratios for BW have ALL been falling since Each has been below the industry averages for the past three years. COGS administrative costs BW u This indicates that COGS and administrative costs may both be too high and a potential problem for BW. u Note, this result is consistent with the low interest coverage ratio.

Summary of Ratio Analyses u Inventories are too high. u May be paying off creditors (accounts payable) too soon. u COGS may be too high. u Selling, general, and administrative costs may be too high. u Inventories are too high. u May be paying off creditors (accounts payable) too soon. u COGS may be too high. u Selling, general, and administrative costs may be too high.

Common-size Analysis An analysis of percentage financial statements where all balance sheet items are divided by total assets and all income statement items are divided by net sales or revenues.

Basket Wonders’ Common Size Balance Sheets

Basket Wonders’ Common Size Income Statements

Index Analyses An analysis of percentage financial statements where all balance sheet or income statement figures for a base year equal (percent) and subsequent financial statement items are expressed as percentages of their values in the base year.

Basket Wonders’ Indexed Balance Sheets

Basket Wonders’ Indexed Income Statements

Funds Analysis, Cash-Flow Analysis, and Financial Planning u Flow of Funds (Sources and Uses) Statement u Accounting Statement of Cash Flows u Cash-Flow Forecasting u Range of Cash-Flow Estimates u Forecasting Financial Statements u Flow of Funds (Sources and Uses) Statement u Accounting Statement of Cash Flows u Cash-Flow Forecasting u Range of Cash-Flow Estimates u Forecasting Financial Statements

Flow of Funds Statement cash flow statement Has been replaced by the cash flow statement (1989) in U.S. audited annual reports. A summary of a firm’s changes in financial position from one period to another; it is also called a sources and uses of funds statement or a statement of changes in financial position.

Why Examine the Flow of Funds Statement QUESTION? Why should we bother to understand a Flow of Funds Statement that is no longer required to appear in U.S. audited annual reports?QUESTION?

Why Examine the Flow of Funds Statement u Includes important noncash transactions while the cash flow statement does not. u Is easy to prepare and often preferred by managers for analysis purposes over the more complex cash flow statement. u Helps you to better understand the cash flow statement, especially if it is prepared under the “indirect method.” u Includes important noncash transactions while the cash flow statement does not. u Is easy to prepare and often preferred by managers for analysis purposes over the more complex cash flow statement. u Helps you to better understand the cash flow statement, especially if it is prepared under the “indirect method.” The Flow of Funds Statement:

Flow of Funds Statement All of the firm’s investments and claims against those investments. beyond just cash Extends beyond just transactions involving cash. All of the firm’s investments and claims against those investments. beyond just cash Extends beyond just transactions involving cash. funds What are “funds”?

Sources and Uses Statement Uses Sources Assets Liabilities The letters labeling the boxes stand for Uses, Sources, Assets, and Liabilities (broadly defined). The pluses (minuses) indicate increases (decreases) in assets or liabilities. AL A L S U

BW’s Determination of Sources and Uses $ S S U U $ 1,140 $ 1,140 N/A 930 N/A (299) N/A $ 631 $ U $ 2,044 $ S S U U $ 1,140 $ 1,140 N/A 930 N/A (299) N/A $ 631 $ U $ 2,044 Cash and C.E. $ 90 Acct. Rec. 394 Inventories 696 Prepaid Exp 5 Accum Tax Prepay 10 Current Assets $ 1,195 Fixed Assets 1030 Less: Acc. Depr. (329) Net Fix. Assets $ 701 Investment, LT 50 Other Assets, LT 223 Total Assets $ 2,169 Assets /- S/U Assets /- S/U

BW’s Determination of Sources and Uses $ 100 $10 S S U U $ 1,140 $ 1,140 N/A 930 N/A (299) N/A $ 631 $ U $ 2,044 $ 100 $10 S S U U $ 1,140 $ 1,140 N/A 930 N/A (299) N/A $ 631 $ U $ 2,044 Cash and C.E. $ 90 Acct. Rec. 394 Inventories 696 Prepaid Exp 5 Accum Tax Prepay 10 Current Assets $ 1,195 Fixed Assets 1030 Less: Acc. Depr. (329) Net Fix. Assets $ 701 Investment, LT 50 Other Assets, LT 223 Total Assets $ 2,169 Assets /- S/U Assets /- S/U

BW’s Determination of Sources and Uses $ U $505 $ 505 N/A S S $ 1086 $ 1086 N/A $ 2,044 $ U $505 $ 505 N/A S S $ 1086 $ 1086 N/A $ 2,044 Notes Payable $ 290 Acct. Payable 94 Accrued Taxes 16 Other Accrued Liab. 100 Current Liab.$ 500 Current Liab. $ 500 Long-Term Debt 530 Shareholders’ Equity Com. Stock ($1 par) 200 Add Pd in Capital 729 Retained Earnings 210 Total Equity $ 1,139 Total Liab/Equity $ 2,169 Liabilities and Equity /- S/U

BW’s Determination of Sources and Uses $ 295 $ 5 U $505 $ 505 N/A S S $ 1086 $ 1086 N/A $ 2,044 $ 295 $ 5 U $505 $ 505 N/A S S $ 1086 $ 1086 N/A $ 2,044 Notes Payable $ 290 Acct. Payable 94 Accrued Taxes 16 Other Accrued Liab. 100 Current Liab.$ 500 Current Liab. $ 500 Long-Term Debt 530 Shareholders’ Equity Com. Stock ($1 par) 200 Add Pd in Capital 729 Retained Earnings 210 Total Equity $ 1,139 Total Liab/Equity $ 2,169 Liabilities and Equity /- S/U

Risk and Return © Pearson Education Limited 2004 Fundamentals of Financial Management, 12/e Created by: Gregory A. Kuhlemeyer, Ph.D. Carroll College, Waukesha, WI

Defining Risk What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank CD or a share of stock? What rate of return do you expect on your investment (savings) this year? What rate will you actually earn? Does it matter if it is a bank CD or a share of stock? The variability of returns from those that are expected.

Determining Expected Return (Discrete Dist.) R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. R =  ( R i )( P i ) R is the expected return for the asset, R i is the return for the i th possibility, P i is the probability of that return occurring, n is the total number of possibilities. n i=1

How to Determine the Expected Return and Standard Deviation Stock BW R i P i (R i )(P i ) Sum Stock BW R i P i (R i )(P i ) Sum The expected return, R, for Stock BW is.09 or 9%

Determining Standard Deviation (Risk Measure)   =  ( R i - R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution.   =  ( R i - R ) 2 ( P i ) Standard Deviation  Standard Deviation, , is a statistical measure of the variability of a distribution around its mean. It is the square root of variance. Note, this is for a discrete distribution. n i=1

How to Determine the Expected Return and Standard Deviation Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) Sum Stock BW R i P i (R i )(P i ) (R i - R ) 2 (P i ) Sum

Determining Standard Deviation (Risk Measure)   =  ( R i - R ) 2 ( P i )   =  %  =.1315 or 13.15%   =  ( R i - R ) 2 ( P i )   =  %  =.1315 or 13.15% n i=1

Coefficient of Variation standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  R CV =  / R CV of BW =.1315 /.09 = 1.46 standard deviation mean The ratio of the standard deviation of a distribution to the mean of that distribution. RELATIVE It is a measure of RELATIVE risk.  R CV =  / R CV of BW =.1315 /.09 = 1.46

Determining Standard Deviation (Risk Measure) n i=1   =  ( R i - R ) 2 ( n ) Note, this is for a continuous distribution where the distribution is for a population. R represents the population mean in this example.   =  ( R i - R ) 2 ( n ) Note, this is for a continuous distribution where the distribution is for a population. R represents the population mean in this example.

R P =  ( W j )( R j ) R P is the expected return for the portfolio, W j is the weight (investment proportion) for the j th asset in the portfolio, R j is the expected return of the j th asset, m is the total number of assets in the portfolio. R P =  ( W j )( R j ) R P is the expected return for the portfolio, W j is the weight (investment proportion) for the j th asset in the portfolio, R j is the expected return of the j th asset, m is the total number of assets in the portfolio. Determining Portfolio Expected Return m j=1

Determining Portfolio Standard Deviation m j=1 m k=1  P  P =  W j W k  jk W j is the weight (investment proportion) for the j th asset in the portfolio, W k is the weight (investment proportion) for the k th asset in the portfolio,  jk is the covariance between returns for the j th and k th assets in the portfolio.  P  P =  W j W k  jk W j is the weight (investment proportion) for the j th asset in the portfolio, W k is the weight (investment proportion) for the k th asset in the portfolio,  jk is the covariance between returns for the j th and k th assets in the portfolio.

What is Covariance?  r  jk =  j  k r  jk  j is the standard deviation of the j th asset in the portfolio,  k is the standard deviation of the k th asset in the portfolio, r jk is the correlation coefficient between the j th and k th assets in the portfolio.  r  jk =  j  k r  jk  j is the standard deviation of the j th asset in the portfolio,  k is the standard deviation of the k th asset in the portfolio, r jk is the correlation coefficient between the j th and k th assets in the portfolio.

Correlation Coefficient A standardized statistical measure of the linear relationship between two variables Its range is from -1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation). A standardized statistical measure of the linear relationship between two variables Its range is from -1.0 (perfect negative correlation), through 0 (no correlation), to +1.0 (perfect positive correlation).

Variance - Covariance Matrix A three asset portfolio: Col 1 Col 2 Col 3 Row 1W 1 W 1  1,1 W 1 W 2  1,2 W 1 W 3  1,3 Row 2W 2 W 1  2,1 W 2 W 2  2,2 W 2 W 3  2,3 Row 3W 3 W 1  3,1 W 3 W 2  3,2 W 3 W 3  3,3  j,k = is the covariance between returns for the j th and k th assets in the portfolio. A three asset portfolio: Col 1 Col 2 Col 3 Row 1W 1 W 1  1,1 W 1 W 2  1,2 W 1 W 3  1,3 Row 2W 2 W 1  2,1 W 2 W 2  2,2 W 2 W 3  2,3 Row 3W 3 W 1  3,1 W 3 W 2  3,2 W 3 W 3  3,3  j,k = is the covariance between returns for the j th and k th assets in the portfolio.

Stock D Stock BW $2,000 Stock BW $3,000Stock D Stock BW 9%13.15% Stock D 8%10.65%correlation coefficient 0.75 You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D. Remember that the expected return and standard deviation of Stock BW is 9% and 13.15% respectively. The expected return and standard deviation of Stock D is 8% and 10.65% respectively. The correlation coefficient between BW and D is What is the expected return and standard deviation of the portfolio? Stock D Stock BW $2,000 Stock BW $3,000Stock D Stock BW 9%13.15% Stock D 8%10.65%correlation coefficient 0.75 You are creating a portfolio of Stock D and Stock BW (from earlier). You are investing $2,000 in Stock BW and $3,000 in Stock D. Remember that the expected return and standard deviation of Stock BW is 9% and 13.15% respectively. The expected return and standard deviation of Stock D is 8% and 10.65% respectively. The correlation coefficient between BW and D is What is the expected return and standard deviation of the portfolio? Portfolio Risk and Expected Return Example

Determining Portfolio Expected Return W BW = $2,000 / $5,000 =.4 W D.6 W D = $3,000 / $5,000 =.6 W D R D R P = ( W BW )(R BW ) + ( W D )(R D ).68% R P = (.4)(9%) + (.6)(8%) 4.8%8.4% R P = (3.6%) + (4.8%) = 8.4% W BW = $2,000 / $5,000 =.4 W D.6 W D = $3,000 / $5,000 =.6 W D R D R P = ( W BW )(R BW ) + ( W D )(R D ).68% R P = (.4)(9%) + (.6)(8%) 4.8%8.4% R P = (3.6%) + (4.8%) = 8.4%

Two-asset portfolio: Col 1 Col 2 Row 1W BW W BW  BW,BW W BW W D  BW,D Row 2 W D W BW  D,BW W D W D  D,D This represents the variance - covariance matrix for the two-asset portfolio. Two-asset portfolio: Col 1 Col 2 Row 1W BW W BW  BW,BW W BW W D  BW,D Row 2 W D W BW  D,BW W D W D  D,D This represents the variance - covariance matrix for the two-asset portfolio. Determining Portfolio Standard Deviation

Two-asset portfolio: Col 1 Col 2 Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105) Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113) This represents substitution into the variance - covariance matrix. Two-asset portfolio: Col 1 Col 2 Row 1 (.4)(.4)(.0173) (.4)(.6)(.0105) Row 2 (.6)(.4)(.0105) (.6)(.6)(.0113) This represents substitution into the variance - covariance matrix. Determining Portfolio Standard Deviation

Two-asset portfolio: Col 1 Col 2 Row 1 (.0028) (.0025) Row 2 (.0025) (.0041) This represents the actual element values in the variance - covariance matrix. Two-asset portfolio: Col 1 Col 2 Row 1 (.0028) (.0025) Row 2 (.0025) (.0041) This represents the actual element values in the variance - covariance matrix. Determining Portfolio Standard Deviation

 P = (2)(.0025)  P = SQRT(.0119)  P =.1091 or 10.91% A weighted average of the individual standard deviations is INCORRECT.  P = (2)(.0025)  P = SQRT(.0119)  P =.1091 or 10.91% A weighted average of the individual standard deviations is INCORRECT.

Stock C Stock D Portfolio Return Return 9.00% 8.00% 8.64%Stand. Dev. Dev.13.15% 10.65% 10.91% CV CV The portfolio has the LOWEST coefficient of variation due to diversification. Stock C Stock D Portfolio Return Return 9.00% 8.00% 8.64%Stand. Dev. Dev.13.15% 10.65% 10.91% CV CV The portfolio has the LOWEST coefficient of variation due to diversification. Summary of the Portfolio Return and Risk Calculation

Combining securities that are not perfectly, positively correlated reduces risk. Diversification and the Correlation Coefficient INVESTMENT RETURN TIME SECURITY E SECURITY F Combination E and F

Systematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Systematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification. Total Risk = Systematic Risk + Unsystematic Risk Total Risk SystematicRisk UnsystematicRisk Total Risk = Systematic Risk + Unsystematic Risk

Total Risk = Systematic Risk + Unsystematic Risk TotalRisk Unsystematic risk Systematic risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors such as changes in nation’s economy, tax reform by the Congress, or a change in the world situation.

Total Risk = Systematic Risk + Unsystematic Risk TotalRisk Unsystematic risk Systematic risk STD DEV OF PORTFOLIO RETURN NUMBER OF SECURITIES IN THE PORTFOLIO Factors unique to a particular company or industry. For example, the death of a key executive or loss of a governmental defense contract.

risk-free rate a premium systematic risk CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security. Capital Asset Pricing Model (CAPM)

1.Capital markets are efficient. 2.Homogeneous investor expectations over a given period. Risk-free 3.Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). systematic risk 4.Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). 1.Capital markets are efficient. 2.Homogeneous investor expectations over a given period. Risk-free 3.Risk-free asset return is certain (use short- to intermediate-term Treasuries as a proxy). systematic risk 4.Market portfolio contains only systematic risk (use S&P 500 Index or similar as a proxy). CAPM Assumptions

Characteristic Line EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Beta Beta = RiseRun Narrower spread is higher correlation Characteristic Line

systematic risk An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. beta The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. systematic risk An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. beta The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio. What is Beta?

Characteristic Lines and Different Betas EXCESS RETURN ON STOCK EXCESS RETURN ON MARKET PORTFOLIO Beta < 1 (defensive) Beta = 1 Beta > 1 (aggressive) characteristic Each characteristic line line has a different slope.

R j R j is the required rate of return for stock j, R f R f is the risk-free rate of return,  j  j is the beta of stock j (measures systematic risk of stock j), R M R M is the expected return for the market portfolio. R j R j is the required rate of return for stock j, R f R f is the risk-free rate of return,  j  j is the beta of stock j (measures systematic risk of stock j), R M R M is the expected return for the market portfolio. Security Market Line R j R f  R M R f R j = R f +  j (R M - R f )

Security Market Line R j R f  R M R f R j = R f +  j (R M - R f )  M 1.0  M = 1.0 Systematic Risk (Beta) RfRfRfRf RMRMRMRM Required Return RiskPremium Risk-freeReturn

Security Market Line u Obtaining Betas u Can use historical data if past best represents the expectations of the future u Can also utilize services like Value Line, Ibbotson Associates, etc. u Adjusted Beta u Betas have a tendency to revert to the mean of 1.0 u Can utilize combination of recent beta and mean u 2.22 (.7) (.3) = = estimate u Obtaining Betas u Can use historical data if past best represents the expectations of the future u Can also utilize services like Value Line, Ibbotson Associates, etc. u Adjusted Beta u Betas have a tendency to revert to the mean of 1.0 u Can utilize combination of recent beta and mean u 2.22 (.7) (.3) = = estimate

6% R f market expected rate of return 10% beta1.2 required rate of return Lisa Miller at Basket Wonders is attempting to determine the rate of return required by their stock investors. Lisa is using a 6% R f and a long-term market expected rate of return of 10%. A stock analyst following the firm has calculated that the firm beta is 1.2. What is the required rate of return on the stock of Basket Wonders? Determination of the Required Rate of Return

R BW R f  R M R f R BW = R f +  j (R M - R f ) R BW 6%1.210%6% R BW = 6% + 1.2(10% - 6%) R BW 10.8% R BW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). R BW R f  R M R f R BW = R f +  j (R M - R f ) R BW 6%1.210%6% R BW = 6% + 1.2(10% - 6%) R BW 10.8% R BW = 10.8% The required rate of return exceeds the market rate of return as BW’s beta exceeds the market beta (1.0). BWs Required Rate of Return

intrinsic value dividend next period $0.50grow 5.8% Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. intrinsic value overunderpriced What is the intrinsic value of the stock? Is the stock over or underpriced? intrinsic value dividend next period $0.50grow 5.8% Lisa Miller at BW is also attempting to determine the intrinsic value of the stock. She is using the constant growth model. Lisa estimates that the dividend next period will be $0.50 and that BW will grow at a constant rate of 5.8%. The stock is currently selling for $15. intrinsic value overunderpriced What is the intrinsic value of the stock? Is the stock over or underpriced? Determination of the Intrinsic Value of BW

intrinsic value $10 The stock is OVERVALUED as the market price ($15) exceeds the intrinsic value ($10). Determination of the Intrinsic Value of BW $ %5.8% 10.8% - 5.8% IntrinsicValue = = $10

Security Market Line Systematic Risk (Beta) RfRfRfRf Required Return Direction of Movement Direction of Movement Stock Y Stock Y (Overpriced) Stock X (Underpriced)