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- 1. 1 VALUATION – BONDS AND STOCKS
- 2. 2 BONDS We hear a lot about the stock market in the popular press, but not much about the bond market It may surprise you to learn that the U.S. bond market is over twice the size of the U.S. stock market Total outstanding debt in 2007: $29.2 trillion Total market value of common stock: $14.2 trillion In general, bonds are less risky than stocks But, like all assets, high-yield bonds have higher risk
- 3. 3 Corporate Bonds Bond ratings go from AAA(Best credit) to CCC. If the rating is D, then it is considered in default. BBB or better is considered investment grade, 0.5% or less chance of default. BB and below, historically default rate is around 4% but has reached above 10% in 90-91, 2001 for example.
- 4. WHICH TO BUY? High Yield vs Investment grades Example AAA 5% with .2% historical default B, 9% with 4% historical default rate 40% recovery rate on defaults Return = (1 – default rate) * interest rate – default rate * (1-recovery rate) Return for A, .998 * .05 - .002*.6 = 4.87%. Return for B, .96 * .09 - .04 * .6 = 6.24%
- 5. 5 Link to corporate and Treasury quotes
- 6. 6 BOND VALUATION The value of a bond represents the present value of future cash flows. Bonds are easier to value than stocks because in the case of bonds, the cash flows are known Coupon amount Par value Investors also know the time remaining to maturity, and the prevailing market interest rate for bonds of similar risk
- 7. 7 Examples Calculate Price, Annual coupon, semi- annual coupon. What happens when interest rates change? How does maturity affect risk? How does coupon affect risk? Discount, Premium, at Par
- 8. 8 Holding period return Assume you buy a 10 year 8% annual coupon bond yielding 8%. 2 years later it is yielding 6%. What is your return?
- 9. 9 Other Issues: Yield to Call The YTM calculation assumes that the bond is held to maturity What if the bond is called by the issuer prior to maturity? The investor would receive only the coupon payments up to the point of call, plus the call price This is called the Yield to Call
- 10. 10 Callable bonds are an advantage for the issuer, but a disadvantage for the investor If interest rates fall, the issuer can recall the more expensive debt and issue new debt at the new lower interest rate The investor is left with cash, just when interest rates are lower The call provision effectively puts a ceiling on the price of a bond If interest rates fall enough, the bond will be called Investors are not stupid – they require higher yields from callable bonds versus otherwise equivalent non-callable bonds
- 11. 11 Example: 20-year bond with 7 percent coupons, semiannual The bond can be called in 5 years at a call price of 1,070 The bond’s market price is $1,106.38. Calculate the Yield to Call: YTC = 2 x 2.875 = 5.75% INPUT 40 -1106.38 35 1070 N I/YR PV PMT FV OUTPUT 2.875
- 12. 12 MUNICIPAL BONDS AND YIELD Municipal bonds appear to offer low yields compared with corporate bonds and Treasury securities. This is because the interest from municipal bonds is tax exempt at the federal level, and generally at the state level as well In order to compare yields, we must compute the after-tax yield on municipal bonds
- 13. 13 Taxable equivalent yield Example: Pre-tax yield on municipal bond is 5%, and investor’s marginal tax rate is 35% Equivalent taxable yield = 5 / (1-.35) = 7.69% Municipal bonds are more attractive to high-income investors (with high marginal tax rates) ratetax-1 yieldMuni YieldTaxableEquivalent =
- 14. DURATION A measure of the effective maturity of a bond The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment Duration is shorter than maturity for all bonds except zero coupon bonds Duration is equal to maturity for zero coupon bonds
- 15. DURATION: CALCULATION t t t w CF y ice= +( )1 Pr D t w t T t= × = ∑1 CF Cash Flow for period tt =
- 16. DURATION CALCULATION 8% Bond Time years Payment PV of CF (10%) Weight C1 X C4 1 80 72.727 .0765 .0765 2 80 66.116 .0690 .1392 Sum 3 1080 811.420 950.263 .8539 1.0000 2.5617 2.7774
- 17. USES OF DURATION Summary measure of length or effective maturity for a portfolio Immunization of interest rate risk (passive management) Net worth immunization Target date immunization Measure of price sensitivity for changes in interest rate
- 18. DURATION/PRICE RELATIONSHIP Price change is proportional to duration and not to maturity ∆P/P = -D x [∆(1+y) / (1+y) D* = modified duration D* = D / (1+y) ∆P/P = - D* x ∆y
- 19. PRICING ERROR FROM CONVEXITY Price Yield Duration Pricing Error from Convexity
- 20. CORRECTION FOR CONVEXITY )(2 1 2 yConvexityyD P P ∆××+∆×−= ∆ Modify the pricing equation: Convexity is Equal to: ( )∑= + ++× N t t t tt y CF P 1 2 2 )1(y)(1 1 Where: CFt is the cashflow (interest and/or principal) at time t.
- 21. Stock Investing: October, this is one of the peculiarly dangerous months to speculate in stocks. The others are July, January September, April, November, May, March, June, December, August and February. Mark Twain, 1899.
- 22. 22 COMMON STOCK Equity securities (stocks) represent ownership in a corporation Common stockholders are residual claimants The have a claim on cash flows only after all other claimants (employees, suppliers, debtholders, the government) have been paid At any point in time the market value of a firm’s common stock depends on many factors including: The company’s profitability (cash flows) The company’s growth potential Current market interest rates Conditions in the overall stock market
- 23. 23 VALUATION APPROACH Examine Economic Environment(Federal Reserve Forecasts is a good place to start) Examine Industry/Sector Environment Examine Company Examine Price Best of all worlds: Finding a good company in a growing industry within an expanding economy that is undervalued. A tall order. We will not focus on the economic and industry environment in this class, but will start with some simple financial statement analysis to determine if we are dealing with a good company, and then look at valuation models to see if it is selling at an attractive price.
- 24. 24 ANALYSIS OF FINANCIAL STATEMENTS
- 25. 25 INTRODUCTION The real value of financial statements lies in the fact that managers, investors, and analysts can use the information in the statements to: Analyze firm performance Plan changes to improve performance Ratio Analysis Calculating and analyzing financial ratios to assess a firm’s performance
- 26. 26 Ratios fall into five groups: Liquidity ratios Asset management ratios Debt management ratios Profitability ratios Market value ratios After managers, analysts, or investors calculate a firm’s ratios they make two comparisons: Trend – comparison to the same firm over time Competitors – comparison to other firms in the same industry
- 27. 27 LIQUIDITY RATIOS Liquidity ratios provide an indication of the ability of the firm to meet its obligations as they come due The two most common liquidity ratios are the current ratio and the quick (or acid-test) ratio.
- 28. 28 The broadest liquidity measure is the current ratio, which measures the dollars of current assets available to pay each dollar of current liabilities Current Ratio = CA / CL Inventory is the least liquid of the current assets, and is the current asset for which book values are the least reliable measure of market value. The quick, or acid-test ratio excludes inventory in the numerator, and measures the firm’s ability to pay off short-term obligations without relying on inventory sales: Quick Ratio = (CA – Inventory) / CL
- 29. 29 ASSET MANAGEMENT RATIOS Asset management ratios measure how efficiently a firm uses its assets Many of these ratios are focused on a specific asset, such as inventory or accounts receivable. We will examine inventory and total asset turnover.
- 30. 30 Inventory Management The inventory turnover ratio measures the dollars of sales produced per dollar of inventory. Often this ratio uses cost of goods sold in the numerator rather than sales since inventory is listed on the balance sheet at cost Inventory Turnover = Sales / Inventory or Inventory Turnover = Cost of Goods Sold / Inventory Total Asset Management The Total Asset Turnover ratio measures the dollars of sales produced per dollar of total assets Total assets turnover ratio = Sales / Total assets
- 31. 31 DEBT MANAGEMENT RATIOS Debt management ratios measure the extent to which the firm uses debt (financial leverage) versus equity to finance its assets. We will examine the following four: The debt ratio measures the percentage of total assets financed with debt. Debt ratio = Total debt / Total assets The debt-to-equity ratio measures the dollars of debt financing used for every dollar of equity financing. Debt-to-equity ratio = Total debt / Total equity
- 32. 32 The Equity Multiplier ratio measures the dollars of assets on the balance sheet for every dollar of equity financing Equity multiplier ratio = Total assets / Total equity The Times Interest Earned ratio measures the number of dollars of operating earnings available to meet each dollar of interest obligations Times interest earned = EBIT / Interest expense
- 33. 33 PROFITABILITY RATIOS These ratios show the combined effect of liquidity, asset management, and debt management on the overall operating results of the firm These ratios are closely monitored by investors Stock prices react very quickly to unexpected changes in these ratios. We will look at the profit margin, ROA, and ROE. The Profit Margin is the percent of sales left after all firm expenses are paid Profit margin = Net income available to common stockholders / Sales
- 34. 34 The Return on Assets (ROA) measures the overall return on the firm’s assets, inclusive of leverage and taxes Return on Assets (ROA) = Net income available to common stockholders / Total Assets The Return on Equity (ROE) measures the return on common stockholders’ investment Return on Equity (ROE) = Net income available to common stockholders / Common stockholders’ equity ROE is affected by net income as well as the amount of financial leverage A high ROE is generally considered to be a positive sign of firm performance Unless it is driven by excessively high leverage
- 35. 35 MARKET VALUE RATIOS While ROE is a very important financial statement ratio, it doesn’t specifically incorporate risk. Market prices of publicly traded firms do incorporate risk, and so ratios that incorporate stock market values are important. We will look at two, Market to book and PE
- 36. 36 The Market-to-Book ratio measures the amount that investors will pay for the firm’s stock per dollar of equity used to finance the firm’s assets Market-to-book ratio = Market price per share / Book value per share Book value per share is an accounting-based number reflecting historical costs This ratio compares the market (current) value of the firm's equity to their historical costs. If liquidity, asset management, and accounting profitability are good for a firm, then the market-to-book ratio will be high
- 37. 37 The Price-Earnings ratio is the best known and most often quoted figure Price-earnings ratio = Market price per share / Earnings per share Measures how much investors are willing to pay for each dollar of earnings A high PE ratio is often an indication of anticipated growth Stocks are classified as growth stocks or value stocks based on the PE ratio
- 38. 38 DUPONT ANALYSIS DuPont analysis is a decomposition model ROA and ROE can be broken down into components in an effort to explain why they may be low (or high). ROE = profit margin x total asset turnover x equity multiplier ROE = NI/Sales x Sales/Total Assets x Total Assets/Total Equity The DuPont model focuses on Expense control (Profit Margin) Asset utilization (TA turnover) Debt utilization (Equity Mult)
- 39. 39 TIME SERIES AND CROSS- SECTIONAL ANALYSIS To analyze ratios in a meaningful way they must be compared to some benchmark There are two types of benchmarks: Performance of the firm over time (time series analysis) Performance of the firm against other companies in the same industry (cross-sectional analysis) Comparative ratios for industries are available from Value Line, Robert Morris Associates, Dun & Bradstreet, Hoover’s Online, and MSN Money
- 40. FUNDAMENTAL STOCK ANALYSIS: MODELS OF EQUITY VALUATION: IS IT UNDERVALUED? Basic Types of Models Balance Sheet Models Dividend Discount Models Price/Earning Ratios Estimating Growth Rates and Opportunities
- 41. DIVIDEND DISCOUNT MODELS: GENERAL MODEL V D k o t t t = += ∞ ∑( )11 V0 = Value of Stock Dt = Dividend k = required return
- 42. NO GROWTH MODEL V D k o = Stocks that have earnings and dividends that are expected to remain constant Preferred Stock
- 43. NO GROWTH MODEL: EXAMPLE V D k o = E1 = D1 = $5.00 k = .15 V0 = $5.00 / .15 = $33.33
- 44. CONSTANT GROWTH MODEL Vo D g k g o = + − ( )1 g = constant perpetual growth rate
- 45. CONSTANT GROWTH MODEL: EXAMPLE Vo D g k g o = + − ( )1 E1 = $5.00 b = 40% k = 15% (1-b) = 60% D1 = $3.00 g = 8% V0 = 3.00 / (.15 - .08) = $42.86
- 46. 46 ADDITIONAL VALUATION METHODS Variable Growth Techniques For high-growth firms, we can’t use the constant growth formula because we know that the firm can’t sustain the high growth forever These firms may have two different growth rates Growth during the supernormal growth period Steady growth after the firm matures We can use a multistage growth formula for these firms, but we can also use discounted cash flows in combination with the constant growth model
- 47. 47 Example: Suppose a firm currently has a dividend of D0 = $5. We expect the firm to grow at a rate of 10% for three years, after which it will grow at 4% forever. The required return is 9%. First we can calculate the dividends: D1 = 5(1+.10) = 5.50 D2 = 5.50(1.10) = 6.05 D3 = 6.05(1.10) = 6.655 D4 = 6.655(1.04) = 6.92
- 48. 48 Now we can calculate the present value of all of the dividends in periods 4 to ∞, where the growth is constant forever P3 = D4/(kg) = 6.92/(.09-.04) = 138.42 Now we have all the cash flows, and we can find P0 P0 = 5.50/1.091 + 6.05/1.092 + (6.655 + 138.42)/1.093 = $122.17
- 49. 49 Estimating some key inputs for Multi-Stage Growth Models Cash flow estimate Dividends Operating Cash Flow Free Cash Flow to Equity (what could be paid out and remain a going concern): NI - (1 – debt ratio) *( Change in Working Capital + Cap. Expend. – Depreciation) Cost of Capital/Required Return Bond Yield + premium, premium 5% or so Capm: Return = risk free + B(Expected Market Return – risk free) Your own personal required return Growth A) Geometric or Average growth rates of Earnings, Sales, Cash Flows B) Intrinsic Growth, ROE (1 – payout ratio) C) Analyst Estimates
- 50. ESTIMATING DIVIDEND GROWTH RATES g ROE b= × g = growth rate in dividends ROE = Return on Equity for the firm b = plowback or retention percentage rate (1- dividend payout percentage rate)
- 51. ESTIMATING GROWTH VIA HISTORICAL INFO. Dividend in 2000 was $1. Dividend in 2006 was $1.80 Growth is (1.80/1)^(1/6)-1 = 10.29%
- 52. FREE CASH FLOW TO EQUITY A much better model is to apply discount models to FCFE which may more accurately reflect a firms value. FCFE = Net Income + depreciation – Cap. Expend. – change in working capital – principal debt repayments + new debt issues. Apply model as per usual.
- 53. FREE CASH FLOW TO EQUITY If the firm finances a fixed percentage of its capital spending and investments in working capital with debt, the calculation of FCFE is simplified. Let DR be the debt ratio, debt as a percentage of assets. In this case, FCFE can be written as FCFE = NI – (1 – DR)(Capital Spending + change in Working Capital – Depreciation) When building FCFE valuation models, the logic, that debt financing is used to finance a constant fraction of investments, is very useful. This equation is pretty common.
- 54. FREE CASH FLOW TO THE FIRM FCFF = EBIT(1-tax rate) + Dep. – Cap. Expenditures – Change in WC – Change in other assets. Again, proceed as normal(replace dividends with FCFF) but discount at firms cost of capital. You find value of firm. To find value of equity, simply subtract off debt.
- 55. LET’S LOOK AT AN EXAMPLE http://faculty.etsu.edu/trainor/FNCE%203300/Lowes.doc Another interesting site you may want to use: http://caps.fool.com/Ticker.aspx?source=icaedilnk9950012&
- 56. 56 THE P/E MODEL The models we have used so far involve computing a stock’s intrinsic value using discounted cash flows to the investor Another approach is to assess a stock’s relative value The price-earnings (P/E) ratio represents the most common valuation yardstick in the investment industry
- 57. 57 The P/E ratio is simply the current price of the stock divided by the last four quarters of earnings per share: The P/E ratio is used as an indication of expected growth of a company Larger growth rates lead to larger P/E ratios High P/E stocks are called growth stocks, whereas low P/E stocks are called value stocks months12lastforearningssharePer pricestockCurrent P/E =
- 58. 58 Estimating Future Stock Prices Multiplying the P/E ratio by expected earnings results in an expected stock price n n gE E PP )1(xx)( 0 +=
- 59. 59 Example: The P/E ratio for Caterpillar is 12.98. The company earned $5.05 per share and paid a $1.10 dividend last year. Analysts estimate that the company will grow at an average annual rate of 12.8% over the next 5 years. Calculate the expected price of Caterpillar’s stock price in 5 years. P5 = (P/E) x E0 x (1 + g)5 = 12.98 x $5.05 x (1.128)5 = $119.70
- 60. OTHER TYPES OF VALUATION Use Price/sales Price/Cash flow All relative valuation models rely on the market to be fairly valued. What is a good Price/Sales ratio? Relies on comparisons which may or may not be valued accurately.
- 61. 61 I leave you with the following: “When it comes to investing, the rear- view mirror is always a lot clearer than the windshield.” Warren Buffett

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