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Bond Valuation Chapter 8, 9 Stock and Bond Valuation Konan Chan Corporate Finance, 2018 Bond Valuation Bond Valuation Bond pricing model Annual vs. semi-annual coupon bonds Yield-to-maturity (YTM) Credit ratings Corporate Finance Konan Chan 3 Bond Cash Flows Annual coupons coupon coupon+par 0 1 2 ……. T Value today = PV of expected cash flows Corporate Finance Konan Chan 4 Bond Characteristics Five basic variables FV : par value (or face value) - usually $1000 to be paid at maturity PMT : annual coupon = par value*coupon rate (paid periodically to bondholder) T : years to maturity r : required rate of return (discount rate) PV : PV of future cash flows (value today) Corporate Finance Konan Chan 5 Bond Pricing Example What is the price of a 6.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 3.9%. Corporate Finance Konan Chan 6 Bond Price and Interest Rate There is a negative relationship between bond price and interest rate (discount rate) If discount rate is higher (lower) than coupon rate, bond prices should be less (more) than par value Corporate Finance Konan Chan 7 Bond Price Over Time 1,080 Price path for 1,060 Premium Bond 1,040 1,020 Both premium and discount bonds 1,000 approach face value as their 980 maturity date approaches Bond Price 960 940 920 Price path for Today Maturity 900 Discount Bond 880 0 5 10 15 20 25 30 Time to Maturity Corporate Finance Konan Chan 8 Bond Cash Flows Annual coupons coupon coupon+par 0 1 2 ……. T Semi-annual coupons coupon/2 coupon/2+par 0 1 2 ……. 2T Value today = PV of expected cash flows Corporate Finance Konan Chan 9 Bond Pricing Example (continued) What is the price of the bond if the required rate of return is 3.9% and the coupons are paid semi- annually? Corporate Finance Konan Chan 10 Bond Yields Current Yield annual coupon payments divided by bond price. Yield To Maturity (YTM) interest rate for which the present value of bond equals the market price total annual expected return if you buy the bond today and hold to the maturity date Corporate Finance Konan Chan 11 Corporate Bond Corporate bond quotation (on Sep 2005) Company Coupon Maturity Last price Last yield Wal-mart 7.55 Sep 30, 2031 125.314 5.675 How to compute yield to maturity? Bond price = 1253.14 Annual coupon = 7.55%*1000 = 75.5 N = 2*26 = 52, PMT = 75.5/2 = 37.75, FV = 1000 The YTM to meet the current price is 5.676% Corporate Finance Konan Chan 12 Yield To Maturity In Excel, RATE(52,37.75,-1253.14,1000,0) Corporate Finance Konan Chan 13 Clean versus Dirty Prices Clean price: quoted price Dirty price: price actually paid = quoted price plus accrued interest Example: Buy a T-bond with annual coupon 8% Ask quote is 132.24 (i.e (132+24/32)% of face value) Number of days since last coupon = 61 Number of days in the coupon period = 184 Accrued interest = (61/184)(8%*1,000/2) = 13.26 Prices: Clean price = 1,327.50 Dirty price = 1,327.50 + 13.26 = 1,340.76 So, you would actually pay $1,340.76 for the bond. Corporate Finance Konan Chan 17 Interest Rate Risk Measures bond price sensitivity to changes in interest rates All things equal, long-term bonds have more interest rate risk than short-term bonds. All things equal, low coupon bonds also have more interest rate risk than high coupon bonds Corporate Finance Konan Chan 15 Interest Rate Risk Example Let’s compare two bonds with everything the same except the time-to-maturity (1 vs. 30 years) PVs of 10% annual coupons with r at 5%, 10%, 15%, 20%. Corporate Finance Konan Chan 16 Bond Price Sensitivity When the interest rate equals the 10% coupon rate, both bonds sell at face value Corporate Finance Konan Chan 17 Credit Rating (default risk) Credit ratings proxy for default risk, the risk that bond issuer may default on its obligations Default premium: difference between corporate bond yield and T-bond yield (assume same coupon, maturity) Bonds are generally classified into two groups Investment grade bonds: BBB and above Junk (speculative grade) bonds: below BBB Investment grade bonds are generally legal for purchase by banks; junk bonds are not Corporate Finance Konan Chan 18 Credit Rating Corporate Finance Konan Chan 19 Credit Rating and Yield, 2011 Price, % of Yield to Issuer Coupon Maturity S&P Rating Face Value Maturity Johnson & Johnson 5.15% 2017 AAA 122.88% 1.27% Walmart 5.38 2017 AA 117.99 1.74 Walt Disney 5.88 2017 A 121.00 2.07 Suntrust Banks 7.13 2017 BBB 109.76 4.04 U.S. Steel 6.05 2017 BB 97.80 6.54 American Stores 7.90 2017 B 97.50 8.49 Caesars Entertainment 5.75 2017 CCC 41.95 25.70 Corporate Finance Konan Chan 20 Yield Spread Corporate Finance Konan Chan 21 Government Bonds Treasury Securities Issued by federal government Examples: T-bills, T-notes, T-bonds No default risk Municipal Securities (munis) Issued by state or local governments Varying degrees of default risk, rated similar to corporate debt Coupons are tax-exempt at the federal level Corporate Finance Konan Chan 22 Inflation Inflation Rate at which prices as a whole are increasing. Nominal Interest Rate Rate at which money invested grows. Real Interest Rate Rate at which the purchasing power of an investment increases. Corporate Finance Konan Chan 23 Fisher Effect (Inflation) Approximation formula Corporate Finance Konan Chan 24 Corporate Bond Yield Factors Real interest Inflation Interest rate risk Default risk premium – bond ratings Taxability premium – municipal versus taxable Liquidity premium – bonds with more trading have lower yield Anything else that affects the risk of the cash flows to the bondholders, will affect the bond yield Corporate Finance Konan Chan 25 Stock Valuation Stock Valuation Dividend discount model Constant growth Zero growth Non-constant growth Expected stock return Multiple valuation Corporate Finance Konan Chan 27 Stock Valuation Dividend discount model (DDM) discount future dividends back to present where T is time horizon for your investment Corporate Finance Konan Chan 28 Stock Valuation We will assume stocks fall into 3 categories Constant growth rate in dividends Zero growth rate in dividends “Supernormal” (non-constant) growth rate in dividends Corporate Finance Konan Chan 29 Constant Growth DDM A dividend discount model where dividends are assume to grow at a constant rate forever Given any combination of variables in the equation, you can solve for the unknown variable. D0: dividend just paid (the most recent dividend) g: constant growth rate of dividends r: required rate of return for stock Corporate Finance Konan Chan 30 Constant Growth DDM D1 = D0 (1 + g) 2 D2 = D1 (1 + g) = D0 (1 + g) Using geometric series formula Corporate Finance Konan Chan 31 Constant Growth DDM - example What is the value of a stock that expects to pay a $3.00 dividend next year, and then increase the dividend at a rate of 8% per year, indefinitely? Assume a 12% expected return Corporate Finance Konan Chan 32 Same example If the same stock is selling for $100 in the stock market, what might the market assume about the growth in dividends? The market assumes the dividend will grow at 9% per year, indefinitely. Corporate Finance Konan Chan 33 Zero Growth DDM If we forecast no growth for the stock (i.e., dividends keep constant forever), the stock will become a perpetuity This is exactly the valuation for preferred stocks Corporate Finance Konan Chan 34 Preferred Stock Stated dividend that must be paid before dividends can be paid to common stockholders Dividends are not a liability of the firm and preferred dividends can be deferred indefinitely Most preferred dividends are cumulative – any missed preferred dividends have to be paid before common dividends can be paid Preferred stock generally does not carry voting rights Corporate Finance Konan Chan 35 What if CGDDM Doesn’t Apply? Any restriction on constant growth DDM? What does it mean? How to deal with it if this restriction exists? Two-stage or multiple stage of growth Corporate Finance Konan Chan 36 Non-constant Growth Model Two stages of growth assume stock has a period of non-constant growth in dividend, and then eventually settles into a normal constant growth pattern Generally, high growth in the first stage, then low growth stage in the second stage Young, start-up firms, or technology firms with new product will have high growth rates Multiple stages if necessary Corporate Finance Konan Chan 37 Non-constant Growth - Example The growth for firm A.net is expected to be 20% for next two years, and 6% thereafter. The current dividend is $1.60, and the firm’s required rate of return is 10%. What’s stock worth today? g1 = 20% g1 = 20% g = 6% Step 1 D1=$1.6(1.2)=$1.92 D2=$1.92(1.2)=$2.304 Step 2 Step 3 Corporate Finance Konan Chan 38 Sustainable Growth Rate Payout ratio Fraction of earnings paid out as dividends Plowback (retention) ratio = 1 - payout ratio Fraction of earnings retained by the firm g = return on equity (ROE) * retention ratio Steady rate at which a firm can grow This estimation of growth rate applies to stable firms only Corporate Finance Konan Chan 39 Estimate Expected Return Given constant growth dividend discount model, we can estimate stock return Expected return = expected dividend yield + growth rate Previous example: r = $3/$75 + 8% = 12% Corporate Finance Konan Chan 40 Components of Expected Return Expected Return r = total income/ purchase price r = [dividend income + capital gain (or loss)]/price r = expected dividend yield + capital gain yield = D1/ P0 + (P1 –P0) / P0 Corporate Finance Konan Chan 41 Growth in Constant Growth DDM P1 / P0 = 1 + g (i.e., the firm will grow constantly) Corporate Finance Konan Chan 42 Chapter 10, 11 Risk and Return Konan Chan Corporate Finance, 2018 Risk and Return Return measures Expected return and risk? Portfolio risk and diversification CAPM (Capital Asset Pricing Model) Beta Calculating Return - Single period Holding period return (HPR) This assumes we only have one investment period.
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