6-1

6-2 Key Concepts and Skills Know the important bond features and bond types Understand: –Bond values and why they fluctuate –Bond ratings and what they mean –The impact of inflation on interest rates –The term structure of interest rates and the determinants of bond yields

6-3 Bond Definitions Bond –Debt contract –Interest-only loan Par value (face value) ~ $1,000 Coupon rate Coupon payment Maturity date Yield to maturity

6-4 Key Features of a Bond Par value: –Face amount –Re-paid at maturity –Assume $1,000 for corporate bonds Coupon interest rate: –Stated interest rate –Usually = YTM at issue –Multiply by par value to get coupon payment

6-5 Key Features of a Bond Maturity: –Years until bond must be repaid Yield to maturity (YTM): –The market required rate of return for bonds of similar risk and maturity –The discount rate used to value a bond –Return if bond held to maturity –Usually = coupon rate at issue –Quoted as an APR

6-6 Bond Value Bond Value = PV(coupons) + PV(par) Bond Value = PV(annuity) + PV(lump sum) Remember: –As interest rates increase present values decrease ( r  → PV  ) –As interest rates increase, bond prices decrease and vice versa

6-7 Spreadsheet Formulas =FV(Rate,Nper,Pmt,PV,0/1) =PV(Rate,Nper,Pmt,FV,0/1) =RATE(Nper,Pmt,PV,FV,0/1) =NPER(Rate,Pmt,PV,FV,0/1) =PMT(Rate,Nper,PV,FV,0/1) Inside parens: (RATE,NPER,PMT,PV,FV,0/1) “0/1” Ordinary annuity = 0 (default) Annuity Due = 1 (must be entered)

6-8 Graphical Relationship Between Price and Yield-to-maturity Bond Price Yield-to-maturity

6-9 Bond Prices: Relationship Between Coupon and Yield Coupon rate = YTM  Price = Par Coupon rate < YTM  Price < Par –“Discount bond” … Why? Coupon rate > YTM  Price > Par –“Premium bond” … Why?

6-10 M Premium 1,000 Discount CR>YTM CR<YTM YTM = CR Bond Value ($) vs Years remaining to Maturity

6-11 Interest Rate Risk Price Risk –Change in price due to changes in interest rates –Long-term bonds have more price risk than short-term bonds –Low coupon rate bonds have more price risk than high coupon rate bonds

6-12 Interest Rate Risk Reinvestment Rate Risk –Uncertainty concerning rates at which cash flows can be reinvested –Short-term bonds have more reinvestment rate risk than long-term bonds –High coupon rate bonds have more reinvestment rate risk than low coupon rate bonds

6-13 Figure 6.2

6-14 Computing Yield-to-Maturity YTM Yield-to-maturity (YTM) = the market required rate of return implied by the current bond price With a financial calculator, –Enter,,., /, and 0 –Remember the sign convention / and 0 need to have the same sign (+). the opposite sign (-) %-

6-15 YTM with Annual Coupons Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $ –Will the yield be more or less than 10%? 15n pv (- for fin calc) 1000fv 100pmt I 11%  Result = YTM Using Excel: =RATE(15, 100, , 1000, 0)

6-16 Table 6.1

6-17 Debt versus Equity Debt –Not an ownership interest –No voting rights –Interest is tax-deductible –Creditors have legal recourse if interest or principal payments are missed –Excess debt can lead to financial distress and bankruptcy Equity –Ownership interest –Common stockholders vote to elect the board of directors and on other issues –Dividends are not tax deductible –Dividends are not a liability of the firm until declared. Stockholders have no legal recourse if dividends are not declared –An all-equity firm cannot go bankrupt

6-18 The Bond Indenture “Deed of Trust” Contract between issuing company and bondholders includes: –Basic terms of the bonds –Total amount of bonds issued –Secured versus Unsecured –Sinking fund provisions –Call provisions Deferred call Call premium –Details of protective covenants Return to Quiz

6-19 Bond Ratings – Investment Quality High Grade –Moody’s Aaa and S&P AAA – capacity to pay is extremely strong –Moody’s Aa and S&P AA – capacity to pay is very strong Medium Grade –Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstances –Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay Return to Quiz

6-20 Bond Ratings - Speculative Low Grade –Moody’s Ba, B, Caa and Ca –S&P BB, B, CCC, CC –Considered speculative with respect to capacity to pay. The “B” ratings are the lowest degree of speculation. Very Low Grade –Moody’s C and S&P C – income bonds with no interest being paid –Moody’s D and S&P D – in default with principal and interest in arrears

6-21 Government Bonds Treasury Securities = Federal government debt –Treasury Bills (T-bills) Pure discount bonds Original maturity of one year or less –Treasury notes Coupon debt Original maturity between one and ten years –Treasury bonds Coupon debt Original maturity greater than ten years

6-22 Zero Coupon Bonds Make no periodic interest payments (coupon rate = 0%) Entire yield-to-maturity comes from the difference between the purchase price and the par value (capital gains) Cannot sell for more than par value Sometimes called zeroes, or deep discount bonds Treasury Bills and U.S. Savings bonds are good examples of zeroes

6-23 Floating Rate Bonds Coupon rate floats depending on some index value Examples – adjustable rate mortgages and inflation-linked Treasuries Less price risk with floating rate bonds –Coupon floats, so is less likely to differ substantially from the yield-to-maturity Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

6-24 Bond Markets Primarily over-the-counter transactions with dealers connected electronically Extremely large number of bond issues, but generally low daily volume in single issues Getting up-to-date prices difficult, particularly on small company or municipal issues Treasury securities are an exception

6-25 Inflation and Interest Rates Real rate of interest =Change in purchasing power Nominal rate of interest = Quoted rate of interest, = Change in purchasing power and inflation The ex ante nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation

6-26 The Fisher Effect The Fisher Effect defines the relationship between real rates, nominal rates and inflation (1 + R) = (1 + r)(1 + h) R = nominal rate (Quoted rate) r = real rate h = expected inflation rate Approximation: R = r + h Return to Quiz

6-27 Example 6.6 If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? –R = (1.1)(1.08) – 1 =.188 = 18.8% –Approximation: R = 10% + 8% = 18% –Because the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation.

6-28 Term Structure of Interest Rates Term structure: The relationship between time to maturity and yields, all else equal –The effect of default risk, different coupons, etc. has been removed. Yield curve: Graphical representation of the term structure –Normal = upward-sloping  L/T > S/T –Inverted = downward-sloping  L/T < S/T Return to Quiz

6-29 Figure 6.5 A – Upward-Sloping Yield Curve REPLACE with FIGURE 6.5 A

6-30 Figure 6.5 B – Downward- Sloping Yield Curve

6-31 Figure 6.6 – Treasury Yield Curve

6-32 Factors Affecting Required Return Default risk premium – bond ratings Taxability premium – municipal versus taxable Liquidity premium – bonds that have more frequent trading will generally have lower required returns Maturity premium – longer term bonds will tend to have higher required returns. Anything else that affects the risk of the cash flows to the bondholders will affect the required returns Return to Quiz

7-33 Key Concepts and Skills Understand how stock prices depend on future dividends and dividend growth Be able to compute stock prices using the dividend growth model Understand how corporate directors are elected Understand how stock markets work Understand how stock prices are quoted

7-34 Cash Flows for Stockholders If you own a share of stock, you can receive cash in two ways –The company pays dividends –You sell your shares, either to another investor in the market or back to the company As with bonds, the price of the stock is the present value of these expected cash flows –Dividends → cash income –Selling → capital gains

7-35 One Period Example Suppose you are thinking of purchasing the stock of Moore Oil, Inc. –You expect it to pay a $2 dividend in one year –You believe you can sell the stock for $14 at that time. –You require a return of 20% on investments of this risk –What is the maximum you would be willing to pay?

7-36 One Period Example D 1 = $2 dividend expected in one year R = 20% P 1 = $14 CF 1 = $2 + $14 = $16 Compute the PV of the expected cash flows

7-37 Two Period Example What if you decide to hold the stock for two years? –D 1 = $2.00CF 1 = $2.00 –D 2 = $2.10 –P 2 = $14.70 –Now how much would you be willing to pay? CF 2 = $ $14.70 = $16.80

7-38 Three Period Example What if you decide to hold the stock for three years? –D 1 = $2.00 CF 1 = $2.00 –D 2 = $2.10 CF 2 = $2.10 –D 3 = $2.205 –P 3 = $ –Now how much would you be willing to pay? CF 3 = $ $ = $17.640

7-39 Developing The Model You could continue to push back when you would sell the stock You would find that the price of the stock is really just the present value of all expected future dividends

7-40 Stock Value = PV of Dividends P 0 = ^ (1+R) 1 (1+R) 2 (1+R) 3 (1+R) ∞ D 1 D 2 D 3 D ∞ + ++…+ How can we estimate all future dividend payments?

7-41 Estimating Dividends Special Cases Constant dividend/Zero Growth –Firm will pay a constant dividend forever –Like preferred stock –Price is computed using the perpetuity formula Constant dividend growth –Firm will increase the dividend by a constant percent every period Supernormal growth –Dividend growth is not consistent initially, but settles down to constant growth eventually

7-42 Zero Growth Dividends expected at regular intervals forever = perpetuity P 0 = D / R Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?

7-43 Constant Growth Stock D 1 = D 0 (1+g) 1 D 2 = D 0 (1+g) 2 D t = D t (1+g) t One whose dividends are expected to grow forever at a constant rate, g. D 0 = Dividend JUST PAID D 1 – D t = Expected dividends

7-44 Projected Dividends D 0 = $2.00 and constant g = 6% D 1 = D 0 (1+g) = 2(1.06) = $2.12 D 2 = D 1 (1+g) = 2.12(1.06) = $ D 3 = D 2 (1+g) = (1.06) = $2.3820

7-45 P 0 = ^D 0 (1+g) R - g = D1D1 Dividend Growth Model “Gordon Growth Model”

7-46 DGM – Example 1 Suppose Big D, Inc. just paid a dividend of $.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for? D 0 = $0.50 g = 2% R = 15%

7-47 Constant Growth Model Conditions 1.Dividend expected to grow at g forever 2.Stock price expected to grow at g forever 3.Expected dividend yield is constant 4.Expected capital gains yield is constant and equal to g 5.Expected total return, R, must be > g 6.Expected total return (R): = expected dividend yield (DY) + expected growth rate (g) = dividend yield + g

7-48 Nonconstant Growth Suppose a firm is expected to increase dividends by 20% in one year and by 15% in two years. After that dividends will increase at a rate of 5% per year indefinitely. If the last dividend was $1 and the required return is 20%, what is the price of the stock? Remember that we have to find the PV of all expected future dividends.

7-49 Nonconstant Growth – Solution Compute the dividends until growth levels off –D 1 = 1(1.2) = $1.20 –D 2 = 1.20(1.15) = $1.38 –D 3 = 1.38(1.05) = $1.449 Find the expected future price at the beginning of the constant growth period: –P 2 = D 3 / (R – g) = / ( ) = 9.66 Find the present value of the expected future cash flows –P 0 = 1.20 / (1.2) + ( ) / (1.2) 2 = 8.67

7-50 Nonconstant + Constant growth Basic PV of all Future Dividends Formula Dividend Growth Model

7-51 Nonconstant + Constant growth

7-52 Using the DGM to Find R Start with the DGM : Rearrange and solve for R:

7-53 Finding the Required Return Example A firm’s stock is selling for $ They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?

7-54 Finding the Required Return Example P 0 = $ D 0 = $1 g = 5% per year. What is the required return?

7-55 Finding the Required Return Example P 0 = $10.50 D 0 = $1 g = 5% per year What is the dividend yield? 1(1.05) / = 10% What is the capital gains yield? g =5% Dividend Capital Gains Yield Yield

7-56 Table 7.1

7-57 Features of Common Stock Voting Rights –Stockholders elect directors –Cumulative voting vs. Straight voting –Proxy voting Classes of stock –Founders’ shares –Class A and Class B shares Return to Quick Quiz

7-58 Features of Common Stock Other Rights –Share proportionally in declared dividends –Share proportionally in remaining assets during liquidation –Preemptive right Right of first refusal to buy new stock issue to maintain proportional ownership if desired Return to Quick Quiz

7-59 Dividend Characteristics Dividends are not a liability of the firm until declared by the Board of Directors –A firm cannot go bankrupt for not declaring dividends Dividends and Taxes –Dividends are not tax deductible for firm –Taxed as ordinary income for individuals –Dividends received by corporations have a minimum 70% exclusion from taxable income