Session S 5 & 6

1. SessionS 5 & 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

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

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

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. 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

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)

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

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?

10. Premium CR>YTM YTM= CR M 1,000 CR<YTM Discount 30 25 20 15 10 5 0 Bond Value ($) vs Years remaining to Maturity

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

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

13. Figure 6.2

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 (-) • %-

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 $928.09. • Will the yield be more or less than 10%? 15 n 928.09pv (- forfincalc) 1000fv 100pmt I11% Result = YTM Using Excel: =RATE(15, 100, -928.09, 1000, 0)

16. Table 6.1

17. 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 Debt versus Equity

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

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

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

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

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

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”

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

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

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

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.

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

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

30. Figure 6.5 B – Downward-Sloping Yield Curve

31. Figure 6.6 – Treasury Yield Curve

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

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

34. Cash Flows for Stockholders • If you own a share of stock, you canreceive cash in two ways • The company pays dividends • You sellyour 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

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?

36. One Period Example • D1 = $2 dividend expected in one year • R = 20% • P1 = $14 • CF1 = $2 + $14 = $16 • Compute the PV of the expected cash flows

37. Two Period Example • What if you decide to hold the stock for two years? • D1 = $2.00 CF1 = $2.00 • D2 = $2.10 • P2 = $14.70 • Now how much would you be willing to pay? CF2 = $2.10 + $14.70 = $16.80

38. Three Period Example • What if you decide to hold the stock for three years? • D1 = $2.00 CF1 = $2.00 • D2 = $2.10 CF2 = $2.10 • D3 = $2.205 • P3 = $15.435 • Now how much would you be willing to pay? CF3 = $2.205 + $15.435 = $17.640

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

40. ^ D1 D2 D3 D∞ P0 = + +…+ + (1+R)1 (1+R)2 (1+R)3 (1+R)∞ Stock Value = PV of Dividends How can we estimate all future dividend payments?

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

42. Zero Growth • Dividends expected at regular intervals forever = perpetuity P0 = 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?

43. Constant Growth Stock One whose dividends are expected to grow forever at a constant rate, g. D1 = D0(1+g)1 D2 = D0(1+g)2 Dt = Dt(1+g)t D0 = Dividend JUST PAID D1 – Dt = Expected dividends

44. Projected Dividends • D0 = $2.00 and constant g = 6% • D1 = D0(1+g) = 2(1.06) = $2.12 • D2 = D1(1+g) = 2.12(1.06) = $2.2472 • D3 = D2(1+g) = 2.2472(1.06) = $2.3820

45. ^ D0(1+g) D1 P0 = = R - g R - g Dividend Growth Model “Gordon Growth Model”

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? • D0= $0.50 • g = 2% • R = 15%

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

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.

49. Nonconstant Growth – Solution • Compute the dividends until growth levels off • D1 = 1(1.2) = $1.20 • D2 = 1.20(1.15) = $1.38 • D3 = 1.38(1.05) = $1.449 • Find the expected future price at the beginning of the constant growth period: • P2 = D3 / (R – g) = 1.449 / (.2 - .05) = 9.66 • Find the present value of the expected future cash flows • P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67

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