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Because learning changes everything.® Chapter 06 Interest Rates and Bond Valuation © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.  Key...

Because learning changes everything.® Chapter 06 Interest Rates and Bond Valuation © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.  Key Concepts and Skills After studying this chapter, you should be able to: Identify important bond features and types of bonds. Describe bond values and why they fluctuate. Discuss bond ratings and what they mean. Evaluate the impact of inflation on interest rates. Explain the term structure of interest rates and the determinants of bond yields. © McGraw Hill, LLC 2  Chapter Outline 6.1 Bonds and Bond Valuation. 6.2 More on Bond Features. 6.3 Bond Ratings. 6.4 Some Different Types of Bonds. 6.5 Bond Markets. 6.6 Inflation and Interest Rates. 6.7 Determinants of Bond Yields. © McGraw Hill, LLC 3  Bond Definitions Bond. Debt contract. Interest-only loan. TERMS: Par value (face value) approximately $1,000. Coupon rate. Coupon payment. Maturity date. Yield to maturity. © McGraw Hill, LLC 4  Bond Definitions © McGraw Hill, LLC 5  Key Features of a Bond 1 Par value: Face amount. Repaid 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. © McGraw Hill, LLC 6  Key Features of a Bond 2 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 equals the coupon rate at issue. Quoted as an APR. © McGraw Hill, LLC 7  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. © McGraw Hill, LLC 8  The Bond-Pricing Equation PV(Annuity) PV(lump sum) C = Coupon payment; F = Face value Return to Quick Quiz © McGraw Hill, LLC 9  Valuing a Discount Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 5 years YTM = 11% Using the formula: B = PV(annuity) + PV(lump sum) B = $369.59 + 593.45 = $963.04 Note: When YTM > Coupon rate → Price < Par = “Discount Bond” © McGraw Hill, LLC 10  Valuing a Premium Bond with Annual Coupons Coupon rate = 10% Annual coupons Par = $1,000 Maturity = 20 years YTM = 8% Using the formula: B = PV(annuity) + PV(lump sum) B = $981.81 + 214.55 = $1196.36 Note: When YTM < Coupon rate → Price > Par = “Premium Bond” © McGraw Hill, LLC 11  Bond Prices: Relationship Between Coupon and Yield Coupon rate = YTM → Price = Par. If the bond's coupon rate is the same as the yield to maturity (YTM), the bond's price is equal to its face value (also called par value). Coupon rate < YTM → Price < Par = Discount Bond If the bond's coupon rate is lower than the YTM, the bond's price will be less than its par value. This happens because investors want a higher return, so they pay less for the bond. Coupon rate > YTM → Price > Par = Premium Bond If the bond's coupon rate is higher than the YTM, the bond's price will be more than its par value. This is because the bond pays more interest than what the market typically expects. © McGraw Hill, LLC 12  The Bond-Pricing Equation Adjusted for Semiannual Coupons C = Annual coupon payment → C ÷ 2 = Semiannual coupon r = Annual yield → r ÷ 2 = Semiannual yield t = Years to maturity → 2t = Number of 6-month periods to maturity © McGraw Hill, LLC 13  Semiannual Bonds Example 6.1 Coupon rate = 14 percent semiannually. r = 16 percent. Maturity = 7 years Number of coupon payments? (2t or N). 14 = 2 × 7 years. Semiannual coupon payment? Semiannual yield? © McGraw Hill, LLC 14  Example 6.1 Semiannual coupon = $70. Semiannual yield = 8%. Periods to maturity = 14. Bond value = © McGraw Hill, LLC 15  Interest Rate Risk 1 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. © McGraw Hill, LLC 16  Interest Rate Risk 2 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. © McGraw Hill, LLC 17  Computing Yield-to-Maturity (YTM) ***Unfortunately, solving for YTM directly in this equation analytically is quite complex. The equation is generally solved using financial calculator Yield-to-maturity (YTM): Market required rate of return implied by the current bond price. With a financial calculator: Enter N, PV, PMT, and FV. Remember the sign convention. PMT and FV need to have the same sign (+). PV the opposite sign (−). CPT I/Y for the yield. © McGraw Hill, LLC 18  YTM with Annual Coupons Consider a bond with a 10 percent annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09. Will the yield be more or less than 10 percent? 15 N 928.09 PV (enter as a negative) 1000 FV 100 PMT CPT PV = 11% ← Result = YTM © McGraw Hill, LLC 19  Table 6.1 1 Table 6.1 Summary of Bond Valuation I. Finding the value of a bond Bond value where: C = Coupon paid each period r = Rate per period t = Number of periods F = Bond’s face value © McGraw Hill, LLC 20  Debt or Equity Debt. Equity. Not an ownership interest. Ownership interest. No voting rights. Common stockholders vote to Interest is tax deductible. elect the board of directors and on other issues. Creditors have legal recourse if interest or Dividends are not tax deductible. principal payments are Dividends are not a liability of the missed. firm until declared. Stockholders have no legal recourse if Excess debt can lead to financial distress and dividends are not declared. bankruptcy. An all-equity firm cannot go bankrupt. © McGraw Hill, LLC 21  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…Cont’d Deferred call. Call premium. Details of protective covenants. Return to Quiz © McGraw Hill, LLC 22  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 © McGraw Hill, LLC 23  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. © McGraw Hill, LLC 24  6.4 Types of Bonds a) Government Bonds : Municipal Securities. Treasury Securities = Federal government debt. Treasury notes. Treasury Bills (T-bills). b) Zero Coupon Bond c) Floating Rates Bond d) Other Bond Types Structured notes. Convertible bonds. Put bonds. © McGraw Hill, LLC 25  Government Bonds 1 Municipal Securities. Debt of state and local governments. Varying degrees of default risk, rated similar to corporate debt. Interest received is tax-exempt at the federal level. Interest usually exempt from state tax in issuing state. © McGraw Hill, LLC 26  Government Bonds 2 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. © McGraw Hill, LLC 27  Example 6.4 A taxable bond has a yield of 8 percent and a municipal bond has a yield of 6 percent. If you are in a 40 percent tax bracket, which bond do you prefer? 8%(1 −.4) = 4.8%. The aftertax return on the corporate bond is 4.8 percent, compared to a 6 percent return on the municipal. At what tax rate would you be indifferent between the two bonds? 8%(1 − t*) = 6%. t* = 25%. © McGraw Hill, LLC 28  Zero Coupon Bonds Make no periodic interest payments (coupon rate = 0 percent). 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. © McGraw Hill, LLC 29  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.” © McGraw Hill, LLC 30  d) Other Bond Types Structured notes. Convertible bonds. Put bonds. Many types of provisions can be added to a bond. Important to recognize how these provisions affect required returns. Who does the provision benefit? © McGraw Hill, LLC 31  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. © McGraw Hill, LLC 32  6.6 Inflation and Interest Rates a) Real rate of interest. Price you actually pay after a discount or increase due to inflation. In the world of bonds, it’s the actual earning power of your interest after considering inflation. Example: If you have a bond paying 5% (nominal rate) in a year when inflation is 3%, your real rate is actually only about 2%, because the value of the money you get is less due to inflation. = Change in purchasing power. © McGraw Hill, LLC 33  6.6 Inflation and Interest Rates b) Nominal rate of interest. The nominal rate is like the sticker price on an item in a store—it's what you see first. For bonds, it's the interest rate stated on the bond, not taking into account any other factors like inflation. Example: If a bond says it'll pay you 5% each year, that's the nominal rate. = 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. © McGraw Hill, LLC 34  The Fisher Effect The Fisher effect defines the relationship between real rates, nominal rates and Inflation. R = Nominal rate (Quoted rate). r = Real rate. h = Expected inflation rate. Approximation: R = r + h. Return to Quiz © McGraw Hill, LLC 35  Example 6.6 If we require a 10 percent real return and we expect inflation to be 8 percent, what is the nominal rate? R = (1.1)(1.08) − 1 =.1880, or 18.80%. 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. © McGraw Hill, LLC 36  Factors Effecting 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 © McGraw Hill, LLC 37  Quick Quiz How do you find the value of a bond and why do bond prices change? (Slide 6.8). What is a bond indenture and what are some of the important features? (Slide 6.31). What are bond ratings and why are they important? (Slide 6.34). How does inflation affect interest rates? (Slide 6.51). What is the term structure of interest rates? (Slide 6.53). What factors determine the required return on bonds? (Slide 6.57). © McGraw Hill, LLC 38  End of Main Content Because learning changes everything.® www.mheducation.com © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.