Comm 324 – W. suo Slide 1

Comm 324 – W. suo Slide 2  Face or par value  Coupon rate Zero coupon bond  Compounding and payments  Indenture  Issuers Bond Characteristics

Comm 324 – W. suo Slide 3  Secured or unsecured  Registered or bearer bonds (Canada)  Call provision  Convertible provision  Retractable and extendible (putable) bonds  Floating rate bond Provisions of Bonds

Comm 324 – W. suo Slide 4 P B =price of the bond C t = interest or coupon payments T = number of periods to maturity r = the appropriate semi-annual discount rate  Quoted price vs Cash Price (or “dirty price”) Accrued interest, day-count convention Bond Pricing

Comm 324 – W. suo Slide 5 C t = 40 (SA) P= 1000 T= 60 periods r= 5% (SA) P B = $ Solving for Price: 10-yr, 8% Coupon Bond, FV = $1,000

Comm 324 – W. suo Slide 6 Yields  Yield to maturity  Yield to first call  Bond Equivalent Yield  Effective Annual Yield  Current Yield (Annual Interest/Market Price)

Comm 324 – W. suo Slide 7 Yield to Maturity Example 10 yr MaturityCoupon Rate = 7% Price = $950 Solve for r = semiannual rate r = %

Comm 324 – W. suo Slide 8 Yield Measures Bond Equivalent Yield 3.86% x 2 = 7.72% Effective Annual Yield (1.0386) = 7.88% Current Yield (Annual Interest/Market Price) $70 / $950 = 7.37 %

Comm 324 – W. suo Slide 9 Realized Yield versus YTM  Reinvestment Assumptions  Holding Period Return Changes in rates affects returns Reinvestment of coupon payments Change in price of the bond

Comm 324 – W. suo Slide 10 Holding-Period Return: Single Period where I = interest payment P 1 = price in one period P 0 = purchase price

Comm 324 – W. suo Slide 11 Holding-Period Example CR = 8% ; YTM = 8%; N=10 years Semiannual Compounding P 0 = $1000 In 6M the rate falls to 7%; P 1 =$ HPR = 10.85% (semiannual)

Comm 324 – W. suo Slide 12 Realized Compound Yield vs. YTM  Requires actual calculation of reinvestment income  Solve for the Internal Rate of Return using the following: Future Value: sale price + future value of coupons Investment: purchase price

Comm 324 – W. suo Slide 13 Example  Two-year bond selling at par, 10% coupon paid once a year. First coupon is reinvested at 8%. Then:

Comm 324 – W. suo Slide 14 Price Paths of Coupon Bonds Price 1,000 Maturity date 0 Discount bond Time Premium bond

Comm 324 – W. suo Slide 15 Zero-Coupon Bonds and Taxation Issues  For constant yields, discount bond prices rise over time and premium bond prices decline over time  Original issue discount bonds’ price appreciation (based on constant yield) is taxed as ordinary income  Price changes stemming from yield changes are taxed as capital gains if the bond is sold

Comm 324 – W. suo Slide 16 Example: Tax  30-year bond with 4% coupon rate, issued at an 8% YTM; if sold one year later, when YTM=7%, for a 36% income tax and a 20% capital gains tax: P 0 =549.69; P 1 (8%)=553.66; P 1 (7%)=631.67

Comm 324 – W. suo Slide 17  Rating companies Moody’s Investor Service Standard & Poor’s Canadian Bond Rating Service (CBRS)  Rating Categories Investment grade Speculative grade Default Risk and Ratings

Comm 324 – W. suo Slide 18  Methods are proprietary  Accounting ratios Coverage ratios Leverage ratio Liquidity ratios Profitability ratios Cash flow to debt  Other qualitative factors Factors Used by Rating Companies

Comm 324 – W. suo Slide 19 Financial Ratios by Rating Class US Industrial LT Debt, Medians AAAABBBB EBIT interest coverage EBITDA interest coverage Funds flow/total debt (%) Free operating CF/debt (%) (4.6) Return on capital (%) Operating income/sales (%) LT debt/capital (%) Total debt/capital (%)

Comm 324 – W. suo Slide 20  Sinking funds  Subordination of future debt  Dividend restrictions  Collateral Protection Against Default

Comm 324 – W. suo Slide 21  Relationship between yield to maturity and maturity  Information on expected future short term rates can be implied from yield curve  The yield curve is a graph that displays the relationship between yield and maturity  Three major theories are proposed to explain the observed yield curve Overview of Term Structure of Interest Rates

Comm 324 – W. suo Slide 22 Important Terms  Bond yields  Spot rates  Forward rates  Yield curve  Term structure or pure yield curve  Structure of forward rates  Using observed rates to predict future rates

Comm 324 – W. suo Slide 23 Yields Maturity Upward Sloping Downward Sloping Flat Yield Curves

Comm 324 – W. suo Slide 24 Measuring the term structure - The bootstrapping method  Derive spot rates from bond yields of varying maturities  Treat each coupon as a mini-zero coupon bond  Use bonds of progressively longer maturities, starting from T-bills  “Clean price” method and “dirty price” method

Comm 324 – W. suo Slide 25 Building zero curve: Boot-strapping  Example: T-bills: 6 month with yield of 4%; One year with yield of 5%  18 month 5% coupon bond traded at $990  2 year 6% coupon bond traded at par This implies y1=2%, y2=5%, y3=2.8664%, y4=3.02% Spot rate: %5%5.81%6.13%

Comm 324 – W. suo Slide 26 Example  Observe prices and yields on August 17, 2004; find the spot rate for December 1, 2005  Observed yields: 3.90%, 4.04% for 6M and 12M, respectively  Observed clean price for 6% bond expiring on December 1, 2005: $  Dirty price = clean price + (time elapsed in semesters) x coupon

Comm 324 – W. suo Slide 27 Bootstrapping example (cont.)  Solving, we find y 3 =2.08%, or 4.16% annually

Comm 324 – W. suo Slide 28 Using Spot Rates to price Coupon Bonds  A coupon bond can be viewed as a series of zero coupon bonds  To find the value, each payment is discounted at the zero coupon rate  Once the bond value is found, one can solve for the yield  It’s the reason for which similar maturity and default risk bonds sell at different yields to maturity

Comm 324 – W. suo Slide 29 Sample Bonds Assuming annual compounding AB Maturity4 years Coupon Rate6%8% Par Value1,000 Cash flow in Cash flow in 41,0601,080

Comm 324 – W. suo Slide 30 Calculation of Price Using Spot Rates (Bond A) PeriodSpot RateCash FlowPV of Cash Flow , Total978.54

Comm 324 – W. suo Slide 31 Calculation of Price Using Spot Rates (Bond B) PeriodSpot RateCash FlowPV of Cash Flow , Total1,047.56

Comm 324 – W. suo Slide 32 Solving for the YTM Bond A  Bond Price =  YTM = 6.63% Bond B  Price = 1,  YTM = 6.61%