1. Investment Valuations Value of Investment = PV of expected future CFs Factors affecting value –Cash Flows Amount (size) and timing –Discount Rate Risk of investment

2. Cash Flows of A Bond Face (Par) Value –At maturity Coupons –At pre-set coupon payment dates 0 1 2 3 N |------|-----|-----|-----|semi-annual C C C C+Face value

3. Bond Rates and Yields Coupon rate –Used for computing coupon payments –Coupon payment = Face value * coupon rate per period Yield-to-Maturity (YTM) –Market interest rate –Used for computing bond value (price) or –Inferred from current market price Current yield –Current yield = Annual coupon payment / Price

4. Bond Valuation Bond value (price) = PV of CFs = PV of Coupon + PV of Par value –Coupon payments per period [PMT] –Par value [FV] –Time to maturity [N] –Discount rate (YTM) per period [I/Y] –Price (value) [PV]

5. An Example: Valuing a Bond You wish to value a bond with a 10% coupon rate per year payable semi- annually, 20 years to maturity, and a par value of $1000. The market interest rate is 10% per year. Period = semi-annual = 2 times per year –Coupon payments = 0.1 x $1000 / 2 = $50 every 6 months –Time to maturity = 20 x 2 = 40 periods –Interest rate per period = 10% (YTM) / 2 = 5% every 6 months –Par value = $1000 at maturity 0 5% 1 2 3……….40 |-----|-----|-----|-----|-----| semi-annual $50 $50 $50 ……$50+$1000 PMT 50, FV 1000, I 5%, N 40 CPT PV -1000 When Price = Par value, a bond is selling at par

6. A Discount Bond (Price < Face Value) Market interest rate increases to 12% per year –Interest rate per period = 12%/2 = 6% every 6 months All other factors remain the same 0 6% 1 2 3……….40 |-----|-----|-----|-----|-----| semi-annual $50 $50 $50 ……$50+$1000 PMT 50, FV 1000, I 6%, N 40 CPT PV -849.537 When Price < Par value, a bond is selling at a discount Price Coupon rate

7. A Premium Bond (Price > Face Value) Market interest rate decreases to 8% per year –Interest rate per period = 8%/2 = 4% every 6 months All other factors remain the same 0 4% 1 2 3……….40 |-----|-----|-----|-----|-----| semi-annual $50 $50 $50 ……$50+$1000 PMT 50, FV 1000, I 4%, N 40 CPT PV –1197.9277 When Price > Par value, a bond is selling at a premium Price > Par value  YTM < Coupon rate

8. Bond Rates and Yields: Example A bond currently sells for $932.90. It pays $35 in coupon payments every 6 months, matures in 10 years, and has a face value of $1000. What are its coupon rate, current yield, and yield to maturity (YTM)? Coupon payments per year = $35 * x = $70 Coupon rate = $70 /$1000 = 7% per year Current yield = $70 /$932.90 = 7.5% per year

9. Bond Rates and Yields: Example Computing YTM Period = semi-annual Time to maturity = 10 * 2 = 20 periods 0 1 2 3 ……… 20 |-----|-----|-----|------|-----|semi-annual $35 $35 $35 $35 + $1000 (Inflow) $932.90 (outflow) PMT 35, FV 1000, PV –932.90, N 20 CPT I 3.9934% every 6 months (x 2 = 7.9869% per year)

10. Graphical Relationship Between Price and YTM

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 Reinvestment Rate Risk –Uncertainty about future rates at which future cash flows can be reinvested –Short-term bonds have more reinvestment rate risk than long-term bonds

12. Figure 6.2

13. Bond Pricing Theorem The following statements about bond pricing are always true. 1.Bond prices and market interest rates move in opposite directions. 2.When a bond’s coupon rate = YTM, price = par value. –coupon rate > YTM  price > par value (premium bond) –coupon rate < YTM  price < par value (discount bond) 3.Longer maturity => greater % price change when interest rate (YTM) changes 4.Lower coupon rate => greater % price change when interest rate (YTM) changes

14. The Bond Indenture Contract between the company and the bondholders and includes –Basic terms Coupon rate, coupon payment dates, maturity dates, etc. –Total amount of bonds issued –May contain the following if applicable Description of property used as security Sinking fund provisions Call provisions –Protective covenants

15. Bond Ratings Bond Rating Agencies –Independent, third party –Moody’s, Standard & Poor, D&B Investment Grade (BBB or higher) Junk (BB or lower)

16. Types of Bonds Government Bonds Municipal Bonds –Tax-exempt –Comparing tax-exempt bonds and taxable bonds –After-tax yield = Taxable yield x (1 - Tax rate) Zero Coupon Bonds Floating-rate Bonds Others

17. Example: Taxable versus tax exempt bond A corporate (taxable) bond has a yield of 8% and a municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you prefer? –After-tax return on the corporate bond = 8%(1 -.4) = 4.8% –After-tax return on the municipal bond = 6% At what tax rate would you be indifferent between the two bonds? AT return on the corporate bond = AT return on the muni 8%(1 – T) = 6% T = 25%

18. Determinants of Interest Rates (Bond Yields) Real Rate –Supply and demand for money Inflation Premium: real versus nominal rates –Fisher Effect: (1 + Nominal) = (1 + real) x (1 + inflation rate) Interest Rate Risk Premium –Maturity, coupon rate, call provisions Default Risk Premium –Bond rating, security, seniority, sinking fund Taxability Premium Liquidity Premium

19. Fisher Effect Example If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? 1+ Nominal R = (1.1)(1.08) – 1 =.188 = 18.8% Interest rates observed are nominal rates. E.g. Return on T-note is 4.5%. Expected inflation rate is 3.5%. What is the implied real return? (1.045) = (1 + real rate) (1.035) Real rate = 0.00966 = 0.966%

20. Term Structure of Interest Rate (Yield curves) Relationship between time to maturity and yields All else equal, i.e. pull out the effect of default risk, different coupons, etc. Yield curve – graphical representation of the term structure –Normal (upward-sloping) long-term yields are higher than short-term yields –Inverted (downward-sloping) long-term yields are lower than short-term yields Today’s yield curve