Bond Prices and Yields

Objectives: 1.Analyze the relationship between bond prices and bond yields. 2.Calculate how bond prices will change over time for a given interest-rate projection. 3.Identify the determinants of bond safety and rating. 4.Analyze how callable, convertible, and sinking fund provisions will affect a bond's equilibrium yield to maturity. 5.Define the yield curve and study its properties

 Long-term debt contract  Fixed interest payment is paid throughout the life of bond  Entire principal payment is paid at maturity date  Coupon rate: determines the fixed interest payment  Yield to maturity: the average return per year that the investors (or the market) require on the bond if they buy and hold the bond until maturity  Coupon rate is fixed, determined by the issuing firm  YTM can fluctuate, depending on the investors in the market  Zero-coupon bond ◦ zero coupon payment ◦ par at maturity date

 T Note maturities range up to 10 years  T bond maturities range from 10 – 30 years  Bid and ask price ◦ Quoted in points and as a percent of par  Accrued interest ◦ Quoted price does not include interest accrued  Example: if the coupon payments are made on May 1 and Nov 1, you buy a bond on June 11. Assume the price on June 11 is 990, how much you have to pay in order to buy the bond. (assume there are 40 days from May 1-June 11

 Most bonds are traded over the counter  Registered  Bearer bonds  Secured and unsecured ◦ Secured:  Collateral  Mortgage ◦ Unsecured  Debentures  Notes  Call provisions: allows issuer to buy back bond before maturity date at a specific call price ◦ Why the company wants to call the bond? ◦ Call provision is in favor of the issuer. So if everything else is the same, callable bond would have to give higher yield, higher coupon to investors than regular bonds

 Convertible bond: a bond with option allowing the bondholder to exchange the bond for a specific number of shares of common stock in the firm ◦ When bondholder want to convert bond into stocks?  Puttable bond: gives the option to bondholder to either exchange the bond for par value at some date or to extend for a given number of year ◦ When bondholders want to exchange for par value before maturity ◦ When bondholders want to extend the bond for a given number of year after maturity  Floating rate bond ◦ coupon rate is tied to current market rates  Preferred stocks

 Federal Home Loan Bank Board  Farm Credit Agencies  Ginnie Mae  Fannie Mae  Freddie Mac

 Reverse floaters ◦ Reverse of floating rate bond  Asset-backed bonds ◦ backed by assets of the firm  Pay-in-kind bonds ◦ issuers may choose to pay interest either in cash or in additional bon  Catastrophe bonds ◦ issued by insurance company, give high yield ◦ In the event of catastrophe, the obligation to pay interest and principal can be delayed or forgiven  Indexed bonds ◦ payments are tied to a general price index or price of a particular commodity ◦ TIPS (Treasury Inflation Protected Securities)

Table 14.1 Principal and Interest Payments for a Treasury Inflation Protected Security TIPS: adjust for inflation Example: n = 3 years, annual coupon, par 1000, coupon 4%

Price of bond = present value of all future coupon payments + present value of the par value P B =Price of the bond C t = interest or coupon payments T = number of periods to maturity r = semi-annual discount rate or the semi-annual yield to maturity P C r Par Value r B t T t T T T      () () 1 1 1

1) 8% coupon, pay annually, 10 years to maturity, par = 1000, YTM = 6% Using formula Using calculator PMT = 80, FV = 1000, n = 10, I/Y = 6 2) The same information, but the bond is paying interest semi- annually. What is the price of the bond?

Yield to maturity is a measure of the average rate of return that will be earned if the bond is held to maturity. YTM is the discount rate that makes the present value of a bond’s payments equal to its price YTM is the solution of : 8% coupon, 30-year bond selling at $1,276.76, what is the yield to maturity?

 Prices and Yields (required rates of return) have an inverse relationship  If YTM increase, then the price decreases and vice versa Market Maturity CouponInterest Bond Value Rate Rate Price $ 1,000 8% 8%$1, $ 1,000 8% 10%$ $ 1,000 8% 6%$1,276.75

rdrd 1-yearChange10-yearChange 5%$1,048$1,386 10%1, % 1, % 15% % % Interest rate risk: change in r d causes bond’s price to change. Bond Prices and Yields Longer time to maturity, higher change in price when interest rate changes (or higher interest rate risk)

,000 1,500 0%5%10%15% 1-year 10-year rdrd Value Bond Prices and Yields

 Yield to Call ◦ Call price replaces par ◦ Call date replaces maturity ◦ Example: 8% coupon, semi-annual, 30 years to maturity, current price = 1150, callable in 10 years, call price = What is the yield to call and yield to maturity

Where P t = Bond Price at time t P t+1 = Bond Price at time t+1

Current yield = Capital gains yield = = YTM = + Annual coupon pmt Current price Change in price Beginning price Expected total return Expected Curr yld Expected cap gains yld

Current yield= = = 10.15%. $90 $887

YTM= Current yield + Capital gains yield. Cap gains yield = YTM - Current yield = 10.91% % = 0.76%. Could also find values in Years 1 and 2, get difference, and divide by value in Year 1. Same answer.

BOND PRICES OVER TIME

 Premium Bond ◦ price > par ◦ Coupon rate exceeds yield to maturity ◦ Bond price will decline to par over its maturity  Discount Bond ◦ price < par ◦ Yield to maturity exceeds coupon rate ◦ Bond price will increase to par over its maturity  Bond selling at par ◦ price = par ◦ Yield to maturity = coupon rate ◦ bond price is constant throughout the life of bond

BOND PRICES OVER TIME

M Bond Value ($) Years remaining to Maturity 1,372 1,211 1, r d = 7%. r d = 13%. r d = 10%.

 At maturity, the value of any bond must equal its par value.  The value of a premium bond would decrease to $1,000.  The value of a discount bond would increase to $1,000.  A par bond stays at $1,000 if r d (YTM) remains constant. BOND PRICES OVER TIME

DEFAULT RISK AND BOND PRICING

 Rating companies ◦ Moody’s Investor Service ◦ Standard & Poor’s ◦ Fitch  Rating Categories ◦ Investment grade ◦ Speculative grade

Investment GradeJunk Bonds Moody’s AaaAaABaaBaBCaaC S&P AAAAAABBBBBBCCCD

 Coverage ratios  Leverage ratios  Liquidity ratios  Profitability ratios  Cash flow to debt

Table 14.3 Financial Ratios and Default Risk by Rating Class, Long- Term Debt

 Sinking funds ◦ A bond that calls for the issuer to periodically repurchase some proportion of the outstanding bonds prior to maturity  Subordination of future debt ◦ Restrictions on additional borrowing that stipulates that senior bondholders will be paid first in the event of bankruptcy  Dividend restrictions ◦ Limit dividend payout to protect bondholders  Collateral ◦ Uses assets to back up bonds: mortgage bond, collateral trust bond, equipment obligation bond. ◦ Collaterals are secured bonds ◦ Unsecured bond: debentures

Figure Callable Bond Issued by Mobil

Default Risk and Yield  Risk structure of interest rates  Default premiums ◦ Yields compared to ratings ◦ Yield spreads over business cycles

Figure Yields on Long-Term Bonds, 1954 – 2006

Inverse relationship between bond prices and bond yields Premium and discount bonds Corporate bonds and default risk Next Class: Managing Bond Portfolios