Chapter 10 Bond Prices and Yields Copyright © 2010 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin
Bond Characteristics Security that obligates issuer to make payments to holder over time Face or par value Coupon rate –Zero coupon bond Indenture 10-2
Treasury Notes and Bonds T Note maturities range up to 10 years T bond maturities range from 10 to 30 years Bid and ask price –Quoted in dollars and 32nds as a percent of par –Typical par = $1,000 Accrued interest –Quoted price does not include interest accrued 10-3
Prices and Yields of U.S. Treasuries 10-4
Corporate Bonds & Debt Most bonds are traded over the counter Registered versus Bearer bonds Call provisions Convertible provision Put provision (putable bonds) Floating rate bonds 10-5
Listing of Corporate Bonds 10-6
Innovations in the Bond Market Inverse floaters –Coupon rate falls when interest rates rise & vice versa Asset-backed bonds –Income from specified assets is used to service the bond Pay-in-kind bonds –Bond issuer may choose to pay interest by giving the investor a bond rather than cash 10-7
Innovations in the Bond Market Catastrophe bonds –In the event of a specified ‘disaster’ the bond issuer’s required payments are reduced or eliminated. Indexed bonds –Payments are tied to a price index or the price of a commodity. TIPS (Treasury Inflation Protected Securities) With TIPS the par value of the bond increases with the Consumer Price Index. 10-8
Principal and Interest Payments on TIPS 10-9
10.2 BOND PRICING 10-10
Bond Prices & Yields a)Bond Price: Coupon (PMT) = 10% Interest rate, yield (I) = 12% Maturity (N) = 10 years, Par = $1, Bond Value ?PV of Coupons$100$ PV of Facevalue$1,000$ TOTAL:$ Semi-Annual Coupons: 1. I = annual coupon/2 =$50 2. n = years to maturity 10x2 =20 3. i d = annual interest rate/2 =6.00% Value of the Bond =$885.30
Bond Pricing Between Coupon Dates If the bond buyer purchases a bond between payment dates the buyer’s invoice price = flat price + accrued interest
Bond Pricing Between Coupon Dates A bond has a flat price of $ and an annual coupon of $ days have passed since the last coupon payment and there are 182 days separating the coupon payments. What is the bond’s invoice price? 10-13
10.3 BOND YIELDS 10-14
Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship When yields get very high the value of the bond will be very low When yields approach zero, the value of the bond approaches the sum of the cash flows 10-15
Yield to Maturity: The rate of return expected on a bond if it is held to maturity. Bond sells for: $1,080.00What is the YTM ? V = I*PVIFA k,n + M*PVIF k,n n=10PMT =$100 If k =9%Value =$1, If k =8%Value =$1, Approximate YTM =I + (M - V)/n (M + V)/2 = 8.85% 3. Using Excel function, Rate, YTM =8.77%
The Inverse Relationship Between Bond Prices and Yields 10-17
Alternative Measures of Yield Current Yield –Annual dollar coupon divided by the price Yield to Call –Call price replaces par –Call date replaces maturity Holding Period Yield –Considers actual reinvestment rate on coupons –Considers any change in price if the bond is sold prior to maturity 10-18
Terminal Value of $1000 invested in a 2 year bond. Holding Period Return? 10-19
Holding Period Return FV=1208 PV= 1000 N = 2 I ?
10.4 BOND PRICES OVER TIME 10-21
Premium and Discount Bonds Premium Bond –Coupon rate exceeds yield to maturity –Bond price will decline to par over its maturity Discount Bond –Yield to maturity exceeds coupon rate –Bond price will increase to par over its maturity Can you explain why these price change will occur? 10-22
Premium and Discount Bonds over Time 10-23
Bond Price Sensitivity Maturity Coupon rate Yield
Bond Value and Maturity Flat
Sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases
Steep Flat A bond’s price sensitivity is inversely related to the bond’s coupon
Steep Sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling Flat