McGraw-Hill/Irwin Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 14 Bond Prices and Yields

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14-7 Bonds Bonds are debt instruments (i.e. loans) Government Bonds include: US Treasury Federal Agency Municipal (Government bonds issued by non Federal entities such as States and Local Governments Corporate Bonds – are private Bonds

14-8 Bond Markets The U.S bond market has grown from $250 billion in 1950 to $22 trillion in 2004

14-9 Bonds Bonds typically make “interest only” payments, and repay the amount borrowed at maturity. New bonds may be issue to repay an issue that is maturing.

14-10 Par Value or Face Value The Par or Face Value is the amount that will be refunded at the maturity date. The par value is usually $1000 (especially for corporate bonds). Assume $1000 par value unless another value is provided.

14-11 Coupon Rate The coupon rate is the annual rate of interest (APR) paid on the bonds par value. E.g % or 6 1/8 Bond coupons historically were in 1/8% increments, but that is becoming less common

14-12 Bond Basics, II. Two basic yield measures for a bond are its coupon rate and its current yield.

14-13 Coupon Payment The coupon payment is the periodic interest payment made to bond holders. Payments per year, P/YR, is the number of coupon payments per year P/YR = 2 for a typical (semiannual) bond If P/YR not stated, assume P/YR=2

14-14 Coupon rate Zero coupon bond Bond Equivalent Yield is the six month yield on a bond, doubled Accrued Interest Indenture Bond Characteristics

14-15 A Quick Note on Bond Quotations, I. We have seen how bond prices are quoted in the financial press, and how to calculate bond prices. Note: If you buy a bond between coupon dates, you will receive the next coupon payment (and might have to pay taxes on it). However, when you buy the bond between coupon payments, you must compensate the seller for any accrued interest.

14-16 A Quick Note on Bond Quotations, II. The convention in bond price quotes is to ignore accrued interest. This results in what is commonly called a clean price (i.e., a quoted price net of accrued interest). Sometimes, this price is also known as a flat price. The price the buyer actually pays is called the dirty price This is because accrued interest is added to the clean price. Note: The price the buyer actually pays is sometimes known as the full price, or invoice price.

14-17 Pricing Example If you purchase an 8% bond quoted at , 47 days after it last coupon (183 day coupon period), what price (ignoring any commissions must you pay for this bond? Accrued Interest = $40 * (47/183) = Purchase price = =

14-18 Different Issuers of Bonds U.S. Treasury Notes and Bonds Corporations Municipalities International Governments and Corporations Innovative Bonds Indexed Bonds Floaters and Inverse Floaters

14-19 Secured or unsecured Call provision Convertible provision Put provision (putable bonds) Floating rate bonds Sinking funds Provisions of Bonds

14-20 P B =Price of the bond C t = interest or coupon payments (an annuity) T = number of periods to maturity y = yield to maturity, or market discount rate (or bond equivalent yield, which is the APR for the bond Bond Pricing

14-21 C t = 40 (Semi Annual) Par= 1000 T= 20 periods YTM= 6% Price: 10-yr, 8% Coupon, Face = $1,000 Assume market rate = 6% This bond is trading at a premium. Why?

14-22 Price: 10-yr, 8% Coupon, Face = $1,000 Assume market rate = 6% (Also called YTM) Calculator Solution: P/YR=2 PV(N=20, I/YR=6, PMT=40, FV=1000) = What if market rate = 10%? PV(N=20, I/YR=10, PMT=40, FV=1000)= Inverse relationship between Yield and Price!

14-23 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. Bond Prices and Yields

14-24 Price Yield Existing Bond Prices vs. YTM’s

14-25 Yield to Maturity Interest rate that makes the present value of the bond’s payments equal to its price. Solve the bond formula for y

14-26 Yield to Maturity Example 10 yr MaturityCoupon Rate = 7% Price = $950 Solve for r = semiannual rate Multiply r by 2 to get YTM r = % YTM = % * 2 = 7.727%

14-27 Solving for YTM using Calculator Data: Price = 950, Maturity=10 years, Coupon Rate = 7.00% I/YR on the HP10BII is an APR P/YR=2 I/YR(N=20, PV=-950, PMT=35,FV=1000) = Press  EFF% = (for EAY)

14-28 Yield Measures (Discount Bond Example) Bond Equivalent Yield – is the APR, that is the 6 month rate doubled 7.72% = 3.86% x 2 Effective Annual Yield (1.0386) = 7.88% Current Yield Annual Interest / Market Price $70 / $950 = 7.37 % Coupon Rate = $70 / $1000 = 7.00%

14-29 Relationship for Yield Measures Consider the “denominator effect” For Discount Bonds YTM > Current Yield > Coupon Rate For Premium Bonds YTM < Current Yield < Coupon Rate For Par Bonds YTM = Current Yield = Coupon Rate

14-30 Realized Yield versus YTM The YTM measure the yield of an investment while it is invested in the bond Investors may be interested in the return on a portfolio and thus must make reinvestment assumptions for the coupon to assess the portfolio If bonds are not held to maturity, one may be interested in the Holding Period Return

14-31 Holding-Period Return: Single Period HPR = [ C + ( P t - P t-1 )] / P t-1 where C = coupon payment P t = price today P t-1 = purchase price last period

14-32 Holding-Period Return Example Your purchase a 7.25% coupon bond with 25 years to maturity when the market rate is 6.135%. You sell it six months later when the market rate is 5.891%. What is your hpr? Step 1. Compute the purchase price Step 2. Compute the current price Step 3. Apply the hpr formula

14-33 hpr: Multiperiod portolfio Requires calculation of reinvestment income Solve for the Internal Rate of Return using the following: Future Value: sales price + future value of coupons Investment: purchase price

14-34 Hpr example: Multiple period portfolio You have a guaranteed account that pays 5% EAR in which you will deposit all coupon payments. You purchase a 6.5% bond (14 years to maturity, market rate 7.142) and hold it for 2.5 years (now market rate is 6.314). What EAR do you earn on your portfolio (bond plus guaranteed account)? Answer: Follow the CF’s

14-35 Taxation of Zero Coupon Bonds Although zero coupon bonds pay no coupon, the IRS requires one pay taxes on the imputed interest each year (assumes “constant yield method”) The imputed interest each year is just the path of capital gains over time Example. Buy a ten year zero for $500. What is the (approx) YTM? What is you taxable interest for the first three years?

14-36 Note: Your actual tax situation depends how long you hold this bond, and whether you sell if for a gain or loss relative to it imputed price

14-37 Taxation of Original Issue Discount Bonds Bonds issued with very low coupons, will realize capital gains over time. The IRS will impute interest on such bond. Assume a 15-year annual coupon bond has a 3% coupon when the market interest rate is 6%. You sell this bond one year from now when the market rate is 7%. What is you before and after tax hpr if you ordinary tax rate is 28%, and your capital gains rate is 15%?

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14-39 Rating companies Moody’s Investor Service Standard & Poor’s Duff and Phelps Fitch Rating Categories Investment grade (AAA – BBB, or Aaa – Baa) Speculative grade Default Risk and Ratings

14-40 Coverage ratios Leverage ratios Liquidity ratios Profitability ratios Cash flow to debt Factors Used by Rating Companies

14-41 Sinking funds Subordination of future debt Dividend restrictions Collateral Protection Against Default