5 - 1 CHAPTER 5 Bonds and Their Valuation  Bonds: Facts and Motivations  Bond valuation  Finding price and yield  Yield-to-maturity: Details  A relationship between price and yield  Premium, discount, and par bonds  Assessing risk  Default risk, interest rate risk, and reinvestment rate risk  Bond ratings  Types of bonds  Bond contract terms and bankruptcy process

5 - 2 Top Five Largest U.S. Corporate Bond Financings, as of July 1999 Issuer Ford Motor Co. AT&T RJR Holdings WorldCom Sprint Date July 1999 Mar 1999 May 1989 Aug 1998 Nov 1998 Amount $8.6 billion $8.0 billion $6.1 billion $5.0 billion

5 - 3 Advantage of Debt over Equity Interest expense is tax-deductible but dividend is not. Avoid earning/ownership dilution Avoid a high flotation cost for issuing stock. Flotation cost = Underwriting fee, Fee to investment banker

5 - 4 Example of Tax Saving with Debt Income Statement Revenue −COGS Profit Margin − Op. CostFirm w/o DebtFirm w/ Debt EBIT$5$5 −Int. Exp01 EBT54 −Tax (30%) Net Income cents savings for every dollar of interest expense

5 - 5 Who Issue a Bond? Domestically, Treasury bill, note, or bond: Issued by federal government, Called “risk-free” securities, about $4 trillion market Municipal bond: “munis” Corporate bond: our focus, about $5 trillion market Internationally, Euro bond (Dollar-denominated bonds sold in Germany by GM) Foreign bond: “Yankee” bond (dollar-denominated bond sold in U.S. by non-U.S. issuer), “Samurai” bond (Yen bonds sold in Japan by a non-Japanese borrower), etc

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5 - 7 AMD (Issuer, Seller, or Borrower) Investor (Buyer, Lender) Price? Coupons at t=1,2, …. T Face Value at T Main Question: How much would be the fair price a buyer is willing to pay for this bond? Bond Pricing: Cash Flow

5 - 8 Elements of Bond Pricing 1.Par value (par): Face amount. paid at maturity. Assume $1, Coupon interest rate (C or INT): Stated interest rate on the bond certificate. Multiply by par value to get dollars of interest to be paid. Generally fixed. 3.Maturity (N): Years until bond must be repaid. Declines over time. 4.Yield-to-Maturity (YTM, r d ): The current market interest rate that is used to discount the future coupon payments and face amount. Or, the required rate of return to be earned from other bonds with same level of risk.

5 - 9 Financial Asset Valuation  PV= CF 1+r r 1n r n. 012n r CF 1 CF n CF 2 Value The value of any financial asset (e.g., a bond, a stock, a loan, etc) is simply the present value of the cash flows the asset is expected to produce.

An AMD Bond Suppose AMD issues a bond with a par value of $1,000 at a coupon rate of 10% for five years. That is, AMD promises to pay you $100 at the end of each of 5 years and $1,000 at the end of 5 th year. Suppose the current market interest rate is 10%. How much would you pay for a bond now? AMD Bond 10% Coupon $1,000 Par 5-year Maturity

The Value of AMD bonds 0125 r=10% 100 =$1,000*10% 1, Present Value...

NI/YR PV PMTFV -1,000 The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at t = 10: $ $1, PV annuity PV maturity value Value of bond ====== INPUTS OUTPUT

What if a price is given?: What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? r d =? 1,000 PV 1. PV 10 PV M 887 Find r d that “works”!...

− NI/YR PV PMTFV  V INT r M r B d N d N  INT 1 + r d   rr dd r d, INPUTS OUTPUT... Watch out a negative sign on PV. Find r d

Semiannual Bonds 1.Multiply years by 2 to get periods = 2n. 2.Divide nominal rate by 2 to get periodic rate = r d /2. 3.Divide annual INT by 2 to get PMT = INT/2. 2n r d /2 OK INT/2OK NI/YR PV PMTFV INPUTS OUTPUT

(10) 13/2 100/ NI/YR PV PMTFV INPUTS OUTPUT N  Multiply by 2 YTM  Divide by 2 INT  Divide by 2 Find the value of 10-year, 10% coupon, semiannual bond if r d = 13%.

What if a price is given with semiannual coupons?: What’s the YTM on a 10-year, 9% semiannual coupon, $1,000 par value bond that sells for $887? In 6 mth periods r d =? 1,000 PV 1. PV 10 PV M 887 Find r d that “works”!...

NI/YR PV PMTFV 5.44 x2 =10.88   rr dd r d, INPUTS OUTPUT... Watch out a negative sign on PV. Don’t forget multiplying 5.44 by 2. Find r d for Semiannual Bonds

Coupon rate = A stated interest rate on the bond at the time of issuance, Usually fixed. Can be used to compute periodic cash flows to investors. Easier to understand. We are dealing with two rates: Coupon rate and YTM

We are dealing with two rates: Coupon rate and YTM Yield-to-maturity The compounded rate of return earned on a bond held to maturity if an investor re-invests all the coupon payments until maturity. Usually, same as the current market interest rate for a similar investment. Also known as the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk. The discount rate that equates a bond’s price with the present value of its future cash flows.

YTM: Example 10% annual coupon bonds, YTM = 15%  Price = $ Now, assume that an investor re-invest first coupon income (t = 1) at 15% for one year. Then, total cash inflows upon maturity in year 2 is equal to 100*1.15 = 115 plus 100 plus 1,000 = 1215 Find I that makes a PV of equal to FV of 1215 when N = 2 N = 2, PV = −918.75, PMT = 0, FV= 1,215  I = 15%

r d = (r* + DRP) + IP + Others. r d = Required rate of return on a debt security. r*= Real risk-free rate. T-bond rate if no inflation; 1% to 4%. DRP= Default risk premium. IP= Inflation premium. Others = Liquidity premium and/or Maturity risk premium. YTM is a function of many factors!

Graphical Relationship Between Price and Yield-to-Maturity Price and Yield move in an opposite direction!

Any explanation?

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NI/YR PV PMTFV When r d rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount. INPUTS OUTPUT What would happen if expected inflation rose by 3%, causing r d = 13%?

What would happen if inflation fell, and r d declined to 7%? NI/YR PV PMTFV -1, If coupon rate > r d, price rises above par, and bond sells at a premium. INPUTS OUTPUT

Premium, Discount, Par Bonds If coupon rate < r d, bond sells at a discount. (Price < Par) If coupon rate = r d, bond sells at its par value. (Price = Par) If coupon rate > r d, bond sells at a premium. (Price > Par) If r d rises, price falls - very important. Price = par at maturity.

Examples: Premium, Discount, and Par Bond Example 1: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 10%. Example 2: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 13%. Example 3: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 7%. Now plot three bonds. Put price on the y-axis and yield on the x-axis.

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

Find current yield and capital gains yield for a 8%, 10-year bond when the bond sells for $ and YTM = 10.91%. Current yield= = = 9.66%. $80 $827.97

YTM= Current yield + Capital gains yield. Cap gains yield = YTM - Current yield = 10.91% % = 1.25%. Could also find values in Years 0 and 1, get difference, and divide by value in Year 1. Same answer.

Premium and Discount Bonds All 10-year Bonds Premium C = 15% YTM = 10.91% Discount C = 8% YTM = 10.91% Current Yield 12.08%9.66% Capital Gain or Loss Yield ─1.17%1.25%

Change in price of a bond over time: Suppose the bond was issued 20 years ago and now has 10 years to maturity. What would happen to its value over time if the required rate of return remained at 10%, or at 13%, or at 7%?

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

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 remains constant. At maturity, the value of any bond must equal its par value. Any economic rationale?

Changes in Bond Price over Time: Reality

Three Risks in the Bond Market Default risk: A seller may not pay me coupons and principal. Interest rate risk: A volatile interest movement may depress the value of my bonds. (also called price risk) Reinvestment risk: I may be forced to re-invest my coupon payments at a lower interest rate.

Bond Ratings Provide One Measure of Default Risk Investment GradeJunk Bonds Moody’s AaaAaABaaBaBCaaC S&P AAAAAABBBBBBCCCD

Importance of Bond Ratings A rating is an indicator of default risk A lower rating means difficulty in selling new bonds as the company needs new financing. A lower rating means a higher interest expense in the future funding. A downgrades may have negative impact on equity prices.

Bond Rating and Market Interest Rates RatingInterest RateSpread over Long Bond Rate AAA7.20%0.20% AA A BBB BB B CCC CC C Source: Applied Corporate Finance by Aswath Damodaran, 1997

What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk? rdrd 1-yearChange10-yearChange 5%$1,048$1,386 10%1, % 1, % 15% % % Interest rate risk: Rising r d causes bond’s price to fall.

,000 1,500 0%5%10%15% 1-year 10-year kdkd Value

What is reinvestment rate risk? The risk that CFs will have to be reinvested in the future at lower rates, reducing income.

r=10% r=10% 100 =$1,000*10% 1, Or, Buying a long-term, 10-year bond in a declining interest rate environment r=7% Buying a short-term bond and rolling over 9 years in a declining interest rate environment

Long-term bonds: High interest rate risk, low reinvestment rate risk. Short-term bonds: Low interest rate risk, high reinvestment rate risk. Nothing is riskless!

True or False: “All 10-year bonds have the same price and reinvestment rate risk.” False! Low coupon bonds have less reinvestment rate risk but more price risk than high coupon bonds. If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the value amount to be received at maturity.

Summary: Risks in Bond Trading Long- Term Bond Short- Term Bond High- Coupon Bond Low- Coupon Bond Interest Rate Risk HigherLower Higher Reinves tment Risk LowerHigher Lower

Other Types of Bonds Treasury Bond: Issued by the federal government Callable bond: The seller has an option to buy back their bonds from bond investors. Convertible bond: The seller grant bondholders the right to exchange each bond for a designated number of common stock shares of the issuing firm. Zero-coupon bonds: “zeros” or “deep discount” bonds Floating-rate bonds

Callable bond: A 10-year, 10% annual coupon,$1,000 par value bond is selling for $1, with an 8% yield to maturity. It can be called after 5 years at $1,050. What’s the bond’s nominal yield to call (YTC)? N I/YR PV PMT FV 7.54% INPUTS OUTPUT Callable Bond

Yield to Call A callable bond allows the issuer to buy back the bond at a specified call price anytime after an initial call protection period, until the bond matures.

How does adding a call provision affect a bond? Issuer can refund if rates decline. That helps the issuer but hurts the investor. Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.

If you bought bonds, would you be more likely to earn YTM or YTC? Coupon rate = 10% vs. YTC = r d = 7.54%. Could raise money by selling new bonds which pay 7.54%. Could thus replace bonds which pay $100/year with bonds that pay only $75.40/year. Investors should expect a call, hence YTC = 7.54%, not YTM = 8%.

In general, if a bond sells at a premium, then (1) coupon > r d, so (2) a call is likely. So, expect to earn: YTC on premium bonds. YTM on par & discount bonds.

Bond Indentures or Provisions Secured versus unsecured debt Debenture: Unsecured bond Senior versus subordinated debt Guarantee provisions Sinking fund provisions Restrictive covenants

Bankruptcy Two main chapters of Federal Bankruptcy Act: Chapter 11, Reorganization Chapter 7, Liquidation Typically, company wants Chapter 11, creditors may prefer Chapter 7.

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Summary A bond is a debt security. YTM = Rate of return to be earned if holding until maturity YTM = Current yield + Capital gains (loss) yield Price and yield are negatively correlated. At maturity, price = par value A premium bond is not necessary “better” investment opportunity than a discount bond. Default risk, reinvestment risk, and price risk are three most important risk factors in trading bonds. Reinvestment risk and price risk can move in opposite direction for a given bond. Callable bond carries a higher reinvestment risk than a straight bond, from the buyer’s perspective.

Bonds Quotation at

Quiz You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10- year semiannual bond. Which would you prefer? The semiannual bond’s EFF% is: