Copyright © 2012 Pearson Prentice Hall. All rights reserved. Chapter 6 Interest Rates And Bond Valuation

© 2012 Pearson Prentice Hall. All rights reserved. 6-2 Bonds and Their Valuation Key features of bonds Bond valuation Measuring yield Assessing risk

Cost of Money Money can be obtained from debts or equity both of which has a cost – Cost of debt = interest – Cost of equity = dividends What is cost for the borrowers of funds is the return for lenders or investors. – Return for bond or debt investors = interest, capital gains – Return for equity investors = dividends, capital gains.

What is a bond? A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.  Key Features of a Bond: Par value – face value of the bond, which is initially borrowed when the bond is sold and then paid at maturity. Coupon interest rate – quoted/stated interest rate (generally fixed) paid by the issuer. We multiply coupon int. rate by par value to get dollar payment of interest called coupon payment. Maturity date – years until the bond must be repaid. Issue date – when the bond was issued. Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”).

Types of Bonds Treasury Bonds: Bonds issued by the federal government. No default risk. Corporate Bonds: Bonds issued by corporations. Different levels of default risk/credit risk. Municipal Bonds: Bonds issued by local government. Foreign Bonds: Bonds issued by foreign government or foreign corporations. Exchange rate risk.

Types of Corporate bonds Mortgage bonds: A mortgage bond is a bond secured by a mortgage on one or more assets. These bonds are typically backed by real estate holdings and/or real property such as equipment. In a default situation, mortgage bondholders have a claim to the underlying property and could sell it off to compensate for the default. Debentures: A debenture is a type of debt instrument that is not secured by physical assets or collateral. Debentures are backed only by the general creditworthiness and reputation of the issuer. Both corporations and governments frequently issue this type of bond in order to secure capital. Ex- T-Bill, T-bond issued by government. Subordinated debentures: A subordinated debenture is a bond classified lower than more senior debt in the event of a default. This means that the holders of more senior securities are paid first, before any residual funds are made available to the holder of the subordinated debenture. Given the higher risk of nonpayment, this security pays out a relatively high interest rate. Investment-grade bonds: An investment grade is a rating that indicates that a municipal or corporate bond has a relatively low risk of default. Junk bonds: A junk bond is a informal term for a high-yield or non-investment grade bond. Junk bonds are fixed-income instruments that carry a rating of 'BB' or lower by Standard & Poor's, or 'Ba' or below by Moody's. Junk bonds are so called because of their higher default risk in relation to investment-grade bonds. © 2012 Pearson Prentice Hall. All rights reserved. 6-6

Types of Bonds Fixed-rate bonds: A bond whose coupon rate is fixed for its entire life. Floating-rate bonds: A bond whose coupon rates fluctuates with shifts in the general level of interest rates. Zero Coupon bond: A bond that pays no periodic coupon. Discount bond: Any bond whose price is lower than the par value. Premium Bond: A bond that sells above it’s par value.

Types of Bonds Convertible bond: A bond that is exchangeable at the option of the holder for the issuing firm’s common stock. Putable bond: A bond that has the provision to allow investors to sell the bond back to the issuer prior to maturity at a prearranged price. Callable bond: A bond with a call provision that gives the issuer right to redeem the bonds prior to maturity date under specified terms. Most bonds have a deferred call and a call premium.

Effect of a call provision A call provision is a provision on a bond or other fixed-income instrument that allows the original issuer to repurchase and retire the bonds. If there is a call provision in place, it will typically come with a time window under which the bond can be called, and a specific price to be paid to bondholders and any accrued interest are defined. Callable bonds will pay a higher yield than comparable non-callable bonds. Allows issuer to refund the bond issue if rates decline (helps the issuer, but hurts the investor). A bond call will almost always favor the issuer over the investor; if it doesn't, the issuer will simply continue to make the current interest payments and keep the debt active. Typically, call options on bonds will be exercised by the issuer when interest rates have fallen. The reason for this is that the issuer can simply issue new debt at a lower rate of interest, effectively reducing the overall cost of their borrowing, instead of continuing to pay the higher effective rate on the borrowings.A bond call © 2012 Pearson Prentice Hall. All rights reserved. 6-9

Sinking Fund Provision Provision to pay off a loan over its life rather than all at maturity (Rather than the issuer repaying the entire principal of a bond on the maturity date, issuer pays it off over bonds maturity period). Generally corporations make semiannual or annual payments that are used to retire the bonds. Similar to amortization on a term loan. Reduces default risk to investor. But not good for investors if rates decline after issuance. Therefore, if interest rates fall and bond prices rise, a firm will benefit from the sinking fund provision that enables it to repurchase its bonds at below-market prices. In this case, the firm's (issuer’s) gain is the bondholder's (investor's) loss – thus callable bonds will typically be issued at a higher coupon rate, reflecting the value of the option.

© 2012 Pearson Prentice Hall. All rights reserved Corporate Bonds: General Features of a Bond Issue Bonds also are occasionally issued with stock purchase warrants, which are instruments that give their holders the right to purchase a certain number of shares of the issuer ’ s common stock at a specified price over a certain period of time. Occasionally attached to bonds as “ sweeteners. ” Including warrants typically allows the firm to raise debt capital at a lower cost than would be possible in their absence.

© 2012 Pearson Prentice Hall. All rights reserved Table 6.4a Characteristics and Priority of Lender’s Claim of Traditional Types of Bonds

© 2012 Pearson Prentice Hall. All rights reserved Table 6.4b Characteristics and Priority of Lender’s Claim of Traditional Types of Bonds

© 2012 Pearson Prentice Hall. All rights reserved Table 6.5 Characteristics of Contemporary Types of Bonds

© 2012 Pearson Prentice Hall. All rights reserved Corporate Bonds: International Bond Issues Companies and governments borrow internationally by issuing bonds in two principal financial markets: –A Eurobond is a bond issued by an international borrower and sold to investors in countries with currencies other than the currency in which the bond is denominated. –In contrast, a foreign bond is a bond issued in a host country ’ s financial market, in the host country ’ s currency, by a foreign borrower. Both markets give borrowers the opportunity to obtain large amounts of long-term debt financing quickly, in the currency of their choice and with flexible repayment terms.

© 2012 Pearson Prentice Hall. All rights reserved Financial Asset Valuation Fundamentals Valuation is the process that links risk and return to determine the worth of an asset. There are three key inputs to the valuation process: 1.Cash flows (returns) 2.Timing 3.A measure of risk, which determines the required return

© 2012 Pearson Prentice Hall. All rights reserved Basic Valuation Model The value of any asset is the present value of all future cash flows it is expected to provide over the relevant time period. The value of any asset at time zero, V 0, can be expressed as where v0v0 =Value of the asset at time zero CF T =cash flow expected at the end of year t r=appropriate required return (discount rate) n=relevant time period 0 12nr CF 1 CF n CF 2 PV CF...

© 2012 Pearson Prentice Hall. All rights reserved Bond Valuation: Bond Fundamentals As noted earlier, bonds are long-term debt instruments used by businesses and government to raise large sums of money, typically from a diverse group of lenders. Most bonds pay interest semiannually at a stated coupon interest rate, have an initial maturity of 10 to 30 years, and have a par value of $1,000 that must be repaid at maturity.

© 2012 Pearson Prentice Hall. All rights reserved Bond Valuation: Basic Bond Valuation The basic model for the value, B 0, of a bond is given by the following equation: OR, B 0 = I*(PVIFA k d, n )+M*(PVIF k d,n ) Where, B0B0 =value of the bond at time zero I=annual interest paid in dollars n=number of years to maturity M=par value in dollars rdrd =required return on a bond

Value of a Bond Two cash flows of a bond are periodic coupon payments and the principal amount (par value) at the end. Thus the value of a bond is k i = k* + IP + MRP + DRP + LP  (b-p-242-timeline)

Value of a Bond

© 2012 Pearson Prentice Hall. All rights reserved Bond Valuation: Basic Bond Valuation (cont.) Mills Company, a large defense contractor, on January 1, 2007, issued a 10% coupon interest rate, 10-year bond with a $1,000 par value that pays interest annually. Investors who buy this bond receive the contractual right to two cash flows: (1) $100 annual interest (10% coupon interest rate  $1,000 par value) at the end of each year and (2) the $1,000 par value at the end of the tenth year. Assuming that interest on the Mills Company bond issue is paid annually and that the required return is equal to the bond ’ s coupon interest rate, I = $100, r d = 10%, M = $1,000, and n = 10 years. So, Here, bond’s price is equal to the face value 1000.

© 2012 Pearson Prentice Hall. All rights reserved Bond Valuation: Bond Value Behavior In practice, the value of a bond in the marketplace is rarely equal to its par value. –Whenever the required return on a bond differs from the bond ’ s coupon interest rate, the bond ’ s value will differ from its par value. –The required return is likely to differ from the coupon interest rate because either (1) economic conditions have changed, causing a shift in the basic cost of long-term funds, or (2) the firm ’ s risk has changed. –Increases in the basic cost of long-term funds or in risk will raise the required return; decreases in the cost of funds or in risk will lower the required return. –Example-1:

© 2012 Pearson Prentice Hall. All rights reserved Table 6.6 Bond Values for Various Required Returns (Mills Company’s 10% Coupon Interest Rate, 10-Year Maturity, $1,000 Par, January 1, 2010, Issue Paying Annual Interest) If, r d >c, bond sells at Discount If, r d =c, bond sells at Par If, r d <c, bond sells at Premium

© 2012 Pearson Prentice Hall. All rights reserved Figure 6.4 Bond Values and Required Returns

Bond values over time At maturity, the value of any bond must equal its par value. If r d remains constant: – The value of a premium bond would decrease over time until it reaches par value. – The value of a discount bond would increase over time, until it reaches par value. – A value of a par bond stays constant.

© 2012 Pearson Prentice Hall. All rights reserved Figure 6.5 Time to Maturity and Bond Values

Bonds with Semiannual Coupons Divide annual coupon payment by 2 (INT/2). Multiply years to maturity by 2 (N X 2). Divide nominal (quoted) interest rate by 2 (r d /2)

© 2012 Pearson Prentice Hall. All rights reserved Bonds with Semiannual Coupons (cont.) The procedure used to value bonds paying interest semiannually is similar to that shown in Chapter 5 for compounding interest more frequently than annually, except that here we need to find present value instead of future value. It involves 1.Converting annual interest, I, to semiannual interest by dividing I by 2. 2.Converting the number of years to maturity, n, to the number of 6-month periods to maturity by multiplying n by 2. 3.Converting the required stated (rather than effective) annual return for similar-risk bonds that also pay semiannual interest from an annual rate, r d, to a semiannual rate by dividing r d by 2.

© 2012 Pearson Prentice Hall. All rights reserved Bonds with Semiannual Coupons (cont.) Assuming that the Mills Company bond pays interest semiannually and that the required stated annual return, r d is 12% for similar risk bonds that also pay semiannual interest, substituting these values into the previous equation yields

Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10% semiannual coupon bond, all else equal? The semiannual bond’s effective rate is: 10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

Bond Yields Yields are the returns on bonds based on market conditions. Yield To Maturity is the rate of return earned on a bond if it is held till maturity. At the time of issue YTM is equal to coupon rate. Yield To Call is the rate of return earned when bonds are held till the call period before maturity.

© 2012 Pearson Prentice Hall. All rights reserved Yield to Maturity (YTM) The yield to maturity (YTM) is the rate of return that investors earn if they buy a bond at a specific price and hold it until maturity. (Assumes that the issuer makes all scheduled interest and principal payments as promised.) The yield to maturity on a bond with a current price equal to its par value will always equal the coupon interest rate. When the bond value differs from par, the yield to maturity will differ from the coupon interest rate.

YTM Current Yield Capital Gain Yield I Premium or discount amount B o YTM should be greater than 10% because Investor bought the bond by 950 (discount bond) which is less than par value So there is a capital gain along with the current yield. *Discount bond is good for investor.

Estimated Yield To Maturity Without a financial calculator it is not possible to find the exact YTM of any bond. However YTM can be estimated using the following formula:

What is the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling for $887? YTM of this bond is 10.91%. This bond sells at a discount, because YTM > coupon rate. Find YTM, if the bond price was $1, YTM of this bond is 7.08%. This bond sells at a premium, because YTM < coupon rate. If, YTM >c, bond sells at Discount If, YTM =c, bond sells at Par If, YTM <c, bond sells at Premium

© 2012 Pearson Prentice Hall. All rights reserved Bond’s Riskiness Interest rate risk is the chance that interest rates will change and thereby change the required return and bond value. The risk of a decline in a bond’s price due to an increase in interest rate. Rising rates, which result in decreasing bond values, are of greatest concern. The shorter the amount of time until a bond ’ s maturity, the less responsive is its market value to a given change in the required return.

© 2012 Pearson Prentice Hall. All rights reserved Bond’s Riskiness Reinvestment Risk: The risk of short-termed bonds due to a decline in interest rates. (It affects YTM which is calculated on the premise that all future coupon payments will be reinvested at the interest rate in effect when the bond was first purchased.) Zero coupon bonds are the only fixed- income instruments to have no reinvestment risk, since they have no interim coupon payments. Which risk is more relevant to an investor depends on his/her investment horizon – Investment horizon is the period of time an investor plans to hold a particular investment.

Bond’s Riskiness Default risk: If an issuer defaults, investors receive less than the promised return. Therefore, the expected return on corporate and municipal bonds is less than the promised return. Influenced by the issuer’s financial strength and the terms of the bond contract.

© 2012 Pearson Prentice Hall. All rights reserved Table 6.1 Debt-Specific Issuer- and Issue-Related Risk Premium Components

Evaluating default risk: Bond ratings Investment GradeJunk Bonds Moody’s Aaa Aa A BaaBa B Caa C S & P AAA AA A BBBBB B CCC D Bond ratings are designed to reflect the probability of a bond issue going into default.

© 2012 Pearson Prentice Hall. All rights reserved Table 6.3 Moody’s and Standard & Poor’s Bond Ratings Bond ratings are designed to reflect the probability of a bond issue going into default.

Bond markets Primarily traded in the over-the-counter (OTC) market. Most bonds are owned by and traded among large financial institutions. Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE.

© 2012 Pearson Prentice Hall. All rights reserved Review of Learning Goals (cont.) LG2Review the legal aspects of bond financing and bond cost. –Corporate bonds are long-term debt instruments indicating that a corporation has borrowed an amount that it promises to repay in the future under clearly defined terms. The bond indenture, enforced by a trustee, states all conditions of the bond issue. It contains both standard debt provisions and restrictive covenants, which may include a sinking- fund requirement and/or a security interest. The cost of a bond to an issuer depends on its maturity, offering size, and issuer risk and on the basic cost of money.

© 2012 Pearson Prentice Hall. All rights reserved Review of Learning Goals (cont.) LG3Discuss the general features, yields, prices, ratings, popular types, and international issues of corporate bonds. –A bond issue may include a conversion feature, a call feature, or stock purchase warrants. The yield, or rate of return, on a bond can be measured by its current yield, yield to maturity (YTM), or yield to call (YTC). Bond prices are typically reported along with their coupon, maturity date, and yield to maturity (YTM). Bond ratings by independent agencies indicate the risk of a bond issue. Various types of traditional and contemporary bonds are available. Eurobonds and foreign bonds enable established creditworthy companies and governments to borrow large amounts internationally.

© 2012 Pearson Prentice Hall. All rights reserved Review of Learning Goals (cont.) LG4Understand the key inputs and basic model used in the valuation process. –Key inputs to the valuation process include cash flows (returns), timing, and risk and the required return. The value of any asset is equal to the present value of all future cash flows it is expected to provide over the relevant time period.

© 2012 Pearson Prentice Hall. All rights reserved Review of Learning Goals (cont.) LG5Apply the basic valuation model to bonds and describe the impact of required return and time to maturity on bond values. –The value of a bond is the present value of its interest payments plus the present value of its par value. The discount rate used to determine bond value is the required return, which may differ from the bond ’ s coupon interest rate. The amount of time to maturity affects bond values. The value of a bond will approach its par value as the bond moves closer to maturity. The chance that interest rates will change and thereby change the required return and bond value is called interest rate risk. The shorter the amount of time until a bond ’ s maturity, the less responsive is its market value to a given change in the required return.

© 2012 Pearson Prentice Hall. All rights reserved Review of Learning Goals (cont.) LG6Explain yield to maturity (YTM), its calculation, and the procedure used to value bonds that pay interest semiannually. –Yield to maturity is the rate of return investors earn if they buy a bond at a specific price and hold it until maturity. YTM can be calculated by using a financial calculator or by using an Excel spreadsheet. Bonds that pay interest semiannually are valued by using the same procedure used to value bonds paying annual interest, except that the interest payments are one-half of the annual interest payments, the number of periods is twice the number of years to maturity, and the required return is one-half of the stated annual required return on similar-risk bonds.