Chapter 6 - Bond Valuation and Interest Rates

CHAPTER 6 Bond Valuation and Interest Rates123 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 2Lecture AgendaLearning ObjectivesImportant TermsBasic Structure of BondsValuing BondsBond YieldsInterest Rate DeterminantsOther Types of Bonds/Debt InstrumentsSummary and ConclusionsConcept Review QuestionsAppendix Bond Duration

The Basic Structure of BondsBond Valuation and Interest Rates6 - 4What is a Bond?In its broadest sense, a bond is any debt instrument that promises a fixed income stream to the holder423 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 5Basic Structure of BondsA typical bond has the following characteristics:A fixed face or par value, paid to the holder of the bond, at maturityA fixed coupon payment, which specifies the interest payable over the life of the bondCoupons are usually paid either annually or semi-annuallyA fixed maturity date523 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 6Basic Structure of BondsNote:The coupon rate, the maturity date, par value are all set (fixed) at the time the bond was originally sold to the market623 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 7Bond indenture - the contract between the issuer of the bond and the investors who hold itThe market price of a bond is equal to the present value of the payments promised by the bond

(See the basic pattern of cash flows from a traditional bond on the next slide)Basic Structure of Bonds723 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 8Cash Flow Pattern of a BondThe Purchase Price or Market Price of a bond is simply the present value of the cash inflows, discounted at the bonds yield-to-maturity0234n1CouponCouponCouponCouponCoupon +Face ValuePurchase PriceCash Inflows to the InvestorCash Outflows to the Investor823 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTBond Features and ProvisionsBond Valuation and Interest Rates6 - 10More Bond TerminologyTerm-to-maturity the time remaining to the bonds maturity dateCoupon rate the annual percentage interest paid on the bonds face value. To calculate the dollar value of the annual coupon, multiply the coupon rate times the face value.If the coupon is paid twice a year, divide the annual coupon by twoExample: A $1000 bond with an 8% coupon rate will have an $80 coupon if paid annually or a $40 coupon if paid semi-annually.

1023 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 11Security & Protective ProvisionsCovenantsPositive covenants things the firm agrees to doSupply periodic financial statementsMaintain certain ratios

Negative covenants things the firm agrees not to doRestrictions on the amount of debt the firm can take onPrevents the firm from acquiring or disposing of assets1123 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTBond ValuationAnnual Coupon PaymentsBond Valuation and Interest Rates6 - 13Bond ValuationThe value of a bond is a function of:The bonds par (face) valueTerm to maturityCoupon rateInvestors required rate of return (discount rate is also known as the bonds yield to maturity)6 - 14Bond ValueGeneral Formula

[ 6-1]Where:I = interest (or coupon ) paymentskb = the bond discount rate (or market rate)n = the term to maturityF = Face (or par) value of the bond6 - 15Bond Valuation: ExampleWhat is the market price of a ten year, $1,000 bond with a 5% coupon, if the bonds yield-to-maturity is 6%?

Calculator Approach:1,000 FV50PMT10NI/Y 6CPT PV926.401523 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTFactors Affecting Bond PricesBond Valuation and Interest Rates6 - 17Coupon Rate Relationship to Yield-to- MaturityThe relationship between the coupon rate and the bonds yield-to-maturity (YTM) determines if the bond will sell at a premium, at a discount or at par

IfThenBond Sells at a:Coupon < YTMMarket < FaceDiscountCoupon = YTMMarket = FaceParCoupon > YTMMarket > FacePremium1723 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 18Factors Affecting Bond PricesInverse Relationship Between Yields and PricesYield to maturity (investors required return)Bond prices go down when the YTM goes upBond prices go up when the YTM goes down

Look at the graph on the next slide. It shows how the price of a 25 year, 10% coupon bond changes as the bonds YTM varies from 1% to 30%Note that the graph is not linear instead it is said to be convex to the origin1823 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 19Price & Yield: 25 Year Bond, 10% Coupon

As interest rates increase, bond prices fall, but fall at a decreasing rate1923 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 20Bond YieldsThe Yield to Maturity = Investors Required Rate of ReturnYield-to-maturity (YTM) the discount rate used to evaluate bondsThe yield earned by a bond investor who:Purchases the bond at the current market priceHolds the bond to maturityIs the bonds Internal Rate of Return (IRR) 2023 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 21Bond Yield to MaturityThe yield to maturity is that discount rate that causes the sum of the present value of promised cash flows to equal the current bond price.

[ 6-2]2123 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 22Solving for YTMTo solve for YTM, solve for YTM in the following formula:

There is a Problem: You cant solve for YTM algebraically; therefore, must either use a financial calculator, Excel, trial & error or approximation formula.

2223 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 23Solving for YTMExample: What is the YTM on a 10 year, 5% coupon bond (annual pay coupons) that is selling for $980?

Financial Calculator1,000FV980 +/-PV PMT NI/Y5.26%2323 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTYTM impIf YTM = coupon rate, then par value = bond priceIf YTM > coupon rate, then par value > bond priceWhy? The discount provides yield above coupon ratePrice below par value, called a discount bondIf YTM < coupon rate, then par value < bond priceWhy? Higher coupon rate causes value above parPrice above par value, called a premium bond

6 - 24Using the Approximation Formula to Solve for Yield to MaturityBond Valuation and Interest Rates6 - 26The Approximation FormulaThis formula gives you a quick estimate of the yield to maturityIt is an estimate because it is based on a linear approximation (again you will remember the exponential nature of compound interest)Should you be concerned with the error inherent in the approximated YTM?NORemember a YTM is an ex ante calculation as a forecast, it is based on assumptions which may or may not hold in this case, therefore as a forecast or estimate, the approximation approach should be fine.6 - 27The Approximation FormulaF = Face Value = Par Value = $1,000B = Bond PriceI = the semi annual coupon interestN = number of semi-annual periods left to maturity

6 - 28ExampleFind the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annually.)Therefore there is coupon interest of $30 paid semi-annuallyThere are 10 semi-annual periods left until maturity 6 - 29Example with SolutionFind the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi-annually.)

The actual answer is 9.87%...so of course, the approximation approach only gives us an approximate answerbut that is just fine for tests and exams.Short-Term Interest RatesBond Valuation and Interest Rates6 - 31Interest Rate DeterminantsInterest is the price of moneyInterest rates go:Up when the demand for loanable funds risesDown when the demand for loanable funds falls3123 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTTerm Structure of Interest Rates(Long-term Interest Rates)Bond Valuation and Interest Rates

6 - 33Term Structure of Interest RatesTerm structure is the relationship between time to maturity and yields, all else equalYield curve graphical representation of the term structureNormal upward-sloping; long-term yields are higher than short-term yieldsInverted downward-sloping; long-term yields are lower than short-term yieldsWhen plotted on a graph, the line is called a Yield Curve

3323 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENT6 - 34Figure 7.6 Upward-Sloping Yield Curve

Figure 7.6 Downward-Sloping Yield Curve6 - 35

6 - 36Theories of the Term StructureThree theories are used to explain the shape of the term structureLiquidity preference theoryInvestors must be paid a liquidity premium to hold less liquid, long-term debtExpectations theoryThe long rate is the average of expected future short interest ratesMarket segmentation theoryDistinct markets exist for securities of different maturities3623 April 2012IFTIKHAR AHMED SANJRANIFINANCIAL MANAGEMENTChart1298.2084013056256.1876517887221.8920338389193.7324796619170.4697228302151.1334246331134.9607495348121.3495523772109.822579604910091.578255335384.313721775978.010045064672.508290250767.679254573663.417448166559.636364747356.264753224153.243668368750.524129800548.06525744845.832781399143.79784685841.936052445440.226673591238.652033209637.196989942535.848520549134.5953779264

Percent YTMPrice per $100 of Face ValuePrice/Yield Relationship

Sheet1010010002035000.011001000-2824.31995017230.021001000-3203.0299723236298.20840130560.031001000-3645.9264321807256.18765178870.041001000-4164.5908287186221.89203383890.051001000-4772.7098817988193.73247966190.06170.46972283020.07151.13342463310.08134.96074953480.09121.34955237720.1109.82257960490.111000.1291.57825533530.1384.31372177590.1478.01004506460.1572.50829025070.1667.67925457360.1763.41744816650.1859.63636474730.1956.26475322410.253.24366836870.2150.52412980050.2248.0652574480.2345.83278139910.2443.7978468580.2541.93605244540.2640.22667359120.2738.65203320960.2837.19698994250.2935.84852054910.334.5953779264

Sheet100000000000000000000000000000

Yield to MaturityPrice per $100 of Face ValuePrice/Yield Relationship

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