Principles of Business Finance

Principles of Business FinanceLecture 6: Interest Rates and Bond ValuationLearning OutcomesBy the end of this lecture, you should be able to:-Understand the importance of bond featuresCalculate bond values and yields Understand the impact on inflation on interest rates.Comprehend the term structure of interest rates and the determinants of bond yields.Try this!

Bond

Bond DefinitionBeck Corporation wants to borrow $1,000 for 30 years. The interest rate on similar debt issued by similar corporation is 12%.CouponFace value or par valueCoupon rateMaturity

Types of Corporate BondsVanilla BondsZero Coupon BondsConvertible BondsBond ValuationHow bonds are price?Estimate the expected future cash flows.Determine the required rate of return.Compute the discounted present value of the future cash flows.Bond Values and YieldsAs time passes, interest rates change in the marketplace.Cash flows from a bond, stay the same.As a result, the value of the bond will fluctuate.When interest rates rise, the present value of the bonds remaining cash flow declines, the bond is worth less.When interest rates fall, the bond is worth more.This negative relation between changes in interest rate and price of a bond is a very important relation in corporate finance.Think!Your stockbroker is trying to sell you a 15-year bond with a 7 percent coupon, and the interest, or yield, on similar bonds is 10 percent. Is the bond selling at premium, par or at a discount?Bond Values and YieldsInterest rate required in the market on a bond is called the bonds yield to maturity (YTM).Bonds YTM should not be confused with its current yield.Current yield = annual coupon/priceCurrent yield is usually higher/lower than the YTM in that it considers only the coupon portion of the return and does not consider the built-in gain/loss from the price of the bond.

Yield To MaturityIs the discount rate that makes the present value of the coupon and principal payments equal to the price of the bond.YTM is viewed as a promised yield.A bonds yield to maturity changes daily as interest rates increase or decrease, but its calculation is always based on the issuers promise to make interest and principal payments as stipulated in the bond contract.Valuing a Discount Bond with Annual CouponsConsider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000, and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond?

Valuing a Premium Bond with Annual CouponsSuppose you are reviewing a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond?Graphical Relationship Between Price and Yield-to-maturity (YTM)

Bond PriceYield-to-maturity (YTM)6.14Bond characteristics: Coupon rate = 8% with annual coupons; Par value = $1,000; Maturity = 10 yearsBond Prices: Relationship Between Coupon and YieldIf 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

The Bond Pricing Equation

Example: Semiannual Coupons An ordinary bond has a coupon rate of 14%, the yield to maturity is quoted at 16% and the bond matures in seven years.Find present values based on the payment periodHow many coupon payments are there?What is the semiannual coupon payment?What is the semiannual yield?B = 70[1 1/(1.08)14] / .08 + 1,000 / (1.08)14 = 917.567-176.17The students can read the example in the book. The basic information is as follows:

Coupon rate = 14%, semiannual couponsYTM = 16%Maturity = 7 yearsPar value = $1,000Interest Rate RiskRisk that arises for bond owners from fluctuating interest rates is called rate risk.How much interest rate risk a bond has depends on how sensitive its price is to interest changes.This sensitivity directly depends on two things:-- - Interest Rate RiskTwo things to keep in mind:-Interest Rate Risk

Exhibit 8.3: Relation between Bond Price Volatility and Coupon Rate

21Computing Yield to MaturityYield to Maturity (YTM) is the rate implied by the current bond price.Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity.It can also be calculated using the interpolation method.

Computing Yield to Maturity Annual CouponsConsider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $928.09.Will the yield be more or less than 10%?B = 100[1 1/(1.10)15] / .11 + 1,000 / (1.10)15 = 928.09YTM = 11%

Computing Yield to Maturity - Semiannual CouponsSuppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,197.93.Is the YTM more or less than 10%?What is the semiannual coupon payment?How many periods are there?B = 50[1 1/(1.04)40] / .04 + 1,000 / (1.04)40 = 1,197.93YTM = 4%*2 = 8%Summary of Bond Valuation

QuestionsBasic (page 254)Q. 2: Suppose you buy a 7% coupon, 20-year bond today when it is first issued. If interest rates suddenly rise to 15%, what happens to the value of your bond? Why?Price and yield move in opposite directions; if interest rates rise, the price of the bond will fall. This is because the fixed coupon payments determined by the fixed coupon rate are not as valuable when interest rates risehence, the price of the bond decreases.

QuestionsQ. 3 Staind, Inc., has 7.5% coupon bonds on the market that have 10 years left to maturity. The bonds makes annual payments. If the YTM on these bonds is 8.75%, what is the current bond price?P = $75(PVIFA8.75%,10) + $1,000(PVIF8.75%,10) = $918.89QuestionsQ.4 Ackerman Co. has 9 percent coupon bonds on the market with nine years left to maturity. The bonds make annual payments. If the bond currently sells for $934 , what is its YTM? P = $934 = $90(PVIFAR%,9) + $1,000(PVIFR%,9) YTM = 10.15%