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Canada
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Ryerson University
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Finance
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FIN 300
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John Currie
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Chapter 7

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CHAPTER 7 INTEREST RATES AND BOND VALUATIONLearning ObjectivesLO1Important bond features and types of bonds LO2 Bond values and yields and why they fluctuate LO3Bond ratings and what they mean LO4How are bond prices quoted LO5The impact of inflation on interest rates LO6The term structure of interest rates and the determinants of bond yieldsAnswers to Concepts Review and Critical Thinking Questions1 LO1 No As interest rates fluctuate the value of a government security will fluctuate Longterm government securities have substantial interest rate risk 2 LO2 All else the same the government security will have lower coupons because of its lower default risk so it will have greater interest rate risk3 LO4 No If the bid were higher than the ask the implication would be that a dealer was willing to sell a bond and immediately buy it back at a higher price How many such transactions would you like to do4 LO4 Prices and yields move in opposite directions Since the bid price must be lower the bid yield must be higher5 LO1 There are two benefits First the company can take advantage of interest rate declines by calling in an issue and replacing it with a lower coupon issue Second a company might wish to eliminate a covenant for some reason Calling the issue does this The cost to the company is a higher coupon A put provision is desirable from an investors standpoint so it helps the company by reducing the coupon rate on the bond The cost to the company is that it may have to buy back the bond at an unattractive price6 LO1 Bond issuers look at outstanding bonds of similar maturity and risk The yields on such bonds are used to establish the coupon rate necessary for a particular issue to initially sell for par value Bond issuers also simply ask potential purchasers what coupon rate would be necessary to attract them The coupon rate is fixed and simply determines what the bonds coupon payments will be The required return is what investors actually demand on the issue and it will fluctuate through time The coupon rate and required return are equal only if the bond sells for exactly par7 LO5 Yes Some investors have obligations that are denominated in dollars ie they are nominal Their primary concern is that an investment provides the needed nominal dollar amounts Pension funds for example often must plan for pension payments many years in the future If those payments are fixed in dollar terms then it is the nominal return on an investment that is important8 LO3 Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell many large investors are prohibited from investing in unrated issues 9 LO3 Government bonds have no credit risk so a rating is not necessary Junk bonds often are not rated because there would no point in an issuer paying a rating agency to assign its bonds a low rating its like paying someone to kick you10 LO6 The term structure is based on pure discount bonds The yield curve is based on couponbearing issues S71 Solutions to Questions and ProblemsNOTE All end of chapter problems were solved using a spreadsheet Many problems require multiple steps Due to space and readability constraints when these intermediate steps are included in this solutions manual rounding may appear to have occurred However the final answer for each problem is found without rounding during any step in the problem Basic1 LO2 The yield to maturity is the required rate of return on a bond expressed as a nominal annual interest rate For noncallable bonds the yield to maturity and required rate of return are interchangeable terms Unlike YTM and required return the coupon rate is not a return used as the interest rate in bond cash flow valuation but is a fixed percentage of par over the life of the bond used to set the coupon payment amount For the example given the coupon rate on the bond is still 10 percent and the YTM is 8 percent2 LO2 Price and yield move in opposite directions if interest rates fall the price of the bond will rise and if interest rates rise the price of the bond will decrease This is because the fixed coupon payments determined by the fixed coupon rate are more valuable when interest rates fall hence the price of the bond decrease when interest rates rose to15 percentNOTE Most problems do not explicitly list a par value for bonds Even though a bond can have any par value in general corporate bonds in Canada will have a par value of 1000 We will use this par value in all problems unless a different par value is explicitly stated3 LO2 The price of any bond is the PV of the interest payment plus the PV of the par value Notice this problem assumes an annual coupon The price of the bond will be10 10 P751110875 0875100011087591889 We would like to introduce shorthand notation here Rather than write or type as the case may be the entire equation for the PV of a lump sum or the PVA equation it is common to abbreviate the equations astPVIF11r Rtwhich stands for Present Value Interest Factort PVIFA 111r rRt which stands for Present Value Interest Factor of an Annuity These abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved We will use this shorthand notation in remainder of the solutions key4 LO2 Here we need to find the YTM of a bond The equation for the bond price is P93490PVIFA1000PVIFR9R9Notice the equation cannot be solved directly for R Using a spreadsheet a financial calculator or trial and error we findRYTM10153 If you are using trial and error to find the YTM of the bond you might be wondering how to pick an interest rate to start the process First we know the YTM has to be higher than the coupon rate since the bond is aS72

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