# Chapter Review and Self-Test Problems. Answers to Chapter Review and Self-Test Problems

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1 236 PART THREE Valuation of Future Cash Flows Chapter Review and Self-Test Problems 7.1 Bond Values A Microgates Industries bond has a 10 percent coupon rate and a \$1,000 face value. Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent yield, what is the bond s value? What is the effective annual yield on the bond? 7.2 Bond Yields A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually. The par value is \$1,000, and the bond matures in six years. If the bond currently sells for \$911.37, what is its yield to maturity? What is the effective annual yield? Answers to Chapter Review and Self-Test Problems 7.1 Because the bond has a 10 percent coupon yield and investors require a 12 percent return, we know that the bond must sell at a discount. Notice that, because the bond pays interest semiannually, the coupons amount to \$100/2 \$50 every six months. The required yield is 12%/2 6% every six months. Finally, the bond matures in 20 years, so there are a total of 40 six-month periods. The bond s value is thus equal to the present value of \$50 every six months for the next 40 six-month periods plus the present value of the \$1,000 face amount: Bond value \$50 [(1 1/ )/.06] 1,000/ \$ ,000/ \$ Notice that we discounted the \$1,000 back 40 periods at 6 percent per period, rather than 20 years at 12 percent. The reason is that the effective annual yield on the bond is %, not 12 percent. We thus could have used percent per year for 20 years when we calculated the present value of the \$1,000 face amount, and the answer would have been the same. 7.2 The present value of the bond s cash flows is its current price, \$ The coupon is \$40 every six months for 12 periods. The face value is \$1,000. So the bond s yield is the unknown discount rate in the following: \$ \$40 [1 1/(1 r) 12 ]/r 1,000/(1 r) 12 The bond sells at a discount. Because the coupon rate is 8 percent, the yield must be something in excess of that. If we were to solve this by trial and error, we might try 12 percent (or 6 percent per six months): Bond value \$40 (1 1/ )/.06 1,000/ \$ This is less than the actual value, so our discount rate is too high. We now know that the yield is somewhere between 8 and 12 percent. With further trial and error (or a little machine assistance), the yield works out to be 10 percent, or 5 percent every six months. By convention, the bond s yield to maturity would be quoted as 2 5% 10%. The effective yield is thus %.

2 CHAPTER 7 Interest Rates and Bond Valuation 237 Concepts Review and Critical Thinking Questions 1. Treasury Bonds Is it true that a U.S. Treasury security is risk-free? 2. Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury bond or a 30-year BB corporate bond? 3. Treasury Pricing With regard to bid and ask prices on a Treasury bond, is it possible for the bid price to be higher? Why or why not? 4. Yield to Maturity Treasury bid and ask quotes are sometimes given in terms of yields, so there would be a bid yield and an ask yield. Which do you think would be larger? Explain. 5. Call Provisions A company is contemplating a long-term bond issue. It is debating whether or not to include a call provision. What are the benefits to the company from including a call provision? What are the costs? How do these answers change for a put provision? 6. Coupon Rate How does a bond issuer decide on the appropriate coupon rate to set on its bonds? Explain the difference between the coupon rate and the required return on a bond. 7. Real and Nominal Returns Are there any circumstances under which an investor might be more concerned about the nominal return on an investment than the real return? 8. Bond Ratings Companies pay rating agencies such as Moody s and S&P to rate their bonds, and the costs can be substantial. However, companies are not required to have their bonds rated in the first place; doing so is strictly voluntary. Why do you think they do it? 9. Bond Ratings U.S. Treasury bonds are not rated. Why? Often, junk bonds are not rated. Why? 10. Term Structure What is the difference between the term structure of interest rates and the yield curve? 11. Crossover Bonds Looking back at the crossover bonds we discussed in the chapter, why do you think split ratings such as these occur? 12. Municipal Bonds Why is it that municipal bonds are not taxed at the federal level, but are taxable across state lines? Why is it that U.S. Treasury bonds are not taxable at the state level? (You may need to dust off the history books for this one.) 13. Bond Market What are the implications for bond investors of the lack of transparency in the bond market? 14. Treasury Market All Treasury bonds are relatively liquid, but some are more liquid than others. Take a look back at Figure 7.4. Which issues appear to be the most liquid? The least liquid? 15. Rating Agencies A controversy erupted regarding bond-rating agencies when some agencies began to provide unsolicited bond ratings. Why do you think this is controversial? 16. Bonds as Equity The 100-year bonds we discussed in the chapter have something in common with junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise. What are the issues here? Why would a company want to sell equity in disguise?

3 238 PART THREE Valuation of Future Cash Flows Questions and Problems Basic (Questions 1 14) 1. Interpreting Bond Yields Is the yield to maturity on a bond the same thing as the required return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on the bond now? The YTM? 2. Interpreting Bond Yields Suppose you buy a 7 percent coupon, 20-year bond today when it s first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why? 3. Bond Prices WMS, Inc., has 7 percent coupon bonds on the market that have 10 years left to maturity. The bonds make annual payments. If the YTM on these bonds is 9 percent, what is the current bond price? 4. Bond Yields Finley Co. has 10 percent coupon bonds on the market with nine years left to maturity. The bonds make annual payments. If the bond currently sells for \$1,075.25, what is its YTM? 5. Coupon Rates Mustaine Enterprises has bonds on the market making annual payments, with 13 years to maturity, and selling for \$850. At this price, the bonds yield 7.4 percent. What must the coupon rate be on Mustaine s bonds? 6. Bond Prices Mullineaux Co. issued 11-year bonds one year ago at a coupon rate of 8.6 percent. The bonds make semiannual payments. If the YTM on these bonds is 7.5 percent, what is the current bond price? 7. Bond Yields Clapper Corp. issued 12-year bonds 2 years ago at a coupon rate of 7.8 percent. The bonds make semiannual payments. If these bonds currently sell for 108 percent of par value, what is the YTM? 8. Coupon Rates Barely Heroes Corporation has bonds on the market with 14.5 years to maturity, a YTM of 9 percent, and a current price of \$850. The bonds make semiannual payments. What must the coupon rate be on Barely Heroes bonds? 9. Calculating Real Rates of Return If Treasury bills are currently paying 8 percent and the inflation rate is 6 percent, what is the approximate real rate of interest? The exact real rate? 10. Inflation and Nominal Returns Suppose the real rate is 3.5 percent and the inflation rate is 3 percent. What rate would you expect to see on a Treasury bill? 11. Nominal and Real Returns An investment offers a 16 percent total return over the coming year. Alan Wingspan thinks the total real return on this investment will be only 10 percent. What does Alan believe the inflation rate will be over the next year? 12. Nominal versus Real Returns Say you own an asset that had a total return last year of 13 percent. If the inflation rate last year was 4 percent, what was your real return? 13. Using Treasury Quotes Locate the Treasury issue in Figure 7.4 maturing in November Is this a note or a bond? What is its coupon rate? What is its bid price? What was the previous day s asked price? 14. Using Treasury Quotes Locate the Treasury bond in Figure 7.4 maturing in November Is this a premium or a discount bond? What is its current yield? What is its yield to maturity? What is the bid-ask spread?

7 242 PART THREE Valuation of Future Cash Flows FRED data, then Interest Rates. You will find listings for Moody s Seasoned Aaa Corporate Bond Yield and Moody s Seasoned Baa Corporate Bond Yield. A default premium can be calculated as the difference between the Aaa bond yield and the Baa bond yield. Calculate the default premium using these two bond indices for the most recent 36 months. Is the default premium the same for every month? Why do you think this is? A B C D E F G H 1 2 Using a spreadsheet for time value of money calculations 3 4 If we invest \$25,000 at 12 percent, how long until we have \$50,000? We need to solve 5 for the unknown of periods, so we use the formal NPER (rate, pmt, pvfv) 6 7 Present Value (pv) \$25,000 8 Future Value (fv) \$50,000 9 Rate (rate) Periods: Spreadsheet Templates 7 5, 7 6, 7 7, 7 18, 7 27 The formal entered in cell B 10 is = NPER: notice that pmt is zero and that pv has a negative sign on it. Also notice that rate is entered as decimal, not a percentage.

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