years to maturity. The bonds make semiannual payments and currently sell for 106.32 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield? needed expansion projects. The company currently has 6 percent coupon bonds on the market with a par value of $1,000 that sell for $967, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par? 23. Accrued Interest [ [ [ LO2] You purchase a bond with an invoice price of $1,053 and a par value of $1,000. The bond has a coupon rate of 5.3 percent, and there are four months to the next semiannual coupon date. What is the clean price of the bond? 24. Accrued Interest [ [ [ LO2] You purchase a bond with a coupon rate of 6.4 percent, a par value of $1,000, and a clean price of $1,027. If the next semiannual coupon payment is due in two months, what is the invoice price? 25. Finding the Bond Maturity [ [ LO2] Milton Corp. has 8 percent coupon bonds making annual payments with a YTM of 7.2 percent. The current yield on these bonds is 7.55 percent. How many years do these bonds have left until they mature? 26. Using Bond Quotes [ [ LO2] Suppose the following bond quotes for IOU Corporation appear in the financial page of today's newspaper. Assume the bond has a face value of $2,000 and the current date is April 19,2021. What is the yield to maturity of the bond? What is the current yield? 27. Bond Prices versus Yields [ [ [ LO2] a. What is the relationship between the price of a bond and its YTM? b. Explain why some bonds sell at a premium over par value while other bonds sell at a discount. What do you know about the relationship between the coupon rate and the YTM for premium bonds? What about for discount bonds? For bonds selling at par value? c. What is the relationship between the current yield and YTM for premium bonds? For discount bonds? For bonds selling at par value? plant expansion, and it has decided to issue 25 -year zero coupon bonds with a par value of $1,000 each to raise the money. The required return on the bonds will be 5.3 percent. Assume semiannual compounding periods. a. What will these bonds sell for at issuance? b. Using the IRS amortization rule, what interest deduction can the company take on these bonds in the first year? In the last year? c. Repeat part (b) using the straight-line method for the interest deduction. (Questions 1-17) 1. Interpreting Bond Yields [ [ ] LO1] 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 then? The YTM? 2. Interpreting Bond Yields [ [ [O LO2] 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. Valuing Bonds [ [ [ LO2] Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of 1,000,27 years to maturity, and a coupon rate of 3.6 percent paid annually. If the yield to maturity is 3.2 percent, what is the current price of the bond in euros? 4. Bond Yields [ [ [ LO2] A Japanese company has a bond outstanding that sells for 96.318 2 percent of its 100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond? with eight years to maturity, a par value of $1,000, and selling for $962. At this price, the bonds yield 5.1 percent. What must the coupon rate be on the bonds? 6. Bond Prices [ [ LO2] Westco Co. issued 15-year bonds a year ago at a coupon rate of 5.4 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 4.5 percent, what is the current price of the bond in dollars? 7. Bond Yields [ [ LO2] Ashburn Corp. issued 25-year bonds two years ago at a coupon rate of 5.6 percent. The bonds make semiannual payments. If these bonds currently sell for 97 percent of par value, what is the YTM? 8. Coupon Rates [ [ LO2] Draiman Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $987. The bonds make semiannual payments. What must the coupon rate be on these bonds? 9. Zero Coupon Bonds [ [ [3 LO2] You find a zero coupon bond with a par value of $10,000 and 24 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the dollar price of the bond? Assume semiannual compounding periods. 10. Valuing Bonds [ [ LO2] Yan Yan Corp. has a \$2,000 par value bond outstanding with a coupon rate of 4.7 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 5.05 percent. What is the dollar price of the bond? d. Based on your answers in (b) and (c), which interest deduction method would the company prefer? Why? 29. Zero Coupon Bonds [ [ LO2] Suppose your company needs to raise $65 million and you want to issue 20-year bonds for this purpose. Assume the required return on your bond issue will be 4.9 percent, and you're evaluating two issue alternatives: a semiannual coupon bond with a coupon rate of 4.9 percent, and a zero coupon bond. The tax rate is 21 percent. Both bonds will have a par value of $1,000. a. How many of the coupon bonds would you need to issue to raise the $65 million? How many of the zeroes would you need to issue? Page242 b. In 20 years, what will your company's repayment be if you issue the coupon bonds? What if you issue the zeroes? c. Based on your answers in parts (a) and (b), why would you ever want to issue the zeroes? To answer, calculate the firm's aftertax cash flows for the first year under the two different scenarios. Assume the IRS amortization rules apply for the zero coupon bonds. 30. Finding the Maturity [ [ LO2] You've just found a 10 percent coupon bond on the market that sells for par value. What is the maturity on this bond? 31. Real Cash Flows [ [O [ 4] You want to have $2.5 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10.1 percent and the inflation rate is 3.4 percent. What real amount must you deposit each year to achieve your goal? CHALLENGE (Questions 32-38) 32. Components of Bond Returns [ [ [LO] Bond P is a premium bond with a coupon rate of 9 percent. Bond D has a coupon rate of 5 percent and is currently selling at a discount. Both bonds make annual payments, have a par value of $1,000, a YTM of 7 percent, and 15 years to maturity. What is the current yield for Bond P? For Bond D? If interest rates remain unchanged, what is the expected capital gains yield over the next year for Bond P? For Bond D ? Explain your answers and the interrelationships among the various types of yields. 33. Holding Period Yield [ [ LO2] The YTM on a bond is the interest rate you earn on your investment if interest rates don't change. If you actually sell the bond before it matures, your realized return is known as the holding period yield (HPY). a. Suppose that today you buy a bond with an annual coupon rate of 7 percent for $1,050. The bond has 17 years to maturity. What rate of return do you expect to earn on your investment? Assume a par value of $1,000. b. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell. What price will your bond sell for? What is the HPY on your investment? Compare this yield to the YTM when you first bought the bond. Why are they different? 34. Valuing Bonds [ [ LO2] Cookie Dough Corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $900 every six months over the subsequent eight years, and finally pays $1,300 every six months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it makes no coupon payments over the life of the 11. Valuing Bonds [ [ LO2] Union Local School District has a bond outstanding with Page 240 a coupon rate of 2.9 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 2.7 percent, and the bond has a par value of $5,000. What is the dollar price of the bond? 12. Calculating Real Rates of Return [ [ [ L 4] If Treasury bills are currently paying 4.6 percent and the inflation rate is 1.9 percent, what is the approximate real rate of interest? The exact real rate? 13. Inflation and Nominal Returns [ [O [ [ Suppose the real rate is 1.8 percent and the inflation rate is 2.7 percent. What rate would you expect to see on a Treasury bill? 14. Nominal and Real Returns [ [ LO4] An investment offers a total return of 11.7 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 9 percent. What does Janice believe the inflation rate will be over the next year? 15. Nominal versus Real Returns [ [ LO4] Say you own an asset that had a total return last year of 14.1 percent. If the inflation rate last year was 2.83 percent, what was your real return? 16. Using Treasury Quotes [ [ LO2] Locate the Treasury issue in Figure 7.5 maturing in February 2029. What is its coupon rate? What is its bid price? What was the previous day's asked price? Assume a par value of $10,000. 17. Using Treasury Quotes [ [ LO2] Locate the Treasury bond in Figure 7.5 maturing in November 2026. 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 in dollars? Assume a par value of $10,000. INTERMEDIATE (Questions 18-31) 18. Bond Price Movements [ [ [CO 2] Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 6.8 percent, has a YTM of 6.2 percent, and has 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6.2 percent, has a YTM of 6.8 percent, and also has 13 years to maturity. The bonds have a par value of $1,000. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 3 years? In 8 years? In 12 years? In 13 years? What's going on here? Illustrate your answers by graphing bond prices versus time to maturity. 19. Interest Rate Risk [ [ LO2] Both Bond Sam and Bond Dave have 7.1 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate risk of longer-term bonds? 20. Interest Rate Risk [ [ LO2] Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds