Valuing Bonds

Chapter 6, Solutions

Cornett, Adair, and Nofsinger

CHAPTER 6 – Valuing Bonds Questions LG1 1. What does a call provision allow the issuer to do, and why would they do it? A call provision on a bond issue allows the issuer to pay off the bond debt early at a cost of the principal plus any call premium. Most of the time a bond issuer is called, it is because interest rates have substantially declined in the economy. The issuer calls the existing bonds and issues new bonds at the lower interest rate. This reduces the interest payments the issuer must pay each year. LG2 2. List the differences between the new TIPS and traditional Treasury bonds. Traditional Treasury bonds have a fixed principal and constant payments. Because the principal and coupon rate are fixed, interest rate changes in the economy cause the market price of the bonds to have large fluctuations. On the other hand, the principal of a TIPS increases with the rate of inflation. Similar to a T-bond, the TIPS has a constant coupon rate. However, since the principal of the TIPS increases over time, the interest payment increases over time. This inflation rate adjustment of a TIPS’ principal every six months reduces the amount of downward price change in the price of the bond when interest rates increase. LG2 3. Explain how mortgage-backed securities work. A large amount of home mortgages are purchased and pooled together. The home owners pay interest and principal monthly on their mortgages. Bonds are issued from the pool of mortgages, using the mortgages as collateral. The interest payments and bond principal payments for these mortgage-backed securities (MBS) originate from the mortgage borrowers and flow through the pool of mortgages. As the home owners pay off their mortgages over time, the MBS are also paid. LG3 4. Provide the definitions of a discount bond and a premium bond. Give examples. A discount bond is simply a bond that is selling below its par value. It would be quoted at a price that is less than 100 percent of par, like 99.05. A premium bond is a bond selling above its par value. Its price will be quoted as over 100 percent of par value, like 101.15. A bond becomes a discount bond when market interest rates rise above the bond’s coupon rate. A bond becomes a premium bond when market interest rates fall below the bond’s coupon rate. LG4 5. Describe the differences in interest payments and bond price between a 5 percent coupon bond and a zero coupon bond.

7-1

Chapter 6, Solutions

Cornett, Adair, and Nofsinger

The 5 percent coupon bond pays annual interest of 5 percent of the bond’s par value. For $1,000 par value bond, this would be $50 per year. This interest might be paid in two payments of $25. The price of the coupon bond tends to stay near its par value. The zero coupon bond pays no interest payments. The bondholder earns a return from the increase of the bond’s market price over time. The bond’s price is initially much lower than its par value. When the zero coupon bond finally matures, the par value is paid. LG5 6. All else equal, which bond’s price is more affected by a change in interest rates, a short-term bond or a longer-term bond? Why? All else equal, a long-term bond experiences larger price changes when interest rates change than a short-term bond. A bond’s price is the present value of all its cash flows. Changes in the discount rate (the interest rate) impact present values more for cash flows that are further out in time. LG5 7. All else equal, which bond’s price is more effected by a change in interest rates, a bond with a large coupon or a small coupon? Why? The price of the bond with the small coupon will be impacted more by a change in interest rates than the price of the large coupon bond. For a small coupon bond, the cash flows are weighted much more toward the maturity date because of the small interest payments. The large coupon bond has high interest payments, many occur soon. These higher cash flows made earlier dampen the impact of interest rate changes because those changes in the discount rate impact the earlier cash flows to a lesser degree than the later cash flows. LG5 8. Explain how a bond’s interest rate can change over time even if interest rates in the economy do not change. Because of the yield curve, there are different interest rates that apply to each time to maturity. So, as a bond gets closer to its maturity date, different interest rates may apply to its discounting even when interest rates in the economy have not changed. LG6 9. Compare and contrast the advantages and disadvantages of the current yield computation versus yield to maturity calculations. The current yield computation is useful because it is a very simple one. It provides a quick and easy assessment of what the bond offers the investor in return. But it measures only the return from the interest rate payments. The full return to an investor also includes the capital gain or loss the bond will experience if it is selling as a discount or premium bond. The yield to maturity computation is more difficult, but it incorporates the full return the bond offers to investors. LG6 10. What is the yield to call and why is it important to a bond investor?

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

Many bonds do not survive until their maturity date because they get paid early through a call provision. The yield to call is the yield that would be earned if the bond is purchased at today’s price and held until it is called by the issuer. The computation incorporates the additional call premium that is paid with the principal. LG6 11. What is the purpose of computing the equivalent taxable yield of a municipal bond? Municipal bonds offer a tax advantage for the bondholder that other kinds of bonds do not offer. Thus, their yield to maturity is not directly comparable to that of other bonds. The equivalent taxable yield (ETY) is an adjustment to the yield to make it comparable to taxable bonds. Bond investors can use the ETY to assess which bond will earn them a higher after-tax return. LG6 12. Explain why high income and wealthy people are more likely to buy a municipal bond than a corporate bond. Individual bondholders do not owe taxes on interest payments received from municipal bonds. This tax advantage is more valuable to individuals who are in a higher marginal tax bracket. Because wealth individuals are usually in a higher tax bracket, this tax advantage is more valuable to them. LG7 13. Why does a Treasury bond offer a lower yield than a corporate bond with the same time to maturity? Could a corporate bond with a different time to maturity offer a lower yield? Explain. The Treasury bond has lower credit risk than the corporate bond. Given the risk/return relationship, lower risk is associated with lower expected return. Thus, all else equal, a Treasury bond will offer a lower yield to maturity than a corporate bond. However, if the yield curve slopes upward, then shorter term to maturity bonds will require a smaller interest rate than longer term bonds. So, it is possible that a short-term corporate bond would offer a lower yield than a long-term Treasury bond. LG7 14. Describe the difference between a bond issued as a high-yield bond and one that has become a “fallen angel.” Both of these bonds would be rated as BB or below. The company referred to as a fallen angel would be a firm that was a successful, financially stable firm that has recently struggled. Many of the bondholders had purchased the bond when it was rated much better. The other company issued bonds when it was already in a less financially stable condition. The purchasers of these bonds bought the bonds while they were rated as a junk bond. LG8 15. What is the difference in the trading volume between Treasury bonds and corporate bonds? Give examples and/or evidence.

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

There is high trading volume in Treasury bonds and low volume in corporate bonds. LG8 16. Explain how the Lehman Brothers Intermediate Bond Index might increase one day while the Merrill Lynch High Yield Index decreases the same day. These two indices use different bonds. This Lehman index uses Treasury bonds with medium terms to maturity. The Merrill Lynch index uses high risk bonds. When investors determine that there is more risk in the economy, the spread between the safer bonds (Treasuries) and riskier bonds (high yield) widen. If risk in the economy is perceived to be declining, this spread will decrease. This question is an example of the spread widening. Problems Basic Problems LG1

6-1 Interest Payments Determine the interest payment for the following three bonds: 3 ½ percent coupon corporate bond (paid semi-annually), 4.25 percent coupon Treasury note, and a corporate zero coupon bond maturing in 10 years. (Assume a $1,000 par value.) 3 ½ percent coupon corporate bond (paid semi-annually): ½ × 3.5% × $1,000 = $17.50 4.25 percent coupon Treasury note: ½ × 4.25% × $1,000 = $21.25 corporate zero coupon bond maturing in 10 years: 0% × $1,000 = $0

LG1

6-2 Interest Payments Determine the interest payment for the following three bonds: 4 ½ percent coupon corporate bond (paid semi-annually), 5.15 percent coupon Treasury note, and a corporate zero coupon bond maturing in 15 years. (Assume a $1,000 par value.) 4 ½ percent coupon corporate bond (paid semi-annually): ½ × 4.5% × $1,000 = $22.50 5.15 percent coupon Treasury note: ½ × 5.15% × $1,000 = $25.75 corporate zero coupon bond maturing in 10 years: 0% × $1,000 = $0

LG1

6-3 Time to Maturity A bond issued by Ford on May 15, 1997 is scheduled to mature on May 15, 2097. If today is November 16, 2008, what is this bond’s time to maturity? May 15, 2097 minus November 16, 2008 = 88 years and 6 months

LG1

6-4 Time to Maturity A bond issued by IBM on December 1, 1996 is scheduled to mature on December 1, 2096. If today is December 2, 2007, what is this bond’s time to maturity? December 1, 2096 minus December 2, 2007 = 89 years

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Chapter 6, Solutions

LG1

Cornett, Adair, and Nofsinger

6-5 Call Premium A 7 percent corporate coupon bond is callable in five years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? principal + call premium = $1,000 + 7%×$1,000 = $1,070

LG1

6-6 Call Premium A 6.5 percent corporate coupon bond is callable in ten years for a call premium of one year of coupon payments. Assuming a par value of $1,000, what is the price paid to the bondholder if the issuer calls the bond? principal + call premium = $1,000 + 6.5%×$1,000 = $1,065

LG2

6-7 TIPS Interest and Par Value A 2 ¾ percent TIPS has an original reference CPI of 185.4. If the current CPI is 210.7, what is the current interest payment and par value of the TIPS? par value = 210.7/185.4 × $1,000 = $1,136.46 interest payment = ½ × 2.75% × $1,136.46 = $15.63

LG2

6-8 TIPS Interest and Par Value A 3 1/8 percent TIPS has an original reference CPI of 180.5. If the current CPI is 206.8, what is the current interest payment and par value of the TIPS? par value = 206.8/180.5 × $1,000 = $1,145.71 interest payment = ½ × 3.125% × $1,145.71 = $17.90

LG3

6-9 Bond Quotes Consider the following three bond quotes; a Treasury note quoted at 97:27, and a corporate bond quoted at 103.25, and a municipal bond quoted at 101.90. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? Treasury note at 97:27: (97+27/32)% × $1,000 = $978.44 Corporate bond at 103.24: 103.24% × $1,000 = $1,032.40 Municipal bond at 101.90: 101.90% × $5,000 = $5,095.00

LG3

6-10 Bond Quotes Consider the following three bond quotes; a Treasury bond quoted at 106:14, and a corporate bond quoted at 96.55, and a municipal bond quoted at 100.95. If the Treasury and corporate bonds have a par value of $1,000 and the municipal bond has a par value of $5,000, what is the price of these three bonds in dollars? Treasury note at 106:14: (106+14/32)% × $1,000 = $1,064.375 Corporate bond at 96.55: 96.55% × $1,000 = $965.50 Municipal bond at 100.95: 100.95% × $5,000 = $5,047.50

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Chapter 6, Solutions

LG4

6-11 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 20 years if the market interest rate is 6.5 percent. use semi-annual compounding: PV =

LG4

Cornett, Adair, and Nofsinger

FVN $1,000 $1,000 = = = $278.23 N 40 3.594 (1 + i ) 1.0325

6-12 Zero Coupon Bond Price Calculate the price of a zero coupon bond that matures in 15 years if the market interest rate is 7.25 percent. : use semi-annual compounding: PV =

LG6

FVN $1,000 $1,000 = = = $343.61 N 30 2.910 (1 + i ) 1.03625

6-13 Current Yield What’s the current yield of a 5.5 percent coupon corporate bond quoted at a price of 102.08? 5.5% ÷ 102.08% = 0.05388 = 5.39%

LG6

6-14 Current Yield What’s the current yield of a 7.2 percent coupon corporate bond quoted at a price of 96.78? 7.2% ÷ 96.78% = 0.07440 = 7.44%

LG6

6-15 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to maturity of 3.5 percent for an investor in the 28 percent marginal tax bracket? Muni yield

3.5%

Use equation 6.4: Equivalent taxable yield = 1 −tax rate = 1 − 0.28 = 4.86% LG6

6-16 Taxable Equivalent Yield What’s the taxable equivalent yield on a municipal bond with a yield to maturity of 2.9 percent for an investor in the 33 percent marginal tax bracket? Muni yield

2.9%

Use equation 6.4: Equivalent taxable yield = 1 −tax rate = 1 − 0.33 = 4.33% LG7

6-17 Credit Risk and Yield Rank order from highest credit risk to lowest risk the following bonds, with the same time to maturity, by their yield to maturity: Treasury bond with yield of 5.55 percent, IBM bond with yield of 7.49 percent, Trump Casino bond with yield of 8.76 percent, and Banc One bond with a yield of 5.99 percent. Trump Casino bond with yield of 8.76 percent IBM bond with yield of 7.49 percent

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

Banc One bond with a yield of 5.99 percent Treasury bond with yield of 5.55 percent LG7

6-18 Credit Risk and Yield Rank the following bonds in order from lowest credit risk to highest risk all with the same time to maturity, by their yield to maturity: Treasury bond with yield of 4.65 percent, United Airline bond with yield of 9.07 percent, Bank of America bond with a yield of 6.25 percent, and Hewlett Packard bond with yield of 6.78 percent. Treasury bond with yield of 4.65 percent Bank of America bond with a yield of 6.25 percent Hewlett Packard bond with yield of 6.78 percent United Airline bond with yield of 9.07 percent

Intermediate Problems 6-19 TIPS Capital Return Consider a 3.5% TIPS with an issue CPI reference of 185.6. At the beginning of this LG2 year, the CPI was 196.2 and was at 201.3 at the end of the year. What was the capital gain of the TIPS in dollars and in percentage terms? gain = end of year value – beginning of year value = 201.3/185.6 × $1,000 − 196.2/185.6 × $1,000 = $1,084.59 − $1,057.11 = $27.48 As a percentage, the gain was = $27.48 ÷ $1,057.11 = 2.60% LG2

6-20 TIPS Capital Return Consider a 2.25% TIPS with an issue CPI reference of 183.5. At the beginning of this year, the CPI was 197.1 and was at 203.8 at the end of the year. What was the capital gain of the TIPS in dollars and in percentage terms? gain = end of year value – beginning of year value = 203.8/183.5 × $1,000 − 197.1/183.5 × $1,000 = $1,110.63 − $1,074.11 = $36.52 As a percentage, the gain was = $36.52 ÷ $1,074.11 = 3.40%

LG4

6-21 Compute Bond Price Compute the price of a 4.5 percent coupon bond with 15 years left to maturity and a market interest rate of 6.8 percent. (Assume interest payments are semi-annual.) Is this a discount or premium bond? 1  1 −(1 +0.034 )30 Bond Price =$22.50 × 0.034   

  1,000 + =$419.05 +$366.76 =$785.81 30  (1 +0.034 )  

Or N=30, I=3.4, PMT=22.5, FV=1000 CPT PV = -785.81 Since this is less then $1,000, it is a discount bond.

7-7

Chapter 6, Solutions

LG4

Cornett, Adair, and Nofsinger

6-22 Compute Bond Price Compute the price of a 5.6 percent coupon bond with 10 years left to maturity and a market interest rate of 7.0 percent. (Assume interest payments are semi-annual.) Is this a discount or premium bond? 1  1 −(1 +0.035) 20 Bond Price =$28.00 × 0.035   

  1,000 + =$397.95 +$502.56 =$900.51 20  (1 +0.035)  

Or N=20, I=3.5, PMT=28, FV=1000 CPT PV = -900.51 Since this is less then $1,000, it is a discount bond. LG4

6-23 Compute Bond Price Calculate the price of a 6.2 percent coupon bond with 18 years left to maturity and a market interest rate of 5.9 percent. (Assume interest payments are semi-annual.) Is this a discount or premium bond? 1  1 −(1 +0.0295)36 Bond Price =$31.00 × 0.0295   

  1,000 + =$681.88 +$351.11 =$1,032.99 36  (1 +0.0295)  

Or N=36, I=2.95, PMT=31, FV=1000 CPT PV = -1,032.99 Since the bond is greater then $1,000, it is a premium bond. LG4

6-24 Compute Bond Price Calculate the price of a 5.7 percent coupon bond with 25 years left to maturity and a market interest rate of 4.8 percent. (Assume interest payments are semi-annual.) Is this a discount or premium bond? 1  1 − (1 +0.024 ) 50 Bond Price =$28.50 × 0.024   

  1,000 + =$824.73 +$305.49 =$1,130.22  (1 +0.024 ) 50  

Or N=50, I=2.4, PMT=28.50, FV=1000 CPT PV = -1,130.22 Since the bond is greater then $1,000, it is a premium bond. LG5

6-25 Bond Prices and Interest Rate Changes A 5.75 percent coupon bond with 10 years left to maturity is priced to offer a 6.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.0 percent. What is the change in price the bond will experience in dollars? Compute the current bond price: 1  1 −(1 +0.0325) 20 Bond Price =$28.75 × 0.0325   

  1,000 + =$418.01 +$527.47 =$945.48 20  (1 +0.0325)  

Or N=20, I=3.25, PMT=28.75, FV=1000 CPT PV = -945.48

7-8

Chapter 6, Solutions

Cornett, Adair, and Nofsinger

Now compute the price in one year: 1  1 −(1 +0.03)18 Bond Price =$28.75 × 0.03   

  1,000 + =$395.41 +$587.40 =$982.81 18 ( 1 + 0.03)   

Or N=18, I=3.0, PMT=28.75, FV=1000 CPT PV = -982.81 So the dollar change in price is: $982.81 − $945.48 = $37.33 LG5

6-26 Bond Prices and Interest Rate Changes A 6.5 percent coupon bond with 14 years left to maturity is priced to offer a 7.2 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.8 percent. What is the change in price the bond will experience in dollars? Compute the current bond price: 1  1 −(1 +0.036 ) 28 Bond Price =$32.50 × 0.036   

  1,000 + =$567.42 +$371.47 =$938.89 28  (1 +0.036 )  

Or N=28, I=3.6, PMT=32.50, FV=1000 CPT PV = -938.89 Now compute the price in one year: 1  1 −(1 +0.034 ) 26 Bond Price =$32.50 × 0.034   

  1,000 + =$555.14 +$419.24 =$974.38 26  (1 +0.034 )  

Or N=26, I=3.4, PMT=32.50, FV=1000 CPT PV = -974.38 So the dollar change in price is: $974.38 − $938.89 = $35.49 LG6

6-27 Yield to Maturity A 6.85 percent coupon bond with 26 years left to maturity is offered for sale at $1,035.25. What yield to maturity is the bond offering? (Assume interest payments are paid semi-annually.) N=52, PV=-1035.25, PMT=34.25, FV=1000 6.57%

LG6

CPT I = 3.264%, YTM = 3.264% × 2 =

6-28 Yield to Maturity A 5.25 percent coupon bond with 14 years left to maturity is offered for sale at $955.75. What yield to maturity is the bond offering? (Assume interest payments are paid semi-annually.) N=28, PV=-955.75, PMT=26.25, FV=1000 5.71%

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CPT I = 2.857%, YTM = 2.857% × 2 =

Chapter 6, Solutions

LG6

Cornett, Adair, and Nofsinger

6-29 Yield to Call A 6.75 percent coupon bond with 26 years left to maturity can be called in 6 years. The call premium is one year of coupon payments. It is offered for sale at $1,135.25. What yield to call of the bond? (Assume that interest payments are paid semi-annually.) N=12, PV=-1135.25, PMT=33.75, FV=1067.50 CPT I = 2.541%, YTC = 2.541% × 2 = 5.08%

LG6

6-30 Yield to Call A 5.25 percent coupon bond with 14 years left to maturity can be called in 4 years. The call premium is one year of coupon payments. It is offered for sale at $1,075.50. What yield to call of the bond? (Assume that interest payments are paid semi-annually.) N=8, PV=-1075.50, PMT=26.25, FV=1052.50 CPT I = 2.193%, YTC = 2.193% × 2 = 4.39%

LG6

6-31 Comparing Bond Yields A client in the 33 percent marginal tax bracket is comparing a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? Muni yield

4.5%

First determine the ETY: Equivalent taxable yield = 1 −tax rate = 1 −0.33 = 6.72% Since 6.72% > 6.45%, the client should take the municipal bond. LG6

6-32 Comparing Bond Yields A client in the 28 percent marginal tax bracket is comparing a municipal bond that offers a 4.5 percent yield to maturity and a similar-risk corporate bond that offers a 6.45 percent yield. Which bond will give the client more profit after taxes? Muni yield

4.5%

First determine the ETY: Equivalent taxable yield = 1 −tax rate = 1 − 0.28 = 6.25% Since 6.25% < 6.45%, the client should take the corporate bond. Advanced Problems 6-33 TIPS Total Return Reconsider the 3.5% TIPS discussed in problem 6-19. It was LG2 issued with CPI reference of 185.6. The bond is purchased at the beginning of the year (after the interest payment), when the CPI was 196.2. For the interest payment in the middle of the year, the CPI was 199.6. Now, at the end of the year, the CPI is 201.3 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? capital gain = end of year value – beginning of year value =

7-10

Chapter 6, Solutions

Cornett, Adair, and Nofsinger

201.3/185.6 × $1,000 − 196.2/185.6 × $1,000 = $1,084.59 − $1,057.11 = $27.48 The mid-year interest payment was: ½ × 3.5% × 199.6/185.6 × $1,000 = $18.82 The end-of-year interest payment was: ½ × 3.5% × 201.3/185.6 × $1,000 = $18.98 Total dollar return = $27.48 + $18.82 + $18.98 = $65.28 As a percentage, the return was = $65.28 ÷ $1,057.11 = 6.18% LG2

6-34 TIPS Total Return Reconsider the 2.25% TIPS discussed in problem 6-20. It was issued with CPI reference of 183.5. The bond is purchased at the beginning of the year (after the interest payment), when the CPI was 197.1. For the interest payment in the middle of the year, the CPI was 200.1. Now, at the end of the year, the CPI is 203.8 and the interest payment has been made. What is the total return of the TIPS in dollars and in percentage terms for the year? gain = end of year value – beginning of year value = 203.8/183.5 × $1,000 − 197.1/183.5 × $1,000 = $1,110.63 − $1,074.11 = $36.52 The mid-year interest payment was: ½ × 2.25% × 200.1/183.5 × $1,000 = $12.27 The end-of-year interest payment was: ½ × 2.25% × 203.8/183.5 × $1,000 = $12.49 Total dollar return = $36.52 + $12.27 + $12.49 = $61.28 As a percentage, the return was = $61.28 ÷ $1,074.11 = 5.71%

LG5

6-35 Bond Prices and Interest Rate Changes A 6.25 percent coupon bond with 22 years left to maturity is priced to offer a 5.5 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.0 percent. If this occurs, what would be the total return of the bond in dollars and percent? Compute the current bond price: 1  1 −(1 +0.0275) 44 Bond Price =$31.25 × 0.0275   

  1,000 + =$791.92 +$303.11 =$1,095.03 44  (1 +0.0275)  

Or N=44, I=2.75, PMT=31.25, FV=1000 CPT PV = -1095.03 Now compute the price in one year: 1  1 −(1 +0.03) 42 Bond Price =$31.15 × 0.03   

  1,000 + =$740.67 +$288.96 =$1,029.63 42  (1 +0.03)  

Or N=42, I=3.0, PMT=31.25, FV=1000 CPT PV = -1029.63 So the dollar change in price + interest payments are: $1,029.63 − $1,095.03 + $62.50 = $-2.90 The percentage return is: -2.90 ÷ 1,095.03 = -0.26% LG5

6-36 Bond Prices and Interest Rate Changes A 7.5 percent coupon bond with 13 years left to maturity is priced to offer a 6.25 percent yield to maturity. You believe that in one

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

year, the yield to maturity will be 7.0 percent. If this occurs, what would be the total return of the bond in dollars and percentage terms? Compute the current bond price: 1  1 −(1 +0.03125) 26 Bond Price =$37.50 × 0.03125   

  1,000 + =$660.84 +$449.30 =$1,110.14 26  (1 +0.03125)  

Or N=26, I=3.125, PMT=37.50, FV=1000 CPT PV = -1110.14 Now compute the price in one year: 1  1 −(1 +0.035) 24 Bond Price =$37.50 × 0.035   

  1,000 + =$602.19 +$437.96 =$1,040.15 24 (  1 +0.035)  

Or N=24, I=3.5, PMT=37.50, FV=1000 CPT PV = -1040.15 So the dollar change in price + interest payments are: $1,040.15 − $1,110.14 + $75.00 = $5.01 The percentage return is: 5.01 ÷ 1,110.14 = 0.45% LG6

6-37 Yields of a Bond A 3.75 percent coupon municipal bond has 14 years left to maturity and has a price quote of 98.45. The bond can be called in 4 years. The call premium is one year of coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax bracket), and yield to call. (Assume interest payments are paid semi-annually and a par value of $5,000.) Current yield = 3.75 ÷ 98.45 = 3.81% YTM: N=28, PV=-4922.50, PMT=93.75, FV=5000 CPT I = 1.947%, YTM = 1.947% × 2 = 3.89% Equivalent taxable yield =

Muni yield 3.89% = = 5.98% 1 −tax rate 1 − 0.35

YTC: N=8, PV=-4922.50, PMT=93.75, FV=5187.50 CPT I = 2.52%, YTM = 2.52% × 2 = 5.04% The current yield is higher than the coupon rate because this is currently a discount bond. This is also shown in a YTM that is greater than the coupon rate. The YTC is comparatively high, but it is currently not likely that the bond will be called early since interest rates are high. LG6

6-38 Yields of a Bond A 4.25 percent coupon municipal bond has 18 years left to maturity and has a price quote of 97.65. The bond can be called in 8 years. The call premium is one year of coupon payments. Compute and discuss the bond’s current yield, yield to maturity, taxable equivalent yield (for an investor in the 35 percent marginal tax

7-12

Chapter 6, Solutions

Cornett, Adair, and Nofsinger

bracket), and yield to call. (Assume interest payments are paid semi-annually and a par value of $5,000.) Current yield = 4.25 ÷ 97.65 = 4.35% YTM: N=36, PV=-4882.50, PMT=106.25, FV=5000 CPT I = 2.22%, YTM = 2.22% × 2 = 4.44% Equivalent taxable yield =

Muni yield 4.44% = = 6.83% 1 −tax rate 1 − 0.35

YTC: N=16, PV=-4882.50, PMT=106.25, FV=5212.50 CPT I = 2.52%, YTM = 2.52% × 2 = 5.04% The current yield is higher than the coupon rate because this is currently a discount bond. This is also shown in a YTM that is greater than the coupon rate. The YTC is comparatively high, but it is currently not likely that the bond will be called early since interest rates are high. LG7

6-39 Bond Ratings and Prices A corporate bond with a 6.5 percent coupon has 15 years left to maturity. It has had a credit rating of BBB and a yield to maturity of 7.2 percent. The firm has recently gotten into some trouble and the rating agency is downgrading the bonds to BB. The new appropriate discount rate will be 8.5 percent. What will be the change in the bond’s price in dollars and percentage terms? (Assume interest payments are paid semi-annually.) Compute the current bond price: 1  1 −(1 +0.036 )30 Bond Price =$32.50 × 0.036   

  1,000 + =$590.32 +$346.11 =$936.43 30  (1 +0.036 )  

Or N=30, I=3.6, PMT=32.50, FV=1000 CPT PV = -936.43 Now compute the price after the rating change: 1  1 −(1 +0.0425 ) 30 Bond Price =$32.50 × 0.0425   

  1,000 + =$545.32 +$286.89 =$832.21 30  (1 +0.0425)  

Or N=30, I=4.25, PMT=32.50, FV=1000 CPT PV = -832.21 So the dollar change in price is: $832.21 − $936.43 = $-104.22 The percentage return is: -104.22 ÷ 936.43 = -11.13% LG7

6-40 Bond Ratings and Prices A corporate bond with a 6.75 percent coupon has 10 years left to maturity. It has had a credit rating of BB and a yield to maturity of 8.2 percent. The firm has recently become more financial stable and the rating agency is upgrading the bonds to BBB. The new appropriate discount rate will be 7.1 percent. What

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

will be the change in the bond’s price in dollars and percentage terms? (Assume interest payments are paid semi-annually.) Compute the current bond price: 1  1 −(1 +0.041) 20 Bond Price =$33.75 × 0.041   

  1,000 + =$454.64 +$447.70 =$902.34 20  (1 +0.041)  

Or N=20, I=4.1, PMT=33.75, FV=1000 CPT PV = -902.34 Now compute the price after the rating change: 1  1 −(1 +0.0355) 20 Bond Price =$33.75 × 0.0355   

  1,000 + =$477.51 +$497.73 =$975.24 20  (1 +0.0355)  

Or N=20, I=3.55 PMT=33.75, FV=1000 CPT PV = -975.24 So the dollar change in price is: $975.24 − $902.34 = $72.90 The percentage return is: 72.90 ÷ 902.34 = 8.08% 6-41 Excel Problem Say that in June of 2008, a company issued bonds that are scheduled to mature in June of 2011. The coupon rate is 5.75% and is paid semi-annually. The bond issue was rated AAA. A. Build a spreadsheet that shows how much money the firm pays for each interest rate payment and when those payments will occur if the bond issue sells 50,000 bonds. B. If the bond issue rating would have been BBB, then the coupon rate would have been 6.30%. Show the interest payments with this rating. Explain why bond ratings are important to firms issuing capital debt. C. Consider that interest rates in the economy increased in the first half of 2008. If the firm would have issued the bonds in January of 2008, then the interest rates would have only been 5.40%. How much extra money per year is the firm paying because it issued the bonds in June instead of January? The spreadsheet might look like: A. Coupon Rate= Par Value = Number of Bonds =

Jun-08 Dec-08 Jun-09 Dec-09

B.

C.

5.75% $1,000 50,000

6.30% $1,000 50,000

5.40% $1,000 50,000

Interest payments 0 $1,437,500 $1,437,500 $1,437,500

Interest payments 0 $1,575,000 $1,575,000 $1,575,000

Interest payments 0 $0 $1,350,000 $1,350,000

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Chapter 6, Solutions

Jun-10 Dec-10 Jun-11 Dec-11 Jun-12

Cornett, Adair, and Nofsinger

$1,437,500 $1,437,500 $1,437,500 $1,437,500

$1,575,000 $1,575,000 $1,575,000 $1,575,000

$1,350,000 $1,350,000 $1,350,000 $1,350,000 $1,350,000

B. The better the bond rating, the lower the interest rate a firm will have to pay. In this example, the firm has to pay $275,000 more each year in interest payment with the lower bond rating. C. The firm is paying $175,000 per year more in interest because it issued its bonds before the rates declined. Research It! Bond Information Online Information on the bond market is widely available in papers like The Wall Street Journal and Barron’s. Bond information can also be found online at financial websites like finance.yahoo.com, the Bond Market Association (www.bondmarkets.com), nasdbondinflo.com. The bond credit rating agencies also maintain websites with their own bond market news. You can follow the bond market easily at places like the Yahoo! Finance website. Click on the Bond link in the menu to go to their Bond Center. Bond yields for various maturity Treasury securities are shown for today and for previous days. The Bond Composite Rates link shows similar comparisons for municipal and corporate bonds too. Bond calculators are also available for free on the Web. Compare a bond price result from your calculator or the price equation with the online bond calculator result at Investopedia at www.investopedia.com/calculator/BondPrice.aspx SOLUTION: All answers will be different. Here is an example answer: An example done on the website…

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

1  1 −(1 +0.02 ) 6 Bond Price =$17.50 × 0.02   

  1,000 + =$98.03 +$887.97 =$986.00 6  (1 +0.02 )  

Or N=6, I=2, PMT=17.50, FV=1000 CPT PV = -985.996 All computations are the same. Integrated Mini Case: Corporate Bond Credit Risk Changes and Bond Prices Land’o’Toys is a profitable, medium sized, retail company. Several years ago it issued a 6½ percent coupon bond, which pays interest semi-annually. The bond will mature in ten years and is currently priced in the market as $1,037.19. The average yields to maturity for 10-year corporate bonds are reported in the following table by bond rating. Bond Rating AAA AA A BBB

Yield (%) 5.4 5.7 6.0 6.5

Bond Rating BB B CCC CC C D

Yield (%) 7.3 8.2 9.2 10.5 12.0 14.5

Periodically, one company will purchase another by buying all of the target firm’s stock. The bonds of the target firm continue to exist. The debt obligation is assumed by the new firm. The credit risk of the bonds often changes because of this type of an event.

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Chapter 6, Solutions

Cornett, Adair, and Nofsinger

Suppose that the firm Treasure Toys makes an announcement that they are purchasing Land’o’Toys. Due to Treasury Toy’s projected financial structure after the purchase, Standard & Poors states that the bond rating Land’o’Toys bonds will change to BB. A. Compute the yield to maturity of Land’o’Toys bonds before the purchase announcement and us it to determine the likely bond rating. B. Assume the bond’s price changes to reflect the new credit rating. What is the new price? Did the price increase or decrease? C. What is the dollar change and percentage change in the bond price? D. How do the bond investors feel about the announcement? SOLUTION: A. YTM: N=20, PV=-1,037.19, PMT=32.50, FV=1000 CPT I = 3.00%, YTM = 3.00% × 2 = 6.00% This bond is likely rated as an “A”. B. The new YTM will likely be 7.3% annually, so the price will change to: N=20, I=3.65, PMT=32.50, FV=1000 CPT PV = -943.91 The price decreased because it got riskier. C. The price change would be $943.91 − $1,037.19 = -$93.28 The change as a percentage would be -$93.28 ÷ $1,037.19 = -8.99% D. In a firm buyout, the stock holders of the target firm earn a nice profit. However, the bondholders of the target firm can be unhappy if the new combined firm has a worse bond rating, like in this case.

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