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# Sample financial questions: bonds, yields, coupon rates, maturity and more...

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Can you please assist me with theses questions?

3. A bond has a coupon rate of 8.5% and 18 years until maturity. If the yield to maturity is 6.7%, what is the price of the bond?

5. A bond sells for \$864.50 and has a coupon rate of 6%. If the bond has 16 years until maturity, what is the yield to maturity of the bond?

8. Sealord Fisheries issues zero coupon bonds on the market at a price of \$150 per bond. Each bond has a face value of \$1,000 payable at maturity in 20 years. What is the yield to maturity for these bonds?

10. If instead the Sealord Fisheries zero coupon bonds referred to above in question # 8, are callable in 10 years at a call price of \$475, what is their yield to call?

11. Dunbar Corp. has bonds on the market with 11.5 years to maturity, a Yield to Maturity of 7.5 percent, and a current price of \$1,084. What must the coupon rate be on Dunbar's bonds?

14. A zero coupon bond with a 9%Yield To Maturity has 15 years to maturity. Two years later, the price of the bond remains the same. What going on here?

16. Bond X is a premium bond with an 8% coupon, a Yield to Maturity of 6 percent, and 15 years to maturity. Bond Y is a discount bond with 8% coupon, a Yield to Maturity of 10 %, and also 15 years to maturity. If interest rates remain unchanged, what do you expect the price of these bonds to be 1 year from now? In 5 years? In 10 years? In 14 years? In 15 Years? What's going on here?

18. Bond J is a 4% coupon bond. Bonk K is a 10% coupon bond. Both bonds have 10 years to maturity and have a Yield To Maturity of 7%. If interest rates suddenly rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

25. A bond with a coupon rate of 7% sells at a yield to maturity of 8%. If the bond matures in 13 years, what is the Macaulay duration of the bond? What is the modified duration?

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3. A bond has a coupon rate of 8.5% and 18 years until maturity. If the yield to maturity is 6.7%, what is the price of the bond?

Annual payment = 1000*8.5% = 85
Number of years = 18
YTM (rate) = 6.7%
FV = 1000
Then by a financial calculator, we can compute PV = \$1185.05

5. A bond sells for \$864.50 and has a coupon rate of 6%. If the bond has 16 years until maturity, what is the yield to maturity of the bond?

Annual payment = 1000*6% = 60
Number of years = 16
FV = 1000
PV = - 864.50
Then by a financial calculator, we can compute YTM (rate) = 7.48%

8. Sealord Fisheries issues zero coupon bonds on the market at a price of \$150 per bond. Each bond has a face value of \$1,000 payable at maturity in 20 years. What is the yield to maturity for these bonds?

Annual payment = 0
Number of years = 20
FV = 1000
PV = -150
Then by a financial calculator, we can compute YTM (rate) = 9.95%

10. If instead the Sealord Fisheries zero coupon bonds referred to above in question # 8, are callable in 10 years at a call price of \$475, what is their yield to call?

Annual payment = ...

#### Solution Summary

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\$2.19

## Yield Curves; Expectations theory; Bond valuation; Yield to maturity and call

6-1: YIELD CURVES The following yields on U.S. Treasury securities were taken from a recent financial publication:

Term Rate
6 months 5.1%
1 year 5.5
2 years 5.6
3 years 5.7
4 years 5.8
5 years 6.0
10 years 6.1
20 years 6.5
30 years 6.3

a. Plot a yield curve based on these data?
b. What type of yield curve is shown?
c. What information does this graph tell you?
d. Based on this yield curve, if you needed to borrow money for longer than 1 year, would it make sense for you to borrow short-term and renew the loan or borrow long-term?

6-15: EXPECTATIONS THEORY Assume that the real risk-free rate is 2% and that the maturity risk premium is zero. If the 1-year bond yield is 5% and a 2-year bond (of similar risk) yields 7%, what is the 1-year interest rate that is expected for Year 2? What inflation rate is expected during Year 2? Comment on why the average interest rate during the 2-year period differs from the 1-year interest rate expected for Year 2.

7-5: BOND VALUATION An investor has two bonds in his portfolio that have a few value of \$1,000 and pay a 10% annual coupon. Bond L matures in 15 years, while Bond S matures in 1 year.

a. What will the value of each bond be if the going interest rate is 5%, 8%, and 12%? Assume that only one more interest payments is to be made on Bond S at its maturity and that 15 more payments are to be made on Bond L.
b. Why does the longer-term bond's price vary more than the price of the shorter-term bond when interest rates change?

7-10: CURRENT YIELD, CAPITAL GAINS YIELD, AND YIELD TO MATURITY Hooper Printing Inc. has bonds outstanding with 9 years left to maturity. The bonds have an 8% annual coupon rate and were issued 1 year ago at their par value of \$1,000. However, due to changes in interest rates, the bond's market price has fallen to \$901.40. The capital gains yield last year was -9.86%.

a. What is the yield to maturity?
b. For the coming year, what are the expected current and capital gains yields?
c. Will the actual realized yields be equal to the expected yields if interest rates change? IF not, how will they differ?

7-19: YIELD TO MATURITY AND YIELD TO CALL Kaufman Enterprises has bonds outstanding with a \$1,000 face value and 10 years left until maturity. They have an 11% annual coupon payment, and their current price is \$1,175. The bonds may be called in 5 years at 109% of face value (Call price = 41,090).

a. What is the yield to maturity?
b. What is the yield to call if they are called in 5 years?
c. Which yield might investors expect to earn on these bonds? Why?
d. The bond's indenture indicates that the call provision gives the firm the right to call the bonds at the end year beginning in Year 5. In Year 5, the bonds may be called at 109% of face value; but in each of the next 4 year, the call percentage will decline by 1%. Thus, in Year 6, they may be called at 108% of face value; in Year 7, they may be called at 107% of face value; and so forth. If the yield curve is horizontal and interest rates remain at their current level, when is the latest that investors might expect the firm to call the bonds?

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