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CHAPTER 7
INTEREST RATES AND BOND
VALUATION
Answers to Concepts Review and Critical Thinking Questions
5. There are two benefits. First, the company can take advantage of interest rate declines by calling in an
8. Companies pay to have their bonds rated simply because unrated bonds can be difficult to sell; many
CHAPTER 7 - 2
12. As a general constitutional principle, the federal government cannot tax the states without their consent
Solutions to Questions and Problems
NOTE: 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.
Basic
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NOTE: 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 the United States will have a par value of $1,000. We will use this par
value in all problems unless a different par value is explicitly stated.
3. The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice this
4. Here we need to find the YTM of a bond. The equation for the bond price is:
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5. Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing
6. To find the price of this bond, we need to realize that the maturity of the bond is 13 years. The bond
7. Here we are finding the YTM of a semiannual coupon bond. The bond price equation is:
8. Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing
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9. The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation
(h) is:
10. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest
rates, and inflation is:
12. The Fisher equation, which shows the exact relationship between nominal interest rates, real interest
rates, and inflation is:
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14. This is a premium bond because it sells for more than 100% of face value. The current yield is:
Intermediate
15. Here we are finding the YTM of annual coupon bonds for various maturity lengths. The bond price
equation is:
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16. Any bond that sells at par has a YTM equal to the coupon rate. Both bonds sell at par, so the initial
17. Initially, at a YTM of 6 percent, the prices of the two bonds are:
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If the YTM declines from 6 percent to 4 percent:
18. The current yield is:
19. The company should set the coupon rate on its new bonds equal to the required return. The required
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20. Accrued interest is the coupon payment for the period times the fraction of the period that has passed
21. Accrued interest is the coupon payment for the period times the fraction of the period that has passed
22. To find the number of years to maturity for the bond, we need to find the price of the bond. Since we
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23. The bond has 16 years to maturity, so the bond price equation is:
24. a. The bond price is the present value of the cash flows from a bond. The YTM is the interest rate
25. The price of a zero coupon bond is the PV of the par, so:
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The interest deduction is the price of the bond at the end of the year, minus the price at the
beginning of the year, so:
26. a. The coupon bonds have a 6 percent coupon which matches the 6 percent required return, so they
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c. The total coupon payment for the coupon bonds will be the number bonds times the coupon
Notice the cash flow for the zeroes is a cash inflow. This is because of the tax deductibility of the
27. We found the maturity of a bond in Problem 22. However, in this case, the maturity is indeterminate.
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Now we can use the future value of an annuity equation to find the annual deposit. Doing so, we find:
Challenge
30. a. The rate of return you expect to earn if you purchase a bond and hold it until maturity is the YTM.
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b. To find our HPY, we need to find the price of the bond in two years. The price of the bond in two
31. The price of any bond (or financial instrument) is the PV of the future cash flows. Even though Bond
32. To calculate this, we need to set up an equation with the callable bond equal to a weighted average of
