# Chapter 8 Valuing Bonds

Valuing Bonds

8-1.A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments.

a.What is the coupon payment for this bond?

b.Draw the cash flows for the bond on a timeline.

a.The coupon payment is:

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b.The timeline for the cash flows for this bond is (the unit of time on this timeline is six-month periods):

[pic]

8-2.Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):

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a.What is the maturity of the bond (in years)?

b.What is the coupon rate (in percent)?

c.What is the face value?

a.The maturity is 10 years.

b.(20/1000) x 2 = 4%, so the coupon rate is 4%.

c.The face value is $1000.

8-3.The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value):

[pic]

a.Compute the yield to maturity for each bond.

b.Plot the zero-coupon yield curve (for the first five years).

c.Is the yield curve upward sloping, downward sloping, or flat?

a.Use the following equation.

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b.The yield curve is as shown below.

[pic]

c.The yield curve is upward sloping.

8-4.Suppose the current zero-coupon yield curve for risk-free bonds is as follows:

[pic]

a.What is the price per $100 face value of a two-year, zero-coupon, risk-free bond?

b.What is the price per $100 face value of a four-year, zero-coupon, risk-free bond?

c.What is the risk-free interest rate for a five-year maturity?

a.[pic]

b.[pic]

c.6.05%

8-5.In the box in Section 8.1, Bloomberg.com reported that the three-month Treasury bill sold for a price of $100.002556 per $100 face value. What is the yield to maturity of this bond, expressed as an EAR?

[pic]

8-6.Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.

a.What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?

b.If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?

a.[pic]

Using the annuity spreadsheet:

| |NPER |Rate |PV |PMT |FV |Excel Formula | |Given: |20 | |-1,034.74 |40 |1,000 | | |Solve For Rate: | |3.75% | | | |=RATE(20,40,-1034.74,1000) |

Therefore, YTM = 3.75% × 2 = 7.50%

b.[pic]

Using the spreadsheet

With a 9% YTM = 4.5% per 6 months, the new price is $934.96 | |NPER |Rate |PV |PMT |FV |Excel Formula | |Given: |20 |4.50% | |40 |1,000 | | |Solve For PV: | | |(934.96) | | |=PV(0.045,20,40,1000) |

8-7.Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?

[pic]

We can use the annuity spreadsheet to solve for the payment. | |NPER |Rate |PV |PMT |FV |Excel Formula | |Given: |5 |6.00% |-900.00 | |1,000 | | |Solve For PMT: | | | |36.26 | |=PMT(0.06,5,-900,1000) |

Therefore,...

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