Chapter 8 Valuing Bonds

Topics: Bond, Bonds, Zero-coupon bond Pages: 25 (4675 words) Published: October 14, 2013
Chapter 8
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:


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


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


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):


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.







b.The yield curve is as shown below.


c.The yield curve is upward sloping.

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


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?




8-5.In the box in Section 8.1, 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?


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?


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%


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?


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) |

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