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Chapter 4: Q.2 (page 114)

What is the formula used to calculate the yield to maturity on a 20-year coupon bond with a current yield of 12% and \(1,000 face value that sells for \)2,500

Short Answer

Expert verified

The yield to maturity is 3.33%

Step by step solution

01

Step 1. Introduction

A coupon is a payment of interest received by a bondholder from the date of issuance to the bond's maturity date. The "coupon rate," which is computed by summing the total number of coupons paid each year and dividing it by the bond's face value, is the most common way of describing coupons.

02

Step 2. Explanation

CouponAmount=CouponRate脳FaceValue=10%脳1000=100YieldtoMaturity=Couponamount+((Facevalue-sellingprice)/n)(Facevalue+sellingprice)/2=100+((1000-2000)/20)(1000+2000)/2=100+(-1000/20)(3000/2)=100-501500=501500=3.33%

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Most popular questions from this chapter

What is the yield to maturity on a \(10,000-face-value discount bond, maturing in one year, which sells for \)9,523.81?

True or False: With a discount bond, the return on the bond is equal to the rate of capital gain.

Would $200, which is to be received in exactly one year, be worth more to you today when the interest rate is 12% or when it is 17%?

The U.S. Treasury issues some bonds as Treasury Inflation Indexed Securities, or TIIS, which are bonds adjusted for inflation; hence the yields can be roughly interpreted as real interest rates. Go to the St. Louis Federal Reserve FRED database, and find data on the following TIIS bonds and their nominal counterparts. Then answer the questions below.

  • 5-year U.S. Treasury (DGS5) and 5-year TIIS (DFII5)
  • 7-year U.S. Treasury (DGS7) and 7-year TIIS (DFII7)
  • 10-year U.S. Treasury (DGS10) and 10-year TIIS (DFII10)
  • 20-year U.S. Treasury (DGS20) and 20-year TIIS (DFII20)
  • 30-year U.S. Treasury (DGS30) and 30-year TIIS (DFII30)

a. Following the Great Recession of 2008鈥� 2009, the 5-, 7-, 10-, and even the 20-year TIIS yields became negative for a period of time. How is this possible?

b. Using the most recent data available, calculate the difference between the yields for each of the pairs of bonds (DGS5 鈥� DFII5, etc.) listed above. What does this difference represent?

c. Based on your answer to part (b), are there significant variations among the differences in the bond-pair yields? Interpret the magnitude of the variation in differences among the pairs.

If interest rates decline, which would you rather be holding, long-term bonds or short-term bonds? Why? Which type of bond has the greater interest-rate risk?
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