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Chapter 4: Q.19 (page 134)

Which \(10,000 bond has the higher yield to maturity, a 20-year bond selling for \)8,000 with a current yield of 20% or a 1-year bond selling for $8,000 with a current yield of 10%?

Short Answer

Expert verified

One year bond has higher to maturity.

Step by step solution

01

Step 1. Introduction

Bonds are debt instruments that are issued by governments or businesses to raise funds. Bu purchasign a bond, an invest lends money to the issuer. In return, the investor gets the principal amount along with the interest at the maturity of the bond.

02

Step 2. Explanation

CurrentYield=AnnualCouponPrice20%=AnnualCoupon8,000AnnualCoupon=$1600Thebondwillpaycouponof1600peryeartill20years.8000=1600(1+r)^n8000=1600(1+r)^1+1600(1+r)^2+1600(1+r)^3+1600(1+r)^4+-------+1600(1+r)^20r=20.13%1yearbindsellingCurrentYield=AnnualCouponPrice10%=AnnualCoupon8000AnnualCoupon=80080000=(10,000+800)(1+r)r=35%

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Most popular questions from this chapter

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?

Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?

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 the interest rate is 15%, what is the present value of a security that pays you \(1,100 next year, \)1,250 the year after, and $1,347 the year after that?

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
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