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Chapter 4: Q.22 (page 134)

What is the price of a perpetuity that has a coupon of $70 per year and a yield to maturity of 1.5%? If the yield to maturity doubles, what will happen to the perpetuity鈥檚 price?

Short Answer

Expert verified

The price of perpetuity will be $2333.3

Step by step solution

01

Step 1. Introduction

A perpetuity is a financial instrument that pays for an indefinite period of time. Perpetuity is a never-ending sequence of identical cash flows in finance. The term "perpetuity" is employed in a number of financial theories, including the dividend discount model (DDM).

02

Step 2. Explanation

PriceofPerpetuityiscalculatedas:PV=Pi=701.5%=$4666.67Iftheyieldgetdoubled,thenthePViscutinhalf:PV=703%=$2333.3

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Most popular questions from this chapter

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?

When is the current yield a good approximation of the yield to maturity?

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.

Property taxes in a particular district are 2% of the purchase price of a home every year. If you just purchased a \(150,000 home, what is the present value of all the future property tax payments? Assume that the house remains worth \)150,000 forever, property tax rates never change, and a 4% interest rate is used for discounting.

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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