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Chapter 4: Q.17 (page 134)

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

Short Answer

Expert verified

Yield to Maturity will be 5%

Step by step solution

01

Step 1. Introduction

The internal rate of return required for the existing cost of all future cash flows of the bond (face cost and coupon bills) to same the present day bond charge is called the yield to maturity (YTM). All coupon bills are reinvested at a yield same to the YTM, and the bond is held to maturity, in line with YTM.

02

Step 2. Explanation

YieldtoMaturity:9523.81=10,000(1+YTM)10,0009523.81=1+YTM1+YTM=1.0499YTM=4.99%YTM=5%(approx)

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Most popular questions from this chapter

To help pay for college, you have just taken out a \(1,000 government loan that makes you pay \)126 per year for 25 years. However, you don’t have to start making these payments until you graduate from college two years from now. Why is the yield to maturity necessarily less than 12%? (This is the yield to maturity on a normal \(1,000 fixed-payment loan on which you pay \)126 per year for 25 years.)

In this chapter, we discussed long-term bonds as if there were only one type, coupon bonds. In fact, investors can also purchase long-term discount bonds. A discount bond is sold at a low price, and the whole return comes in the form of a price appreciation. You can easily compute the current price of a discount bond by using the financial calculator at http://www .treasurydirect.gov/indiv/tools/tools_savingsbondcalc.htm.

To compute the values for savings bonds, read the instructions on the page and click on Get Started. Fill in the information (you do not need to fill in the Bond Serial Number field) and click on Calculate.

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’s price?
Consider a bond with a 6% annual coupon and a face value of $1,000. Complete the following table. What relationships do you observe between years to maturity, yield to maturity, and the current price?

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