PRIN.OF CORPORATE FINANCE
PRIN.OF CORPORATE FINANCE
13th Edition
ISBN: 9781260013900
Author: BREALEY
Publisher: RENT MCG
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Chapter 23, Problem 1PS

Expected yield You own a 5% bond maturing in two years and priced at 87%. Suppose that there is a 10% chance that at maturity the bond will default and you will receive only 40% of the promised payment. What is the bond’s promised yield to maturity? What is its expected yield (i.e., the possible yields weighted by their probabilities)?

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Summary Introduction

To determine: The bonds promised yield to maturity and expected yield.

Yield to maturity (YTM) is the overall return anticipated on a bond throughout its maturity period and it is considered as a long-term bond yield and represented as an annual rate.

Explanation of Solution

Computation of bonds promised yield to maturity and expected yield is as follows:

Price=CF1(1+IRR)+CF2(1+IRR)2$870=$50(1+IRR)+$1,050(1+IRR)2By solving,IRR=0.1277or12.77%

Therefore, to ascertain the expected yield, the expected pay off at maturity is needed and given a 10% probability that only 40% of the promised payment will be received.

Expected pay off=(0.90×$1,050)+0.10(0.40×$1,050)=$945+$42=$987

Therefore, the expected yield is as follows:

Price=CF1(1+IRR)+CF2(1+IRR)2$870=$50(1+IRR)+$987(1+IRR)2By solving,IRR=0.0942or9.42%

Therefore, the bonds promised yield to maturity and expected yield is 12.77% and 9.42% respectively.

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