   Chapter 6, Problem 10P Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977

Solutions

Chapter
Section Fundamentals of Financial Manageme...

14th Edition
Eugene F. Brigham + 1 other
ISBN: 9781285867977
Textbook Problem

INFLATION Due to a recession, expected inflation this year is only 3%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3%. Assume that the expectations theory holds and the real risk-free rate (r*) is 2%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2%, what inflation rate is expected after Year 1?

Summary Introduction

To identify: The expected inflation rate after a year.

Expectation Theory:

Expectation theory estimates the future interest without taking maturity risk into consideration. According to the expectation theory, the yield curve of investment totally depends upon the future expectation of investors.

Explanation

Solution:

In order to compute the expected inflation after a year; 1-year Treasury bond yield, 3-year treasury bonds yield, 2-year treasury bonds yield need to calculate.

Compute the 1-year Treasury bond yield

Given,

Real risk-free rate is 2%.

The one year inflation rate is 3%.

Formula to calculate the 1-year Treasury bond,

Yieldof1-yearTreasuryBond=r*+IP

Where,

• r* is real risk-free rate.
• IP for inflation premium.

Substitute 2% for r* and 3% for IP.

Yieldof1-yearTreasuryBond=2%+3%=5%

The yield of 1-year Treasury bond is 5%.

Compute the 3-year Treasury bond yield

The yield of 1-year Treasury bond is 5%. (Calculated)

The additional yield of 3-year Treasury bond than 1-year Treasury bond is 2%.

Formula to calculate the 3-year Treasury bond,

Yieldof3-yearTreasuryBond=Yieldof1-yearTreasuryBond+MoreYield

Substitute 5% for yield of 1-year Treasury bond and 2% for more yield.

Yieldof3-yearTreasuryBond=5%+2%=7%

The yield of 3-year Treasury bond is 7%.

Compute the 2-year treasury bonds yield

Calculated,

The yield of 1-year Treasury bond is 5% or 0.05.

The yield of 3-year Treasury bond is 7% or 0.07

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