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Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250

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BuyFindarrow_forward

Fundamentals of Financial Manageme...

15th Edition
Eugene F. Brigham + 1 other
ISBN: 9781337395250
Textbook Problem

INFLATION Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r″) is 2.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 1.5%, what inflation rate is expected after Year 1?

Summary Introduction

To identify: The expected inflation rate after a year.

Introduction:

Expectation Theory:

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

Explanation

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 2.5%.

The one year inflation rate is 3.25%.

Formula to calculate the 1-year Treasury bond,

Yieldof1-yeartreasurybond=r*+IP

Where,

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

Substitute 2.5% for r* and 3.25% for IP.

Yieldof1-yeartreasurybond=2.5%+3.25%=5.75%

The yield of 1-year Treasury bond is 5.75%.

Compute the 3-year Treasury bond yield:

The yield of 1-year Treasury bond is 5.75%. (Calculated)

The more yield of 3-year Treasury bond than 1-year Treasury bond is 1.5%.

Formula to calculate the 3-year Treasury bond,

Yieldof3-yearTreasuryBond=Yieldof1-yeartreasurybond+Moreyield

Substitute 5.75% for yield of 1-year Treasury bond and 1.5% for more yield.

Yieldof3-yeartreasurybond=5.75%+1.5%=7.25%

The yield of 3-year Treasury bond is 7.25%.

Compute the 2-year treasury bonds yield

Calculated,

The yield of 1-year Treasury bond is 5.75% or 0.0575.

The yield of 3-year Treasury bond is 7.25% or 0.0725.

Formula to calculate the yield of 2-year treasury securities today,

(1+Yieldof2-yearTreasurySecurities)2=(1+Yieldof3-yearTreasurySecurities)3(1+Yieldof1-yearTreasurySecurities)1

Substitute 0

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