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Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937

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Fundamentals of Financial Manageme...

9th Edition
Eugene F. Brigham + 1 other
ISBN: 9781305635937
Textbook Problem
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INTEREST RATE PREMIUMS A 5-year Treasury bond has a 5.2% yield. A 10-year Treasury bond yields 6.4%, and a 10-year corporate bond yields 8.4%. The market expects that inflation will average 2.5% over the next 10 years (IP10 = 2.5%). Assume that there is no maturity risk premium (MRP = 0) and that the annual real risk-free rate, r″, will remain constant over the next 10 years. (Hint: Remember that the default risk premium and the liquidity premium are zero for Treasury securities: DRP = LP = 0.) A 5-year corporate bond has the same default risk premium and liquidity premium as the 10-year corporate bond described. What is the yield on this 5-year corporate bond?

Summary Introduction

To identify: The expected yield on 5-year Treasury bond.

Introduction:

Yield:

The yield is the percentage of the securities at which the return is provided by the company to its investors. Yield can be used in the form of dividend and interest.

Explanation

In order to compute the yield on 5-year Treasury bond; the real risk-free rate of10-year Treasury bond, the inflation premium on 5-year Treasury bond, and the total value of liquidity premium and default risk premium on 10-year bond need to calculate.

Compute the real risk-free rate

Given,

The yield of 10-year Treasury bond is 6.4%.

The inflation rate at 10-year is 2.5%.

Formula to calculate the real risk-free rate derives from the formula of expected yield,

rT10=r*+IP10r*=rT10IP10

Where,

  • r* is the real-risk free rate.
  • rT10 is yield of treasury bonds.
  • IP10 is inflation premium.

Substitute 6.4% for rT10 and 2.5% for IP.

r*=6.4%2.5%=3.9% (1)

The real risk-free rate is 3.9%.

Compute the inflation premium on 5-year Treasury bond

The yield at 5-year Treasury securities is 5.2%. (Given)

The real risk-free rate is 3.9%. (Calculated in equation (1))

Formula to calculate the inflation premium derives from the formula of expectedyield,

rT5=r*+IP5IP5=rT5r*

Where,

  • r* is real-risk free rate.
  • rT5 is yield of treasury bonds.
  • IP5 is inflation premium.

Substitute 5.2% for rT5 and 3.9% for r*.

IP5=5.2%3.9%=1.3% (2)

The inflation premium of 5 year is 1.3%.

Compute the liquidity premium and default risk premium

The yield of 10-year corporate bond is 8.4%. (Given)

The real risk-free rate is3.9%. (Calculated in equation (1))

The inflation premium of 10 year is 2.5%. (Given)

Formula to calculate the default risk premium, liquidity premium derives from the formula of yield,

rC10=r*+IP10+DRP10+LP10DRP10+LP10=rC10(r*+IP10)

Where,

  • DRP10 is the default risk premium

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