   Chapter 6, Problem 12P Fundamentals of Financial Manageme...

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

Solutions

Chapter
Section Fundamentals of Financial Manageme...

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

MATURITY RISK PREMIUM An investor in Treasury securities expects inflation to be 2.1% in Year 1, 2.7% in Year 2, and 3.65% each year thereafter. Assume that the real risk-free rate is 1.95% and that this rate will remain constant. Three-year Treasury securities yield 5.20%, while 5-year Treasury securities yield 6.00%. What is the difference in the maturity risk premiums (MRPs) on the two securities; that is, what is MRP5 − MRP3?

Summary Introduction

To identify: The maturity risk premium.

Introduction:

A premium, which is paid by the borrower to its lender in the form of compensation of the interest rate uncertainty in regards of the maturity risk, is known as the maturity risk premium.

Explanation

The items required for the calculation of the maturity risk are risk free rate, Treasury bill yield and inflation premium.

Year 3

The yield is 5.20%. (Given)

The risk free rate is 1.95%. (Given)

The inflation premium on 3 year treasury security is 2.82%. (Working note)

Formula to calculate the maturity risk premium derives from the formula of corporate bond yield,

r=r*+IP+MRPMRP=r(r*+IP)

Where,

• MRP is the maturity risk premium.
• r is the corporate bond yield.
• r* is the risk free rate.
• IP is the inflation premium.

Substitute 5.20% for r, 1.95% for r* and 2.82% for IP.

MRP3=5.20%(1.95%+2.82%)=5.20%4.77%=0.43%

The maturity risk premium on year 3 treasury security is 0.43%.

Year 5

The yield is 6%. (Given)

The risk free rate is 1.95%. (Given)

The inflation premium on 5 year treasury security is 3.15%. (Working note)

Substitute 6.8% for r, 2.75% for r* and 2.82% for IP.

MRP5=6%(1.95%+3.15%)=6%5.1%=0.9%

The maturity risk premium on year 5 treasury security is 0.9%.

Compute the difference between two maturity risks

Calculated,

MRP3 is 0.43%.

MRP5 is 0.9%.

Formula to calculate the difference between two maturity risks,

Differencebetweentwomaturityrisks=MRP5MRP3

Substitute, 0.43% for MRP3 and 0.9% for MRP5

Differencebetweentwomaturityrisks=0.9%0.43%=0

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