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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

YIELD CURVES Suppose the inflation rate is expected to be 7% next year, 5% the following year, and 3% thereafter. Assume that the real risk-free rate, r″, will remain at 2% and that maturity risk premiums on Treasury securities rise from zero on very short-term bonds (those that mature in a few days) to 0.2% for 1-year securities. Furthermore, maturity risk premiums increase 0.2% for each year to maturity, up to a limit of 1.0% on 5-year or longer-term T-bonds.

  1. a. Calculate the interest rate on 1-, 2-, 3-, 4-, 5-, 10-, and 20-year Treasury securities and plot the yield curve.
  2. b. Suppose a AAA-rated company (which is the highest bond rating a firm can have) had bonds with the same maturities as the Treasury bonds. Estimate and plot what you believe a AAA-rated company’s yield curve would look like on the same graph with the Treasury bond yield curve. (Hint: Think about the default risk premium on its long-term versus its short-term bonds.)
  3. c. On the same graph, plot the approximate yield curve of a much riskier lower-rated company with a much higher risk of defaulting on its bonds.

a.

Summary Introduction

To identify: The interest on Treasury securities, and yield curve.

Yield:

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

Yield Curve:

The graphical representation of the expected return, provided by the company to its investors during the years is known as the yield curve.

Explanation

Given,

The risk free rate is 2% or 0.02.

Inflation rate for the first year is 7% or 0.07.

The inflation rate of second year is 5% or 0.05.

The inflation rate after two years is 3% or 0.03.

The maturity risk premium for the first year is 0.2% or 0.002 and it will increase by 0.2% every year till 1%.

Formula to calculate the interest rate,

r=r*+IP+MRP

Where,

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

Statement to show the calculation of interest rate

Maturity

Real Risk-Free Rate

(%)

(r*)

Inflation Rate

(%)

(IP)

Maturity Risk Premium

(MRP)

b.

Summary Introduction

To identify: The interest rate on AAA rated securities, and the yield curve.

c.

Summary Introduction

To identify: The interest rate on lower rated bonds, and the yield curve.

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