Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
11th Edition
ISBN: 9780077861759
Author: Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher: McGraw-Hill Education
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Chapter 8, Problem 19QP

Interest Rate Risk The Faulk Corp. has a 6 percent coupon bond outstanding. The Gonas Company has a 14 percent bond outstanding. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 10 percent. If interest rates suddenly rise by 2 percent, what is the percentage change in the price of these bonds? What if interest rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower coupon bonds?

Expert Solution & Answer
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Summary Introduction

To determine: The percentage change in the price of the bonds.

Coupon Rate:

The coupon rate refers to the rate at which interest is earned on the face value of a bond every year. This is the rate at which yield is funded from a fixed-income security.

Yield to Maturity:

The yield to maturity is the total yield or return, which is derived from a bond until the time of the maturity. For this, it is assumed that the bond will be held until the maturity and would not be called.

Interest Rate Risk:

The interest rate risk refers to the risk, which is associated with a bond because of the fluctuations of the interest rate. The value of the bond differs with the change in the interest rate.

Explanation of Solution

Solution:

Given,

The yield to maturity of the bonds of both companies is 10%.

The bonds of both the company mature after 12 years.

The F Company has a 6% coupon rate outstanding.

The G Company has a 14% coupon rate outstanding.

Calculation of the change in the price of bonds when the interest rate is increased by 2%:

The formula to calculate the change in price is,

Changeinprice=NewpriceOriginalpriceOriginalprice

For F company,

Substitute $623.53 (refer working note) for the new price and $724 for the original price in the above formula.

Changeinprice=$623.53$724$724=($100.47)$724=(0.1387)or(13.87%)

The change in bonds price is (13.87%).

For G company,

Substitute $1,125.57 (refer working note) for the new price and $1,276 for the original price in the above formula.

Changeinprice=$1,125.57$1,276$1,276=($150.43)$1,276=(0.1179)or(11.79%)

The change in bonds price is (11.79%).

Calculation of the change in the price of bonds when the interest rate is decreased by 2%:

The formula to calculate the change in price is,

Changeinprice=NewpriceOriginalpriceOriginalprice

For F company,

Substitute $847.41 (refer working note) for the new price and $724 for the original price in the above formula.

Changeinprice=$847.41$724$724=$123.41$724=0.1704or17.04%

The change in bonds price is 17.04%.

For G company,

Substitute $1,457.29 (refer working note) for the new price and $1,276 for the original price in the above formula.

Changeinprice=$1,457.29$1,276$1,276=$181.29$1,276=0.1420or14.21%

The change in bonds price is 14.21%.

Working note:

Calculation of the semi-annual interest on bonds of F Company:

Semi-annualinterest=Facevalue×Interestrate×12=$1,000×6%×12=$60×12=$30

The semi-annual interest is $30.

Calculation of the semi-annual interest on bonds of G Company:

Semi-annualinterest=Facevalue×Interestrate×12=$1,000×14%×12=$140×12=$70

The semi-annual interest is $70.

Calculation of the price of bonds if yield to maturity is 10%:

For F Company,

Valueofbond=[(Interestvalue×PVIFA5%,24)+(Principalvalue×PVIF5%,24)]=($30×13.8)+($1,000×0.310)=$414+$310=$724

The value of the bond is $724.

For G Company,

Valueofbond=[(Interestvalue×PVIFA5%,24)+(Principalvalue×PVIF5%,24)]=($70×13.8)+($1,000×0.310)=$966+$310=$1,276

The value of the bond is $1,276.

Calculation of the price of bonds if yield to maturity is 12%:

For F Company,

Valueofbond=[(Interestvalue×PVIFA6%,24)+(Principalvalue×PVIF6%,24)]=($30×12.551)+($1,000×0.247)=$376.53+$247=$623.53

The value of the bond is $623.53.

For G Company,

Valueofbond=[(Interestvalue×PVIFA6%,24)+(Principalvalue×PVIF6%,24)]=($70×12.551)+($1,000×0.247)=$878.57+$247=$1,125.57

The value of the bond is $1,125.57.

Calculation of the price of bonds if yield to maturity is 8%:

For F Company,

Valueofbond=[(Interestvalue×PVIFA4%,24)+(Principalvalue×PVIF4%,24)]=($30×15.247)+($1,000×0.390)=$457.41+$390=$847.41

The value of the bond is $847.41.

For G Company,

Valueofbond=[(Interestvalue×PVIFA4%,24)+(Principalvalue×PVIF4%,24)]=($70×15.247)+($1,000×0.390)=$1,067.29+$390=$1,457.29

The value of the bond is $1,457.29.

Calculation of PVIFA5%,24 :

PVIFA5%,24=[11(1+r)nr]=[11(1+0.05)240.05]=13.8

Calculation of PVIF5%,24 :

PVIF5%,24=[1(1+r)n]=[1(1+0.05)24]=0.310

Calculation of PVIFA6%,24 :

PVIFA6%,24=[11(1+r)nr]=[11(1+0.06)240.06]=12.551

Calculation of PVIF6%,24 :

PVIF6%,24=[1(1+r)]=[1(1+0.06)24]=0.247

Calculation of PVIFA4%,24 :

PVIFA4%,24=[11(1+r)nr]=[11(1+0.04)240.04]=15.247

Calculation of PVIF4%,24 :

PVIF4%,24=[1(1+r)]=[1(1+0.04)24]=0.3901

Conclusion

Thus, the percentage change in price when the rate isincreased by 2% for F Company is (13.87%) and for G Company is (11.79%). The percentage change in price when the rate is decreased by 2% for F Company is 17.04% and for G Company is 14.21%.

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Chapter 8 Solutions

Corporate Finance (The Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)

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