Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
12th Edition
ISBN: 9781259144387
Author: Richard A Brealey, Stewart C Myers, Franklin Allen
Publisher: McGraw-Hill Education
bartleby

Videos

Textbook Question
Book Icon
Chapter 3, Problem 30PS

Prices and yields If a bond’s yield to maturity does not change, the return on the bond each year will be equal to the yield to maturity. Confirm this with a simple example of a four-year bond selling at a premium to face value. Now do the same for a four-year bond selling at a discount. For convenience, assume annual coupon payments.

a)

Expert Solution
Check Mark
Summary Introduction

To discuss: Illustrate on return on bond equals yield to maturity (YTM).

Explanation of Solution

4-year bond selling at a premium to face value and the 3% coupon bond is 2%.

PV=(0.03×$1,000)×((10.02)[10.02×(1+0.02)4])+[$1,000(1+0.02)4]=$30×(($50[$46.19]))+[$1,0001.0824]=$30×($3.81)+$923.87=$1,038.17

If the yield to maturity remain same, 1 year later the bond will sell as follows:

PV=(0.03×$1,000)×((10.02)[10.02×(1+0.02)3])+[$1,000(1+0.02)3]=$30×(($50$47.125))+[$1,0001.061208]=$30×($2.875)+$942.322=$1,028.57

Calculation of interest rate:

r=($30+[$1,028.84$1,038.08 $1,038.08])=1.999%or2%

Thus, the interest rate equals yield to maturity.

b)

Expert Solution
Check Mark
Summary Introduction

To discuss: Illustrate on return on bond equals yield to maturity (YTM).

Explanation of Solution

4-year bond selling at discount to face value and the 3% coupon bond is 4%.

PV=(0.03×$1,000)×((10.04)[10.04×(1+0.04)4])+[$1,000(1+0.04)4]0.046799=$30×((25[$21.368]))+[$1,0001.1699]=$30×($3.632)+$854.77=$963.73

If the yield to maturity remain same, 1 year later the bond will sell as follows:

PV=(0.03×$1,000)×((10.04)[10.04×(1+0.04)3])+[$1,0001.1249]=$30×(($25$22.22))+[$1,0001.1249]=$30×($2.78)+$888.97=$972.37

Calculation of interest rate:

r=($30+[$972.25$963.70 $963.70])=0.040or4%

Thus, the interest rate equals yield to maturity.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Consider a 4-years bond with a 8% annual coupon rate and semi-annual payments. Let us suppose that the zero coupon curve rate today with annual compounding is given by the one in Table 1.(a) Calculate the discount factors for all the previous maturities and then the bond price.(b) Calculate the equivalent continuous compounding rates. What do you expect as result for the bond price with these rates? Should it be lower, higher or equal to the one in part (a)? Why? The equivalent continuous compounding rates should be lower than the annual rates. Why?
In calculating the current price of a bond paying semiannual coupons, one needs to O use double the number of years for the number of payments made. O use the semiannual coupon. O use the semiannual rate as the discount rate. O All of the above needs to be done.
When you use the effective annual yield on a semi-annual coupon bond to price the corresponding annual coupon bond, do you get the same price?

Chapter 3 Solutions

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

Knowledge Booster
Background pattern image
Finance
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Essentials Of Investments
Finance
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Mcgraw-hill Education,
Text book image
FUNDAMENTALS OF CORPORATE FINANCE
Finance
ISBN:9781260013962
Author:BREALEY
Publisher:RENT MCG
Text book image
Financial Management: Theory & Practice
Finance
ISBN:9781337909730
Author:Brigham
Publisher:Cengage
Text book image
Foundations Of Finance
Finance
ISBN:9780134897264
Author:KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:Pearson,
Text book image
Fundamentals of Financial Management (MindTap Cou...
Finance
ISBN:9781337395250
Author:Eugene F. Brigham, Joel F. Houston
Publisher:Cengage Learning
Text book image
Corporate Finance (The Mcgraw-hill/Irwin Series i...
Finance
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
Journalizing Bonds Payable/Amortization of a Premium; Author: TLC Tutoring;https://www.youtube.com/watch?v=5gEpAFFnIE8;License: Standard YouTube License, CC-BY
Investing Basics: Bonds; Author: TD Ameritrade;https://www.youtube.com/watch?v=IuyejHOGCro;License: Standard YouTube License, CC-BY