(a)
To Discuss:
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%.
To use a financial calculator or spreadsheet to find the price of the bond if its yield to maturity falls to 7%.
Introduction:
When specified payments are made by the issuer to the holder for a given period of time due to an obligation created by a security,then that security is known as Bond.The amount the holder will receive on maturity along with the coupon rate which is also known as the interest rate of the bond is known as the face value of the bond.The discount rate due to which the present payments from the bond become equal to its price i.e. it is the average
The time taken by the bond to change based on the interest rate changes is displayed by Convexity. Duration measures approximately a
Answer to Problem 26PS
Price of Bond using a financial calculator if yield to maturity falls to 7% is 1620.45.
Explanation of Solution
Price of the bond when the yield to maturity is 8% using a financial calculator can be calculated as below:
So, the price of the bond with 8% yield is 1450.31.
So, the price of the bond with 7% yield is 1620.45.
(b)
To Discuss:
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4The bond currently sells at a yield to maturity of 8%.
To predict the price using the duration rule.
Introduction:
When specified payments are made by the issuer to the holder for a given period of time due to an obligation created by a security, then that security is known as Bond. The amount the holder will receive on maturity along with the coupon rate which is also known as the interest rate of the bond is known as the face value of the bond. The discount rate due to which the present payments from the bond become equal to its price i.e. it is the average rate of return which a holder can expect from a bond, is known as Yield to Maturity.
The time taken by the bond to change based on the interest rate changes are displayed by Convexity.
Duration measures approximately a bond's price sensitivity to interest rates changes.
Answer to Problem 26PS
Price of Bond using the duration rule if yield to maturity falls to 7% is 1605.28.
Explanation of Solution
The price of the bond with 8% yield is 1450.31.
Price of the Bond using the duration rule, if yield to maturity falls to 7%:
Predicted Price change =
=
=154.97
Predicted new price=1450.31+154.97=1605.28
(c)
To Discuss:
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4.The bond currently sells at a yield to maturity of 8%.
To predict the price using the duration with convexity rule.
Introduction:
When specified payments are made by the issuer to the holder for a given period of time due to an obligation created by a security,then that security is known as Bond.The amount the holder will receive on maturity along with the coupon rate which is also known as the interest rate of the bond is known as the face value of the bond.The discount rate due to which the present payments from the bond become equal to its price i.e. it is the average rate of return which a holder can expect from a bond,is known as Yield to Maturity.
The time taken by the bond to change based on the interest rate changes is displayed by Convexity. Duration measures approximately a bond's price sensitivity to interest rates changes.
Answer to Problem 26PS
Price of Bond using the duration with convexity rule if yield to maturity falls to 7% is 1619.23.
Explanation of Solution
So, the price of the bond with 8% yield is 1450.31.
Price of the Bond using Duration-with-Convexity Rule, if yield to maturity falls to 7%:
Predicted price change =
=
=168.92
Predicted new price=1450.31+168.92=1619.23
(d)
To Discuss:
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%.
To determine the percent error for each rule and to conclude about the accuracy of the two rules.
Introduction:
When specified payments are made by the issuer to the holder for a given period of time due to an obligation created by a security,then that security is known as Bond.The amount the holder will receive on maturity along with the coupon rate which is also known as the interest rate of the bond is known as the face value of the bond.The discount rate due to which the present payments from the bond become equal to its price i.e. it is the average rate of return which a holder can expect from a bond,is known as Yield to Maturity.
The time taken by the bond to change based on the interest rate changes is displayed by Convexity. Duration measures approximately a bond's price sensitivity to interest rates changes.
Answer to Problem 26PS
The percentage error of duration rule is -.98% and percentage error of duration with convexity rule is -.075%.
Conclusion: The duration-with-convexity rule provides more accurate approximations tothe true change in price.
Explanation of Solution
Percent error for duration rule =
= -0.0094
= -0.94%
Percent error for duration with convexity rule=
= -0.00075
= -0.075%
The duration-with-convexity rule provides more accurate approximations to
the true change in price.
Conclusion: The percentage error using convexity with duration is less than one-tenth the error using only duration to estimate the price change.
(e)
To Discuss:
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration of 11.54 years and convexity of 192.4The bond currently sells at a yield to maturity of 8%.
To repeat the analysis if the bond's yield to maturity increases to 9% and to determine whether the conclusions about the accuracy of the two rules with parts (a)-(d) were consistent.
Introduction:
When specified payments are made by the issuer to the holder for a given period of time due to an obligation created by a security,then that security is known as Bond.The amount the holder will receive on maturity along with the coupon rate which is also known as the interest rate of the bond is known as the face value of the bond.The discount rate due to which the present payments from the bond become equal to its price i.e. it is the average rate of return which a holder can expect from a bond,is known as Yield to Maturity.
The time taken by the bond to change based on the interest rate changes is displayed by Convexity. Duration measures approximately a bond's price sensitivity to interest rates changes.
Answer to Problem 26PS
The conclusions about the accuracy of the two rules with parts (a)-(d) were consistent on repeating the analysis if the bond's yield to maturity increases to 9%.
Explanation of Solution
So, the price of the bond with 9% yield is 1308.21.
Price of the Bond using the duration rule, if yield to maturity rises to 9%:
Predicted Price change =
=
=-154.97
Predicted new price=1450.31-154.97
=1295.34
Percent error=
= -0.0098
= -0.98%
Price of the Bond using Duration-with-Convexity Rule, if yield to maturity rises to 9%:
Predicted price change =
=
= -141.02
Predicted new price=1450.31-141.02=1309.29
Percent error=
=0.00083
=0.083%
The percentage error using convexity with duration is less than one-tenth the error using only duration to estimate the price change.
The previous conclusion about the duration with convexity rule being more accurate is consistent with parts (a) - (d) if the bond's yield to maturity rises to 9%.
Want to see more full solutions like this?
Chapter 11 Solutions
Essentials Of Investments
- 15-year maturity, 8% coupon bond paying coupons monthly is callable in 6 years at a callprice of $1,050. The bond currently sells at a yield to maturity of 11%.a. What is the yield to call?b. What is the yield to call if the call price is $1,100 and the bond can be called in 4 yearsinstead of 6 years?arrow_forwardSuppose you open a savings account with Hillside Bank, where you also have your salaryaccount. The bank will deduct $20 from your salary account every month and put it into thesavings account. The first deposit will take place immediately after you open the account. Ifyou are planning to maintain the account for the next 5 years, how much money will youhave when you close your account 5 years from now? Suppose the interest rate is 7% please show work.arrow_forwardProject Mean Green has an initial after-tax cost of $500,000. The project is expected to produceafter-tax CFs of $100,000 at the end of each year for the next five years and has a WACC of10%.There’s a 20% probability that the project’s growth opportunities will have an NPV of $3million at t=5, and a 80% probability that the NPV will be -1.2 million at t=5.Is it feasible for the company to expand the project after 5 years? plase show workarrow_forward
- Project panther has an initial after-tax cost of $150,000 at t=0. The project is expected toproduce after-tax cash flows of $60,000 for the next three years. The project’s WACC is 12%.The project’s CFs depend critically upon customer’s acceptance of the product. There’s a 50%probability that the product will be successful and generate annual after-tax CFs of $100,000,and a 50% probability that it will not be successful and hence produce annual after-tax CFs of-$10,000.Should the company abandon the project after a year?arrow_forwarda. A semi-annual bond with a face value of $1,000 has an annual coupon rate of 8%. If 23days have passed since the last coupon payment, how much will be the accrued interest onthe bond? What will be invoice price if the bond is selling at its par value?b. What will be the invoice price if the bond is a discount bond with a yield to maturity(YTM) of 9% and a maturity of 7 years? please show work.arrow_forwarda. Krannert Inc. issues a bond with a coupon rate of 7% and a YTM of 10%. If the bond isselling for $815.66, what is the maturity of the bond?b. How much would the bond be selling for if it was a quarterly bond with a maturity of 6years?arrow_forward
- Travis just won a lottery which gives him a choice between the following two paymentoptions:a. He will receive a one-time payment of $100,000 right now, ORb. He will receive $10,000 every year for the next 20 years.Which option Travis should go for? Suppose the interest rate is 5%. please show work.arrow_forwardProject Falcon has an upfront after-tax cost of $100,000. The project is expected to produceafter-tax cash flows of $35,000 at the end of each of the next four years. The project has aWACC of 11%.However, if the company waits a year, they will find out more information about marketcondition and its effect on the project’s expected after-tax cash flows. If they wait a year,• There’s a 60% chance that the market will be strong and the expected after-tax CFs willbe $45,000 a year for four years.• There’s a 40% chance that the market will be weak and the expected after-tax CFs willbe $25,000 a year for four years.• Project’s initial after-tax cost (at t=1) will still be $100,000.Should the company go ahead with the project today or wait for one more year? please show work.arrow_forwardMake a report on Human Resource Development Practices in Nepalese Private Sector Business Industries.arrow_forward
- Eccles Inc., a zero-growth firm, has an expected EBIT of $100.000 and a corporate tax rate of 30%. Eccles uses $500,000 of 12.0% debt, and the cost of equity to an unlevered firm in the same risk class is 16.0%. If the effective personal tax rates on debt income and stock income are Td = 25% and TS = 20% respectively, what is the value of the firm according to the Miller model (Based on the same unlevered firm value in the earlier question)? a. $475,875 b. $536,921 c. $587,750 d. $623,050 e. $564,167arrow_forwardRefer to the data for Eccles Inc. earlier. If the effective personal tax rates on debt income and stock income are Td = 25% and TS = 20% respectively, what is the value of the firm according to the Miller model (Based on the same unlevered firm value in the earlier question)? a. $475,875 b. $536,921 c. $587,750 d. $623,050 O $564,167arrow_forwardWarren Supply Inc. wants to use debt and common equity for its capital budget of $800,000 in the coming year, but it will not issue any new common stock. It is forecasting an EPS of $3.00 on its 500,000 outstanding shares of stock and is committed to maintaining a $2.00 dividend per share. Given these constraints, what percentage of the capital budget must be financed with debt? a. 33.84% b. 37.50% c. 32.15% d. 30.54% e. 35.63%arrow_forward
- Essentials Of InvestmentsFinanceISBN:9781260013924Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.Publisher:Mcgraw-hill Education,
Foundations Of FinanceFinanceISBN:9780134897264Author:KEOWN, Arthur J., Martin, John D., PETTY, J. WilliamPublisher:Pearson,
Fundamentals of Financial Management (MindTap Cou...FinanceISBN:9781337395250Author:Eugene F. Brigham, Joel F. HoustonPublisher:Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i...FinanceISBN:9780077861759Author: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 ProfessorPublisher:McGraw-Hill Education