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
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Question
Chapter 3, Problem 33PS
Summary Introduction
To prove: The duration of a bond makes an equal payment each year in perpetuity.
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Students have asked these similar questions
Which has morereinvestment rate risk: a 1-year bond or a 10-yearbond?
(a) Determine what is the payment stream of the bond.
(b) Determine the effective duration of the bond's payments if interest is
compounded annually at rate 3%. State your answer to three significant figures.
(c) Find the duration of the bond's payments if interest is compounded
continuously at rate 3%. State your answer to three significant figures.
What is the Macaulay duration of a $1 per year annuity-immediate payable for 10 years based on an annual
interest rate of 5%?
It can be calculated using the below formula,
Macaulay Duration Formula
t-C n-M
+
(1+y) (1+y)
с
Current Bond Price
Macaulay Duration
tx C
+
Macaulay =
Duration Formula
(1+ y)
nxM
(1+ y)n
Current Bond Price
13
Chapter 3 Solutions
Principles of Corporate Finance (Mcgraw-hill/Irwin Series in Finance, Insurance, and Real Estate)
Ch. 3 - (PRICE) In February 2009, Treasury 8.5s of 2020...Ch. 3 - (YLD) On the same day, Treasury 3.5s of 2018 were...Ch. 3 - (DURATION) What was the duration of the Treasury...Ch. 3 - (MDURATION) What was the modified duration of the...Ch. 3 - Prob. 1PSCh. 3 - Bond prices and yields The following statements...Ch. 3 - Prob. 3PSCh. 3 - Bond prices and yields A 10-year German government...Ch. 3 - Bond prices and yields Construct some simple...Ch. 3 - Spot interest rates and yields Which comes first...
Ch. 3 - Prob. 7PSCh. 3 - Spot interest rates and yields Assume annual...Ch. 3 - Prob. 9PSCh. 3 - Prob. 10PSCh. 3 - Duration True or false? Explain. a....Ch. 3 - Duration Calculate the durations and volatilities...Ch. 3 - Term-structure theories The one-year spot interest...Ch. 3 - Real interest rates The two-year interest rate is...Ch. 3 - Duration Here are the prices of three bonds with...Ch. 3 - Prob. 16PSCh. 3 - Prob. 17PSCh. 3 - Spot interest rates and yields A 6% six-year bond...Ch. 3 - Spot interest rates and yields Is the yield on...Ch. 3 - Prob. 20PSCh. 3 - Prob. 21PSCh. 3 - Duration Find the spreadsheet for Table 3.4 in...Ch. 3 - Prob. 23PSCh. 3 - Prob. 25PSCh. 3 - Prob. 26PSCh. 3 - Prob. 27PSCh. 3 - Prob. 28PSCh. 3 - Prob. 29PSCh. 3 - Prices and yields If a bonds yield to maturity...Ch. 3 - Prob. 31PSCh. 3 - Price and spot interest rates Find the arbitrage...Ch. 3 - Prob. 33PSCh. 3 - Prices and spot interest rates What spot interest...Ch. 3 - Prices and spot interest rates Look one more time...
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Similar questions
- What is the Macaulay duration of a $1 per year annuity-immediate payable for 10 years based on an annual interest rate of 5%? It can be calculated using the below formula, Macaulay Duration Formula t-C -M + (1+y) (1+y) Current Bond Price Macaulay Duration Macaulay = Duration Formula tx C + (1+ y) nxM (1+ y)n Current Bond Price www 13arrow_forwardAccording to the expectations theory of the term structure of interest, if the 1-year bond rate today is 6% p.a. and the 2-year bond rate today is 7% p.a., what is the 1-year bond rate next year? A. 6% B. 6.75% C. 7.5% D. 8%arrow_forwardConsider a one-year discount bond that has a present value of P1,500. If the rate of discount is 4 percent, the future value of the bond (the amount the bond pays in one year) is * P1,560.00 P1,540.00 P1,440.00 P1,442.31arrow_forward
- Assume that there is a bond that pays $50 at the and of year 1 and $50 at the end of year 2. It sells at $100. The Macauley duration of the bond isarrow_forwardAssume that a bond makes 30 equal annual payments of \$1,000$1,000 starting one year from today. (This security is sometimes referred to as an amortizing bond.) If the discount rate is 3.5\%3.5% per annum, what is the current price of the bond?arrow_forwardExplain the relation between current and future expected one-year bond yields and the yield on a five-year bond.arrow_forward
- 3. Present Value of Annuity and Perpetuity - Show your steps! (You must simplify your answer use the formula for Geometric series.) 1 A bond with a face value of y pays out interest at rate r annually. The discount rate you should use for the bond is i. (That is, the present value of $1 received a year from now is $11, and the present value of 1 dollar received 2 years from now is $- .) What is the present value of owning the bond that pays its first interest a year from now if (a) The bond pays interest for n years and pays back the face value at the last year. (b) The bond pays interest forever and never pays back the face value. (1+i)²arrow_forwardAssume you have the following asset and liability in your balance sheet Asset - Bond AModified Duration = 1.5 yearsValue = RM1 million Liability - Bond BModified Duration 2.6 yearsValue = RM2 million a. Calculate the duration gaps?b. What is the expected change in Net worth if interest increases by 1%?c. What should or could you to achieve immunised balance sheet?arrow_forward1) Suppose that today's one-year interest rate is 5%. Consider the following one-year interest rates expected to occur over the next four years: 6%, 7%, 8% and 9%.a. Calculate the interest rate for two-year bonds, based on the expectations theory.b. What about five-year bonds?arrow_forward
- What is the present value of a 10-year bond outstanding with 8 years left in “year-to-maturity,” 6% annual required rate, and 4% annual payment rate?arrow_forwardAccording to the expectations theory, what will be the interest rate on a three-year bond if the two-year term premium is 1.0% while the three-year term premium is 2.0%, and a one-year bond has an interest rate of 4% and is expected to have an interest rate of 5% next year and 6% in two year? Select one: Oa. 6.0% O b. 15.0% Oc. 5.0% O d. 4.0%arrow_forward1. Suppose the interest rate on a one-year bond today is 6% per year, the interest rate on a one-year bond one year from now is expected to be 4% per year, and the interest rate on a one-year bond two years from now is expected to be 3% per year. The term premium on a two-year bond is 0.5% per year and the term premium on a three-year bond is 1.0 % per year. In equilibrium, what is the interest rate today on a two-year bond? On a three-year bond? What is the shape of the yield curve?arrow_forward
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