A 30-year maturity bond making annual coupon payments with a coupon rate of 14.0% has duration of 11.36 years and convexity of 186.4. The bond currently sells at a yield to maturity of 8%. a. Find the price of the bond if its yield to maturity falls to 7%. (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Price of the bond b. What price would be predicted by the duration rule? (Do not round Intermediate calculations. Round your answer to 2 decim places.) Predicted price c. What price would be predicted by the duration-with-convexity rule? (Do not round Intermediate calculations. Round your ans to 2 decimal places.) Predicted price

A 30-year maturity bond making annual coupon payments with a coupon rate of 14.0% has duration of 11.36 years and convexity of 186.4. The bond currently sells at a yield to maturity of 8%. a. Find the price of the bond if its yield to maturity falls to 7%. (Do not round Intermediate calculations. Round your answer to 2 decimal places.) Price of the bond b. What price would be predicted by the duration rule? (Do not round Intermediate calculations. Round your answer to 2 decim places.) Predicted price c. What price would be predicted by the duration-with-convexity rule? (Do not round Intermediate calculations. Round your ans to 2 decimal places.) Predicted price

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has (modified) duration of 11.54 years and convexity of 192.4. The bond currently sells at a yield to maturity of 8%. a) Find the price of the bond if ytm falls to 7% (use financial calculator or spreadsheet). b) What price would be predicted using duration only? c) What price would be predicted using duration and convexity? d) What is the error (in %) for each rule? What do you conclude about accuracy of the two rules? e) Repeat the analysis with yields rising to 9%. Do your conclusions about accuracy hold up?
Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (b) Using answers from (a), calculate the modified duration of this bond. (c) Using answers from (a) and (b), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule?
Find the duration of a bond with a settlement date of May 27, 2025, and maturity date November 15, 2036. The coupon rate of the bond is 6.0%, and the bond pays coupons semiannually. The bond is selling at a bond-equivalent yield to maturity of 8.0%. Use Spreadsheet 16.3. Note: Do not round intermediate calculations. Round your answers to 2 decimal places. X Answer is complete but not entirely correct. Macaulay duration Modified duration 11.98 X 11.52 X
Consider a bond with a coupon of 4.6 percent, five years to maturity, and a current price of $1,047.80. Suppose the yield on the bond suddenly increases by 2 percent. a. Use duration to estimate the new price of the bond. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Price b. Calculate the new bond price using the usual bond pricing formula. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Price
The current zero-coupon yield curve for risk-free bonds is as follows: coupon, risk-free bond? . What is the price per $100 face value of a two-year, zero- The price per $100 face value of the two-year, zero-coupon, risk-free bond is $ (Round to the nearest cent.) Data table (Click on the following icon in order to copy its contents into a spreadsheet.) Maturity (years) 1 2 3 YTM 4.95% 5.49% 5.76% 4 5.97% 5 6.09% Print Done -
There are three bonds that mature at the same time, have the same par value, and are expected to pay their first annual coupon 1 next year. The bonds are detailed in the below table. Bond A B с PV PV PV Present Value B ? ? ? PV B If ca r, then what can we say about the prices of the bonds today? (Enter >, <, or ?) PV C PV Yield to Maturity C r rb Coupon Rate ca с с
A 30-year maturity bond making annual coupon payments with a coupon rate of 14.5% has duration of 10.64 years. The bond currently sells at a yield to maturity of 9%. Required: a. Find the price of the bond if its yield to maturity falls to 8%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of the bond b. What price would be predicted by the duration rule, if its yield to maturity falls to 8% ? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Predicted price
Suppose you purchase a $1000 Face-Value Zero-Coupon Bond with maturity 30 years and yield to maturity 4% quoted with annual compounding. Show the bond cash flows on a time line and compute the current price of the bond Draw a graph to illustrate how the price of this bond will change as it gets closer to maturity – Price (on y axis) vs Time (on x axis). Why is a zero-coupon bond more sensitive to interest rate changes than similar coupon bearing bonds (2 or 3 sentences)?
A 30-year maturity bond making annual coupon payments with a coupon rate of 11.00% has a ation of 13.50 years. The bond currently sells at a yield to maturity of 5.75%. Ducation a. Find the exact dollar price of the bond if its yield to maturity falls to 4.75%. What is the % change in price? b. Assume that you need to make a quick approximation using the duration rule. What is the % change in price as approximated by the duration rule when the yield to maturity falls to 4.75%? c. Does the duration-rule provide a good approximation of the % price change in this case? Why or why not?
Consider a semi-annual bond that has a par value of 100, a 15-year maturity, a 5% coupon rate. Monthly interest rate is 0.412%. (a) Calculate the annualized semi-annual compounding yield. (b) What is the price of the bond (without calculation)? And explain why you can determine the price of the bond without calculation? (c) Using answers from (b), calculate the modified duration of this bond. (d) Using answers from (b) and (c), suppose that the bond’s yield to maturity decreases to 3.5%. How much will the bond price increase by applying the duration rule? (e) Do you agree with the following statement, and explain why? “If two bonds have the same duration, then the percentage change in price of the two bonds will be the same for a given change in interest rates.” (f) Discuss the problems with the traditional bond pricing approach by using the yield to maturity. (300 words Maximum)
Consider a bond with a coupon of 7 percent, five years to maturity, and a current price of $1,025.30. Suppose the yield on the bond suddenly increases by 2 percent. a. Use duration to estimate the new price of the bond. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price b. Calculate the new bond price using the usual bond pricing formula. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price
Find the duration of a bond with a settlement date of May 27, 2025, and maturity date November 15, 2036. The coupon rate of the bond is 8.0%, and the bond pays coupons semiannually. The bond is selling at a bond- equivalent yield to maturity of 8.0%. Use Spreadsheet 16.3 Note: Do not round intermediate calculations. Round your answers to 2 decimal places. Macaulay duration Modified duration

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