Question
In: Finance
What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a...
What is the approximate modified duration of a 22-year bond, making semiannual coupon payments, with a coupon rate of 5% and a current price of 69.18 per 100 of par value, considering a 50 bps change in discount rate?
Solutions
Expert Solution
| Par Value | $ 100.00 |
| Nper | 44 |
| Coupon (semi annual) | $ 2.50 |
| Coupon Rate | 5% |
| Coupon per year | 2 |
| Years to maturity | 22 |
| Current Price | $ 69.18 |
| Yield to maturity (YTM) | 8.0% |
| Formula Explained | |
| Nper |
Total number of payment periods Coupon per year * years of maturity |
| PMT | Interest Payments, Par value*Coupon rate divided by coupons per year |
| PV | The current price of the bond, which is negative because it’s the cost to buy today |
| FV | Par value, because this is the future value of the bond at maturity |
| Type | 0, default |
| Re annualizing | Coupon per year |
|
|||
| YTM 1 | 8.50% | ||
| YTM 2 | 7.50% | ||
| Price of bond for YTM 1 | $65.42 | ||
| Price of bond for YTM 2 | $73.26 | ||
| Modified Duration | 11.33948121 |
|
Formula for Modified Duration |
(Price of bond with YTM 2 -Price of bond with YTM 1) divided by (2* Initial price* change in yield) |
Please like the answer if your query has been solved. Thanks!
jeff jeffy answered 1 year agoRelated Solutions
Calculate the approximate modified duration of a 4-year, 5% coupon, semi-annual bond if yields change by...
Calculate the approximate modified duration of a 4-year, 5%
coupon, semi-annual bond if yields change by 50bps. Assume the bond
currently sells at 5% yield to maturity (YTM).
a) 1.79
b) 3.59
c) 7.17
d) 11.95
e) None of the above
a. Find the duration of a 10% coupon bond making annual coupon payments if it has...
a. Find the duration of a 10% coupon bond making annual coupon
payments if it has three years until maturity and has a yield to
maturity of 10%. Note: The face value of the bond is $1,000.
b. What is the duration if the yield to maturity is 13%? Note:
The face value of the bond is $1,000.
a. Find the duration of a 6% coupon bond making (semiannually) coupon payments if it has...
a. Find the duration of a 6% coupon bond making
(semiannually) coupon payments if it has three
years until maturity and has a yield to maturity of 6%.
b. What is the duration if the yield to maturity is 10%?
A 28-year maturity bond making annual coupon payments with a coupon rate of 10% has duration...
A 28-year maturity bond making annual coupon payments with a
coupon rate of 10% has duration of 12.14 years and convexity of
190.6. The bond currently sells at a yield to maturity of 7%.
Required:
(a)
Find the price of the bond if its yield to maturity falls to 6%
or rises to 8%. (Round your answers to 2 decimal places.
Omit the "$" sign in your response.)
Yield to maturity of 6%
$
Yield to maturity of 8%
$ ...
A 28-year maturity bond making annual coupon payments with a coupon rate of 10% has duration...
A 28-year maturity bond making annual coupon payments with a
coupon rate of 10% has duration of 12.14 years and convexity of
190.6. The bond currently sells at a yield to maturity of 7%.
Required:
(a)
Find the price of the bond if its yield to maturity falls to 6%
or rises to 8%. (Round your answers to 2 decimal places.
Omit the "$" sign in your response.)
Yield to maturity of 6%
$
Yield to maturity of 8%
$ ...
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration...
A 30-year maturity bond making annual coupon payments with a
coupon rate of 12% has duration of 11.54 years and convexity of
190.8. The bond currently sells at a yield to maturity of 8%.
Required:
(a)
Find the price of the bond if its yield to maturity falls to 7%
or rises to 9%. (Round your answers to 2 decimal places.
Omit the "$" sign in your response.)
Yield to maturity of 7%
$
Yield to maturity of 9%
$ ...
A 30-year maturity bond making annual coupon payments with a coupon rate of 15.0% has duration...
A 30-year maturity bond making annual coupon payments with a
coupon rate of 15.0% has duration of 9.41 years and convexity of
129.3. The bond currently sells at a yield to maturity of
11%.
a. Find the price of the bond if its yield to
maturity falls to 10%. (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...
A 30-year maturity bond making annual coupon payments with a coupon rate of 12% has duration...
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%.
Please find the price of the bond if its yield to maturity
falls to 7% or rise to 9%.
What prices for the bond at these new yields would be predicted
by the duration rule and the duration-with-convexity rule? What is
the percent error for each...
A 30-year maturity bond making annual coupon payments with a coupon rate of 11% has duration...
A 30-year maturity bond making annual coupon payments with a
coupon rate of 11% has duration of 12.44 years and convexity of
221.07. The bond currently sells at a yield to maturity of
7%.
a. Find the price of the bond if its yield to
maturity falls to 6%.
b. What price would be predicted by the
duration rule?
c. What price would be predicted by the
duration-with-convexity rule?
d-1. What is the percent error for each
rule?
d-2. What...
A 30-year maturity bond making annual coupon payments with a coupon rate of 10% has duration...
A 30-year maturity bond making annual coupon payments with a
coupon rate of 10% has duration of 10.37 years and convexity of
157.28. The bond currently sells at a yield to maturity of 10%.
a. Find the price of the bond if its yield to
maturity falls to 9%. (Do not round intermediate
calculations. Round your answers to 2 decimal places.)
b. What price would be predicted by the
duration rule? (Do not round intermediate calculations.
Round your answers to...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Why would UnderArmour want to be sure that consumers can clearly see different models ( about...
- Five years ago, Miguel invested a stock with price $35 per share. The stock price at...
- You are touring a distant planet on which the magnitude of the gravitational acceleration is 65%...
- GDP increased from $16.55 trillion to $17.28 trillion. What was the growth rate of GDP? The...
- Forming an Accountable Care Organization in a hospital setting What is an ACO and its reimbursement?...
- Implement a method that meets the following requirements: (a) Has the same requirements as the above...
- The Good’n’Fresh Grocery Store has two checkout lanes and four employees. Employees are equally skilled, and...
ADVERTISEMENT