Problem 1a (20 points): Calculate the duration of a $1,000, 6% coupon bond with three years to maturity. Assume that all market interest rates are 7%. Solution to 1a: Payments PV of Payments Year 1 Year 2 Year 3 Time Weighted PV of Payments Time Weighted PV of Payments Divided by Price Curent bond price Duration of the Bond: Problem 1b (20 points): Consider the bond in Problem 1a. Calculate the expected price change if interest rates drop to 6.75% using the duration approximation. Also calculate the actual price change using discounted cash flow. Solution to 1b: Using the duration approximation, the price change is calculated as: Duration of the Bond: Change in interest rates Curent bond price Bond price change New Bond price after interest rate change Now using a discounted cash flow approach to get the new bond price with the interest rate change: Payments PV of payments New Bond price after interest rate change Year 1 Sum Year 2 Year 3 Sum
Problem 1a (20 points): Calculate the duration of a $1,000, 6% coupon bond with three years to maturity. Assume that all market interest rates are 7%. Solution to 1a: Payments PV of Payments Year 1 Year 2 Year 3 Time Weighted PV of Payments Time Weighted PV of Payments Divided by Price Curent bond price Duration of the Bond: Problem 1b (20 points): Consider the bond in Problem 1a. Calculate the expected price change if interest rates drop to 6.75% using the duration approximation. Also calculate the actual price change using discounted cash flow. Solution to 1b: Using the duration approximation, the price change is calculated as: Duration of the Bond: Change in interest rates Curent bond price Bond price change New Bond price after interest rate change Now using a discounted cash flow approach to get the new bond price with the interest rate change: Payments PV of payments New Bond price after interest rate change Year 1 Sum Year 2 Year 3 Sum
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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You must use formulas and cell references PV of Payments when computing all values in the green cells
Problem 1: Calculate the duration of a $1,000, 6% coupon bond with three years to maturity. Assume that all market interest rates are 7%
Problem 1b: Consider the bond in Problem 1a. Calculate
the expected price change if interest rates
drop to 6.75% using the duration approximation.
Also calculate the actual price change using discounted cash flow.
Transcribed Image Text:Problem 1a (20 points): Calculate the duration of a $1,000, 6% coupon bond with three years to maturity. Assume that all market interest rates are 7%.
Solution to 1a:
Payments
PV of Payments
Year 1
Year 2
Year 3
Time Weighted PV of Payments
Time Weighted PV of Payments Divided by Price
Curent bond price
Duration of the Bond:
Problem 1b (20 points): Consider the bond in Problem 1a. Calculate
the expected price change if interest rates
drop to 6.75% using the duration approximation.
Also calculate the actual price change using discounted cash flow.
Solution to 1b:
Using the duration approximation, the price change is calculated as:
Duration of the Bond:
Change in interest rates
Curent bond price
Bond price change
New Bond price after interest rate change
Now using a discounted cash flow approach to get the new bond price with the interest rate change:
Payments
PV of payments
New Bond price after interest rate change
Year 1
Sum
Year 2
Year 3
Sum
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