Asked by Madison Bradford on May 06, 2024
Verified
Jackson Central has a 6-year, 8% annual coupon bond with a $1,000 par value. Earls Enterprises has a 12-year, 8% annual coupon bond with a $1,000 par value. Both bonds currently have a yield to maturity of 6%. Which of the following statements are correct if the market yield increases to 7%?
A) Both bonds would decrease in value by 4.61%.
B) The Earls bond will increase in value by $88.25.
C) The Jackson bond will increase in value by 4.61%.
D) The Earls bond will decrease in value by 7.56%.
E) The Earls bond will decrease in value by $50.68.
Yield To Maturity
The total return anticipated on a bond if it is held until the maturity date, factoring in its current market price, par value, interest payments, and time to maturity.
Annual Coupon
The yearly interest paid to bondholders, typically expressed as a percentage of the bond's face value.
Market Yield
The annual income returned on an investment divided by its current market price.
- Absorb knowledge on the relationship between interest rates and bond prices, including the influence of maturity, coupon rates, and yield to maturity on the assessment of bond value.
- Familiarize yourself with the notion of interest rate risk and analyze how maturity and coupon rates, as features of a bond, influence its responsiveness to interest rate variations.
Verified Answer
MP
Megha PatelMay 12, 2024
Final Answer :
D
Explanation :
When market yield increases, bond prices decrease. The longer the time to maturity, the more sensitive the bond price is to changes in market yield. Therefore, the Earls bond with a longer maturity will experience a greater change in value than the Jackson bond.
To calculate the change in value, we can use the following formula:
Change in value = -(C × (1 - 1/(1 + r)^n)/r) - (F/(1 + r)^n)
Where:
C = coupon payment
r = market yield
n = number of years to maturity
F = par value
For the Jackson bond:
C = $80 ($1,000 × 8%)
r = 7%
n = 6 years
F = $1,000
Using the formula, we get:
Change in value = -($80 × (1 - 1/1.07^6)/0.07) - ($1,000/1.07^6) = -$45.95
So the Jackson bond will decrease in value by $45.95 or 4.60%.
For the Earls bond:
C = $80
r = 7%
n = 12 years
F = $1,000
Using the formula, we get:
Change in value = -($80 × (1 - 1/1.07^12)/0.07) - ($1,000/1.07^12) = -$75.68
So the Earls bond will decrease in value by $75.68 or 7.57%.
Therefore, the correct choice is D. Choice A is incorrect because the Jackson bond will decrease in value by a smaller percentage than the Earls bond. Choice B and C are incorrect because the change in value for the Earls bond is negative, not positive. Choice E is incorrect because the change in value for the Earls bond is greater than $50.68.
To calculate the change in value, we can use the following formula:
Change in value = -(C × (1 - 1/(1 + r)^n)/r) - (F/(1 + r)^n)
Where:
C = coupon payment
r = market yield
n = number of years to maturity
F = par value
For the Jackson bond:
C = $80 ($1,000 × 8%)
r = 7%
n = 6 years
F = $1,000
Using the formula, we get:
Change in value = -($80 × (1 - 1/1.07^6)/0.07) - ($1,000/1.07^6) = -$45.95
So the Jackson bond will decrease in value by $45.95 or 4.60%.
For the Earls bond:
C = $80
r = 7%
n = 12 years
F = $1,000
Using the formula, we get:
Change in value = -($80 × (1 - 1/1.07^12)/0.07) - ($1,000/1.07^12) = -$75.68
So the Earls bond will decrease in value by $75.68 or 7.57%.
Therefore, the correct choice is D. Choice A is incorrect because the Jackson bond will decrease in value by a smaller percentage than the Earls bond. Choice B and C are incorrect because the change in value for the Earls bond is negative, not positive. Choice E is incorrect because the change in value for the Earls bond is greater than $50.68.
Learning Objectives
- Absorb knowledge on the relationship between interest rates and bond prices, including the influence of maturity, coupon rates, and yield to maturity on the assessment of bond value.
- Familiarize yourself with the notion of interest rate risk and analyze how maturity and coupon rates, as features of a bond, influence its responsiveness to interest rate variations.