Asked by kenyana jones on Jul 15, 2024
Verified
J&J Manufacturing just issued a bond with a $1,000 face value and a coupon rate of 7%. If the bond has a life of 30 years, pays annual coupons, and the yield to maturity is 6.8%, what is the total present value of the bond's coupon payments?
A) $138.95
B) $241.15
C) $886.37
D) $921.12
E) $1,025.32
Coupon Rate
The interest rate on a bond or fixed-income security, representing the annual interest payment compared to its face value.
Yield To Maturity
The total return anticipated on a bond if it is held until the date of its maturity, accounting for all payments from the bond over its remaining life.
Present Value
The current value of a future amount of money or stream of cash flows, discounted at a specific interest rate.
- Compute the current value of bonds, encompassing both zero-coupon and coupon-bearing variants.
- Gain knowledge of and apply yield to maturity and coupon rates to estimate bond prices.
Verified Answer
JT
jessica thomasJul 21, 2024
Final Answer :
C
Explanation :
The total present value of the bond's coupon payments can be calculated using the formula for the present value of an annuity: PV = P * [1 - (1 + r)^-n] / r, where P is the payment (in this case, the annual coupon payment), r is the yield to maturity, and n is the number of periods. Here, P = $1,000 * 7% = $70, r = 6.8% or 0.068, and n = 30. Plugging these values into the formula gives PV = $70 * [1 - (1 + 0.068)^-30] / 0.068, which calculates to approximately $886.37.
Learning Objectives
- Compute the current value of bonds, encompassing both zero-coupon and coupon-bearing variants.
- Gain knowledge of and apply yield to maturity and coupon rates to estimate bond prices.