Final answer:
To find the price of the Matt Carp bonds with a 5-year maturity, $1,000 par value, and an 8% coupon rate when the market interest rate is 6.5%, we calculate the present value of the bond's future cash flows using a formula that accounts for the annual coupon payments, market interest rate, number of years till maturity, and face value.
Step-by-step explanation:
To determine the price of the Matt Carp bonds that mature in 5 years, have a par value of $1,000, and a coupon rate of 8% while the market requires a return of 6.5% on these bonds, we must calculate the present value of the bond's future cash flows. The bond's annual coupon payment is (8% of $1,000) which equals $80.
The bond price is found using the formula:
Price = (C x (1 - (1 + r)^-n) / r) + (F / (1 + r)^n
Where
- C = Annual coupon payment ($80)
- r = Market interest rate (6.5% or 0.065)
- n = Number of years until maturity (5)
- F = Face value of the bond ($1,000)
Plugging the numbers into the formula gives us:
Price = ($80 x (1 - (1 + 0.065)^-5) / 0.065) + ($1,000 / (1 + 0.065)^5)
Doing the calculations provides us with the current price of the bond. Since the coupon rate is higher than the market interest rate, the bond will sell for a premium above its face value.