moussawi ltd's outstanding bonds have a $1000 par value, and they mature in 5 years. their yield to maturity is 9%, based on semiannual compounding, and the current market price is $853.61. what is the bonds annual coupon interest rate?
5.30
To find the bond's annual coupon interest rate, we need to use the following formula:
Coupon Interest Rate = (Coupon Payment / Par Value) * 100
First, let's calculate the Coupon Payment using the information given:
1. Determine the number of periods: Since the bond pays semiannual coupons and matures in 5 years, there will be 10 coupon periods (2 coupons per year for 5 years).
2. Calculate the semiannual coupon payment:
Market Price = PV of Coupons + PV of Face Value
We know the market price is $853.61, the face value (par value) is $1000, and the yield to maturity is 9% (based on semiannual compounding).
Using a financial calculator or spreadsheet software, you can solve for PV of Coupons:
PV of Coupons = Market Price - PV of Face Value
PV of Face Value = Face Value / (1 + Yield/2) ^ (2 * n)
PV of Face Value = $1000 / (1 + 0.09/2) ^ (2 * 5)
Now, substitute the values and solve for PV of Coupons:
PV of Coupons = $853.61 - PV of Face Value
Next, calculate the Coupon Payment per period:
Coupon Payment = PV of Coupons / Number of Periods
Now, we have all the necessary information to find the bond's annual coupon interest rate:
Coupon Interest Rate = (Coupon Payment / Par Value) * 100
Simply insert the calculated values into the formula and solve for the coupon interest rate.