(Bond valuation) RCA made a coupon payment yesterday on its 6.25% bonds that mature in 11.5 years. If the required return on these bonds is 9.2% nominal annual, what should be the
market price of these bonds?
To calculate the market price of the bonds, we need to determine the present value of the future cash flows, including the coupon payments and the final maturity payment.
Step 1: Calculate the coupon payment per year
The coupon payment is given as a percentage of the face value of the bond. In this case, it is 6.25%. To calculate the coupon payment per year, multiply the coupon rate by the face value of the bond.
Coupon payment per year = Coupon rate * Face value of the bond
Step 2: Determine the number of coupon payments
The bonds mature in 11.5 years, so the number of coupon payments will be equal to the number of years until maturity multiplied by the frequency of the payments per year.
Number of coupon payments = Number of years until maturity * Frequency of coupon payments per year
Step 3: Calculate the present value of the coupon payments
Using the required return, we can discount each coupon payment back to its present value. The present value of each coupon payment is calculated by dividing the coupon payment by (1 + required return)^n, where n is the number of coupon payments until maturity.
Present value of coupon payments = Coupon payment per year * [1 - (1 + required return)^(-n)] / required return
Step 4: Determine the present value of the maturity payment
At maturity, the bondholder receives the face value of the bond. The present value of the maturity payment can be calculated by dividing the face value of the bond by (1 + required return)^n, where n is the number of coupon payments until maturity.
Present value of maturity payment = Face value of the bond / (1 + required return)^n
Step 5: Calculate the market price of the bonds
To calculate the market price of the bonds, add the present value of the coupon payments (Step 3) to the present value of the maturity payment (Step 4).
Market price of the bonds = Present value of coupon payments + Present value of maturity payment
By plugging in the values provided in the question (coupon rate, required return, maturity period), you can calculate the market price of the bond.