a company has an outstanding issue of 1,000 face value bonds with a 9.5% annual coupon and 20 years remaining until maturity. The bonds are currently selling at a price of 90 (90% of face value).
To understand the current price of the bonds, we need to calculate the present value of the cash flows generated by these bonds.
Step 1: Calculate the annual coupon payment
The annual coupon payment is calculated by multiplying the face value of the bond ($1,000) by the coupon rate (9.5%). Therefore, the annual coupon payment is $1,000 * 9.5% = $95.
Step 2: Calculate the number of periods remaining until maturity
In this case, the bonds have 20 years remaining until maturity. Since the coupon payments are made annually, the number of periods remaining is equal to 20.
Step 3: Calculate the present value of the coupon payments
To calculate the present value of the future cash flows generated by the coupon payments, we need to discount them to their present value. We will be using the discount rate as determined by the bond price.
To calculate the present value of the coupon payments, we'll use the following formula:
PV of coupon payments = (Annual coupon payment / Discount rate) * [1 - (1 / (1 + Discount rate)^Number of periods)]
Assuming the discount rate is the same as the market price (90%), we can calculate the PV of the coupon payments as follows:
PV of coupon payments = ($95 / 0.90) * [1 - (1 / (1 + 0.90)^20)] = $1,055.53
Step 4: Calculate the present value of the face value amount at maturity
The face value of the bond is $1,000, and we will be using the same discount rate (90%) to calculate its present value.
PV of face value amount = Face value / (1 + Discount rate)^Number of periods
PV of face value amount = $1,000 / (1 + 0.90)^20 = $367.08
Step 5: Calculate the total present value of the bond
To calculate the total present value of the bond, we add the present value of the coupon payments to the present value of the face value amount at maturity.
Total present value = PV of coupon payments + PV of face value amount
Total present value = $1,055.53 + $367.08 = $1,422.61
Therefore, the current selling price of the bonds at 90% of the face value is $1,422.61.