To calculate the price of the bond, we need to find the present value of all future cash flows (interest payments and principal repayment) discounted at the current market rate of 10%.
Step 1: Calculate the annual interest payment
The bond has a $1,000 face value and a 12% coupon rate, so the annual interest payment is:
Annual interest payment = Coupon rate x Face value
Annual interest payment = 12% x $1,000
Annual interest payment = $120
Step 2: Determine the number of periods remaining until maturity
The bond has 16 years remaining until maturity, and it pays interest annually. Therefore, there are 16 periods remaining.
Step 3: Calculate the present value of the interest payments
To calculate the present value of the interest payments, we can use the formula for the present value of an annuity:
PV = C x [(1 - (1 + r)^-n) / r]
Where:
PV = Present value of the annuity
C = Annual cash flow (in this case, the annual interest payment)
r = Discount rate (the current market rate of 10%)
n = Number of periods (in this case, 16)
Plugging in the numbers, we get:
PV = $120 x [(1 - (1 + 0.10)^-16) / 0.10]
PV = $120 x 9.712
PV = $1,165.44
Step 4: Calculate the present value of the principal repayment
To calculate the present value of the principal repayment, we can simply discount the face value of the bond at the current market rate of 10%. The present value of the principal repayment is:
PV = Face value / (1 + r)^n
PV = $1,000 / (1 + 0.10)^16
PV = $1,000 / 4.355
PV = $229.59
Step 5: Calculate the total present value of the bond
The total present value of the bond is the sum of the present value of the interest payments and the present value of the principal repayment:
Total PV = PV of interest payments + PV of principal repayment
Total PV = $1,165.44 + $229.59
Total PV = $1,395.03
Therefore, the Complex Systems bonds should sell for $1,395.03 today if bonds of similar risk are