Answer:
To calculate the price you should be willing to pay for the bond, we can follow these steps:
1. Determine the total number of coupon payments the bond will make until maturity. Since it is a semi-annual bond with 6 years to maturity, there will be 6 x 2 = 12 coupon payments.
2. Calculate the present value of each coupon payment. Since the coupon rate is 8% per year and the coupon payments are made semi-annually, the coupon payment for each period will be 8% / 2 = 4% of the bond's face value.
3. Calculate the present value of the bond's face value (the final payment at maturity). This can be calculated by discounting the future value using the required rate of return.
4. Determine the present value of the future cash flows (coupon payments and the final payment at maturity) by discounting them using the required rate of return.
5. Sum up the present value of all the cash flows to obtain the price you should be willing to pay for the bond.
Let's calculate it step by step:
Step 1: The bond will make a total of 12 coupon payments (6 years x 2 coupon payments per year).
Step 2: Calculate the present value of each coupon payment.
Since the coupon payment is 4% of the bond's face value, we need to divide it by 2 (because there are semi-annual payments) and discount it using the required rate of return.
The present value of each coupon payment can be calculated as follows:
PV(coupon payment) = Coupon payment / (1 + required rate of return/2)^period
Where the period ranges from 1 to 12.
Step 3: Calculate the present value of the bond's face value.
To calculate the present value of the final payment at maturity, we need to discount it using the required rate of return.
The present value of the face value can be calculated as follows:
PV(face value) = Face value / (1 + required rate of return/2)^number of periods (number of periods remaining until maturity)
Step 4: Determine the present value of the future cash flows.
Sum up the present value of each coupon payment and the present value of the face value to get the total present value of the cash flows.
Step 5: The sum obtained in step 4 represents the price you should be willing to pay for the bond.
It's important to note that the required rate of return is equal to the coupon rate in this case, which is 8%.
Please provide the face value of the bond in order to proceed with the calculations.