Target Company issues bonds with a par value of $900,000 on their stated issue date. The bonds mature in 10 years and pay 10% annual interest in semiannual payments. On the issue date, the annual market rate for the bonds is 12%. What is the selling price of the bond
To calculate the selling price of a bond, you can use the present value of the bond's cash flows formula. Here's how you can calculate the selling price of the bond in this scenario:
Step 1: Calculate the semiannual interest payment
The bond pays 10% annual interest, which is then divided into semiannual payments. So, the semiannual interest payment can be calculated as follows:
Semiannual interest payment = (10% / 2) * $900,000
Step 2: Determine the number of periods
Since the bond matures in 10 years and makes semiannual payments, the total number of periods is 10 * 2 = 20.
Step 3: Calculate the semiannual discount rate
The annual market rate for the bond is 12%, but since the bond makes semiannual payments, we need to adjust it. Divide the annual rate by 2 to get the semiannual rate:
Semiannual discount rate = 12% / 2
Step 4: Determine the present value of the interest payments
Using the present value formula for an annuity, you can calculate the present value of the interest payments as follows:
Present value of interest payments = Semiannual interest payment * [(1 - (1 + Semiannual discount rate)^-Number of periods) / Semiannual discount rate]
Step 5: Determine the present value of the bond's par value
The par value of the bond is $900,000, which is the amount received by the bondholder at maturity. Since there is no further interest payment for the last period, the present value of the bond's par value can be calculated as follows:
Present value of par value = $900,000 / (1 + Semiannual discount rate)^Number of periods
Step 6: Calculate the selling price of the bond
The selling price of the bond is the sum of the present value of the interest payments and the present value of the bond's par value:
Selling price of the bond = Present value of interest payments + Present value of par value
By plugging in the values from the given information into the above formulas, you can calculate the selling price of the bond.