Question

Spongebob Corporation issued $700,000, 10%, 23 year bonds on December 31, 2018, when the market rate of interest was 12%. The bonds pay interest semi-annually each June 30 and December 31. Using your present value tables, compute the price of the bond. Round to the nearest whole dollar. exact number, no tolerance

Answer 1

1. Price of the bond can be calculated by the following formula:

Bond price = Present value of interest payment + Present value of bond payment at maturity

Semi annual bond interest = 10% * $700000 * 1/2 = $35000

Bond interest payments will be semi annual every year, so it is an annuity. While calculating the present value of bond interest payment, we will use the present value of annuity (PVA) of $1 table and bond payment at maturity is a one time payment, so we will use the present value (PV) of $1 table. The interest rate that will be used in calculating the required present values will be the semi annual market rate, which is 12% /2 = 6%, with 23*2 = 46 periods.

Now,

Bond price = $35000 * PVA (6%, 46 years) + $700000 * PV (6%, 46 years)

We will now find the values of PVA (6%, 46 years) and PV (6%, 46 years) from the table given and solve this equation.

Bond price = ($35000 * 15.52) + ($700000 * 0.07)

Bond price = $543200 + $49000

Bond price = $592200

2. 1- Discount

Since the par value of the bond was $700000 and issue price was $592200, so it was issued at discount.

3. Discount amount = Par value - Issue price

Discount amount = $700000 - $592200 = $107800