RJ Toys issues $500,000 of 12%, 10-year bonds that pay interest semiannually. The market rate of interest is 11%. RJ's bond would be trading at what price when issued?Group of answer choices$487,567.90$515,000.34$529,875.96$105,979.78
Question
RJ Toys issues 487,567.90529,875.96$105,979.78
Solution
To calculate the price at which RJ's bond would be trading when issued, we need to calculate the present value of the bond's cash flows, which consist of semi-annual interest payments and the repayment of the bond's face value at the end of its term.
Step 1: Calculate the semi-annual interest payment. The bond pays 12% interest annually, so the semi-annual interest rate is 12%/2 = 6%. The semi-annual interest payment is 6% of the bond's face value, which is 500,000 * 6% = $30,000.
Step 2: Calculate the present value of the interest payments. The bond pays interest semi-annually for 10 years, so there are 10*2 = 20 interest payments. The market rate of interest is 11%, so the semi-annual market rate is 11%/2 = 5.5%. The present value of the interest payments is 343,775.90.
Step 3: Calculate the present value of the bond's face value. The bond's face value is repaid at the end of its term, so we need to discount it back to the present using the semi-annual market rate of interest. The present value of the bond's face value is 143,792.
Step 4: Add the present value of the interest payments and the present value of the bond's face value to get the price at which the bond would be trading when issued. So, the bond would be trading at 143,792 = $487,567.90 when issued.
So, the correct answer is $487,567.90.
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