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RJ Toys issues $100,000 of 10%, 8-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$105,979.78$94,768.92$112,500.54$99,560.55

Question

RJ Toys issues 100,000of10100,000 of 10%, 8-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 choices105,979.7894,768.9294,768.92112,500.54$99,560.55

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Solution

The price of a bond is calculated using the formula for the present value of an annuity for the bond's interest payments plus the present value of a lump sum for the bond's face value payment at maturity.

Here's how to calculate it:

  1. First, calculate the semiannual interest payment. The bond has a 10% annual interest rate, but it pays interest semiannually, so the semiannual interest rate is 10% / 2 = 5%. The semiannual interest payment is 5% of the 100,000facevalue,or100,000 face value, or 5,000.

  2. Next, calculate the present value of the interest payments. This is an annuity of 5,000for8years∗2=16periods.Themarketinterestrateis115,000 for 8 years * 2 = 16 periods. The market interest rate is 11% annually, but we need the semiannual rate, so we divide by 2 to get 5.5%. The present value of an annuity is calculated as PVA = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment per period, r is the interest rate per period, and n is the number of periods. Plugging in the numbers, we get PVA = 5,000 * [(1 - (1 + 0.055)^-16) / 0.055] = $57,434.92.

  3. Then, calculate the present value of the face value payment at maturity. This is a lump sum of 100,000in16periods.ThepresentvalueofalumpsumiscalculatedasPV=FV/(1+r)n,whereFVisthefuturevalue,ristheinterestrateperperiod,andnisthenumberofperiods.Plugginginthenumbers,wegetPV=100,000 in 16 periods. The present value of a lump sum is calculated as PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods. Plugging in the numbers, we get PV = 100,000 / (1 + 0.055)^16 = $37,334.00.

  4. Finally, add the present value of the interest payments and the present value of the face value to get the price of the bond. The price is 57,434.92+57,434.92 + 37,334.00 = $94,768.92.

So, RJ's bond would be trading at $94,768.92 when issued.

This problem has been solved

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