Question

On January 1, Year 1, Greenfield, Inc. issues $100,000 of 9% bonds maturing in 10 years when the market rate of interest is 8%. Interest is paid semiannually on June 30 and December 31. When using a financial calculator to compute the issue price of the bonds, the applicable periodic interest rate ("I") is:

Answer 1

To compute the issue price of bonds with a semiannual interest payment, use half of the market interest rate as the periodic rate. A two-year bond's present value is calculated using this interest rate and considering both the interest payments and the principal repayment. Applicable periodic interest rate = 4%

Step-by-step explanation:

The student's question relates to calculating the issue price of bonds when the coupon rate is different from the market interest rate. In this case, the bond has a 9% coupon rate, and they are issued when the market interest rate is 8%. Because interest is paid semiannually, the periodic interest rate used in the financial calculator for computing the issue price is half of the annual market rate, which is 4% (8% divided by 2).

Applicable periodic interest rate = Market rate of interest / Number of compounding periods per year

Applicable periodic interest rate = 8% / 2

= 4%

To calculate the present value of the bond when the discount rate is 8% and then at 11%, the student must discount the annual interest payments and the principal repayment back to their present value. Using the present value formula, the student would calculate the present value of each payment separately and then sum these amounts to find the total present value of the bond.

For example, if we consider a two-year bond with a principal of $3,000 and an 8% interest rate, it will pay $240 in interest each year. To calculate the present value of these interest payments and the principal repayment at the end of the second year when the discount rate is 8%, each cash flow must be discounted back to its present value. And if the market interest rate rises to 11%, the discount rate changes accordingly, impacting the bond's present value due to the higher opportunity cost.

Answer 2

When using a financial calculator to compute the issue price of the bonds, the applicable periodic interest rate ("I") is 3.923%

Step-by-step explanation:

Hi, first, the discount interest rate that you have to choose is 8%, because 9% is the coupon rate (which in our case would be 9%/2=4.5% and this is used only to find the amount to be paid semi-annually).

Now we know we have to choose 8%, but this is an effective rate (I know this is an effective rate because no units were mentioned), and by definition it is a periodic rate, but it is not the rate that we need since the payments are going to be made in a semi-annual way, therefore we need to use the following equation.

`r(semi-annual)=[1+r(annual)]^{(1)/(2) } -1`

So, everything should look like this.

`r(semi-annual)=[1+0.08]^{(1)/(2) } -1=0.03923`

Therefore, the periodic interest that yuo have to use to calculate the price of the bond is 3.923%

Best of luck.