On December 31, 2009, $150,000 of 14% bonds were issued. The market interest rate at the time of issuance was 15%. The bonds pay interest on June 30 and December 31 and mature in 8 years. Compute the selling price of a single $1,000 bond on December 31, 2009
To compute the selling price of a bond, you need to calculate the present value of the bond's future cash flows. In this case, the bond pays semi-annual interest, so you'll need to calculate the present value of the coupon payments and the present value of the principal repayment.
Here's how you can calculate the selling price of the bond on December 31, 2009:
Step 1: Determine the coupon payment.
The bond has a face value of $1,000 and a coupon rate of 14%. Since the coupon is paid semi-annually, the coupon payment is calculated as follows:
Coupon Payment = (Face Value * Coupon Rate) / 2
Coupon Payment = ($1,000 * 14%) / 2
Coupon Payment = $70
Step 2: Determine the number of coupon payments.
Since the bond matures in 8 years and interest is paid semi-annually, the number of coupon payments is 8 * 2 = 16.
Step 3: Determine the discount rate.
The market interest rate at the time of issuance is 15%, which will be used as the discount rate.
Step 4: Calculate the present value of the coupon payments.
To calculate the present value of the coupon payments, you need to discount each coupon payment using the discount rate. Since the coupon payments are semi-annual, you'll need to divide the discount rate by 2. The formula to calculate the present value of the coupon payments is:
Present Value of Coupon Payments = Coupon Payment * (1 - (1 + Discount Rate / 2)^-Number of Coupon Payments) / (Discount Rate / 2)
Present Value of Coupon Payments = $70 * (1 - (1 + 15% / 2)^-16) / (15% / 2)
Step 5: Calculate the present value of the principal repayment.
To calculate the present value of the principal repayment, you'll need to discount the face value of the bond using the discount rate. The formula to calculate the present value of the principal repayment is:
Present Value of Principal Repayment = Face Value / (1 + Discount Rate / 2)^Number of Coupon Payments
Present Value of Principal Repayment = $1,000 / (1 + 15% / 2)^16
Step 6: Calculate the selling price of the bond.
The selling price of the bond is the sum of the present value of the coupon payments and the present value of the principal repayment.
Selling Price of the Bond = Present Value of Coupon Payments + Present Value of Principal Repayment
Selling Price of the Bond = Present Value of Coupon Payments + Present Value of Principal Repayment
The result will be the selling price of a single $1,000 bond on December 31, 2009.